From cbcacc4b574c1101d613896f383e2436d5a180fd Mon Sep 17 00:00:00 2001
From: Don Cross <cosinekitty@gmail.com>
Date: Sun, 18 Apr 2021 21:15:17 -0400
Subject: [PATCH] Improved agreement of precision among the 4 supported
 languages.

Before making these changes, I had the following discrepancies
between the calculations made by the different programming
language implementations of Astronomy Engine:

    C vs C#: 5.55112e-17, worst line number = 6
    C vs JS: 2.78533e-12, worst line number = 196936
    C vs PY: 1.52767e-12, worst line number = 159834

Now the results are:

    Diffing calculations: C vs C#
    ctest(Diff): Maximum numeric difference = 5.55112e-17, worst line number = 5

    Diffing calculations: C vs JS
    ctest(Diff): Maximum numeric difference = 1.02318e-12, worst line number = 133677

    Diffing calculations: C vs PY
    ctest(Diff): Maximum numeric difference = 5.68434e-14, worst line number = 49066

    Diffing calculations: JS vs PY
    ctest(Diff): Maximum numeric difference = 1.02318e-12, worst line number = 133677

Here is how I did this:

1. Use new constants HOUR2RAD, RAD2HOUR that directly convert between radians and sidereal hours.
   This reduces tiny roundoff errors in the conversions.

2. In VSOP longitude calculations, keep clamping the angular sum to
   the range [-2pi, +2pi], to prevent it from accumulating thousands
   of radians. This reduces the accumulated error in the final result
   before it is fed into trig functions.

The remaining discrepancies are largely because of an "azimuth amplification" effect:
When converting equatorial coordinates to horizontal coordinates, an object near
the zenith (or nadir) has an azimuth that is highly sensitive to the input
equatorial coordinates. A tiny change in right ascension (RA) can cause a much
larger change in azimuth.

I tracked down the RA discrepancy, and it is due to a different behavior
of the atan2 function in C and JavaScript. There are cases where the least
significant decimal digit is off by 1, as if due to a difference of opinion
about rounding policy.

My best thought is to go back and have a more nuanced diffcalc that
applies less strict tests for azimuth values than the other calculated values.
It seems like every other computed quantity is less sensitive, because solar
system bodies tend to stay away from "poles" of other angular coordinate
systems: their ecliptic latitudes and equatorial declinations are usually
reasonably close to zero. Therefore, right ascensions and ecliptic longitudes
are usually insensitive to changes in the cartesian coordinates they
are calculated from.
---
 README.md                                  |     2 +-
 demo/browser/astronomy.browser.js          |    61 +-
 demo/nodejs/astronomy.js                   |    61 +-
 demo/nodejs/test/camera_correct.txt        |     2 +-
 demo/python/astronomy.py                   |    28 +-
 demo/python/test/camera_correct.txt        |     4 +-
 generate/.gitignore                        |     2 +
 generate/ctest.c                           |    31 +-
 generate/diffcalc                          |    21 +
 generate/dotnet/csharp_test/csharp_test.cs |     6 +-
 generate/run                               |     6 +-
 generate/template/astronomy.c              |    42 +-
 generate/template/astronomy.cs             |    44 +-
 generate/template/astronomy.py             |    28 +-
 generate/template/astronomy.ts             |    60 +-
 generate/test.js                           |    40 +-
 generate/test.py                           |    20 +-
 source/c/README.md                         |    34 +-
 source/c/astronomy.c                       |    42 +-
 source/c/astronomy.h                       |    16 +-
 source/csharp/README.md                    |    16 +
 source/csharp/astronomy.cs                 |    44 +-
 source/js/README.md                        |    20 +-
 source/js/astronomy.browser.js             |    61 +-
 source/js/astronomy.browser.min.js         |   270 +-
 source/js/astronomy.d.ts                   |    12 +-
 source/js/astronomy.js                     |    61 +-
 source/js/astronomy.min.js                 |    30 +-
 source/js/astronomy.ts                     |    60 +-
 source/js/esm/astronomy.js                 |    55 +-
 source/python/astronomy.py                 |    28 +-
 website/src/assets/documentation.json      | 20363 ++++++++++---------
 32 files changed, 11067 insertions(+), 10503 deletions(-)
 create mode 100755 generate/diffcalc

diff --git a/README.md b/README.md
index 23641279..228fca43 100644
--- a/README.md
+++ b/README.md
@@ -148,7 +148,7 @@ of complexity. So I decided to create Astronomy Engine with the following engine
 
 - Support JavaScript, C, C#, and Python with the same algorithms, and verify them to produce identical results.
 - No external dependencies! The code must not require anything outside the standard library for each language.
-- Minified JavaScript code less than 100K. (The current size is <!--MINIFIED_SIZE-->94787 bytes.)
+- Minified JavaScript code less than 100K. (The current size is <!--MINIFIED_SIZE-->94894 bytes.)
 - Accuracy always within 1 arcminute of results from NOVAS.
 - It would be well documented, relatively easy to use, and support a wide variety of common use cases.
 
diff --git a/demo/browser/astronomy.browser.js b/demo/browser/astronomy.browser.js
index fa536b0f..bed61a5b 100644
--- a/demo/browser/astronomy.browser.js
+++ b/demo/browser/astronomy.browser.js
@@ -34,21 +34,29 @@
  */
 'use strict';
 Object.defineProperty(exports, "__esModule", { value: true });
-exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2DEG = exports.DEG2RAD = exports.KM_PER_AU = void 0;
-exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = void 0;
+exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = void 0;
+exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = void 0;
 /**
  * @brief The number of kilometers per astronomical unit.
  */
 exports.KM_PER_AU = 1.4959787069098932e+8;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 exports.DEG2RAD = 0.017453292519943296;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+exports.HOUR2RAD = 0.2617993877991494365;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 exports.RAD2DEG = 57.295779513082321;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+exports.RAD2HOUR = 3.819718634205488;
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1972,10 +1980,10 @@ function vector2radec(pos, time) {
             return new EquatorialCoordinates(0, -90, dist, vec);
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
-    let ra = Math.atan2(vec.y, vec.x) / (exports.DEG2RAD * 15);
+    let ra = exports.RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / exports.DEG2RAD;
+    const dec = exports.RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 function spin(angle, pos) {
@@ -2036,8 +2044,8 @@ function Horizon(date, observer, ra, dec, refraction) {
     const coslon = Math.cos(observer.longitude * exports.DEG2RAD);
     const sindc = Math.sin(dec * exports.DEG2RAD);
     const cosdc = Math.cos(dec * exports.DEG2RAD);
-    const sinra = Math.sin(ra * 15 * exports.DEG2RAD);
-    const cosra = Math.cos(ra * 15 * exports.DEG2RAD);
+    const sinra = Math.sin(ra * exports.HOUR2RAD);
+    const cosra = Math.cos(ra * exports.HOUR2RAD);
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
     //
@@ -2083,7 +2091,7 @@ function Horizon(date, observer, ra, dec, refraction) {
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * exports.RAD2DEG;
+        az = -exports.RAD2DEG * Math.atan2(pw, pn);
         if (az < 0)
             az += 360;
     }
@@ -2093,7 +2101,7 @@ function Horizon(date, observer, ra, dec, refraction) {
         az = 0;
     }
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * exports.RAD2DEG;
+    let zd = exports.RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
     if (refraction) {
@@ -2111,7 +2119,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             }
             proj = Math.sqrt(pr[0] * pr[0] + pr[1] * pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * exports.RAD2DEG / 15;
+                out_ra = exports.RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
@@ -2119,7 +2127,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * exports.RAD2DEG;
+            out_dec = exports.RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
     return new HorizontalCoordinates(az, 90 - zd, out_ra, out_dec);
@@ -2373,7 +2381,7 @@ function GeoMoon(date) {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 exports.GeoMoon = GeoMoon;
-function VsopFormula(formula, t) {
+function VsopFormula(formula, t, clamp_angle) {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2381,7 +2389,10 @@ function VsopFormula(formula, t) {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2; // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2419,26 +2430,28 @@ function VsopRotate(eclip) {
 function VsopSphereToRect(lon, lat, radius) {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 function CalcVsop(model, time) {
     const t = time.tt / DAYS_PER_MILLENNIUM; // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
 function CalcVsopPosVel(model, tt) {
     const t = tt / DAYS_PER_MILLENNIUM;
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
     const drad_dt = VsopDeriv(model[RAD_INDEX], t);
@@ -3087,7 +3100,7 @@ exports.HelioVector = HelioVector;
 function HelioDistance(body, date) {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
diff --git a/demo/nodejs/astronomy.js b/demo/nodejs/astronomy.js
index f11e9f8f..2c7dafa0 100644
--- a/demo/nodejs/astronomy.js
+++ b/demo/nodejs/astronomy.js
@@ -33,21 +33,29 @@
  */
 'use strict';
 Object.defineProperty(exports, "__esModule", { value: true });
-exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2DEG = exports.DEG2RAD = exports.KM_PER_AU = void 0;
-exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = void 0;
+exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = void 0;
+exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = void 0;
 /**
  * @brief The number of kilometers per astronomical unit.
  */
 exports.KM_PER_AU = 1.4959787069098932e+8;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 exports.DEG2RAD = 0.017453292519943296;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+exports.HOUR2RAD = 0.2617993877991494365;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 exports.RAD2DEG = 57.295779513082321;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+exports.RAD2HOUR = 3.819718634205488;
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1971,10 +1979,10 @@ function vector2radec(pos, time) {
             return new EquatorialCoordinates(0, -90, dist, vec);
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
-    let ra = Math.atan2(vec.y, vec.x) / (exports.DEG2RAD * 15);
+    let ra = exports.RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / exports.DEG2RAD;
+    const dec = exports.RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 function spin(angle, pos) {
@@ -2035,8 +2043,8 @@ function Horizon(date, observer, ra, dec, refraction) {
     const coslon = Math.cos(observer.longitude * exports.DEG2RAD);
     const sindc = Math.sin(dec * exports.DEG2RAD);
     const cosdc = Math.cos(dec * exports.DEG2RAD);
-    const sinra = Math.sin(ra * 15 * exports.DEG2RAD);
-    const cosra = Math.cos(ra * 15 * exports.DEG2RAD);
+    const sinra = Math.sin(ra * exports.HOUR2RAD);
+    const cosra = Math.cos(ra * exports.HOUR2RAD);
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
     //
@@ -2082,7 +2090,7 @@ function Horizon(date, observer, ra, dec, refraction) {
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * exports.RAD2DEG;
+        az = -exports.RAD2DEG * Math.atan2(pw, pn);
         if (az < 0)
             az += 360;
     }
@@ -2092,7 +2100,7 @@ function Horizon(date, observer, ra, dec, refraction) {
         az = 0;
     }
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * exports.RAD2DEG;
+    let zd = exports.RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
     if (refraction) {
@@ -2110,7 +2118,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             }
             proj = Math.sqrt(pr[0] * pr[0] + pr[1] * pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * exports.RAD2DEG / 15;
+                out_ra = exports.RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
@@ -2118,7 +2126,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * exports.RAD2DEG;
+            out_dec = exports.RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
     return new HorizontalCoordinates(az, 90 - zd, out_ra, out_dec);
@@ -2372,7 +2380,7 @@ function GeoMoon(date) {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 exports.GeoMoon = GeoMoon;
-function VsopFormula(formula, t) {
+function VsopFormula(formula, t, clamp_angle) {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2380,7 +2388,10 @@ function VsopFormula(formula, t) {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2; // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2418,26 +2429,28 @@ function VsopRotate(eclip) {
 function VsopSphereToRect(lon, lat, radius) {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 function CalcVsop(model, time) {
     const t = time.tt / DAYS_PER_MILLENNIUM; // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
 function CalcVsopPosVel(model, tt) {
     const t = tt / DAYS_PER_MILLENNIUM;
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
     const drad_dt = VsopDeriv(model[RAD_INDEX], t);
@@ -3086,7 +3099,7 @@ exports.HelioVector = HelioVector;
 function HelioDistance(body, date) {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
diff --git a/demo/nodejs/test/camera_correct.txt b/demo/nodejs/test/camera_correct.txt
index e50aee5f..3c2fbc7e 100644
--- a/demo/nodejs/test/camera_correct.txt
+++ b/demo/nodejs/test/camera_correct.txt
@@ -1,5 +1,5 @@
 Moon horizontal position: azimuth = 274.486, altitude = 52.101
-Moon check: x = 1, y = -2.0725886704096896e-16, z = 8.290354681638758e-17
+Moon check: x = 1, y = -2.072588670409689e-16, z = -2.901624138573565e-16
 Sun vector: x = -0.088530, y = -0.319391, z = -0.939663
 Tilt angle of sunlit side of the Moon = -108.773 degrees counterclockwise from up.
 Moon magnitude = -10.27, phase angle = 84.22 degrees.
diff --git a/demo/python/astronomy.py b/demo/python/astronomy.py
index 374daee1..d0d810da 100644
--- a/demo/python/astronomy.py
+++ b/demo/python/astronomy.py
@@ -56,6 +56,8 @@ CALLISTO_RADIUS_KM = 2410.3     #<const> The mean radius of Jupiter's moon Calli
 
 _CalcMoonCount = 0
 
+_RAD2HOUR  =  3.819718634205488         # 12/pi = factor to convert radians to sidereal hours
+_HOUR2RAD  =  0.2617993877991494365     # pi/12 = factor to convert sidereal hours to radians
 _DAYS_PER_TROPICAL_YEAR = 365.24217
 _PI2 = 2.0 * math.pi
 _EPOCH = datetime.datetime(2000, 1, 1, 12)
@@ -1465,7 +1467,7 @@ def _vector2radec(pos, time):
         else:
             dec = +90.0
     else:
-        ra = math.degrees(math.atan2(pos[1], pos[0])) / 15.0
+        ra = _RAD2HOUR * math.atan2(pos[1], pos[0])
         if ra < 0:
             ra += 24
         dec = math.degrees(math.atan2(pos[2], math.sqrt(xyproj)))
@@ -3085,11 +3087,16 @@ _vsop = [
 ],
 ]
 
-def _VsopFormula(formula, t):
+def _VsopFormula(formula, t, clamp_angle):
     tpower = 1.0
     coord = 0.0
     for series in formula:
-        coord += tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        incr = tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        if clamp_angle:
+            # Longitude angles can be hundreds of radians.
+            # Improve precision by keeping each increment within [-2*pi, +2*pi].
+            incr = math.fmod(incr, _PI2)
+        coord += incr
         tpower *= t
     return coord
 
@@ -3136,7 +3143,9 @@ def _VsopSphereToRect(lon, lat, rad):
 
 def _CalcVsop(model, time):
     t = time.tt / _DAYS_PER_MILLENNIUM
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
     eclip = _VsopSphereToRect(lon, lat, rad)
     return _VsopRotate(eclip).ToAstroVector(time)
 
@@ -3149,7 +3158,10 @@ class _body_state_t:
 def _CalcVsopPosVel(model, tt):
     t = tt / _DAYS_PER_MILLENNIUM
 
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
+
     (dlon_dt, dlat_dt, drad_dt) = [_VsopDeriv(formula, t) for formula in model]
 
     # Use spherical coords and spherical derivatives to calculate
@@ -3209,7 +3221,7 @@ def _VsopHelioDistance(model, time):
     # The caller only wants to know the distance between the planet and the Sun.
     # So we only need to calculate the radial component of the spherical coordinates.
     # There is no need to translate coordinates.
-    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM)
+    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM, False)
 
 def _CalcEarth(time):
     return _CalcVsop(_vsop[Body.Earth.value], time)
@@ -4314,7 +4326,7 @@ def Horizon(time, observer, ra, dec, refraction):
     latrad = math.radians(observer.latitude)
     lonrad = math.radians(observer.longitude)
     decrad = math.radians(dec)
-    rarad = math.radians(ra * 15.0)
+    rarad = ra * _HOUR2RAD
 
     sinlat = math.sin(latrad)
     coslat = math.cos(latrad)
@@ -4407,7 +4419,7 @@ def Horizon(time, observer, ra, dec, refraction):
             pr = [(((p[j] - coszd0 * uz[j]) / sinzd0)*sinzd + uz[j]*coszd) for j in range(3)]
             proj = math.sqrt(pr[0]*pr[0] + pr[1]*pr[1])
             if proj > 0:
-                hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
+                hor_ra = _RAD2HOUR * math.atan2(pr[1], pr[0])
                 if hor_ra < 0:
                     hor_ra += 24
             else:
diff --git a/demo/python/test/camera_correct.txt b/demo/python/test/camera_correct.txt
index a76cf3db..1c2640d9 100644
--- a/demo/python/test/camera_correct.txt
+++ b/demo/python/test/camera_correct.txt
@@ -1,6 +1,6 @@
 Moon horizontal position: azimuth = 274.486, altitude = 52.101
-Moon check: (1.0, -2.0725886704096896e-16, 1.2435532022458137e-16, 2021-03-22T02:45:00.000Z)
-Sun vector: (-0.0885303206557285, -0.3193912784902719, -0.9396631499852888, 2021-03-22T02:45:00.000Z)
+Moon check: (1.0, -2.072588670409689e-16, -1.0362943352048446e-16, 2021-03-22T02:45:00.000Z)
+Sun vector: (-0.08853032065573567, -0.31939127849027193, -0.9396631499852881, 2021-03-22T02:45:00.000Z)
 Tilt angle of sunlit side of the Moon = -108.773 degrees counterclockwise from up.
 Moon magnitude = -10.27, phase angle = 84.22 degrees.
 Angle between Moon and Sun as seen from Earth = 95.64 degrees.
diff --git a/generate/.gitignore b/generate/.gitignore
index ca542ff1..74531f19 100644
--- a/generate/.gitignore
+++ b/generate/.gitignore
@@ -1,3 +1,5 @@
+atan2.js
+issue_103.txt
 generate_c_docs
 generate
 lnxp1600p2200.405
diff --git a/generate/ctest.c b/generate/ctest.c
index 88d9e7b0..c46bfff7 100644
--- a/generate/ctest.c
+++ b/generate/ctest.c
@@ -91,6 +91,7 @@ static int Transit(void);
 static int DistancePlot(astro_body_t body, double ut1, double ut2, const char *filename);
 static int GeoidTest(void);
 static int JupiterMoonsTest(void);
+static int Issue103(void);
 
 typedef int (* unit_test_func_t) (void);
 
@@ -109,6 +110,7 @@ static unit_test_t UnitTests[] =
     {"elongation",              ElongationTest},
     {"geoid",                   GeoidTest},
     {"global_solar_eclipse",    GlobalSolarEclipseTest},
+    {"issue_103",               Issue103},
     {"jupiter_moons",           JupiterMoonsTest},
     {"local_solar_eclipse",     LocalSolarEclipseTest},
     {"lunar_eclipse",           LunarEclipseTest},
@@ -2217,7 +2219,7 @@ static int Test_EQJ_ECL(void)
     et = Astronomy_RotateVector(r, ee);
     CHECK(VectorDiff(et, ev, &diff));
     DEBUG("C Test_EQJ_ECL  ev diff=%lg\n", diff);
-    if (diff > 2.0e-16)
+    if (diff > 2.3e-16)
         FAIL("C Test_EQJ_ECL: EXCESSIVE REVERSE ROTATION ERROR\n");
 
     error = 0;
@@ -2323,7 +2325,7 @@ static int Test_EQD_HOR(astro_body_t body)
     DEBUG("C Test_EQD_HOR %s: trusted alt=%0.3lf, az=%0.3lf; test alt=%0.3lf, az=%0.3lf; diff_alt=%lg, diff_az=%lg\n",
         Astronomy_BodyName(body), hor.altitude, hor.azimuth, sphere.lat, sphere.lon, diff_alt, diff_az);
 
-    if (diff_alt > 3.0e-14 || diff_az > 8e-14)
+    if (diff_alt > 3.2e-14 || diff_az > 1.2e-13)
         FAIL("C Test_EQD_HOR: EXCESSIVE HORIZONTAL ERROR.\n");
 
     /* Confirm that we can convert back to horizontal vector. */
@@ -2339,7 +2341,7 @@ static int Test_EQD_HOR(astro_body_t body)
     CHECK_VECTOR(check_eqd, Astronomy_RotateVector(rot, vec_hor));
     CHECK(VectorDiff(check_eqd, vec_eqd, &diff));
     DEBUG("C Test_EQD_HOR %s: OFDATE inverse rotation diff = %lg\n", Astronomy_BodyName(body), diff);
-    if (diff > 2.0e-15)
+    if (diff > 2.1e-15)
         FAIL("C Test_EQD_HOR: EXCESSIVE OFDATE INVERSE HORIZONTAL ERROR.\n");
 
     /* Exercise HOR to EQJ translation. */
@@ -3740,3 +3742,26 @@ fail:
 }
 
 /*-----------------------------------------------------------------------------------------------------------*/
+
+static int Issue103(void)
+{
+    /* https://github.com/cosinekitty/astronomy/issues/103 */
+
+    astro_observer_t observer = Astronomy_MakeObserver(29.0, -81.0, 10.0);
+    double ut = -51279.9420508868643083;
+    astro_time_t time = Astronomy_TimeFromDays(ut);
+    astro_body_t body = BODY_MOON;
+    astro_equatorial_t ofdate = Astronomy_Equator(body, &time, observer, EQUATOR_OF_DATE, ABERRATION);
+    astro_horizon_t hor;
+
+    printf("tt  = %23.16lf\n", time.tt);
+    printf("ra  = %23.16lf\n", ofdate.ra);
+    printf("dec = %23.16lf\n", ofdate.dec);
+    hor = Astronomy_Horizon(&time, observer, ofdate.ra, ofdate.dec, REFRACTION_NONE);
+    printf("az  = %23.16lf\n", hor.azimuth);
+    printf("alt = %23.16lf\n", hor.altitude);
+
+    return 0;
+}
+
+/*-----------------------------------------------------------------------------------------------------------*/
diff --git a/generate/diffcalc b/generate/diffcalc
new file mode 100755
index 00000000..ab87ffa3
--- /dev/null
+++ b/generate/diffcalc
@@ -0,0 +1,21 @@
+#!/bin/bash
+
+echo ""
+echo "Diffing calculations: C vs C#"
+./ctest diff temp/c_check.txt dotnet/csharp_test/csharp_check.txt || exit $?
+
+echo ""
+echo "Diffing calculations: C vs JS"
+./ctest diff temp/{c,js}_check.txt || exit $?
+
+echo ""
+echo "Diffing calculations: C vs PY"
+./ctest diff temp/{c,py}_check.txt || exit $?
+
+echo ""
+echo "Diffing calculations: JS vs PY"
+./ctest diff temp/{js,py}_check.txt || exit $?
+
+echo ""
+echo "diffcalc: PASS"
+exit 0
diff --git a/generate/dotnet/csharp_test/csharp_test.cs b/generate/dotnet/csharp_test/csharp_test.cs
index 74e39b29..b99eb714 100644
--- a/generate/dotnet/csharp_test/csharp_test.cs
+++ b/generate/dotnet/csharp_test/csharp_test.cs
@@ -1420,7 +1420,7 @@ namespace csharp_test
             AstroVector et = Astronomy.RotateVector(r, ee);
             diff = VectorDiff(et, ev);
             Debug("C# Test_EQJ_ECL  ev diff={0}", diff);
-            if (diff > 2.0e-16)
+            if (diff > 2.3e-16)
             {
                 Console.WriteLine("C# Test_EQJ_ECL: EXCESSIVE REVERSE ROTATION ERROR");
                 return 1;
@@ -1485,7 +1485,7 @@ namespace csharp_test
             Debug("C# Test_EQD_HOR {0}: trusted alt={1}, az={2}; test alt={3}, az={4}; diff_alt={5}, diff_az={6}",
                 body, hor.altitude, hor.azimuth, sphere.lat, sphere.lon, diff_alt, diff_az);
 
-            if (diff_alt > 3.0e-14 || diff_az > 8.0e-14)
+            if (diff_alt > 3.2e-14 || diff_az > 1.2e-13)
             {
                 Console.WriteLine("C# Test_EQD_HOR: EXCESSIVE HORIZONTAL ERROR.");
                 return 1;
@@ -1506,7 +1506,7 @@ namespace csharp_test
             AstroVector check_eqd = Astronomy.RotateVector(rot, vec_hor);
             diff = VectorDiff(check_eqd, vec_eqd);
             Debug("C# Test_EQD_HOR {0}: OFDATE inverse rotation diff = {1}", body, diff);
-            if (diff > 2.0e-15)
+            if (diff > 2.1e-15)
             {
                 Console.WriteLine("C# Test_EQD_HOR: EXCESSIVE OFDATE INVERSE HORIZONTAL ERROR.");
                 return 1;
diff --git a/generate/run b/generate/run
index 16c1befa..029254c5 100755
--- a/generate/run
+++ b/generate/run
@@ -131,11 +131,7 @@ cd .. || Fail "Could not change to parent directory."
 ./unit_test_c $1 || exit $?
 ./unit_test_python $1 || exit $?
 
-echo ""
-echo "Diffing calculations."
-./ctest diff temp/c_check.txt dotnet/csharp_test/csharp_check.txt || Fail "Diff(c,c#) failure."
-./ctest diff temp/{c,js}_check.txt || Fail "Diff(c,js) failure."
-./ctest diff temp/{c,py}_check.txt || Fail "Diff(c,py) failure."
+./diffcalc || exit $?
 
 echo ""
 echo "Testing example programs."
diff --git a/generate/template/astronomy.c b/generate/template/astronomy.c
index 0c5a8b77..3a50df31 100644
--- a/generate/template/astronomy.c
+++ b/generate/template/astronomy.c
@@ -1342,7 +1342,7 @@ static astro_equatorial_t vector2radec(const double pos[3], astro_time_t time)
     }
     else
     {
-        equ.ra = atan2(pos[1], pos[0]) / (DEG2RAD * 15.0);
+        equ.ra = RAD2HOUR * atan2(pos[1], pos[0]);
         if (equ.ra < 0)
             equ.ra += 24.0;
 
@@ -1866,6 +1866,7 @@ static const vsop_model_t vsop[] =
 static void VsopCoords(const vsop_model_t *model, double t, double sphere[3])
 {
     int k, s, i;
+    double incr;
 
     for (k=0; k < 3; ++k)
     {
@@ -1879,9 +1880,12 @@ static void VsopCoords(const vsop_model_t *model, double t, double sphere[3])
             for (i=0; i < series->nterms; ++i)
             {
                 const vsop_term_t *term = &series->term[i];
-                sum += term->amplitude * cos(term->phase + (t * term->frequency));
+                sum  += term->amplitude * cos(term->phase + (t * term->frequency));
             }
-            sphere[k] += tpower * sum;
+            incr = tpower * sum;
+            if (k == LON_INDEX)
+                incr = fmod(incr, PI2);     /* improve precision for longitudes, which can be hundreds of radians */
+            sphere[k] += incr;
             tpower *= t;
         }
     }
@@ -1909,8 +1913,10 @@ static terse_vector_t VsopRotate(const double ecl[3])
 static void VsopSphereToRect(double lon, double lat, double radius, double pos[3])
 {
     double r_coslat = radius * cos(lat);
-    pos[0] = r_coslat * cos(lon);
-    pos[1] = r_coslat * sin(lon);
+    double coslon = cos(lon);
+    double sinlon = sin(lon);
+    pos[0] = r_coslat * coslon;
+    pos[1] = r_coslat * sinlon;
     pos[2] = radius * sin(lat);
 }
 
@@ -2965,20 +2971,26 @@ astro_horizon_t Astronomy_Horizon(
     astro_time_t *time, astro_observer_t observer, double ra, double dec, astro_refraction_t refraction)
 {
     astro_horizon_t hor;
+    double latrad, lonrad, decrad, rarad;
     double uze[3], une[3], uwe[3];
     double uz[3], un[3], uw[3];
     double p[3], pz, pn, pw, proj;
     double az, zd;
     double spin_angle;
 
-    double sinlat = sin(observer.latitude * DEG2RAD);
-    double coslat = cos(observer.latitude * DEG2RAD);
-    double sinlon = sin(observer.longitude * DEG2RAD);
-    double coslon = cos(observer.longitude * DEG2RAD);
-    double sindc = sin(dec * DEG2RAD);
-    double cosdc = cos(dec * DEG2RAD);
-    double sinra = sin(ra * 15 * DEG2RAD);
-    double cosra = cos(ra * 15 * DEG2RAD);
+    latrad = observer.latitude * DEG2RAD;
+    lonrad = observer.longitude * DEG2RAD;
+    decrad = dec * DEG2RAD;
+    rarad = ra * HOUR2RAD;
+
+    double sinlat = sin(latrad);
+    double coslat = cos(latrad);
+    double sinlon = sin(lonrad);
+    double coslon = cos(lonrad);
+    double sindc = sin(decrad);
+    double cosdc = cos(decrad);
+    double sinra = sin(rarad);
+    double cosra = cos(rarad);
 
     /*
         Calculate three mutually perpendicular unit vectors
@@ -3090,7 +3102,7 @@ astro_horizon_t Astronomy_Horizon(
             proj = sqrt(pr[0]*pr[0] + pr[1]*pr[1]);
             if (proj > 0)
             {
-                hor.ra = atan2(pr[1], pr[0]) * (RAD2DEG / 15.0);
+                hor.ra = RAD2HOUR * atan2(pr[1], pr[0]);
                 if (hor.ra < 0.0)
                     hor.ra += 24.0;
             }
@@ -3098,7 +3110,7 @@ astro_horizon_t Astronomy_Horizon(
             {
                 hor.ra = 0.0;
             }
-            hor.dec = atan2(pr[2], proj) * RAD2DEG;
+            hor.dec = RAD2DEG * atan2(pr[2], proj);
         }
     }
 
diff --git a/generate/template/astronomy.cs b/generate/template/astronomy.cs
index 5de550cb..3f3e93ab 100644
--- a/generate/template/astronomy.cs
+++ b/generate/template/astronomy.cs
@@ -1943,11 +1943,22 @@ $ASTRO_ADDSOL()
         /// </summary>
         public const double RAD2DEG = 57.295779513082321;
 
+        /// <summary>
+        /// The factor to convert radians to sidereal hours = 12/pi.
+        /// </summary>
+        public const double RAD2HOUR  = 3.819718634205488;
+
         /// <summary>
         /// The factor to convert degrees to radians = pi/180.
         /// </summary>
         public const double DEG2RAD = 0.017453292519943296;
 
+        /// <summary>
+        /// The factor to convert sidereal hours to radians = pi/12.
+        /// </summary>
+        public const double HOUR2RAD = 0.2617993877991494365;
+
+
         // Jupiter radius data are nominal values obtained from:
         // https://www.iau.org/static/resolutions/IAU2015_English.pdf
         // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -2278,7 +2289,7 @@ $ASTRO_CSHARP_VSOP(Neptune)
             }
         }
 
-        private static double VsopFormulaCalc(vsop_formula_t formula, double t)
+        private static double VsopFormulaCalc(vsop_formula_t formula, double t, bool clamp_angle)
         {
             double coord = 0.0;
             double tpower = 1.0;
@@ -2287,7 +2298,10 @@ $ASTRO_CSHARP_VSOP(Neptune)
                 double sum = 0.0;
                 foreach (vsop_term_t term in series.term)
                     sum += term.amplitude * Math.Cos(term.phase + (t * term.frequency));
-                coord += tpower * sum;
+                double incr = tpower * sum;
+                if (clamp_angle)
+                    incr %= PI2;    // improve precision: longitude angles can be hundreds of radians
+                coord += incr;
                 tpower *= t;
             }
             return coord;
@@ -2319,9 +2333,9 @@ $ASTRO_CSHARP_VSOP(Neptune)
             double t = time.tt / DAYS_PER_MILLENNIUM;    /* millennia since 2000 */
 
             /* Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates. */
-            double lat = VsopFormulaCalc(model.lat, t);
-            double lon = VsopFormulaCalc(model.lon, t);
-            double rad = VsopFormulaCalc(model.rad, t);
+            double lon = VsopFormulaCalc(model.lon, t, true);
+            double lat = VsopFormulaCalc(model.lat, t, false);
+            double rad = VsopFormulaCalc(model.rad, t, false);
 
             /* Convert ecliptic spherical coordinates to ecliptic Cartesian coordinates. */
             TerseVector eclip = VsopSphereToRect(lon, lat, rad);
@@ -2401,14 +2415,14 @@ $ASTRO_CSHARP_VSOP(Neptune)
             double t = tt / DAYS_PER_MILLENNIUM;    /* millennia since 2000 */
 
             /* Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates. */
-            double lat = VsopFormulaCalc(model.lat, t);
-            double lon = VsopFormulaCalc(model.lon, t);
-            double rad = VsopFormulaCalc(model.rad, t);
+            double lon = VsopFormulaCalc(model.lon, t, true);
+            double lat = VsopFormulaCalc(model.lat, t, false);
+            double rad = VsopFormulaCalc(model.rad, t, false);
 
             TerseVector eclip_pos = VsopSphereToRect(lon, lat, rad);
 
-            double dlat_dt = VsopDerivCalc(model.lat, t);
             double dlon_dt = VsopDerivCalc(model.lon, t);
+            double dlat_dt = VsopDerivCalc(model.lat, t);
             double drad_dt = VsopDerivCalc(model.rad, t);
 
             /* Use spherical coords and spherical derivatives to calculate */
@@ -3136,7 +3150,7 @@ $ASTRO_IAU_DATA()
             }
             else
             {
-                ra = Math.Atan2(pos.y, pos.x) / (DEG2RAD * 15.0);
+                ra = RAD2HOUR * Math.Atan2(pos.y, pos.x);
                 if (ra < 0)
                     ra += 24.0;
 
@@ -3325,7 +3339,7 @@ $ASTRO_IAU_DATA()
                 case Body.Saturn:
                 case Body.Uranus:
                 case Body.Neptune:
-                    return VsopFormulaCalc(vsop[(int)body].rad, time.tt / DAYS_PER_MILLENNIUM);
+                    return VsopFormulaCalc(vsop[(int)body].rad, time.tt / DAYS_PER_MILLENNIUM, false);
 
                 default:
                     /* For non-VSOP objects, fall back to taking the length of the heliocentric vector. */
@@ -3589,8 +3603,8 @@ $ASTRO_IAU_DATA()
             double coslon = Math.Cos(observer.longitude * DEG2RAD);
             double sindc = Math.Sin(dec * DEG2RAD);
             double cosdc = Math.Cos(dec * DEG2RAD);
-            double sinra = Math.Sin(ra * 15 * DEG2RAD);
-            double cosra = Math.Cos(ra * 15 * DEG2RAD);
+            double sinra = Math.Sin(ra * HOUR2RAD);
+            double cosra = Math.Cos(ra * HOUR2RAD);
 
             // Calculate three mutually perpendicular unit vectors
             // in equatorial coordinates: uze, une, uwe.
@@ -3679,7 +3693,7 @@ $ASTRO_IAU_DATA()
                     proj = Math.Sqrt(prx*prx + pry*pry);
                     if (proj > 0.0)
                     {
-                        hor_ra = Math.Atan2(pry, prx) * (RAD2DEG / 15.0);
+                        hor_ra = RAD2HOUR * Math.Atan2(pry, prx);
                         if (hor_ra < 0.0)
                             hor_ra += 24.0;
                     }
@@ -3687,7 +3701,7 @@ $ASTRO_IAU_DATA()
                     {
                         hor_ra = 0.0;
                     }
-                    hor_dec = Math.Atan2(prz, proj) * RAD2DEG;
+                    hor_dec = RAD2DEG * Math.Atan2(prz, proj);
                 }
             }
             else if (refraction != Refraction.None)
diff --git a/generate/template/astronomy.py b/generate/template/astronomy.py
index 8bd1d9c0..b3c586a6 100644
--- a/generate/template/astronomy.py
+++ b/generate/template/astronomy.py
@@ -56,6 +56,8 @@ CALLISTO_RADIUS_KM = 2410.3     #<const> The mean radius of Jupiter's moon Calli
 
 _CalcMoonCount = 0
 
+_RAD2HOUR  =  3.819718634205488         # 12/pi = factor to convert radians to sidereal hours
+_HOUR2RAD  =  0.2617993877991494365     # pi/12 = factor to convert sidereal hours to radians
 _DAYS_PER_TROPICAL_YEAR = 365.24217
 _PI2 = 2.0 * math.pi
 _EPOCH = datetime.datetime(2000, 1, 1, 12)
@@ -929,7 +931,7 @@ def _vector2radec(pos, time):
         else:
             dec = +90.0
     else:
-        ra = math.degrees(math.atan2(pos[1], pos[0])) / 15.0
+        ra = _RAD2HOUR * math.atan2(pos[1], pos[0])
         if ra < 0:
             ra += 24
         dec = math.degrees(math.atan2(pos[2], math.sqrt(xyproj)))
@@ -1234,11 +1236,16 @@ _vsop = [
     $ASTRO_LIST_VSOP(Neptune),
 ]
 
-def _VsopFormula(formula, t):
+def _VsopFormula(formula, t, clamp_angle):
     tpower = 1.0
     coord = 0.0
     for series in formula:
-        coord += tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        incr = tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        if clamp_angle:
+            # Longitude angles can be hundreds of radians.
+            # Improve precision by keeping each increment within [-2*pi, +2*pi].
+            incr = math.fmod(incr, _PI2)
+        coord += incr
         tpower *= t
     return coord
 
@@ -1285,7 +1292,9 @@ def _VsopSphereToRect(lon, lat, rad):
 
 def _CalcVsop(model, time):
     t = time.tt / _DAYS_PER_MILLENNIUM
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
     eclip = _VsopSphereToRect(lon, lat, rad)
     return _VsopRotate(eclip).ToAstroVector(time)
 
@@ -1298,7 +1307,10 @@ class _body_state_t:
 def _CalcVsopPosVel(model, tt):
     t = tt / _DAYS_PER_MILLENNIUM
 
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
+
     (dlon_dt, dlat_dt, drad_dt) = [_VsopDeriv(formula, t) for formula in model]
 
     # Use spherical coords and spherical derivatives to calculate
@@ -1358,7 +1370,7 @@ def _VsopHelioDistance(model, time):
     # The caller only wants to know the distance between the planet and the Sun.
     # So we only need to calculate the radial component of the spherical coordinates.
     # There is no need to translate coordinates.
-    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM)
+    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM, False)
 
 def _CalcEarth(time):
     return _CalcVsop(_vsop[Body.Earth.value], time)
@@ -2284,7 +2296,7 @@ def Horizon(time, observer, ra, dec, refraction):
     latrad = math.radians(observer.latitude)
     lonrad = math.radians(observer.longitude)
     decrad = math.radians(dec)
-    rarad = math.radians(ra * 15.0)
+    rarad = ra * _HOUR2RAD
 
     sinlat = math.sin(latrad)
     coslat = math.cos(latrad)
@@ -2377,7 +2389,7 @@ def Horizon(time, observer, ra, dec, refraction):
             pr = [(((p[j] - coszd0 * uz[j]) / sinzd0)*sinzd + uz[j]*coszd) for j in range(3)]
             proj = math.sqrt(pr[0]*pr[0] + pr[1]*pr[1])
             if proj > 0:
-                hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
+                hor_ra = _RAD2HOUR * math.atan2(pr[1], pr[0])
                 if hor_ra < 0:
                     hor_ra += 24
             else:
diff --git a/generate/template/astronomy.ts b/generate/template/astronomy.ts
index 0a38e3be..a8b86ac6 100644
--- a/generate/template/astronomy.ts
+++ b/generate/template/astronomy.ts
@@ -42,15 +42,26 @@ export type FlexibleDateTime = Date | number | AstroTime;
 export const KM_PER_AU = 1.4959787069098932e+8;
 
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 export const DEG2RAD = 0.017453292519943296;
 
+/**
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+export const HOUR2RAD = 0.2617993877991494365;
+
  /**
-  * @brief The factor to convert degrees to radians = 180/pi.
+  * @brief The factor to convert radians to degrees = 180/pi.
   */
 export const RAD2DEG = 57.295779513082321;
 
+ /**
+  * @brief The factor to convert radians to sidereal hours = 12/pi.
+  */
+export const RAD2HOUR = 3.819718634205488;
+
+
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1314,10 +1325,10 @@ function vector2radec(pos: ArrayVector, time: AstroTime): EquatorialCoordinates
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
 
-    let ra = Math.atan2(vec.y, vec.x) / (DEG2RAD * 15);
+    let ra = RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / DEG2RAD;
+    const dec = RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 
@@ -1381,8 +1392,8 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     const coslon = Math.cos(observer.longitude * DEG2RAD);
     const sindc  = Math.sin(dec * DEG2RAD);
     const cosdc  = Math.cos(dec * DEG2RAD);
-    const sinra  = Math.sin(ra * 15 * DEG2RAD);
-    const cosra  = Math.cos(ra * 15 * DEG2RAD);
+    const sinra  = Math.sin(ra * HOUR2RAD);
+    const cosra  = Math.cos(ra * HOUR2RAD);
 
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
@@ -1438,7 +1449,7 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * RAD2DEG;
+        az = -RAD2DEG * Math.atan2(pw, pn);
         if (az < 0) az += 360;
     } else {
         // The body is straight up/down, so it does not have an azimuth.
@@ -1447,7 +1458,7 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     }
 
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * RAD2DEG;
+    let zd = RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
 
@@ -1466,14 +1477,14 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
             }
             proj = Math.sqrt(pr[0]*pr[0] + pr[1]*pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * RAD2DEG / 15;
+                out_ra = RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
             } else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * RAD2DEG;
+            out_dec = RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
 
@@ -1746,7 +1757,7 @@ export function GeoMoon(date: FlexibleDateTime): Vector {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 
-function VsopFormula(formula: any, t: number): number {
+function VsopFormula(formula: any, t: number, clamp_angle: boolean): number {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -1754,7 +1765,10 @@ function VsopFormula(formula: any, t: number): number {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2;    // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -1800,18 +1814,20 @@ function VsopRotate(eclip: ArrayVector): TerseVector {
 function VsopSphereToRect(lon: number, lat: number, radius: number): ArrayVector {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 
 function CalcVsop(model: any[], time: AstroTime): Vector {
     const t = time.tt / DAYS_PER_MILLENNIUM;   // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
@@ -1820,9 +1836,9 @@ function CalcVsopPosVel(model: any[], tt: number): body_state_t {
     const t = tt / DAYS_PER_MILLENNIUM;
 
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
 
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
@@ -2422,7 +2438,7 @@ export function HelioVector(body: Body, date: FlexibleDateTime): Vector {
 export function HelioDistance(body: Body, date: FlexibleDateTime): number {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
@@ -5663,7 +5679,7 @@ function GeoidIntersect(shadow: ShadowInfo): GlobalSolarEclipseInfo {
 
         // Adjust longitude for Earth's rotation at the given UT.
         const gast = sidereal_time(peak);
-        longitude = (RAD2DEG * Math.atan2(py, px) - (15*gast)) % 360.0;
+        longitude = (RAD2DEG*Math.atan2(py, px) - (15*gast)) % 360.0;
         if (longitude <= -180.0) {
             longitude += 360.0;
         } else if (longitude > +180.0) {
diff --git a/generate/test.js b/generate/test.js
index b63e840e..097c0397 100644
--- a/generate/test.js
+++ b/generate/test.js
@@ -2,8 +2,6 @@
 const fs = require('fs');
 const Astronomy = require('../source/js/astronomy.min.js');
 let Verbose = false;
-const DEG2RAD = 0.017453292519943296;
-const RAD2DEG = 57.295779513082321;
 
 function Fail(message) {
     console.trace();
@@ -406,11 +404,13 @@ function LunarEclipse() {
 }
 
 function VectorFromAngles(lat, lon) {
-    const coslat = cos(DEG2RAD * lat);
+    const latrad = Astronomy.DEG2RAD * lat;
+    const lonrad = Astronomy.DEG2RAD * lon;
+    const coslat = cos(latrad);
     return [
-        cos(DEG2RAD * lon) * coslat,
-        sin(DEG2RAD * lon) * coslat,
-        sin(DEG2RAD * lat)
+        cos(lonrad) * coslat,
+        sin(lonrad) * coslat,
+        sin(latrad)
     ];
 }
 
@@ -425,7 +425,7 @@ function AngleDiff(alat, alon, blat, blon) {
     if (dot >= +1.0) {
         return 0.0;
     }
-    return v(RAD2DEG * Math.acos(dot));
+    return v(Astronomy.RAD2DEG * Math.acos(dot));
 }
 
 
@@ -1269,7 +1269,7 @@ function Rotation() {
         const et = Astronomy.RotateVector(ir, ee);
         const idiff = VectorDiff(et, ev);
         if (Verbose) console.log(`JS Test_EQJ_ECL ev diff = ${idiff}`);
-        if (idiff > 2.0e-16)
+        if (idiff > 2.3e-16)
             throw 'Test_EQJ_ECL: EXCESSIVE REVERSE ROTATION ERROR';
     }
 
@@ -1333,7 +1333,7 @@ function Rotation() {
         const diff_az = abs(xsphere.lon - hor.azimuth);
 
         if (Verbose) console.log(`JS Test_EQD_HOR ${body}: trusted alt=${hor.altitude}, az=${hor.azimuth}; test alt=${xsphere.lat}, az=${xsphere.lon}; diff_alt=${diff_alt}, diff_az=${diff_az}`);
-        if (diff_alt > 4.0e-14 || diff_az > 1.0e-13)
+        if (diff_alt > 4.3e-14 || diff_az > 1.2e-13)
             throw 'Test_EQD_HOR: EXCESSIVE HORIZONTAL ERROR.';
 
         /* Confirm that we can convert back to horizontal vector. */
@@ -1348,7 +1348,7 @@ function Rotation() {
         const check_eqd = Astronomy.RotateVector(irot, vec_hor);
         diff = VectorDiff(check_eqd, vec_eqd);
         if (Verbose) console.log(`JS Test_EQD_HOR ${body}: OFDATE inverse rotation diff = ${diff}`);
-        if (diff > 2.0e-15)
+        if (diff > 2.1e-15)
             throw 'Test_EQD_HOR: EXCESSIVE OFDATE INVERSE HORIZONTAL ERROR.';
 
         /* Exercise HOR to EQJ translation. */
@@ -1976,11 +1976,31 @@ function JupiterMoons() {
 }
 
 
+function Issue103() {
+    // https://github.com/cosinekitty/astronomy/issues/103
+
+    const observer = new Astronomy.Observer(29, -81, 10);
+    const ut = -51279.9420508868643083;
+    const time = Astronomy.MakeTime(ut);
+    const ofdate = Astronomy.Equator(Astronomy.Body.Moon, time, observer, true, true);
+
+    console.log(`tt  = ${time.tt.toFixed(16)}`);
+    console.log(`ra  = ${ofdate.ra.toFixed(16)}`);
+    console.log(`dec = ${ofdate.dec.toFixed(16)}`);
+    const hor = Astronomy.Horizon(time, observer, ofdate.ra, ofdate.dec, false);
+    console.log(`az  = ${hor.azimuth.toFixed(16)}`);
+    console.log(`alt = ${hor.altitude.toFixed(16)}`);
+
+    return 0;
+}
+
+
 const UnitTests = {
     constellation:          Constellation,
     elongation:             Elongation,
     geoid:                  Geoid,
     global_solar_eclipse:   GlobalSolarEclipse,
+    issue_103:              Issue103,
     jupiter_moons:          JupiterMoons,
     local_solar_eclipse:    LocalSolarEclipse,
     lunar_apsis:            LunarApsis,
diff --git a/generate/test.py b/generate/test.py
index b76f2da1..55ff492f 100755
--- a/generate/test.py
+++ b/generate/test.py
@@ -850,7 +850,7 @@ def Test_EQJ_ECL():
     et = astronomy.RotateVector(ir, ee)
     idiff = VectorDiff(et, ev)
     Debug('PY Test_EQJ_ECL ev diff = {}'.format(idiff))
-    if idiff > 2.0e-16:
+    if idiff > 2.3e-16:
         print('PY Test_EQJ_ECL: EXCESSIVE REVERSE ROTATION ERROR')
         sys.exit(1)
 
@@ -921,7 +921,7 @@ def Test_EQD_HOR(body):
     Debug('PY Test_EQD_HOR {}: trusted alt={}, az={}; test alt={}, az={}; diff_alt={}, diff_az={}'.format(
         body.name, hor.altitude, hor.azimuth, xsphere.lat, xsphere.lon, diff_alt, diff_az))
 
-    if diff_alt > 4.0e-14 or diff_az > 1.0e-13:
+    if diff_alt > 4.0e-14 or diff_az > 1.2e-13:
         print('PY Test_EQD_HOR: EXCESSIVE HORIZONTAL ERROR.')
         sys.exit(1)
 
@@ -1780,11 +1780,27 @@ def JupiterMoons():
 
 #-----------------------------------------------------------------------------------------------------------
 
+def Issue103():
+    # https://github.com/cosinekitty/astronomy/issues/103
+    observer = astronomy.Observer(29, -81, 10)
+    ut = -39864.1907264927140204
+    time = astronomy.Time(ut)
+    body = astronomy.Body.Venus
+    ofdate = astronomy.Equator(body, time, observer, True, True)
+    hor = astronomy.Horizon(time, observer, ofdate.ra, ofdate.dec, astronomy.Refraction.Airless)
+    print('tt  = {:23.16f}'.format(time.tt))
+    print('az  = {:23.16f}'.format(hor.azimuth))
+    print('alt = {:23.16f}'.format(hor.altitude))
+    return 0
+
+#-----------------------------------------------------------------------------------------------------------
+
 UnitTests = {
     'constellation':            Constellation,
     'elongation':               Elongation,
     'geoid':                    Geoid,
     'global_solar_eclipse':     GlobalSolarEclipse,
+    'issue_103':                Issue103,
     'jupiter_moons':            JupiterMoons,
     'local_solar_eclipse':      LocalSolarEclipse,
     'lunar_apsis':              LunarApsis,
diff --git a/source/c/README.md b/source/c/README.md
index 50aed1a4..6c097f84 100644
--- a/source/c/README.md
+++ b/source/c/README.md
@@ -2321,7 +2321,7 @@ Calculates the non-negative length of the given vector. The length is expressed
 <a name="DEG2RAD"></a>
 ### `DEG2RAD`
 
-**The factor to convert radians to degrees = pi/180.** 
+**The factor to convert degrees to radians = pi/180.** 
 
 
 
@@ -2361,6 +2361,21 @@ Calculates the non-negative length of the given vector. The length is expressed
 
 
 
+---
+
+<a name="HOUR2RAD"></a>
+### `HOUR2RAD`
+
+**The factor to convert sidereal hours to radians = pi/12.** 
+
+
+
+```C
+#define HOUR2RAD  0.2617993877991494365
+```
+
+
+
 ---
 
 <a name="IO_RADIUS_KM"></a>
@@ -2546,7 +2561,7 @@ Calculates the non-negative length of the given vector. The length is expressed
 <a name="RAD2DEG"></a>
 ### `RAD2DEG`
 
-**The factor to convert degrees to radians = 180/pi.** 
+**The factor to convert radians to degrees = 180/pi.** 
 
 
 
@@ -2556,6 +2571,21 @@ Calculates the non-negative length of the given vector. The length is expressed
 
 
 
+---
+
+<a name="RAD2HOUR"></a>
+### `RAD2HOUR`
+
+**The factor to convert radians to sidereal hours = 12/pi.** 
+
+
+
+```C
+#define RAD2HOUR  3.819718634205488
+```
+
+
+
 ---
 
 <a name="TIME_TEXT_BYTES"></a>
diff --git a/source/c/astronomy.c b/source/c/astronomy.c
index 527f9eb1..090fbc1b 100644
--- a/source/c/astronomy.c
+++ b/source/c/astronomy.c
@@ -1420,7 +1420,7 @@ static astro_equatorial_t vector2radec(const double pos[3], astro_time_t time)
     }
     else
     {
-        equ.ra = atan2(pos[1], pos[0]) / (DEG2RAD * 15.0);
+        equ.ra = RAD2HOUR * atan2(pos[1], pos[0]);
         if (equ.ra < 0)
             equ.ra += 24.0;
 
@@ -2872,6 +2872,7 @@ static const vsop_model_t vsop[] =
 static void VsopCoords(const vsop_model_t *model, double t, double sphere[3])
 {
     int k, s, i;
+    double incr;
 
     for (k=0; k < 3; ++k)
     {
@@ -2885,9 +2886,12 @@ static void VsopCoords(const vsop_model_t *model, double t, double sphere[3])
             for (i=0; i < series->nterms; ++i)
             {
                 const vsop_term_t *term = &series->term[i];
-                sum += term->amplitude * cos(term->phase + (t * term->frequency));
+                sum  += term->amplitude * cos(term->phase + (t * term->frequency));
             }
-            sphere[k] += tpower * sum;
+            incr = tpower * sum;
+            if (k == LON_INDEX)
+                incr = fmod(incr, PI2);     /* improve precision for longitudes, which can be hundreds of radians */
+            sphere[k] += incr;
             tpower *= t;
         }
     }
@@ -2915,8 +2919,10 @@ static terse_vector_t VsopRotate(const double ecl[3])
 static void VsopSphereToRect(double lon, double lat, double radius, double pos[3])
 {
     double r_coslat = radius * cos(lat);
-    pos[0] = r_coslat * cos(lon);
-    pos[1] = r_coslat * sin(lon);
+    double coslon = cos(lon);
+    double sinlon = sin(lon);
+    pos[0] = r_coslat * coslon;
+    pos[1] = r_coslat * sinlon;
     pos[2] = radius * sin(lat);
 }
 
@@ -4191,20 +4197,26 @@ astro_horizon_t Astronomy_Horizon(
     astro_time_t *time, astro_observer_t observer, double ra, double dec, astro_refraction_t refraction)
 {
     astro_horizon_t hor;
+    double latrad, lonrad, decrad, rarad;
     double uze[3], une[3], uwe[3];
     double uz[3], un[3], uw[3];
     double p[3], pz, pn, pw, proj;
     double az, zd;
     double spin_angle;
 
-    double sinlat = sin(observer.latitude * DEG2RAD);
-    double coslat = cos(observer.latitude * DEG2RAD);
-    double sinlon = sin(observer.longitude * DEG2RAD);
-    double coslon = cos(observer.longitude * DEG2RAD);
-    double sindc = sin(dec * DEG2RAD);
-    double cosdc = cos(dec * DEG2RAD);
-    double sinra = sin(ra * 15 * DEG2RAD);
-    double cosra = cos(ra * 15 * DEG2RAD);
+    latrad = observer.latitude * DEG2RAD;
+    lonrad = observer.longitude * DEG2RAD;
+    decrad = dec * DEG2RAD;
+    rarad = ra * HOUR2RAD;
+
+    double sinlat = sin(latrad);
+    double coslat = cos(latrad);
+    double sinlon = sin(lonrad);
+    double coslon = cos(lonrad);
+    double sindc = sin(decrad);
+    double cosdc = cos(decrad);
+    double sinra = sin(rarad);
+    double cosra = cos(rarad);
 
     /*
         Calculate three mutually perpendicular unit vectors
@@ -4316,7 +4328,7 @@ astro_horizon_t Astronomy_Horizon(
             proj = sqrt(pr[0]*pr[0] + pr[1]*pr[1]);
             if (proj > 0)
             {
-                hor.ra = atan2(pr[1], pr[0]) * (RAD2DEG / 15.0);
+                hor.ra = RAD2HOUR * atan2(pr[1], pr[0]);
                 if (hor.ra < 0.0)
                     hor.ra += 24.0;
             }
@@ -4324,7 +4336,7 @@ astro_horizon_t Astronomy_Horizon(
             {
                 hor.ra = 0.0;
             }
-            hor.dec = atan2(pr[2], proj) * RAD2DEG;
+            hor.dec = RAD2DEG * atan2(pr[2], proj);
         }
     }
 
diff --git a/source/c/astronomy.h b/source/c/astronomy.h
index aee5ffa1..66f17c5c 100644
--- a/source/c/astronomy.h
+++ b/source/c/astronomy.h
@@ -44,16 +44,28 @@ extern "C" {
 
 /**
  * \def DEG2RAD
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 #define DEG2RAD     0.017453292519943296
 
+/**
+ * \def HOUR2RAD
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+#define HOUR2RAD    0.2617993877991494365
+
 /**
  * \def RAD2DEG
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 #define RAD2DEG     57.295779513082321
 
+/**
+ * \def RAD2HOUR
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+#define RAD2HOUR    3.819718634205488
+
 /*
     Jupiter radius data are nominal values obtained from:
     https://www.iau.org/static/resolutions/IAU2015_English.pdf
diff --git a/source/csharp/README.md b/source/csharp/README.md
index 666bd910..5b189144 100644
--- a/source/csharp/README.md
+++ b/source/csharp/README.md
@@ -178,6 +178,14 @@ these are used in function and type names.
 **The The mean radius of Jupiter's moon Ganymede, expressed in kilometers.**
 
 
+---
+
+<a name="Astronomy.HOUR2RAD"></a>
+### `const double Astronomy.HOUR2RAD = 0.26179938779914946;`
+
+**The factor to convert sidereal hours to radians = pi/12.**
+
+
 ---
 
 <a name="Astronomy.IO_RADIUS_KM"></a>
@@ -226,6 +234,14 @@ these are used in function and type names.
 **The factor to convert radians to degrees = 180/pi.**
 
 
+---
+
+<a name="Astronomy.RAD2HOUR"></a>
+### `const double Astronomy.RAD2HOUR = 3.819718634205488;`
+
+**The factor to convert radians to sidereal hours = 12/pi.**
+
+
 ---
 
 <a name="functions"></a>
diff --git a/source/csharp/astronomy.cs b/source/csharp/astronomy.cs
index 21fecfbd..99fac5e9 100644
--- a/source/csharp/astronomy.cs
+++ b/source/csharp/astronomy.cs
@@ -2048,11 +2048,22 @@ namespace CosineKitty
         /// </summary>
         public const double RAD2DEG = 57.295779513082321;
 
+        /// <summary>
+        /// The factor to convert radians to sidereal hours = 12/pi.
+        /// </summary>
+        public const double RAD2HOUR  = 3.819718634205488;
+
         /// <summary>
         /// The factor to convert degrees to radians = pi/180.
         /// </summary>
         public const double DEG2RAD = 0.017453292519943296;
 
+        /// <summary>
+        /// The factor to convert sidereal hours to radians = pi/12.
+        /// </summary>
+        public const double HOUR2RAD = 0.2617993877991494365;
+
+
         // Jupiter radius data are nominal values obtained from:
         // https://www.iau.org/static/resolutions/IAU2015_English.pdf
         // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -3210,7 +3221,7 @@ namespace CosineKitty
             }
         }
 
-        private static double VsopFormulaCalc(vsop_formula_t formula, double t)
+        private static double VsopFormulaCalc(vsop_formula_t formula, double t, bool clamp_angle)
         {
             double coord = 0.0;
             double tpower = 1.0;
@@ -3219,7 +3230,10 @@ namespace CosineKitty
                 double sum = 0.0;
                 foreach (vsop_term_t term in series.term)
                     sum += term.amplitude * Math.Cos(term.phase + (t * term.frequency));
-                coord += tpower * sum;
+                double incr = tpower * sum;
+                if (clamp_angle)
+                    incr %= PI2;    // improve precision: longitude angles can be hundreds of radians
+                coord += incr;
                 tpower *= t;
             }
             return coord;
@@ -3251,9 +3265,9 @@ namespace CosineKitty
             double t = time.tt / DAYS_PER_MILLENNIUM;    /* millennia since 2000 */
 
             /* Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates. */
-            double lat = VsopFormulaCalc(model.lat, t);
-            double lon = VsopFormulaCalc(model.lon, t);
-            double rad = VsopFormulaCalc(model.rad, t);
+            double lon = VsopFormulaCalc(model.lon, t, true);
+            double lat = VsopFormulaCalc(model.lat, t, false);
+            double rad = VsopFormulaCalc(model.rad, t, false);
 
             /* Convert ecliptic spherical coordinates to ecliptic Cartesian coordinates. */
             TerseVector eclip = VsopSphereToRect(lon, lat, rad);
@@ -3333,14 +3347,14 @@ namespace CosineKitty
             double t = tt / DAYS_PER_MILLENNIUM;    /* millennia since 2000 */
 
             /* Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates. */
-            double lat = VsopFormulaCalc(model.lat, t);
-            double lon = VsopFormulaCalc(model.lon, t);
-            double rad = VsopFormulaCalc(model.rad, t);
+            double lon = VsopFormulaCalc(model.lon, t, true);
+            double lat = VsopFormulaCalc(model.lat, t, false);
+            double rad = VsopFormulaCalc(model.rad, t, false);
 
             TerseVector eclip_pos = VsopSphereToRect(lon, lat, rad);
 
-            double dlat_dt = VsopDerivCalc(model.lat, t);
             double dlon_dt = VsopDerivCalc(model.lon, t);
+            double dlat_dt = VsopDerivCalc(model.lat, t);
             double drad_dt = VsopDerivCalc(model.rad, t);
 
             /* Use spherical coords and spherical derivatives to calculate */
@@ -4336,7 +4350,7 @@ namespace CosineKitty
             }
             else
             {
-                ra = Math.Atan2(pos.y, pos.x) / (DEG2RAD * 15.0);
+                ra = RAD2HOUR * Math.Atan2(pos.y, pos.x);
                 if (ra < 0)
                     ra += 24.0;
 
@@ -4525,7 +4539,7 @@ namespace CosineKitty
                 case Body.Saturn:
                 case Body.Uranus:
                 case Body.Neptune:
-                    return VsopFormulaCalc(vsop[(int)body].rad, time.tt / DAYS_PER_MILLENNIUM);
+                    return VsopFormulaCalc(vsop[(int)body].rad, time.tt / DAYS_PER_MILLENNIUM, false);
 
                 default:
                     /* For non-VSOP objects, fall back to taking the length of the heliocentric vector. */
@@ -4789,8 +4803,8 @@ namespace CosineKitty
             double coslon = Math.Cos(observer.longitude * DEG2RAD);
             double sindc = Math.Sin(dec * DEG2RAD);
             double cosdc = Math.Cos(dec * DEG2RAD);
-            double sinra = Math.Sin(ra * 15 * DEG2RAD);
-            double cosra = Math.Cos(ra * 15 * DEG2RAD);
+            double sinra = Math.Sin(ra * HOUR2RAD);
+            double cosra = Math.Cos(ra * HOUR2RAD);
 
             // Calculate three mutually perpendicular unit vectors
             // in equatorial coordinates: uze, une, uwe.
@@ -4879,7 +4893,7 @@ namespace CosineKitty
                     proj = Math.Sqrt(prx*prx + pry*pry);
                     if (proj > 0.0)
                     {
-                        hor_ra = Math.Atan2(pry, prx) * (RAD2DEG / 15.0);
+                        hor_ra = RAD2HOUR * Math.Atan2(pry, prx);
                         if (hor_ra < 0.0)
                             hor_ra += 24.0;
                     }
@@ -4887,7 +4901,7 @@ namespace CosineKitty
                     {
                         hor_ra = 0.0;
                     }
-                    hor_dec = Math.Atan2(prz, proj) * RAD2DEG;
+                    hor_dec = RAD2DEG * Math.Atan2(prz, proj);
                 }
             }
             else if (refraction != Refraction.None)
diff --git a/source/js/README.md b/source/js/README.md
index cf16c3b8..9fca91ca 100644
--- a/source/js/README.md
+++ b/source/js/README.md
@@ -725,7 +725,15 @@ The calculations are performed from the point of view of a geocentric observer.
 
 ## DEG2RAD
 **Kind**: global variable  
-**Brief**: The factor to convert radians to degrees = pi/180.  
+**Brief**: The factor to convert degrees to radians = pi/180.  
+
+* * *
+
+<a name="HOUR2RAD"></a>
+
+## HOUR2RAD
+**Kind**: global variable  
+**Brief**: The factor to convert sidereal hours to radians = pi/12.  
 
 * * *
 
@@ -733,7 +741,15 @@ The calculations are performed from the point of view of a geocentric observer.
 
 ## RAD2DEG
 **Kind**: global variable  
-**Brief**: The factor to convert degrees to radians = 180/pi.  
+**Brief**: The factor to convert radians to degrees = 180/pi.  
+
+* * *
+
+<a name="RAD2HOUR"></a>
+
+## RAD2HOUR
+**Kind**: global variable  
+**Brief**: The factor to convert radians to sidereal hours = 12/pi.  
 
 * * *
 
diff --git a/source/js/astronomy.browser.js b/source/js/astronomy.browser.js
index fa536b0f..bed61a5b 100644
--- a/source/js/astronomy.browser.js
+++ b/source/js/astronomy.browser.js
@@ -34,21 +34,29 @@
  */
 'use strict';
 Object.defineProperty(exports, "__esModule", { value: true });
-exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2DEG = exports.DEG2RAD = exports.KM_PER_AU = void 0;
-exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = void 0;
+exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = void 0;
+exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = void 0;
 /**
  * @brief The number of kilometers per astronomical unit.
  */
 exports.KM_PER_AU = 1.4959787069098932e+8;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 exports.DEG2RAD = 0.017453292519943296;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+exports.HOUR2RAD = 0.2617993877991494365;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 exports.RAD2DEG = 57.295779513082321;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+exports.RAD2HOUR = 3.819718634205488;
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1972,10 +1980,10 @@ function vector2radec(pos, time) {
             return new EquatorialCoordinates(0, -90, dist, vec);
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
-    let ra = Math.atan2(vec.y, vec.x) / (exports.DEG2RAD * 15);
+    let ra = exports.RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / exports.DEG2RAD;
+    const dec = exports.RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 function spin(angle, pos) {
@@ -2036,8 +2044,8 @@ function Horizon(date, observer, ra, dec, refraction) {
     const coslon = Math.cos(observer.longitude * exports.DEG2RAD);
     const sindc = Math.sin(dec * exports.DEG2RAD);
     const cosdc = Math.cos(dec * exports.DEG2RAD);
-    const sinra = Math.sin(ra * 15 * exports.DEG2RAD);
-    const cosra = Math.cos(ra * 15 * exports.DEG2RAD);
+    const sinra = Math.sin(ra * exports.HOUR2RAD);
+    const cosra = Math.cos(ra * exports.HOUR2RAD);
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
     //
@@ -2083,7 +2091,7 @@ function Horizon(date, observer, ra, dec, refraction) {
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * exports.RAD2DEG;
+        az = -exports.RAD2DEG * Math.atan2(pw, pn);
         if (az < 0)
             az += 360;
     }
@@ -2093,7 +2101,7 @@ function Horizon(date, observer, ra, dec, refraction) {
         az = 0;
     }
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * exports.RAD2DEG;
+    let zd = exports.RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
     if (refraction) {
@@ -2111,7 +2119,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             }
             proj = Math.sqrt(pr[0] * pr[0] + pr[1] * pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * exports.RAD2DEG / 15;
+                out_ra = exports.RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
@@ -2119,7 +2127,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * exports.RAD2DEG;
+            out_dec = exports.RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
     return new HorizontalCoordinates(az, 90 - zd, out_ra, out_dec);
@@ -2373,7 +2381,7 @@ function GeoMoon(date) {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 exports.GeoMoon = GeoMoon;
-function VsopFormula(formula, t) {
+function VsopFormula(formula, t, clamp_angle) {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2381,7 +2389,10 @@ function VsopFormula(formula, t) {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2; // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2419,26 +2430,28 @@ function VsopRotate(eclip) {
 function VsopSphereToRect(lon, lat, radius) {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 function CalcVsop(model, time) {
     const t = time.tt / DAYS_PER_MILLENNIUM; // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
 function CalcVsopPosVel(model, tt) {
     const t = tt / DAYS_PER_MILLENNIUM;
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
     const drad_dt = VsopDeriv(model[RAD_INDEX], t);
@@ -3087,7 +3100,7 @@ exports.HelioVector = HelioVector;
 function HelioDistance(body, date) {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
diff --git a/source/js/astronomy.browser.min.js b/source/js/astronomy.browser.min.js
index c9bdcfca..11b17ce4 100644
--- a/source/js/astronomy.browser.min.js
+++ b/source/js/astronomy.browser.min.js
@@ -35,16 +35,16 @@ $jscomp.polyfillUnisolated=function(q,t,e,A){e=$jscomp.global;q=q.split(".");for
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 $jscomp.polyfill("Number.isInteger",function(q){return q?q:function(t){return Number.isFinite(t)?t===Math.floor(t):!1}},"es6","es3");$jscomp.polyfill("Number.isSafeInteger",function(q){return q?q:function(t){return Number.isInteger(t)&&Math.abs(t)<=Number.MAX_SAFE_INTEGER}},"es6","es3");
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+P;}P=e[M]={exports:{}};t[M][0].call(P.exports,function(ra){return v(t[M][1][ra]||ra)},P,P.exports,q,t,e,A)}return e[M].exports}for(var L="function"==typeof require&&require,S=0;S<A.length;S++)v(A[S]);return v}return q}()({1:[function(q,t,e){function A(a){if(!0!==a&&!1!==a)throw console.trace(),"Value is not boolean: "+a;return a}function v(a){if(!Number.isFinite(a))throw console.trace(),"Value is not a finite number: "+a;return a}function L(a){return a-Math.floor(a)}function S(a,b){var c=a.x*a.x+
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-b-1900,b=a*a,-2.79+1.494119*a-.0598939*b+.0061966*a*b-1.97E-4*b*b;if(1941>b)return a=b-1920,b=a*a,21.2+.84493*a-.0761*b+.0020936*a*b;if(1961>b)return a=b-1950,b=a*a,29.07+.407*a-b/233+a*b/2547;if(1986>b)return a=b-1975,b=a*a,45.45+1.067*a-b/260-a*b/718;if(2005>b)return a=b-2E3,b=a*a,c=a*b,63.86+.3345*a-.060374*b+.0017275*c+6.51814E-4*b*b+2.373599E-5*b*c;if(2050>b)return a=b-2E3,62.92+.32217*a+.005589*a*a;if(2150>b)return a=(b-1820)/100,-20+32*a*a-.5628*(2150-b);a=(b-1820)/100;return-20+32*a*a}function O(a){return a+
+b-1900,b=a*a,-2.79+1.494119*a-.0598939*b+.0061966*a*b-1.97E-4*b*b;if(1941>b)return a=b-1920,b=a*a,21.2+.84493*a-.0761*b+.0020936*a*b;if(1961>b)return a=b-1950,b=a*a,29.07+.407*a-b/233+a*b/2547;if(1986>b)return a=b-1975,b=a*a,45.45+1.067*a-b/260-a*b/718;if(2005>b)return a=b-2E3,b=a*a,c=a*b,63.86+.3345*a-.060374*b+.0017275*c+6.51814E-4*b*b+2.373599E-5*b*c;if(2050>b)return a=b-2E3,62.92+.32217*a+.005589*a*a;if(2150>b)return a=(b-1820)/100,-20+32*a*a-.5628*(2150-b);a=(b-1820)/100;return-20+32*a*a}function P(a){return a+
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 -.02,0,0,1,0,2,2);g(-45.099,-.02,0,-.001,1,0,2,0);g(-.179,-9.52,0,-.0833,1,0,2,-2);g(-.301,-.33,0,.0014,1,0,2,-4);g(-6.382,-3.37,0,-.0481,1,0,-2,2);g(39.528,85.13,0,-.7136,1,0,-2,0);g(9.366,.71,0,-.0112,1,0,-2,-2);g(.202,.02,0,0,1,0,-2,-4);g(.415,.1,0,.0013,0,1,2,0);g(-2.152,-2.26,0,-.0066,0,1,2,-2);g(-1.44,-1.3,0,.0014,0,1,-2,2);g(.384,-.04,0,0,0,1,-2,-2);g(1.938,3.6,-.145,.0401,4,0,0,0);g(-.952,-1.58,.052,-.013,4,0,0,-2);g(-.551,-.94,.032,-.0097,3,1,0,0);g(-.482,-.57,.005,-.0045,3,1,0,-2);g(.681,
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 1,-2).y;z+=-6*k(1,0,1,-4).y;z+=20.599*k(-1,0,1,0).y;z+=-30.598*k(-1,0,1,-2).y;z+=-24.649*k(-2,0,1,0).y;z+=-2*k(-2,0,1,-2).y;z+=-22.571*k(0,1,1,-2).y;z+=10.985*k(0,-1,1,-2).y;p+=.82*l(.7736-62.5512*a)+.31*l(.0466-125.1025*a)+.35*l(.5785-25.1042*a)+.66*l(.4591+1335.8075*a)+.64*l(.313-91.568*a)+1.14*l(.148+1331.2898*a)+.21*l(.5918+1056.5859*a)+.44*l(.5784+1322.8595*a)+.24*l(.2275-5.7374*a)+.28*l(.2965+2.6929*a)+.33*l(.3132+6.3368*a);a=V+r/W;a=(1.000002708+139.978*ca)*(18518.511+1.189+sa)*Math.sin(a)-
-6.24*Math.sin(3*a)+z;return{geo_eclip_lon:P*L((Ja+p/W)/P),geo_eclip_lat:Math.PI/648E3*a,distance_au:W*Ec/(.999953253*ba)}}function bb(a,b,c){b=cb(b,c);return[b.rot[0][0]*a[0]+b.rot[1][0]*a[1]+b.rot[2][0]*a[2],b.rot[0][1]*a[0]+b.rot[1][1]*a[1]+b.rot[2][1]*a[2],b.rot[0][2]*a[0]+b.rot[1][2]*a[1]+b.rot[2][2]*a[2]]}function cb(a,b){a=a.tt/36525;var c=84381.406,d=((((3.337E-7*a-4.67E-7)*a-.00772503)*a+.0512623)*a-.025754)*a+c;c*=4.84813681109536E-6;var f=((((-9.51E-8*a+1.32851E-4)*a-.00114045)*a-1.0790069)*
+6.24*Math.sin(3*a)+z;return{geo_eclip_lon:O*L((Ja+p/W)/O),geo_eclip_lat:Math.PI/648E3*a,distance_au:W*Ec/(.999953253*ba)}}function bb(a,b,c){b=cb(b,c);return[b.rot[0][0]*a[0]+b.rot[1][0]*a[1]+b.rot[2][0]*a[2],b.rot[0][1]*a[0]+b.rot[1][1]*a[1]+b.rot[2][1]*a[2],b.rot[0][2]*a[0]+b.rot[1][2]*a[1]+b.rot[2][2]*a[2]]}function cb(a,b){a=a.tt/36525;var c=84381.406,d=((((3.337E-7*a-4.67E-7)*a-.00772503)*a+.0512623)*a-.025754)*a+c;c*=4.84813681109536E-6;var f=((((-9.51E-8*a+1.32851E-4)*a-.00114045)*a-1.0790069)*
 a+5038.481507)*a*4.84813681109536E-6;d*=4.84813681109536E-6;var h=((((-5.6E-8*a+1.70663E-4)*a-.00121197)*a-2.3814292)*a+10.556403)*a*4.84813681109536E-6;a=Math.sin(c);c=Math.cos(c);var l=Math.sin(-f);f=Math.cos(-f);var k=Math.sin(-d);d=Math.cos(-d);var g=Math.sin(h),m=Math.cos(h);h=m*f-l*g*d;var n=m*l*c+g*d*f*c-a*g*k,p=m*l*a+g*d*f*a+c*g*k,r=-g*f-l*m*d,w=-g*l*c+m*d*f*c-a*m*k;g=-g*l*a+m*d*f*a+c*m*k;l*=k;m=-k*f*c-a*d;a=-k*f*a+d*c;if(b===H.Into2000)return new K([[h,n,p],[r,w,g],[l,m,a]]);if(b===H.From2000)return new K([[h,
 r,l],[n,w,m],[p,g,a]]);throw"Invalid precess direction";}function ka(a){var b=a.tt/36525,c=15*Ga(a).ee;a=(.779057273264+.00273781191135448*a.ut+a.ut%1)%1*360;0>a&&(a+=360);b=((c+.014506+((((-3.68E-8*b-2.9956E-5)*b-4.4E-7)*b+1.3915817)*b+4612.156534)*b)/3600+a)%360/15;0>b&&(b+=24);return b}function Bb(a,b){var c=a.latitude*e.DEG2RAD,d=Math.sin(c);c=Math.cos(c);var f=1/Math.sqrt(c*c+.9933056020041345*d*d),h=a.height/1E3,l=6378.1366*f+h;b=(15*b+a.longitude)*e.DEG2RAD;a=Math.sin(b);b=Math.cos(b);return{pos:[l*
 c*b/e.KM_PER_AU,l*c*a/e.KM_PER_AU,(6335.438815127603*f+h)*d/e.KM_PER_AU],vel:[-7.292115E-5*l*c*a*86400,7.292115E-5*l*c*b*86400,0]}}function Cb(a,b,c){b=db(b,c);return[b.rot[0][0]*a[0]+b.rot[1][0]*a[1]+b.rot[2][0]*a[2],b.rot[0][1]*a[0]+b.rot[1][1]*a[1]+b.rot[2][1]*a[2],b.rot[0][2]*a[0]+b.rot[1][2]*a[1]+b.rot[2][2]*a[2]]}function db(a,b){a=Ga(a);var c=a.mobl*e.DEG2RAD,d=a.tobl*e.DEG2RAD,f=4.84813681109536E-6*a.dpsi;a=Math.cos(c);c=Math.sin(c);var h=Math.cos(d),l=Math.sin(d);d=Math.cos(f);var k=Math.sin(f);
 f=-k*a;var g=-k*c,m=k*h,n=d*a*h+c*l,p=d*c*h-a*l;k*=l;var r=d*a*l-c*h;a=d*c*l+a*h;if(b===H.From2000)return new K([[d,m,k],[f,n,r],[g,p,a]]);if(b===H.Into2000)return new K([[d,f,g],[m,n,p],[k,r,a]]);throw"Invalid precess direction";}function La(a,b,c){return c===H.Into2000?bb(Cb(a,b,c),b,c):Cb(bb(a,b,c),b,c)}function Db(a,b){var c=ka(a);b=Bb(b,c).pos;return La(b,a,H.Into2000)}function Fc(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;
-for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}function Eb(a,b){b=new D(a[0],a[1],a[2],b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return 0>b.z?new ua(0,-90,d,b):new ua(0,90,d,b)}var f=Math.atan2(b.y,b.x)/(15*e.DEG2RAD);0>f&&(f+=24);return new ua(f,Math.atan2(a[2],Math.sqrt(c))/e.DEG2RAD,d,b)}function la(a,b){var c=a*e.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}function Ma(a,b,c,d,f){a=
-y(a);ma(b);v(c);v(d);var h=Math.sin(b.latitude*e.DEG2RAD),l=Math.cos(b.latitude*e.DEG2RAD),k=Math.sin(b.longitude*e.DEG2RAD),g=Math.cos(b.longitude*e.DEG2RAD);b=Math.sin(d*e.DEG2RAD);var m=Math.cos(d*e.DEG2RAD),n=Math.sin(15*c*e.DEG2RAD),p=Math.cos(15*c*e.DEG2RAD),r=[l*g,l*k,h];h=[-h*g,-h*k,l];k=[k,-g,0];l=-15*ka(a);a=la(l,r);r=la(l,h);k=la(l,k);b=[m*p,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];m=b[0]*r[0]+b[1]*r[1]+b[2]*r[2];r=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];p=Math.sqrt(m*m+r*r);0<p?(m=-Math.atan2(r,m)*
-e.RAD2DEG,0>m&&(m+=360)):m=0;n=Math.atan2(p,n)*e.RAD2DEG;p=d;if(f&&(d=n,f=va(f,90-n),n-=f,0<f&&3E-4<n)){c=Math.sin(n*e.DEG2RAD);p=Math.cos(n*e.DEG2RAD);r=Math.sin(d*e.DEG2RAD);d=Math.cos(d*e.DEG2RAD);f=[];for(k=0;3>k;++k)f.push((b[k]-d*a[k])/r*c+a[k]*p);p=Math.sqrt(f[0]*f[0]+f[1]*f[1]);0<p?(c=Math.atan2(f[1],f[0])*e.RAD2DEG/15,0>c&&(c+=24)):c=0;p=Math.atan2(f[2],p)*e.RAD2DEG}return new Fb(m,90-n,c,p)}function ma(a){if(!(a instanceof Gb))throw"Not an instance of the Observer class: "+a;v(a.latitude);
-v(a.longitude);v(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}function Hb(a){a=y(a).AddDays(-.005775518331089121);var b=R(I.Earth,a),c=$jscomp.makeIterator(La([-b.x,-b.y,-b.z],a,H.From2000));b=c.next().value;var d=c.next().value,f=c.next().value,h=e.DEG2RAD*Ga(a).tobl;c=Math.cos(h);h=Math.sin(h);a=new D(b,d,f,a);return Ib(a,c,h)}function Na(a,b,c,d,f){ma(c);A(d);A(f);b=y(b);c=Db(b,c);a=X(a,b,f);a=[a.x-c[0],a.y-c[1],a.z-c[2]];
-if(!d)return Eb(a,b);d=La(a,b,H.From2000);return Eb(d,b)}function Ib(a,b,c){var d=a.x,f=a.y*b+a.z*c;c=-a.y*c+a.z*b;var h=Math.sqrt(d*d+f*f);b=0;0<h&&(b=e.RAD2DEG*Math.atan2(f,d),0>b&&(b+=360));h=e.RAD2DEG*Math.atan2(c,h);a=new D(d,f,c,a.t);return new Jb(a,h,b)}function wa(a){void 0===Oa&&(Oa=e.DEG2RAD*Ga(y(eb)).mobl,Kb=Math.cos(Oa),Lb=Math.sin(Oa));return Ib(a,Kb,Lb)}function Y(a){a=y(a);var b=ia(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),
-b.distance_au*Math.sin(b.geo_eclip_lat)];var d=ra(a)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);b=bb([b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],a,H.Into2000);return new D(b[0],b[1],b[2],a)}function da(a,b){var c=1,d=0;a=$jscomp.makeIterator(a);for(var f=a.next();!f.done;f=a.next()){var h=0;f=$jscomp.makeIterator(f.value);for(var l=f.next();!l.done;l=f.next()){var k=$jscomp.makeIterator(l.value);l=k.next().value;var g=k.next().value;k=k.next().value;h+=l*Math.cos(g+b*k)}d+=c*h;c*=b}return d}function fb(a,b){var c=
-1,d=0,f=0,h=0;a=$jscomp.makeIterator(a);for(var l=a.next();!l.done;l=a.next()){var k=0,g=0;l=$jscomp.makeIterator(l.value);for(var m=l.next();!m.done;m=l.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var p=n.next().value;n=n.next().value;p+=b*n;k+=m*n*Math.sin(p);0<h&&(g+=m*Math.cos(p))}f+=h*d*g-c*k;d=c;c*=b;++h}return f}function gb(a){return new E(a[0]+4.4036E-7*a[1]-1.90919E-7*a[2],-4.79966E-7*a[0]+.917482137087*a[1]-.397776982902*a[2],.397776982902*a[1]+.917482137087*a[2])}function Mb(a,
-b,c){var d=c*Math.cos(b);return[d*Math.cos(a),d*Math.sin(a),c*Math.sin(b)]}function R(a,b){var c=b.tt/365250,d=da(a[0],c),f=da(a[1],c);a=da(a[2],c);d=Mb(d,f,a);return gb(d).ToAstroVector(b)}function Pa(a,b,c,d){d/=d+2.959122082855911E-4;b=R(I[c],b);a.x+=d*b.x;a.y+=d*b.y;a.z+=d*b.z}function Qa(a,b,c,d){d/=d+2.959122082855911E-4;var f=I[c],h=b/365250;c=da(f[0],h);var l=da(f[1],h),k=da(f[2],h),g=fb(f[0],h),m=fb(f[1],h);h=fb(f[2],h);var n=Math.cos(c),p=Math.sin(c),r=Math.cos(l),w=Math.sin(l);f=+(h*r*
-n)-k*w*n*m-k*r*p*g;g=+(h*r*p)-k*w*p*m+k*r*n*g;m=+(h*w)+k*r*m;c=Mb(c,l,k);l=[f/365250,g/365250,m/365250];c=gb(c);l=gb(l);b=new Ra(b,c,l);a.r.incr(b.r.mul(d));a.v.incr(b.v.mul(d));return b}function xa(a,b,c){a=c.sub(a);c=a.quadrature();return a.mul(b/(c*Math.sqrt(c)))}function Sa(a,b,c,d){return new E(b.x+a*(c.x+a*d.x/2),b.y+a*(c.y+a*d.y/2),b.z+a*(c.z+a*d.z/2))}function hb(a,b){var c=a-b.tt,d=new Ta(a),f=Sa(c,b.r,b.v,b.a),h=d.Acceleration(f).mean(b.a);f=Sa(c,b.r,b.v,h);b=b.v.add(h.mul(c));c=d.Acceleration(f);
-a=new Nb(a,f,b,c);return new Ob(d,a)}function Pb(a,b){a=Math.floor(a);return 0>a?0:a>=b?b-1:a}function ib(a){var b=$jscomp.makeIterator(a);a=b.next().value;var c=$jscomp.makeIterator(b.next().value);var d=c.next().value;var f=c.next().value;c=c.next().value;var h=$jscomp.makeIterator(b.next().value);b=h.next().value;var l=h.next().value;h=h.next().value;d=new Ra(a,new E(d,f,c),new E(b,l,h));a=new Ta(d.tt);f=d.r.add(a.Sun.r);c=d.v.add(a.Sun.v);b=a.Acceleration(f);d=new Nb(d.tt,f,c,b);return new Ob(a,
-d)}function Qb(a,b,c){a=ib(a);for(var d=Math.ceil((b-a.grav.tt)/c),f=0;f<d;++f)a=hb(f+1===d?b:a.grav.tt+c,a.grav);return a}function ya(a,b){b=y(b);if(a in I)return R(I[a],b);if(a===u.Pluto){a=b.tt;var c=ea[0][0];if(a<c||a>ea[40][0])a=null;else{a=Pb((a-c)/36500,40);if(!jb[a]){c=jb[a]=[];c[0]=ib(ea[a]).grav;c[146]=ib(ea[a+1]).grav;var d,f=c[0].tt;for(d=1;146>d;++d)c[d]=hb(f+=250,c[d-1]).grav;f=c[146].tt;var h=[];h[146]=c[146];for(d=145;0<d;--d)h[d]=hb(f-=250,h[d+1]).grav;for(d=145;0<d;--d)f=d/146,c[d].r=
-c[d].r.mul(1-f).add(h[d].r.mul(f)),c[d].v=c[d].v.mul(1-f).add(h[d].v.mul(f)),c[d].a=c[d].a.mul(1-f).add(h[d].a.mul(f))}a=jb[a]}(c=a)?(d=Pb((b.tt-c[0].tt)/250,146),a=c[d],d=c[d+1],h=a.a.mean(d.a),c=Sa(b.tt-a.tt,a.r,a.v,h),d=Sa(b.tt-d.tt,d.r,d.v,h),a=(b.tt-a.tt)/250,a=c.mul(1-a).add(d.mul(a)),c=new Ta(b.tt)):(c=b.tt<ea[0][0]?Qb(ea[0],b.tt,-250):Qb(ea[40],b.tt,250),a=c.grav.r,c=c.bary);return a.sub(c.Sun.r).ToAstroVector(b)}if(a===u.Sun)return new D(0,0,0,b);if(a===u.Moon)return a=R(I.Earth,b),c=Y(b),
-new D(a.x+c.x,a.y+c.y,a.z+c.z,b);if(a===u.EMB)return a=R(I.Earth,b),c=Y(b),new D(a.x+c.x/82.30056,a.y+c.y/82.30056,a.z+c.z/82.30056,b);if(a===u.SSB)return a=new D(0,0,0,b),Pa(a,b,u.Jupiter,2.825345909524226E-7),Pa(a,b,u.Saturn,8.459715185680659E-8),Pa(a,b,u.Uranus,1.292024916781969E-8),Pa(a,b,u.Neptune,1.524358900784276E-8),a;throw'HelioVector: Unknown body "'+a+'"';}function fa(a,b){b=y(b);return a in I?da(I[a][2],b.tt/365250):ya(a,b).Length()}function X(a,b,c){A(c);b=y(b);if(a===u.Moon)return Y(b);
-if(a===u.Earth)return new D(0,0,0,b);for(var d=null,f,h=0,l=b,k=0;10>k;++k){f=ya(a,l);c?d=R(I.Earth,l):d||(d=R(I.Earth,b));f=new D(f.x-d.x,f.y-d.y,f.z-d.z,b);var g=b.AddDays(-f.Length()/173.1446326846693);h=Math.abs(g.tt-l.tt);if(1E-9>h)return f;l=g}throw"Light-travel time solver did not converge: dt="+h;}function Gc(a,b,c,d,f){var h=(f+c)/2-d;c=(f-c)/2;if(0==h){if(0==c)return null;d=-d/c;if(-1>d||1<d)return null}else{d=c*c-4*h*d;if(0>=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*h);f=(-c-f)/(2*h);if(-1<=
-d&&1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{x:d,t:a+d*b,df_dt:(2*h*d+c)/b}}function G(a,b,c,d){var f=v(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var h=d&&d.init_f1||a(b),l=d&&d.init_f2||a(c),k=NaN,g=0;d=d&&d.iter_limit||20;for(var m=!0;;){if(++g>d)throw"Excessive iteration in Search()";var n=new N(b.ut+.5*(c.ut-b.ut)),p=n.ut-b.ut;if(Math.abs(p)<f)return n;m?k=a(n):m=!0;var r=Gc(n.ut,c.ut-n.ut,h,k,l);if(r){var w=y(r.t),B=a(w);if(0!==r.df_dt){if(Math.abs(B/
+for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}function Eb(a,b){b=new D(a[0],a[1],a[2],b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return 0>b.z?new ua(0,-90,d,b):new ua(0,90,d,b)}var f=e.RAD2HOUR*Math.atan2(b.y,b.x);0>f&&(f+=24);return new ua(f,e.RAD2DEG*Math.atan2(a[2],Math.sqrt(c)),d,b)}function la(a,b){var c=a*e.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}function Ma(a,b,c,d,f){a=
+y(a);ma(b);v(c);v(d);var h=Math.sin(b.latitude*e.DEG2RAD),l=Math.cos(b.latitude*e.DEG2RAD),k=Math.sin(b.longitude*e.DEG2RAD),g=Math.cos(b.longitude*e.DEG2RAD);b=Math.sin(d*e.DEG2RAD);var m=Math.cos(d*e.DEG2RAD),n=Math.sin(c*e.HOUR2RAD),p=Math.cos(c*e.HOUR2RAD),r=[l*g,l*k,h];h=[-h*g,-h*k,l];k=[k,-g,0];l=-15*ka(a);a=la(l,r);r=la(l,h);k=la(l,k);b=[m*p,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];m=b[0]*r[0]+b[1]*r[1]+b[2]*r[2];r=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];p=Math.sqrt(m*m+r*r);0<p?(m=-e.RAD2DEG*Math.atan2(r,
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+b);d=La(a,b,H.From2000);return Eb(d,b)}function Ib(a,b,c){var d=a.x,f=a.y*b+a.z*c;c=-a.y*c+a.z*b;var h=Math.sqrt(d*d+f*f);b=0;0<h&&(b=e.RAD2DEG*Math.atan2(f,d),0>b&&(b+=360));h=e.RAD2DEG*Math.atan2(c,h);a=new D(d,f,c,a.t);return new Jb(a,h,b)}function wa(a){void 0===Oa&&(Oa=e.DEG2RAD*Ga(y(eb)).mobl,Kb=Math.cos(Oa),Lb=Math.sin(Oa));return Ib(a,Kb,Lb)}function Y(a){a=y(a);var b=ia(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)];
+var d=ra(a)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);b=bb([b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],a,H.Into2000);return new D(b[0],b[1],b[2],a)}function da(a,b,c){var d=1,f=0;a=$jscomp.makeIterator(a);for(var h=a.next();!h.done;h=a.next()){var l=0;h=$jscomp.makeIterator(h.value);for(var k=h.next();!k.done;k=h.next()){var g=$jscomp.makeIterator(k.value);k=g.next().value;var m=g.next().value;g=g.next().value;l+=k*Math.cos(m+b*g)}l*=d;c&&(l%=O);f+=l;d*=b}return f}function fb(a,b){var c=1,d=0,f=0,h=0;a=$jscomp.makeIterator(a);
+for(var l=a.next();!l.done;l=a.next()){var k=0,g=0;l=$jscomp.makeIterator(l.value);for(var m=l.next();!m.done;m=l.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var p=n.next().value;n=n.next().value;p+=b*n;k+=m*n*Math.sin(p);0<h&&(g+=m*Math.cos(p))}f+=h*d*g-c*k;d=c;c*=b;++h}return f}function gb(a){return new E(a[0]+4.4036E-7*a[1]-1.90919E-7*a[2],-4.79966E-7*a[0]+.917482137087*a[1]-.397776982902*a[2],.397776982902*a[1]+.917482137087*a[2])}function Mb(a,b,c){var d=c*Math.cos(b);return[d*
+Math.cos(a),d*Math.sin(a),c*Math.sin(b)]}function R(a,b){var c=b.tt/365250,d=da(a[0],c,!0),f=da(a[1],c,!1);a=da(a[2],c,!1);d=Mb(d,f,a);return gb(d).ToAstroVector(b)}function Pa(a,b,c,d){d/=d+2.959122082855911E-4;b=R(I[c],b);a.x+=d*b.x;a.y+=d*b.y;a.z+=d*b.z}function Qa(a,b,c,d){d/=d+2.959122082855911E-4;var f=I[c],h=b/365250;c=da(f[0],h,!0);var l=da(f[1],h,!1),k=da(f[2],h,!1),g=fb(f[0],h),m=fb(f[1],h);h=fb(f[2],h);var n=Math.cos(c),p=Math.sin(c),r=Math.cos(l),w=Math.sin(l);f=+(h*r*n)-k*w*n*m-k*r*p*
+g;g=+(h*r*p)-k*w*p*m+k*r*n*g;m=+(h*w)+k*r*m;c=Mb(c,l,k);l=[f/365250,g/365250,m/365250];c=gb(c);l=gb(l);b=new Ra(b,c,l);a.r.incr(b.r.mul(d));a.v.incr(b.v.mul(d));return b}function xa(a,b,c){a=c.sub(a);c=a.quadrature();return a.mul(b/(c*Math.sqrt(c)))}function Sa(a,b,c,d){return new E(b.x+a*(c.x+a*d.x/2),b.y+a*(c.y+a*d.y/2),b.z+a*(c.z+a*d.z/2))}function hb(a,b){var c=a-b.tt,d=new Ta(a),f=Sa(c,b.r,b.v,b.a),h=d.Acceleration(f).mean(b.a);f=Sa(c,b.r,b.v,h);b=b.v.add(h.mul(c));c=d.Acceleration(f);a=new Nb(a,
+f,b,c);return new Ob(d,a)}function Pb(a,b){a=Math.floor(a);return 0>a?0:a>=b?b-1:a}function ib(a){var b=$jscomp.makeIterator(a);a=b.next().value;var c=$jscomp.makeIterator(b.next().value);var d=c.next().value;var f=c.next().value;c=c.next().value;var h=$jscomp.makeIterator(b.next().value);b=h.next().value;var l=h.next().value;h=h.next().value;d=new Ra(a,new E(d,f,c),new E(b,l,h));a=new Ta(d.tt);f=d.r.add(a.Sun.r);c=d.v.add(a.Sun.v);b=a.Acceleration(f);d=new Nb(d.tt,f,c,b);return new Ob(a,d)}function Qb(a,
+b,c){a=ib(a);for(var d=Math.ceil((b-a.grav.tt)/c),f=0;f<d;++f)a=hb(f+1===d?b:a.grav.tt+c,a.grav);return a}function ya(a,b){b=y(b);if(a in I)return R(I[a],b);if(a===u.Pluto){a=b.tt;var c=ea[0][0];if(a<c||a>ea[40][0])a=null;else{a=Pb((a-c)/36500,40);if(!jb[a]){c=jb[a]=[];c[0]=ib(ea[a]).grav;c[146]=ib(ea[a+1]).grav;var d,f=c[0].tt;for(d=1;146>d;++d)c[d]=hb(f+=250,c[d-1]).grav;f=c[146].tt;var h=[];h[146]=c[146];for(d=145;0<d;--d)h[d]=hb(f-=250,h[d+1]).grav;for(d=145;0<d;--d)f=d/146,c[d].r=c[d].r.mul(1-
+f).add(h[d].r.mul(f)),c[d].v=c[d].v.mul(1-f).add(h[d].v.mul(f)),c[d].a=c[d].a.mul(1-f).add(h[d].a.mul(f))}a=jb[a]}(c=a)?(d=Pb((b.tt-c[0].tt)/250,146),a=c[d],d=c[d+1],h=a.a.mean(d.a),c=Sa(b.tt-a.tt,a.r,a.v,h),d=Sa(b.tt-d.tt,d.r,d.v,h),a=(b.tt-a.tt)/250,a=c.mul(1-a).add(d.mul(a)),c=new Ta(b.tt)):(c=b.tt<ea[0][0]?Qb(ea[0],b.tt,-250):Qb(ea[40],b.tt,250),a=c.grav.r,c=c.bary);return a.sub(c.Sun.r).ToAstroVector(b)}if(a===u.Sun)return new D(0,0,0,b);if(a===u.Moon)return a=R(I.Earth,b),c=Y(b),new D(a.x+c.x,
+a.y+c.y,a.z+c.z,b);if(a===u.EMB)return a=R(I.Earth,b),c=Y(b),new D(a.x+c.x/82.30056,a.y+c.y/82.30056,a.z+c.z/82.30056,b);if(a===u.SSB)return a=new D(0,0,0,b),Pa(a,b,u.Jupiter,2.825345909524226E-7),Pa(a,b,u.Saturn,8.459715185680659E-8),Pa(a,b,u.Uranus,1.292024916781969E-8),Pa(a,b,u.Neptune,1.524358900784276E-8),a;throw'HelioVector: Unknown body "'+a+'"';}function fa(a,b){b=y(b);return a in I?da(I[a][2],b.tt/365250,!1):ya(a,b).Length()}function X(a,b,c){A(c);b=y(b);if(a===u.Moon)return Y(b);if(a===
+u.Earth)return new D(0,0,0,b);for(var d=null,f,h=0,l=b,k=0;10>k;++k){f=ya(a,l);c?d=R(I.Earth,l):d||(d=R(I.Earth,b));f=new D(f.x-d.x,f.y-d.y,f.z-d.z,b);var g=b.AddDays(-f.Length()/173.1446326846693);h=Math.abs(g.tt-l.tt);if(1E-9>h)return f;l=g}throw"Light-travel time solver did not converge: dt="+h;}function Gc(a,b,c,d,f){var h=(f+c)/2-d;c=(f-c)/2;if(0==h){if(0==c)return null;d=-d/c;if(-1>d||1<d)return null}else{d=c*c-4*h*d;if(0>=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*h);f=(-c-f)/(2*h);if(-1<=d&&
+1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{x:d,t:a+d*b,df_dt:(2*h*d+c)/b}}function G(a,b,c,d){var f=v(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var h=d&&d.init_f1||a(b),l=d&&d.init_f2||a(c),k=NaN,g=0;d=d&&d.iter_limit||20;for(var m=!0;;){if(++g>d)throw"Excessive iteration in Search()";var n=new N(b.ut+.5*(c.ut-b.ut)),p=n.ut-b.ut;if(Math.abs(p)<f)return n;m?k=a(n):m=!0;var r=Gc(n.ut,c.ut-n.ut,h,k,l);if(r){var w=y(r.t),B=a(w);if(0!==r.df_dt){if(Math.abs(B/
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 a.time);k=Ea(l,k);k.x+=a.target.x;k.y+=a.target.y;k.z+=a.target.z;a=Fa(1736,a.time,k,a.dir);if(1E-9<a.r||0>a.r)throw"Unexpected shadow distance from geoid intersection = "+a.r;h=.014<a.k?"total":"annular"}return new oc(h,b,c,f,d)}a=c.AddDays(10)}throw"Failed to find solar eclipse within 12 full moons.";}function pc(a){return a.p-a.r}function qc(a){return Math.abs(a.k)-a.r}function Ya(a,b,c,d,f){d=G(function(h){h=sb(h,a);return b*c(h)},d,f);if(!d)throw"Local eclipse transition search failed.";return rc(a,
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-e.HorizontalCoordinates=e.MakeRotation=e.RotationMatrix=e.EquatorialCoordinates=e.Spherical=e.StateVector=e.Vector=e.CalcMoonCount=e.MakeTime=e.AstroTime=e.SetDeltaTFunction=e.DeltaT_JplHorizons=e.DeltaT_EspenakMeeus=e.Body=e.AngleBetween=e.CALLISTO_RADIUS_KM=e.GANYMEDE_RADIUS_KM=e.EUROPA_RADIUS_KM=e.IO_RADIUS_KM=e.JUPITER_MEAN_RADIUS_KM=e.JUPITER_POLAR_RADIUS_KM=e.JUPITER_EQUATORIAL_RADIUS_KM=e.RAD2DEG=e.DEG2RAD=e.KM_PER_AU=void 0;e.LocalSolarEclipseInfo=e.EclipseEvent=e.NextGlobalSolarEclipse=e.SearchGlobalSolarEclipse=
-e.NextLunarEclipse=e.GlobalSolarEclipseInfo=e.SearchLunarEclipse=e.LunarEclipseInfo=e.Constellation=e.ConstellationInfo=e.Rotation_HOR_ECL=e.Rotation_ECL_HOR=e.Rotation_ECL_EQD=e.Rotation_EQD_ECL=e.Rotation_EQJ_HOR=e.Rotation_HOR_EQJ=e.Rotation_HOR_EQD=e.Rotation_EQD_HOR=e.Rotation_EQD_EQJ=e.Rotation_EQJ_EQD=e.Rotation_ECL_EQJ=e.Rotation_EQJ_ECL=e.RotateState=e.RotateVector=e.InverseRefraction=e.Refraction=e.VectorFromHorizon=e.HorizonFromVector=e.SphereFromVector=e.EquatorFromVector=e.VectorFromSphere=
-e.Pivot=e.IdentityMatrix=e.CombineRotation=e.InverseRotation=e.NextPlanetApsis=e.SearchPlanetApsis=e.NextLunarApsis=e.SearchLunarApsis=e.Apsis=e.SearchPeakMagnitude=e.SearchMaxElongation=e.Elongation=e.ElongationEvent=e.Seasons=e.SeasonInfo=e.SearchHourAngle=e.HourAngleEvent=e.SearchRiseSet=e.NextMoonQuarter=void 0;e.NextTransit=e.SearchTransit=e.TransitInfo=e.NextLocalSolarEclipse=e.SearchLocalSolarEclipse=void 0;e.KM_PER_AU=1.4959787069098932E8;e.DEG2RAD=.017453292519943295;e.RAD2DEG=57.29577951308232;
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-.0017121518344796,8.2822409843551E-4]],[73E3,[-27.3620419812795,18.4265651225706,13.9975343005914],[-.001169093462134,-.0027143131627458,-4.9312695340367E-4]],[109500,[38.3556091850032,-8.7643800131842,-14.2951819118807],[.0012922798115839,.0022032141141126,2.9606522103424E-4]],[146E3,[7.3929490279056,44.3826789515344,11.6295002148543],[-.002193281545383,-2.1751799585364E-4,5.9556516201114E-4]],[182500,[-5.8649529029432,-29.1987619981354,-7.3502494912123],[.0031339384323665,-7.4205968379701E-4,-.0011783357537604]],
-[219E3,[38.4269476345329,30.5667598351632,-2.0378379641214],[-.0010958945370084,.0016194885149659,8.3705272532546E-4]],[255500,[-28.6586488201636,15.0309000931701,13.3365724093667],[-9.4611899595408E-4,-.0028506813871559,-6.0508645822989E-4]],[292E3,[39.8319806717528,-6.0784057667647,-13.9098153586562],[.0011117769689167,.0022362097830152,3.6230548231153E-4]],[328500,[4.837152376403,44.072311954153,12.3146147867802],[-.0022164547537724,-3.6790365636785E-4,5.5542723844616E-4]],[365E3,[-2.2619763759487,
--29.8581508706765,-8.6502366418978],[.0031821176368396,-4.0915169873994E-4,-.0010895893040652]],[401500,[37.1576590087419,32.3528396259588,-1.0950381786229],[-.001198841260683,.0015356290902995,8.4339118209852E-4]],[438E3,[-29.5767402292299,11.8635359435865,12.6313230398719],[-7.2292830060955E-4,-.0029587820140709,-7.08242964503E-4]],[474500,[40.9541099577599,-3.658980594537,-13.499469956395],[9.5387298337127E-4,.0022572135462477,4.1826529781128E-4]],[511E3,[2.4859523114116,43.6181887566155,12.8914184596699],
-[-.0022339745420393,-5.1034757181916E-4,5.1485330196245E-4]],[547500,[1.0594791441638,-30.1357921778687,-9.7458684762963],[.0031921591684898,-1.130531279615E-4,-9.9954096945965E-4]],[584E3,[35.8778640130144,33.8942263660709,-.2245246362769],[-.0012941245730845,.0014560427668319,8.4762160640137E-4]],[620500,[-30.2026537318923,8.7794211940578,11.8609238187578],[-4.9002221381806E-4,-.0030438768469137,-8.0605935262763E-4]],[657E3,[41.8536204011376,-1.3790965838042,-13.0624345337527],[8.0674627557124E-4,
-.0022702374399791,4.6832587475465E-4]],[693500,[.2468843977112,43.0303960481227,13.3909343344167],[-.0022436121787266,-6.5238074250728E-4,4.7172729553196E-4]],[73E4,[4.2432528370899,-30.1182016908248,-10.7074412313491],[.0031725847067411,1.609846120227E-4,-9.0672150593868E-4]]],E=function(a,b,c){this.x=a;this.y=b;this.z=c};E.prototype.ToAstroVector=function(a){return new D(this.x,this.y,this.z,a)};E.prototype.quadrature=function(){return this.x*this.x+this.y*this.y+this.z*this.z};E.prototype.add=
-function(a){return new E(this.x+a.x,this.y+a.y,this.z+a.z)};E.prototype.sub=function(a){return new E(this.x-a.x,this.y-a.y,this.z-a.z)};E.prototype.incr=function(a){this.x+=a.x;this.y+=a.y;this.z+=a.z};E.prototype.decr=function(a){this.x-=a.x;this.y-=a.y;this.z-=a.z};E.prototype.mul=function(a){return new E(a*this.x,a*this.y,a*this.z)};E.prototype.div=function(a){return new E(this.x/a,this.y/a,this.z/a)};E.prototype.mean=function(a){return new E((this.x+a.x)/2,(this.y+a.y)/2,(this.z+a.z)/2)};var Ra=
-function(a,b,c){this.tt=a;this.r=b;this.v=c},Ta=function(a){var b=new Ra(a,new E(0,0,0),new E(0,0,0));this.Jupiter=Qa(b,a,u.Jupiter,2.825345909524226E-7);this.Saturn=Qa(b,a,u.Saturn,8.459715185680659E-8);this.Uranus=Qa(b,a,u.Uranus,1.292024916781969E-8);this.Neptune=Qa(b,a,u.Neptune,1.524358900784276E-8);this.Jupiter.r.decr(b.r);this.Jupiter.v.decr(b.v);this.Saturn.r.decr(b.r);this.Saturn.v.decr(b.v);this.Uranus.r.decr(b.r);this.Uranus.v.decr(b.v);this.Neptune.r.decr(b.r);this.Neptune.v.decr(b.v);
-this.Sun=new Ra(a,b.r.mul(-1),b.v.mul(-1))};Ta.prototype.Acceleration=function(a){var b=xa(a,2.959122082855911E-4,this.Sun.r);b.incr(xa(a,2.825345909524226E-7,this.Jupiter.r));b.incr(xa(a,8.459715185680659E-8,this.Saturn.r));b.incr(xa(a,1.292024916781969E-8,this.Uranus.r));b.incr(xa(a,1.524358900784276E-8,this.Neptune.r));return b};var Nb=function(a,b,c,d){this.tt=a;this.r=b;this.v=c;this.a=d},Ob=function(a,b){this.bary=a;this.grav=b},jb=[],Rc=new K([[.9994327653386544,-.03367710746976414,0],[.030395942890628476,
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-[3.52747346169E-5,2.1256287034578,1.2727416567E-4]],zeta:[[3.142172466014E-4,2.7964219722923,-.002315096098],[9.04169207946E-5,1.0477061879627,-5.6920638196E-4]]},{mu:2.82483274392893E-7,al:[-.3735263437471362,1.76932271112347],a:[[.0044871037804314,0,0],[4.324367498E-7,1.819645606291,1.7822295777568]],l:[[8.576433172936E-4,4.3188693178264,.01303413830805],[4.549582875086E-4,1.4936531751079,.01293892881962],[3.248939825174E-4,1.8196494533458,1.7822295777568],[-3.074250079334E-4,4.9377037005911,.01358483286724],
-[1.982386144784E-4,1.907986905476,.00305101212869],[1.834063551804E-4,2.1402853388529,.00145009789338],[-1.434383188452E-4,5.622214036663,.89111478887838],[-7.71939140944E-5,4.300272437235,2.6733443704266]],z:[[-.0093589104136341,4.0899396509039,-.01290686414666],[2.988994545555E-4,5.9097265185595,1.7693227079462],[2.13903639035E-4,2.1256289300016,1.2727418407E-4],[1.980963564781E-4,2.743516829265,6.7797343009E-4],[1.210388158965E-4,5.5839943711203,3.20566149E-5],[8.37042048393E-5,1.6094538368039,
--.90402165808846],[8.23525166369E-5,1.4461887708689,3.5515522949802]],zeta:[[.0040404917832303,1.0477063169425,-5.692064054E-4],[2.200421034564E-4,3.3368857864364,-1.2491307307E-4],[1.662544744719E-4,2.4134862374711,0],[5.90282470983E-5,5.9719930968366,-3.056160225E-5]]},{mu:2.82498184184723E-7,al:[.2874089391143348,.878207923589328],a:[[.0071566594572575,0,0],[1.393029911E-6,1.1586745884981,2.6733443704266]],l:[[2.310797886226E-4,2.1402987195942,.00145009784384],[-1.828635964118E-4,4.3188672736968,
-.01303413828263],[1.512378778204E-4,4.9373102372298,.01358483481252],[-1.163720969778E-4,4.300265986149,2.6733443704266],[-9.55478069846E-5,1.4936612842567,.01293892879857],[8.15246854464E-5,5.6222137132535,.89111478887838],[-8.01219679602E-5,1.2995922951532,1.0034433456729],[-6.07017260182E-5,.64978769669238,.50172167043264]],z:[[.0014289811307319,2.1256295942739,1.2727413029E-4],[7.71093122676E-4,5.5836330003496,3.20643411E-5],[5.925911780766E-4,4.0899396636448,-.01290686414666],[2.045597496146E-4,
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-a:[[.0125879701715314,0,0],[3.595204947E-6,.64965776007116,.50172168165034],[2.7580210652E-6,1.808423578151,3.1750660413359]],l:[[5.586040123824E-4,2.1404207189815,.00145009793231],[-3.805813868176E-4,2.7358844897853,2.972965062E-5],[2.205152863262E-4,.649796525964,.5017216724358],[1.877895151158E-4,1.8084787604005,3.1750660413359],[7.66916975242E-5,6.2720114319755,1.3928364636651],[7.47056855106E-5,1.2995916202344,1.0034433456729]],z:[[.0073755808467977,5.5836071576084,3.206509914E-5],[2.065924169942E-4,
-5.9209831565786,.37648624194703],[1.589869764021E-4,.28744006242623,.8782079244252],[-1.561131605348E-4,2.1257397865089,1.2727441285E-4],[1.486043380971E-4,1.4462134301023,3.5515522949802],[6.35073108731E-5,5.9096803285954,1.7693227129285],[5.99351698525E-5,4.1125517584798,-2.7985797954589],[5.40660842731E-5,5.5390350845569,.00286834082283],[-4.89596900866E-5,4.6218149483338,-.62695712529519]],zeta:[[.0038422977898495,2.4133922085557,0],[.0022453891791894,5.9721736773277,-3.056125525E-5],[-2.604479450559E-4,
-3.3368746306409,-1.2491309972E-4],[3.3211214323E-5,5.5604137742337,.00290037688507]]}],yc=function(a){this.moon=a};e.JupiterMoonsInfo=yc;e.JupiterMoons=function(a){a=new N(a);for(var b=[],c=$jscomp.makeIterator(Sc),d=c.next();!d.done;d=c.next()){var f=b,h=f.push;d=d.value;for(var l=a.tt+18262.5,k=[0,d.al[0]+l*d.al[1],0,0,0,0],g=$jscomp.makeIterator(d.a),m=g.next();!m.done;m=g.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var p=n.next().value;n=n.next().value;k[0]+=m*Math.cos(p+l*n)}g=
-$jscomp.makeIterator(d.l);for(m=g.next();!m.done;m=g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=n.next().value,n=n.next().value,k[1]+=m*Math.sin(p+l*n);k[1]%=P;0>k[1]&&(k[1]+=P);g=$jscomp.makeIterator(d.z);for(m=g.next();!m.done;m=g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=n.next().value,n=n.next().value,p+=l*n,k[2]+=m*Math.cos(p),k[3]+=m*Math.sin(p);g=$jscomp.makeIterator(d.zeta);for(m=g.next();!m.done;m=g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=
-n.next().value,n=n.next().value,p+=l*n,k[4]+=m*Math.cos(p),k[5]+=m*Math.sin(p);g=k[0];n=k[1];m=k[2];p=k[3];l=k[4];k=k[5];var r=Math.sqrt(d.mu/(g*g*g));d=n+m*Math.sin(n)-p*Math.cos(n);do{var w=Math.cos(d);var B=Math.sin(d);w=(n-d+m*B-p*w)/(1-m*w-p*B);d+=w}while(1E-12<=Math.abs(w));w=Math.cos(d);B=Math.sin(d);n=p*w-m*B;var z=-m*w-p*B,sa=1/(1+z),ba=1/(1+Math.sqrt(1-m*m-p*p));d=g*(w-m-ba*p*n);n=g*(B-p+ba*m*n);p=r*sa*g*(-B-ba*p*z);g=r*sa*g*(+w+ba*m*z);m=2*Math.sqrt(1-l*l-k*k);r=1-2*k*k;w=1-2*l*l;B=2*k*
-l;d=new ob(d*r+n*B,d*B+n*w,(l*n-d*k)*m,p*r+g*B,p*B+g*w,(l*g-p*k)*m,a);d=dc(Rc,d);h.call(f,d)}return new yc(b)};e.HelioVector=ya;e.HelioDistance=fa;e.GeoVector=X;e.Search=G;e.SearchSunLongitude=Rb;e.LongitudeFromSun=kb;e.AngleFromSun=na;e.EclipticLongitude=ha;var Sb=function(a,b,c,d,f,h,l,k){this.time=a;this.mag=b;this.phase_angle=c;this.helio_dist=d;this.geo_dist=f;this.gc=h;this.hc=l;this.ring_tilt=k;this.phase_fraction=(1+Math.cos(e.DEG2RAD*c))/2};e.IlluminationInfo=Sb;e.Illumination=Ua;e.SearchRelativeLongitude=
-oa;e.MoonPhase=lb;e.SearchMoonPhase=Ba;var Ub=function(a,b){this.quarter=a;this.time=b};e.MoonQuarter=Ub;e.SearchMoonQuarter=Tb;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Tb(a)};e.SearchRiseSet=function(a,b,c,d,f){function h(w){var B=Na(a,w,b,!0,!0);w=Ma(w,b,B.ra,B.dec).altitude+l/B.dist*e.RAD2DEG+Qc;return c*w}ma(b);v(f);a:switch(a){case u.Sun:var l=Oc;break a;case u.Moon:l=Pc;break a;default:l=0}if(a===u.Earth)throw"Cannot find rise or set time of the Earth.";
-if(1===c){var k=12;var g=0}else if(-1===c)k=0,g=12;else throw"SearchRiseSet: Invalid direction parameter "+c+" -- must be +1 or -1";d=y(d);var m=h(d);var n;if(0<m){m=Ca(a,b,k,d);var p=m.time;m=h(p)}else p=d;var r=Ca(a,b,g,p);for(n=h(r.time);;){if(0>=m&&0<n&&(p=G(h,p,r.time,{init_f1:m,init_f2:n})))return p;m=Ca(a,b,k,r.time);r=Ca(a,b,g,m.time);if(m.time.ut>=d.ut+f)return null;p=m.time;m=h(m.time);n=h(r.time)}};var Vb=function(a,b){this.time=a;this.hor=b};e.HourAngleEvent=Vb;e.SearchHourAngle=Ca;var zc=
-function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=zc;e.Seasons=function(a){function b(l,k,g){k=new Date(Date.UTC(a,k-1,g));l=Rb(l,k,4);if(!l)throw"Cannot find season change near "+k.toISOString();return l}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+a+" is neither a Date nor a safe integer.";var c=b(0,3,19),d=b(90,6,19),f=b(180,9,
-21),h=b(270,12,20);return new zc(c,d,f,h)};var Xb=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=Xb;e.Elongation=Wb;e.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);m=m.AddDays(.005);n=na(a,n);m=na(a,m);return(n-m)/.01}b=y(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only.";for(var f=0;2>=++f;){var h=ha(a,b),l=ha(u.Earth,b),k=za(h-l),g=h=l=
-void 0;k>=-d.s1&&k<+d.s1?(g=0,l=+d.s1,h=+d.s2):k>=+d.s2||k<-d.s2?(g=0,l=-d.s2,h=-d.s1):0<=k?(g=-Aa(a)/4,l=+d.s1,h=+d.s2):(g=-Aa(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(g);l=oa(a,l,k);h=oa(a,h,l);k=c(l);if(0<=k)throw"SearchMaxElongation: internal error: m1 = "+k;g=c(h);if(0>=g)throw"SearchMaxElongation: internal error: m2 = "+g;k=G(c,l,h,{init_f1:k,init_f2:g,dt_tolerance_seconds:10});if(!k)throw"SearchMaxElongation: failed search iter "+f+" (t1="+l.toString()+", t2="+h.toString()+")";if(k.tt>=b.tt)return Wb(a,
-k);b=h.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};e.SearchPeakMagnitude=function(a,b){function c(g){var m=g.AddDays(-.005);g=g.AddDays(.005);m=Ua(a,m).mag;return(Ua(a,g).mag-m)/.01}if(a!==u.Venus)throw"SearchPeakMagnitude currently works for Venus only.";b=y(b);for(var d=0;2>=++d;){var f=ha(a,b),h=ha(u.Earth,b),l=za(f-h),k=f=h=void 0;-10<=l&&10>l?(k=0,h=10,f=30):30<=l||-30>l?(k=0,h=-30,f=-10):0<=l?(k=-Aa(a)/4,h=10,f=30):(k=-Aa(a)/4,h=-30,f=-10);l=b.AddDays(k);h=oa(a,
-h,l);f=oa(a,f,h);l=c(h);if(0<=l)throw"SearchPeakMagnitude: internal error: m1 = "+l;k=c(f);if(0>=k)throw"SearchPeakMagnitude: internal error: m2 = "+k;l=G(c,h,f,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+h.toString()+", t2="+f.toString()+")";if(l.tt>=b.tt)return Ua(a,l);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Da=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};
-e.Apsis=Da;e.SearchLunarApsis=Yb;e.NextLunarApsis=function(a){var b=Yb(a.time.AddDays(11));if(1!==b.kind+a.kind)throw"NextLunarApsis INTERNAL ERROR: did not find alternating apogee/perigee: prev="+a.kind+" @ "+a.time.toString()+", next="+b.kind+" @ "+b.time.toString();return b};e.SearchPlanetApsis=$b;e.NextPlanetApsis=function(a,b){if(0!==b.kind&&1!==b.kind)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*Z[a].OrbitalPeriod);a=$b(a,c);if(1!==a.kind+b.kind)throw"Internal error: previous apsis was "+
-b.kind+", but found "+a.kind+" for next apsis.";return a};e.InverseRotation=pa;e.CombineRotation=qa;e.IdentityMatrix=function(){return new K([[1,0,0],[0,1,0],[0,0,1]])};e.Pivot=function(a,b,c){if(0!==b&&1!==b&&2!==b)throw"Invalid axis "+b+". Must be [0, 1, 2].";var d=v(c)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);var f=(b+1)%3,h=(b+2)%3,l=[[0,0,0],[0,0,0],[0,0,0]];l[f][f]=c*a.rot[f][f]-d*a.rot[f][h];l[f][h]=d*a.rot[f][f]+c*a.rot[f][h];l[f][b]=a.rot[f][b];l[h][f]=c*a.rot[h][f]-d*a.rot[h][h];l[h][h]=d*
-a.rot[h][f]+c*a.rot[h][h];l[h][b]=a.rot[h][b];l[b][f]=c*a.rot[b][f]-d*a.rot[b][h];l[b][h]=d*a.rot[b][f]+c*a.rot[b][h];l[b][b]=a.rot[b][b];return new K(l)};e.VectorFromSphere=mb;e.EquatorFromVector=ac;e.SphereFromVector=nb;e.HorizonFromVector=function(a,b){a=nb(a);a.lon=bc(a.lon);a.lat+=va(b,a.lat);return a};e.VectorFromHorizon=function(a,b,c){var d=bc(a.lon);c=a.lat+cc(c,a.lat);a=new Va(c,d,a.dist);return mb(a,b)};e.Refraction=va;e.InverseRefraction=cc;e.RotateVector=Ea;e.RotateState=dc;e.Rotation_EQJ_ECL=
-ec;e.Rotation_ECL_EQJ=function(){return new K([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=pb;e.Rotation_EQD_EQJ=qb;e.Rotation_EQD_HOR=rb;e.Rotation_HOR_EQD=fc;e.Rotation_HOR_EQJ=gc;e.Rotation_EQJ_HOR=function(a,b){a=gc(a,b);return pa(a)};e.Rotation_EQD_ECL=hc;e.Rotation_ECL_EQD=ic;e.Rotation_ECL_HOR=jc;e.Rotation_HOR_ECL=function(a,b){a=jc(a,b);return pa(a)};var Tc=[["And","Andromeda"],["Ant","Antila"],["Aps","Apus"],["Aql","Aquila"],
-["Aqr","Aquarius"],["Ara","Ara"],["Ari","Aries"],["Aur","Auriga"],["Boo","Bootes"],["Cae","Caelum"],["Cam","Camelopardis"],["Cap","Capricornus"],["Car","Carina"],["Cas","Cassiopeia"],["Cen","Centaurus"],["Cep","Cepheus"],["Cet","Cetus"],["Cha","Chamaeleon"],["Cir","Circinus"],["CMa","Canis Major"],["CMi","Canis Minor"],["Cnc","Cancer"],["Col","Columba"],["Com","Coma Berenices"],["CrA","Corona Australis"],["CrB","Corona Borealis"],["Crt","Crater"],["Cru","Crux"],["Crv","Corvus"],["CVn","Canes Venatici"],
-["Cyg","Cygnus"],["Del","Delphinus"],["Dor","Dorado"],["Dra","Draco"],["Equ","Equuleus"],["Eri","Eridanus"],["For","Fornax"],["Gem","Gemini"],["Gru","Grus"],["Her","Hercules"],["Hor","Horologium"],["Hya","Hydra"],["Hyi","Hydrus"],["Ind","Indus"],["Lac","Lacerta"],["Leo","Leo"],["Lep","Lepus"],["Lib","Libra"],["LMi","Leo Minor"],["Lup","Lupus"],["Lyn","Lynx"],["Lyr","Lyra"],["Men","Mensa"],["Mic","Microscopium"],["Mon","Monoceros"],["Mus","Musca"],["Nor","Norma"],["Oct","Octans"],["Oph","Ophiuchus"],
-["Ori","Orion"],["Pav","Pavo"],["Peg","Pegasus"],["Per","Perseus"],["Phe","Phoenix"],["Pic","Pictor"],["PsA","Pisces Austrinus"],["Psc","Pisces"],["Pup","Puppis"],["Pyx","Pyxis"],["Ret","Reticulum"],["Scl","Sculptor"],["Sco","Scorpius"],["Sct","Scutum"],["Ser","Serpens"],["Sex","Sextans"],["Sge","Sagitta"],["Sgr","Sagittarius"],["Tau","Taurus"],["Tel","Telescopium"],["TrA","Triangulum Australe"],["Tri","Triangulum"],["Tuc","Tucana"],["UMa","Ursa Major"],["UMi","Ursa Minor"],["Vel","Vela"],["Vir",
-"Virgo"],["Vol","Volans"],["Vul","Vulpecula"]],Uc=[[83,0,8640,2112],[83,2880,5220,2076],[83,7560,8280,2068],[83,6480,7560,2064],[15,0,2880,2040],[10,3300,3840,1968],[15,0,1800,1920],[10,3840,5220,1920],[83,6300,6480,1920],[33,7260,7560,1920],[15,0,1263,1848],[10,4140,4890,1848],[83,5952,6300,1800],[15,7260,7440,1800],[10,2868,3300,1764],[33,3300,4080,1764],[83,4680,5952,1680],[13,1116,1230,1632],[33,7350,7440,1608],[33,4080,4320,1596],[15,0,120,1584],[83,5040,5640,1584],[15,8490,8640,1584],[33,4320,
-4860,1536],[33,4860,5190,1512],[15,8340,8490,1512],[10,2196,2520,1488],[33,7200,7350,1476],[15,7393.2,7416,1462],[10,2520,2868,1440],[82,2868,3030,1440],[33,7116,7200,1428],[15,7200,7393.2,1428],[15,8232,8340,1418],[13,0,876,1404],[33,6990,7116,1392],[13,612,687,1380],[13,876,1116,1368],[10,1116,1140,1368],[15,8034,8232,1350],[10,1800,2196,1344],[82,5052,5190,1332],[33,5190,6990,1332],[10,1140,1200,1320],[15,7968,8034,1320],[15,7416,7908,1316],[13,0,612,1296],[50,2196,2340,1296],[82,4350,4860,1272],
-[33,5490,5670,1272],[15,7908,7968,1266],[10,1200,1800,1260],[13,8232,8400,1260],[33,5670,6120,1236],[62,735,906,1212],[33,6120,6564,1212],[13,0,492,1200],[62,492,600,1200],[50,2340,2448,1200],[13,8400,8640,1200],[82,4860,5052,1164],[13,0,402,1152],[13,8490,8640,1152],[39,6543,6564,1140],[33,6564,6870,1140],[30,6870,6900,1140],[62,600,735,1128],[82,3030,3300,1128],[13,60,312,1104],[82,4320,4350,1080],[50,2448,2652,1068],[30,7887,7908,1056],[30,7875,7887,1050],[30,6900,6984,1044],[82,3300,3660,1008],
-[82,3660,3882,960],[8,5556,5670,960],[39,5670,5880,960],[50,3330,3450,954],[0,0,906,882],[62,906,924,882],[51,6969,6984,876],[62,1620,1689,864],[30,7824,7875,864],[44,7875,7920,864],[7,2352,2652,852],[50,2652,2790,852],[0,0,720,840],[44,7920,8214,840],[44,8214,8232,828],[0,8232,8460,828],[62,924,978,816],[82,3882,3960,816],[29,4320,4440,816],[50,2790,3330,804],[48,3330,3558,804],[0,258,507,792],[8,5466,5556,792],[0,8460,8550,770],[29,4440,4770,768],[0,8550,8640,752],[29,5025,5052,738],[80,870,978,
-736],[62,978,1620,736],[7,1620,1710,720],[51,6543,6969,720],[82,3960,4320,696],[30,7080,7530,696],[7,1710,2118,684],[48,3558,3780,684],[29,4770,5025,684],[0,0,24,672],[80,507,600,672],[7,2118,2352,672],[37,2838,2880,672],[30,7530,7824,672],[30,6933,7080,660],[80,690,870,654],[25,5820,5880,648],[8,5430,5466,624],[25,5466,5820,624],[51,6612,6792,624],[48,3870,3960,612],[51,6792,6933,612],[80,600,690,600],[66,258,306,570],[48,3780,3870,564],[87,7650,7710,564],[77,2052,2118,548],[0,24,51,528],[73,5730,
-5772,528],[37,2118,2238,516],[87,7140,7290,510],[87,6792,6930,506],[0,51,306,504],[87,7290,7404,492],[37,2811,2838,480],[87,7404,7650,468],[87,6930,7140,460],[6,1182,1212,456],[75,6792,6840,444],[59,2052,2076,432],[37,2238,2271,420],[75,6840,7140,388],[77,1788,1920,384],[39,5730,5790,384],[75,7140,7290,378],[77,1662,1788,372],[77,1920,2016,372],[23,4620,4860,360],[39,6210,6570,344],[23,4272,4620,336],[37,2700,2811,324],[39,6030,6210,308],[61,0,51,300],[77,2016,2076,300],[37,2520,2700,300],[61,7602,
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-7680,48],[61,7680,7728,48],[61,7920,8190,48],[61,7800,7920,42],[20,2526,2592,36],[77,1290,1662,0],[59,1662,1680,0],[20,2592,2910,0],[85,5280,5430,0],[58,6420,6570,0],[16,954,1182,-42],[77,1182,1290,-42],[73,5430,5856,-78],[59,1680,1830,-96],[59,2100,2247,-96],[73,6420,6468,-96],[73,6570,6690,-96],[3,6690,6792,-96],[66,8190,8580,-96],[45,3870,4146,-144],[85,4146,4260,-144],[66,0,120,-168],[66,8580,8640,-168],[85,5130,5280,-192],[58,5730,5856,-192],[3,7200,7392,-216],[4,7680,7872,-216],[58,6180,6468,
--240],[54,2100,2910,-264],[35,1770,1830,-264],[59,1830,2100,-264],[41,2910,3012,-264],[74,3450,3870,-264],[85,4260,4620,-264],[58,6330,6360,-280],[3,6792,7200,-288.8],[35,1740,1770,-348],[4,7392,7680,-360],[73,6180,6570,-384],[72,6570,6792,-384],[41,3012,3090,-408],[58,5856,5895,-438],[41,3090,3270,-456],[26,3870,3900,-456],[71,5856,5895,-462],[47,5640,5730,-480],[28,4530,4620,-528],[85,4620,5130,-528],[41,3270,3510,-576],[16,600,954,-585.2],[35,954,1350,-585.2],[26,3900,4260,-588],[28,4260,4530,
--588],[47,5130,5370,-588],[58,5856,6030,-590],[16,0,600,-612],[11,7680,7872,-612],[4,7872,8580,-612],[16,8580,8640,-612],[41,3510,3690,-636],[35,1692,1740,-654],[46,1740,2202,-654],[11,7200,7680,-672],[41,3690,3810,-700],[41,4530,5370,-708],[47,5370,5640,-708],[71,5640,5760,-708],[35,1650,1692,-720],[58,6030,6336,-720],[76,6336,6420,-720],[41,3810,3900,-748],[19,2202,2652,-792],[41,4410,4530,-792],[41,3900,4410,-840],[36,1260,1350,-864],[68,3012,3372,-882],[35,1536,1650,-888],[76,6420,6900,-888],
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-6480,7320,-1368],[38,7920,8400,-1368],[40,1152,1260,-1380],[64,1800,1980,-1380],[12,2340,2460,-1392],[63,0,480,-1404],[35,480,780,-1404],[63,8400,8640,-1404],[32,1560,1650,-1416],[56,5520,5911.5,-1440],[43,7320,7680,-1440],[64,1980,2160,-1464],[18,5460,5520,-1464],[5,5911.5,5970,-1464],[18,5370,5460,-1526],[5,5970,6030,-1526],[64,2160,2460,-1536],[12,2460,3252,-1536],[14,4050,4260,-1536],[27,4260,4620,-1536],[14,4620,5232,-1536],[18,4860,4920,-1560],[5,6030,6060,-1560],[40,780,1152,-1620],[69,1152,
-1650,-1620],[18,5310,5370,-1620],[5,6060,6300,-1620],[60,6300,6480,-1620],[81,7920,8400,-1620],[32,1650,2370,-1680],[18,4920,5310,-1680],[79,5310,6120,-1680],[81,0,480,-1800],[42,1260,1650,-1800],[86,2370,3252,-1800],[12,3252,4050,-1800],[55,4050,4920,-1800],[60,6480,7680,-1800],[43,7680,8400,-1800],[81,8400,8640,-1800],[81,270,480,-1824],[42,0,1260,-1980],[17,2760,4920,-1980],[2,4920,6480,-1980],[52,1260,2760,-2040],[57,0,8640,-2160]],wb,Ac,Bc=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=
-c;this.dec1875=d};e.ConstellationInfo=Bc;e.Constellation=function(a,b){v(a);v(b);if(-90>b||90<b)throw"Invalid declination angle. Must be -90..+90.";a%=24;0>a&&(a+=24);wb||(wb=pb(new N(-45655.74141261017)),Ac=new N(0));a=new Va(b,15*a,1);a=mb(a,Ac);a=Ea(wb,a);a=ac(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Uc),f=d.next();!f.done;f=d.next()){f=f.value;var h=f[1]*c,l=f[2]*c;if(f[3]*b<=a.dec&&h<=a.ra&&a.ra<l)return b=Tc[f[0]],new Bc(b[0],b[1],a.ra,a.dec)}throw"Unable to find constellation for given coordinates.";
-};var mc=function(a,b,c,d,f){this.kind=a;this.peak=b;this.sd_penum=c;this.sd_partial=d;this.sd_total=f};e.LunarEclipseInfo=mc;var Jc=function(a,b,c,d,f,h,l){this.time=a;this.u=b;this.r=c;this.k=d;this.p=f;this.target=h;this.dir=l};e.SearchLunarEclipse=lc;var oc=function(a,b,c,d,f){this.kind=a;this.peak=b;this.distance=c;this.latitude=d;this.longitude=f};e.GlobalSolarEclipseInfo=oc;e.NextLunarEclipse=function(a){a=a.AddDays(10);return lc(a)};e.SearchGlobalSolarEclipse=nc;e.NextGlobalSolarEclipse=function(a){a=
-a.AddDays(10);return nc(a)};var sc=function(a,b){this.time=a;this.altitude=b};e.EclipseEvent=sc;var uc=function(a,b,c,d,f,h){this.kind=a;this.partial_begin=b;this.total_begin=c;this.peak=d;this.total_end=f;this.partial_end=h};e.LocalSolarEclipseInfo=uc;e.SearchLocalSolarEclipse=tc;e.NextLocalSolarEclipse=function(a,b){a=a.AddDays(10);return tc(a,b)};var xc=function(a,b,c,d){this.start=a;this.peak=b;this.finish=c;this.separation=d};e.TransitInfo=xc;e.SearchTransit=wc;e.NextTransit=function(a,b){b=
-b.AddDays(100);return wc(a,b)}},{}]},{},[1])(1)});
+c=vc(a,c,b.time,f,1);a=60*na(a,b.time);return new xc(d,b.time,c,a)}b=d.AddDays(10)}}Object.defineProperty(e,"__esModule",{value:!0});e.SearchMoonPhase=e.MoonPhase=e.SearchRelativeLongitude=e.Illumination=e.IlluminationInfo=e.EclipticLongitude=e.AngleFromSun=e.LongitudeFromSun=e.SearchSunLongitude=e.Search=e.GeoVector=e.HelioDistance=e.HelioVector=e.JupiterMoons=e.JupiterMoonsInfo=e.GeoMoon=e.Ecliptic=e.ObserverVector=e.Equator=e.SunPosition=e.Observer=e.Horizon=e.EclipticCoordinates=e.HorizontalCoordinates=
+e.MakeRotation=e.RotationMatrix=e.EquatorialCoordinates=e.Spherical=e.StateVector=e.Vector=e.CalcMoonCount=e.MakeTime=e.AstroTime=e.SetDeltaTFunction=e.DeltaT_JplHorizons=e.DeltaT_EspenakMeeus=e.Body=e.AngleBetween=e.CALLISTO_RADIUS_KM=e.GANYMEDE_RADIUS_KM=e.EUROPA_RADIUS_KM=e.IO_RADIUS_KM=e.JUPITER_MEAN_RADIUS_KM=e.JUPITER_POLAR_RADIUS_KM=e.JUPITER_EQUATORIAL_RADIUS_KM=e.RAD2HOUR=e.RAD2DEG=e.HOUR2RAD=e.DEG2RAD=e.KM_PER_AU=void 0;e.NextGlobalSolarEclipse=e.SearchGlobalSolarEclipse=e.NextLunarEclipse=
+e.GlobalSolarEclipseInfo=e.SearchLunarEclipse=e.LunarEclipseInfo=e.Constellation=e.ConstellationInfo=e.Rotation_HOR_ECL=e.Rotation_ECL_HOR=e.Rotation_ECL_EQD=e.Rotation_EQD_ECL=e.Rotation_EQJ_HOR=e.Rotation_HOR_EQJ=e.Rotation_HOR_EQD=e.Rotation_EQD_HOR=e.Rotation_EQD_EQJ=e.Rotation_EQJ_EQD=e.Rotation_ECL_EQJ=e.Rotation_EQJ_ECL=e.RotateState=e.RotateVector=e.InverseRefraction=e.Refraction=e.VectorFromHorizon=e.HorizonFromVector=e.SphereFromVector=e.EquatorFromVector=e.VectorFromSphere=e.Pivot=e.IdentityMatrix=
+e.CombineRotation=e.InverseRotation=e.NextPlanetApsis=e.SearchPlanetApsis=e.NextLunarApsis=e.SearchLunarApsis=e.Apsis=e.SearchPeakMagnitude=e.SearchMaxElongation=e.Elongation=e.ElongationEvent=e.Seasons=e.SeasonInfo=e.SearchHourAngle=e.HourAngleEvent=e.SearchRiseSet=e.NextMoonQuarter=e.SearchMoonQuarter=e.MoonQuarter=void 0;e.NextTransit=e.SearchTransit=e.TransitInfo=e.NextLocalSolarEclipse=e.SearchLocalSolarEclipse=e.LocalSolarEclipseInfo=e.EclipseEvent=void 0;e.KM_PER_AU=1.4959787069098932E8;e.DEG2RAD=
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+12.3146147867802],[-.0022164547537724,-3.6790365636785E-4,5.5542723844616E-4]],[365E3,[-2.2619763759487,-29.8581508706765,-8.6502366418978],[.0031821176368396,-4.0915169873994E-4,-.0010895893040652]],[401500,[37.1576590087419,32.3528396259588,-1.0950381786229],[-.001198841260683,.0015356290902995,8.4339118209852E-4]],[438E3,[-29.5767402292299,11.8635359435865,12.6313230398719],[-7.2292830060955E-4,-.0029587820140709,-7.08242964503E-4]],[474500,[40.9541099577599,-3.658980594537,-13.499469956395],[9.5387298337127E-4,
+.0022572135462477,4.1826529781128E-4]],[511E3,[2.4859523114116,43.6181887566155,12.8914184596699],[-.0022339745420393,-5.1034757181916E-4,5.1485330196245E-4]],[547500,[1.0594791441638,-30.1357921778687,-9.7458684762963],[.0031921591684898,-1.130531279615E-4,-9.9954096945965E-4]],[584E3,[35.8778640130144,33.8942263660709,-.2245246362769],[-.0012941245730845,.0014560427668319,8.4762160640137E-4]],[620500,[-30.2026537318923,8.7794211940578,11.8609238187578],[-4.9002221381806E-4,-.0030438768469137,-8.0605935262763E-4]],
+[657E3,[41.8536204011376,-1.3790965838042,-13.0624345337527],[8.0674627557124E-4,.0022702374399791,4.6832587475465E-4]],[693500,[.2468843977112,43.0303960481227,13.3909343344167],[-.0022436121787266,-6.5238074250728E-4,4.7172729553196E-4]],[73E4,[4.2432528370899,-30.1182016908248,-10.7074412313491],[.0031725847067411,1.609846120227E-4,-9.0672150593868E-4]]],E=function(a,b,c){this.x=a;this.y=b;this.z=c};E.prototype.ToAstroVector=function(a){return new D(this.x,this.y,this.z,a)};E.prototype.quadrature=
+function(){return this.x*this.x+this.y*this.y+this.z*this.z};E.prototype.add=function(a){return new E(this.x+a.x,this.y+a.y,this.z+a.z)};E.prototype.sub=function(a){return new E(this.x-a.x,this.y-a.y,this.z-a.z)};E.prototype.incr=function(a){this.x+=a.x;this.y+=a.y;this.z+=a.z};E.prototype.decr=function(a){this.x-=a.x;this.y-=a.y;this.z-=a.z};E.prototype.mul=function(a){return new E(a*this.x,a*this.y,a*this.z)};E.prototype.div=function(a){return new E(this.x/a,this.y/a,this.z/a)};E.prototype.mean=
+function(a){return new E((this.x+a.x)/2,(this.y+a.y)/2,(this.z+a.z)/2)};var Ra=function(a,b,c){this.tt=a;this.r=b;this.v=c},Ta=function(a){var b=new Ra(a,new E(0,0,0),new E(0,0,0));this.Jupiter=Qa(b,a,u.Jupiter,2.825345909524226E-7);this.Saturn=Qa(b,a,u.Saturn,8.459715185680659E-8);this.Uranus=Qa(b,a,u.Uranus,1.292024916781969E-8);this.Neptune=Qa(b,a,u.Neptune,1.524358900784276E-8);this.Jupiter.r.decr(b.r);this.Jupiter.v.decr(b.v);this.Saturn.r.decr(b.r);this.Saturn.v.decr(b.v);this.Uranus.r.decr(b.r);
+this.Uranus.v.decr(b.v);this.Neptune.r.decr(b.r);this.Neptune.v.decr(b.v);this.Sun=new Ra(a,b.r.mul(-1),b.v.mul(-1))};Ta.prototype.Acceleration=function(a){var b=xa(a,2.959122082855911E-4,this.Sun.r);b.incr(xa(a,2.825345909524226E-7,this.Jupiter.r));b.incr(xa(a,8.459715185680659E-8,this.Saturn.r));b.incr(xa(a,1.292024916781969E-8,this.Uranus.r));b.incr(xa(a,1.524358900784276E-8,this.Neptune.r));return b};var Nb=function(a,b,c,d){this.tt=a;this.r=b;this.v=c;this.a=d},Ob=function(a,b){this.bary=a;this.grav=
+b},jb=[],Rc=new K([[.9994327653386544,-.03367710746976414,0],[.030395942890628476,.902057912352809,.43054338854229507],[-.014499455966335291,-.43029916940910073,.902569881273754]]),Sc=[{mu:2.82489428433814E-7,al:[1.446213296021224,3.5515522861824],a:[[.0028210960212903,0,0]],l:[[-1.925258348666E-4,4.9369589722645,.01358483658305],[-9.70803596076E-5,4.3188796477322,.01303413843243],[-8.988174165E-5,1.9080016428617,.00305064867158],[-5.53101050262E-5,1.4936156681569,.01293892891155]],z:[[.0041510849668155,
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+1.8196494533458,1.7822295777568],[-3.074250079334E-4,4.9377037005911,.01358483286724],[1.982386144784E-4,1.907986905476,.00305101212869],[1.834063551804E-4,2.1402853388529,.00145009789338],[-1.434383188452E-4,5.622214036663,.89111478887838],[-7.71939140944E-5,4.300272437235,2.6733443704266]],z:[[-.0093589104136341,4.0899396509039,-.01290686414666],[2.988994545555E-4,5.9097265185595,1.7693227079462],[2.13903639035E-4,2.1256289300016,1.2727418407E-4],[1.980963564781E-4,2.743516829265,6.7797343009E-4],
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+2.1402987195942,.00145009784384],[-1.828635964118E-4,4.3188672736968,.01303413828263],[1.512378778204E-4,4.9373102372298,.01358483481252],[-1.163720969778E-4,4.300265986149,2.6733443704266],[-9.55478069846E-5,1.4936612842567,.01293892879857],[8.15246854464E-5,5.6222137132535,.89111478887838],[-8.01219679602E-5,1.2995922951532,1.0034433456729],[-6.07017260182E-5,.64978769669238,.50172167043264]],z:[[.0014289811307319,2.1256295942739,1.2727413029E-4],[7.71093122676E-4,5.5836330003496,3.20643411E-5],
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+{mu:2.82492144889909E-7,al:[-.3620341291375704,.376486233433828],a:[[.0125879701715314,0,0],[3.595204947E-6,.64965776007116,.50172168165034],[2.7580210652E-6,1.808423578151,3.1750660413359]],l:[[5.586040123824E-4,2.1404207189815,.00145009793231],[-3.805813868176E-4,2.7358844897853,2.972965062E-5],[2.205152863262E-4,.649796525964,.5017216724358],[1.877895151158E-4,1.8084787604005,3.1750660413359],[7.66916975242E-5,6.2720114319755,1.3928364636651],[7.47056855106E-5,1.2995916202344,1.0034433456729]],
+z:[[.0073755808467977,5.5836071576084,3.206509914E-5],[2.065924169942E-4,5.9209831565786,.37648624194703],[1.589869764021E-4,.28744006242623,.8782079244252],[-1.561131605348E-4,2.1257397865089,1.2727441285E-4],[1.486043380971E-4,1.4462134301023,3.5515522949802],[6.35073108731E-5,5.9096803285954,1.7693227129285],[5.99351698525E-5,4.1125517584798,-2.7985797954589],[5.40660842731E-5,5.5390350845569,.00286834082283],[-4.89596900866E-5,4.6218149483338,-.62695712529519]],zeta:[[.0038422977898495,2.4133922085557,
+0],[.0022453891791894,5.9721736773277,-3.056125525E-5],[-2.604479450559E-4,3.3368746306409,-1.2491309972E-4],[3.3211214323E-5,5.5604137742337,.00290037688507]]}],yc=function(a){this.moon=a};e.JupiterMoonsInfo=yc;e.JupiterMoons=function(a){a=new N(a);for(var b=[],c=$jscomp.makeIterator(Sc),d=c.next();!d.done;d=c.next()){var f=b,h=f.push;d=d.value;for(var l=a.tt+18262.5,k=[0,d.al[0]+l*d.al[1],0,0,0,0],g=$jscomp.makeIterator(d.a),m=g.next();!m.done;m=g.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;
+var p=n.next().value;n=n.next().value;k[0]+=m*Math.cos(p+l*n)}g=$jscomp.makeIterator(d.l);for(m=g.next();!m.done;m=g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=n.next().value,n=n.next().value,k[1]+=m*Math.sin(p+l*n);k[1]%=O;0>k[1]&&(k[1]+=O);g=$jscomp.makeIterator(d.z);for(m=g.next();!m.done;m=g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=n.next().value,n=n.next().value,p+=l*n,k[2]+=m*Math.cos(p),k[3]+=m*Math.sin(p);g=$jscomp.makeIterator(d.zeta);for(m=g.next();!m.done;m=
+g.next())n=$jscomp.makeIterator(m.value),m=n.next().value,p=n.next().value,n=n.next().value,p+=l*n,k[4]+=m*Math.cos(p),k[5]+=m*Math.sin(p);g=k[0];n=k[1];m=k[2];p=k[3];l=k[4];k=k[5];var r=Math.sqrt(d.mu/(g*g*g));d=n+m*Math.sin(n)-p*Math.cos(n);do{var w=Math.cos(d);var B=Math.sin(d);w=(n-d+m*B-p*w)/(1-m*w-p*B);d+=w}while(1E-12<=Math.abs(w));w=Math.cos(d);B=Math.sin(d);n=p*w-m*B;var z=-m*w-p*B,sa=1/(1+z),ba=1/(1+Math.sqrt(1-m*m-p*p));d=g*(w-m-ba*p*n);n=g*(B-p+ba*m*n);p=r*sa*g*(-B-ba*p*z);g=r*sa*g*(+w+
+ba*m*z);m=2*Math.sqrt(1-l*l-k*k);r=1-2*k*k;w=1-2*l*l;B=2*k*l;d=new ob(d*r+n*B,d*B+n*w,(l*n-d*k)*m,p*r+g*B,p*B+g*w,(l*g-p*k)*m,a);d=dc(Rc,d);h.call(f,d)}return new yc(b)};e.HelioVector=ya;e.HelioDistance=fa;e.GeoVector=X;e.Search=G;e.SearchSunLongitude=Rb;e.LongitudeFromSun=kb;e.AngleFromSun=na;e.EclipticLongitude=ha;var Sb=function(a,b,c,d,f,h,l,k){this.time=a;this.mag=b;this.phase_angle=c;this.helio_dist=d;this.geo_dist=f;this.gc=h;this.hc=l;this.ring_tilt=k;this.phase_fraction=(1+Math.cos(e.DEG2RAD*
+c))/2};e.IlluminationInfo=Sb;e.Illumination=Ua;e.SearchRelativeLongitude=oa;e.MoonPhase=lb;e.SearchMoonPhase=Ba;var Ub=function(a,b){this.quarter=a;this.time=b};e.MoonQuarter=Ub;e.SearchMoonQuarter=Tb;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Tb(a)};e.SearchRiseSet=function(a,b,c,d,f){function h(w){var B=Na(a,w,b,!0,!0);w=Ma(w,b,B.ra,B.dec).altitude+l/B.dist*e.RAD2DEG+Qc;return c*w}ma(b);v(f);a:switch(a){case u.Sun:var l=Oc;break a;case u.Moon:l=Pc;break a;default:l=
+0}if(a===u.Earth)throw"Cannot find rise or set time of the Earth.";if(1===c){var k=12;var g=0}else if(-1===c)k=0,g=12;else throw"SearchRiseSet: Invalid direction parameter "+c+" -- must be +1 or -1";d=y(d);var m=h(d);var n;if(0<m){m=Ca(a,b,k,d);var p=m.time;m=h(p)}else p=d;var r=Ca(a,b,g,p);for(n=h(r.time);;){if(0>=m&&0<n&&(p=G(h,p,r.time,{init_f1:m,init_f2:n})))return p;m=Ca(a,b,k,r.time);r=Ca(a,b,g,m.time);if(m.time.ut>=d.ut+f)return null;p=m.time;m=h(m.time);n=h(r.time)}};var Vb=function(a,b){this.time=
+a;this.hor=b};e.HourAngleEvent=Vb;e.SearchHourAngle=Ca;var zc=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=zc;e.Seasons=function(a){function b(l,k,g){k=new Date(Date.UTC(a,k-1,g));l=Rb(l,k,4);if(!l)throw"Cannot find season change near "+k.toISOString();return l}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+a+" is neither a Date nor a safe integer.";
+var c=b(0,3,19),d=b(90,6,19),f=b(180,9,21),h=b(270,12,20);return new zc(c,d,f,h)};var Xb=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=Xb;e.Elongation=Wb;e.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);m=m.AddDays(.005);n=na(a,n);m=na(a,m);return(n-m)/.01}b=y(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only.";for(var f=0;2>=++f;){var h=
+ha(a,b),l=ha(u.Earth,b),k=za(h-l),g=h=l=void 0;k>=-d.s1&&k<+d.s1?(g=0,l=+d.s1,h=+d.s2):k>=+d.s2||k<-d.s2?(g=0,l=-d.s2,h=-d.s1):0<=k?(g=-Aa(a)/4,l=+d.s1,h=+d.s2):(g=-Aa(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(g);l=oa(a,l,k);h=oa(a,h,l);k=c(l);if(0<=k)throw"SearchMaxElongation: internal error: m1 = "+k;g=c(h);if(0>=g)throw"SearchMaxElongation: internal error: m2 = "+g;k=G(c,l,h,{init_f1:k,init_f2:g,dt_tolerance_seconds:10});if(!k)throw"SearchMaxElongation: failed search iter "+f+" (t1="+l.toString()+", t2="+
+h.toString()+")";if(k.tt>=b.tt)return Wb(a,k);b=h.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};e.SearchPeakMagnitude=function(a,b){function c(g){var m=g.AddDays(-.005);g=g.AddDays(.005);m=Ua(a,m).mag;return(Ua(a,g).mag-m)/.01}if(a!==u.Venus)throw"SearchPeakMagnitude currently works for Venus only.";b=y(b);for(var d=0;2>=++d;){var f=ha(a,b),h=ha(u.Earth,b),l=za(f-h),k=f=h=void 0;-10<=l&&10>l?(k=0,h=10,f=30):30<=l||-30>l?(k=0,h=-30,f=-10):0<=l?(k=-Aa(a)/4,h=10,f=30):
+(k=-Aa(a)/4,h=-30,f=-10);l=b.AddDays(k);h=oa(a,h,l);f=oa(a,f,h);l=c(h);if(0<=l)throw"SearchPeakMagnitude: internal error: m1 = "+l;k=c(f);if(0>=k)throw"SearchPeakMagnitude: internal error: m2 = "+k;l=G(c,h,f,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+h.toString()+", t2="+f.toString()+")";if(l.tt>=b.tt)return Ua(a,l);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Da=function(a,b,c){this.time=a;
+this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Da;e.SearchLunarApsis=Yb;e.NextLunarApsis=function(a){var b=Yb(a.time.AddDays(11));if(1!==b.kind+a.kind)throw"NextLunarApsis INTERNAL ERROR: did not find alternating apogee/perigee: prev="+a.kind+" @ "+a.time.toString()+", next="+b.kind+" @ "+b.time.toString();return b};e.SearchPlanetApsis=$b;e.NextPlanetApsis=function(a,b){if(0!==b.kind&&1!==b.kind)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*Z[a].OrbitalPeriod);a=$b(a,
+c);if(1!==a.kind+b.kind)throw"Internal error: previous apsis was "+b.kind+", but found "+a.kind+" for next apsis.";return a};e.InverseRotation=pa;e.CombineRotation=qa;e.IdentityMatrix=function(){return new K([[1,0,0],[0,1,0],[0,0,1]])};e.Pivot=function(a,b,c){if(0!==b&&1!==b&&2!==b)throw"Invalid axis "+b+". Must be [0, 1, 2].";var d=v(c)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);var f=(b+1)%3,h=(b+2)%3,l=[[0,0,0],[0,0,0],[0,0,0]];l[f][f]=c*a.rot[f][f]-d*a.rot[f][h];l[f][h]=d*a.rot[f][f]+c*a.rot[f][h];
+l[f][b]=a.rot[f][b];l[h][f]=c*a.rot[h][f]-d*a.rot[h][h];l[h][h]=d*a.rot[h][f]+c*a.rot[h][h];l[h][b]=a.rot[h][b];l[b][f]=c*a.rot[b][f]-d*a.rot[b][h];l[b][h]=d*a.rot[b][f]+c*a.rot[b][h];l[b][b]=a.rot[b][b];return new K(l)};e.VectorFromSphere=mb;e.EquatorFromVector=ac;e.SphereFromVector=nb;e.HorizonFromVector=function(a,b){a=nb(a);a.lon=bc(a.lon);a.lat+=va(b,a.lat);return a};e.VectorFromHorizon=function(a,b,c){var d=bc(a.lon);c=a.lat+cc(c,a.lat);a=new Va(c,d,a.dist);return mb(a,b)};e.Refraction=va;e.InverseRefraction=
+cc;e.RotateVector=Ea;e.RotateState=dc;e.Rotation_EQJ_ECL=ec;e.Rotation_ECL_EQJ=function(){return new K([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=pb;e.Rotation_EQD_EQJ=qb;e.Rotation_EQD_HOR=rb;e.Rotation_HOR_EQD=fc;e.Rotation_HOR_EQJ=gc;e.Rotation_EQJ_HOR=function(a,b){a=gc(a,b);return pa(a)};e.Rotation_EQD_ECL=hc;e.Rotation_ECL_EQD=ic;e.Rotation_ECL_HOR=jc;e.Rotation_HOR_ECL=function(a,b){a=jc(a,b);return pa(a)};var Tc=[["And",
+"Andromeda"],["Ant","Antila"],["Aps","Apus"],["Aql","Aquila"],["Aqr","Aquarius"],["Ara","Ara"],["Ari","Aries"],["Aur","Auriga"],["Boo","Bootes"],["Cae","Caelum"],["Cam","Camelopardis"],["Cap","Capricornus"],["Car","Carina"],["Cas","Cassiopeia"],["Cen","Centaurus"],["Cep","Cepheus"],["Cet","Cetus"],["Cha","Chamaeleon"],["Cir","Circinus"],["CMa","Canis Major"],["CMi","Canis Minor"],["Cnc","Cancer"],["Col","Columba"],["Com","Coma Berenices"],["CrA","Corona Australis"],["CrB","Corona Borealis"],["Crt",
+"Crater"],["Cru","Crux"],["Crv","Corvus"],["CVn","Canes Venatici"],["Cyg","Cygnus"],["Del","Delphinus"],["Dor","Dorado"],["Dra","Draco"],["Equ","Equuleus"],["Eri","Eridanus"],["For","Fornax"],["Gem","Gemini"],["Gru","Grus"],["Her","Hercules"],["Hor","Horologium"],["Hya","Hydra"],["Hyi","Hydrus"],["Ind","Indus"],["Lac","Lacerta"],["Leo","Leo"],["Lep","Lepus"],["Lib","Libra"],["LMi","Leo Minor"],["Lup","Lupus"],["Lyn","Lynx"],["Lyr","Lyra"],["Men","Mensa"],["Mic","Microscopium"],["Mon","Monoceros"],
+["Mus","Musca"],["Nor","Norma"],["Oct","Octans"],["Oph","Ophiuchus"],["Ori","Orion"],["Pav","Pavo"],["Peg","Pegasus"],["Per","Perseus"],["Phe","Phoenix"],["Pic","Pictor"],["PsA","Pisces Austrinus"],["Psc","Pisces"],["Pup","Puppis"],["Pyx","Pyxis"],["Ret","Reticulum"],["Scl","Sculptor"],["Sco","Scorpius"],["Sct","Scutum"],["Ser","Serpens"],["Sex","Sextans"],["Sge","Sagitta"],["Sgr","Sagittarius"],["Tau","Taurus"],["Tel","Telescopium"],["TrA","Triangulum Australe"],["Tri","Triangulum"],["Tuc","Tucana"],
+["UMa","Ursa Major"],["UMi","Ursa Minor"],["Vel","Vela"],["Vir","Virgo"],["Vol","Volans"],["Vul","Vulpecula"]],Uc=[[83,0,8640,2112],[83,2880,5220,2076],[83,7560,8280,2068],[83,6480,7560,2064],[15,0,2880,2040],[10,3300,3840,1968],[15,0,1800,1920],[10,3840,5220,1920],[83,6300,6480,1920],[33,7260,7560,1920],[15,0,1263,1848],[10,4140,4890,1848],[83,5952,6300,1800],[15,7260,7440,1800],[10,2868,3300,1764],[33,3300,4080,1764],[83,4680,5952,1680],[13,1116,1230,1632],[33,7350,7440,1608],[33,4080,4320,1596],
+[15,0,120,1584],[83,5040,5640,1584],[15,8490,8640,1584],[33,4320,4860,1536],[33,4860,5190,1512],[15,8340,8490,1512],[10,2196,2520,1488],[33,7200,7350,1476],[15,7393.2,7416,1462],[10,2520,2868,1440],[82,2868,3030,1440],[33,7116,7200,1428],[15,7200,7393.2,1428],[15,8232,8340,1418],[13,0,876,1404],[33,6990,7116,1392],[13,612,687,1380],[13,876,1116,1368],[10,1116,1140,1368],[15,8034,8232,1350],[10,1800,2196,1344],[82,5052,5190,1332],[33,5190,6990,1332],[10,1140,1200,1320],[15,7968,8034,1320],[15,7416,
+7908,1316],[13,0,612,1296],[50,2196,2340,1296],[82,4350,4860,1272],[33,5490,5670,1272],[15,7908,7968,1266],[10,1200,1800,1260],[13,8232,8400,1260],[33,5670,6120,1236],[62,735,906,1212],[33,6120,6564,1212],[13,0,492,1200],[62,492,600,1200],[50,2340,2448,1200],[13,8400,8640,1200],[82,4860,5052,1164],[13,0,402,1152],[13,8490,8640,1152],[39,6543,6564,1140],[33,6564,6870,1140],[30,6870,6900,1140],[62,600,735,1128],[82,3030,3300,1128],[13,60,312,1104],[82,4320,4350,1080],[50,2448,2652,1068],[30,7887,7908,
+1056],[30,7875,7887,1050],[30,6900,6984,1044],[82,3300,3660,1008],[82,3660,3882,960],[8,5556,5670,960],[39,5670,5880,960],[50,3330,3450,954],[0,0,906,882],[62,906,924,882],[51,6969,6984,876],[62,1620,1689,864],[30,7824,7875,864],[44,7875,7920,864],[7,2352,2652,852],[50,2652,2790,852],[0,0,720,840],[44,7920,8214,840],[44,8214,8232,828],[0,8232,8460,828],[62,924,978,816],[82,3882,3960,816],[29,4320,4440,816],[50,2790,3330,804],[48,3330,3558,804],[0,258,507,792],[8,5466,5556,792],[0,8460,8550,770],[29,
+4440,4770,768],[0,8550,8640,752],[29,5025,5052,738],[80,870,978,736],[62,978,1620,736],[7,1620,1710,720],[51,6543,6969,720],[82,3960,4320,696],[30,7080,7530,696],[7,1710,2118,684],[48,3558,3780,684],[29,4770,5025,684],[0,0,24,672],[80,507,600,672],[7,2118,2352,672],[37,2838,2880,672],[30,7530,7824,672],[30,6933,7080,660],[80,690,870,654],[25,5820,5880,648],[8,5430,5466,624],[25,5466,5820,624],[51,6612,6792,624],[48,3870,3960,612],[51,6792,6933,612],[80,600,690,600],[66,258,306,570],[48,3780,3870,
+564],[87,7650,7710,564],[77,2052,2118,548],[0,24,51,528],[73,5730,5772,528],[37,2118,2238,516],[87,7140,7290,510],[87,6792,6930,506],[0,51,306,504],[87,7290,7404,492],[37,2811,2838,480],[87,7404,7650,468],[87,6930,7140,460],[6,1182,1212,456],[75,6792,6840,444],[59,2052,2076,432],[37,2238,2271,420],[75,6840,7140,388],[77,1788,1920,384],[39,5730,5790,384],[75,7140,7290,378],[77,1662,1788,372],[77,1920,2016,372],[23,4620,4860,360],[39,6210,6570,344],[23,4272,4620,336],[37,2700,2811,324],[39,6030,6210,
+308],[61,0,51,300],[77,2016,2076,300],[37,2520,2700,300],[61,7602,7680,300],[37,2271,2496,288],[39,6570,6792,288],[31,7515,7578,284],[61,7578,7602,284],[45,4146,4272,264],[59,2247,2271,240],[37,2496,2520,240],[21,2811,2853,240],[61,8580,8640,240],[6,600,1182,238],[31,7251,7308,204],[8,4860,5430,192],[61,8190,8580,180],[21,2853,3330,168],[45,3330,3870,168],[58,6570,6718.4,150],[3,6718.4,6792,150],[31,7500,7515,144],[20,2520,2526,132],[73,6570,6633,108],[39,5790,6030,96],[58,6570,6633,72],[61,7728,
+7800,66],[66,0,720,48],[73,6690,6792,48],[31,7308,7500,48],[34,7500,7680,48],[61,7680,7728,48],[61,7920,8190,48],[61,7800,7920,42],[20,2526,2592,36],[77,1290,1662,0],[59,1662,1680,0],[20,2592,2910,0],[85,5280,5430,0],[58,6420,6570,0],[16,954,1182,-42],[77,1182,1290,-42],[73,5430,5856,-78],[59,1680,1830,-96],[59,2100,2247,-96],[73,6420,6468,-96],[73,6570,6690,-96],[3,6690,6792,-96],[66,8190,8580,-96],[45,3870,4146,-144],[85,4146,4260,-144],[66,0,120,-168],[66,8580,8640,-168],[85,5130,5280,-192],[58,
+5730,5856,-192],[3,7200,7392,-216],[4,7680,7872,-216],[58,6180,6468,-240],[54,2100,2910,-264],[35,1770,1830,-264],[59,1830,2100,-264],[41,2910,3012,-264],[74,3450,3870,-264],[85,4260,4620,-264],[58,6330,6360,-280],[3,6792,7200,-288.8],[35,1740,1770,-348],[4,7392,7680,-360],[73,6180,6570,-384],[72,6570,6792,-384],[41,3012,3090,-408],[58,5856,5895,-438],[41,3090,3270,-456],[26,3870,3900,-456],[71,5856,5895,-462],[47,5640,5730,-480],[28,4530,4620,-528],[85,4620,5130,-528],[41,3270,3510,-576],[16,600,
+954,-585.2],[35,954,1350,-585.2],[26,3900,4260,-588],[28,4260,4530,-588],[47,5130,5370,-588],[58,5856,6030,-590],[16,0,600,-612],[11,7680,7872,-612],[4,7872,8580,-612],[16,8580,8640,-612],[41,3510,3690,-636],[35,1692,1740,-654],[46,1740,2202,-654],[11,7200,7680,-672],[41,3690,3810,-700],[41,4530,5370,-708],[47,5370,5640,-708],[71,5640,5760,-708],[35,1650,1692,-720],[58,6030,6336,-720],[76,6336,6420,-720],[41,3810,3900,-748],[19,2202,2652,-792],[41,4410,4530,-792],[41,3900,4410,-840],[36,1260,1350,
+-864],[68,3012,3372,-882],[35,1536,1650,-888],[76,6420,6900,-888],[65,7680,8280,-888],[70,8280,8400,-888],[36,1080,1260,-950],[1,3372,3960,-954],[70,0,600,-960],[36,600,1080,-960],[35,1392,1536,-960],[70,8400,8640,-960],[14,5100,5370,-1008],[49,5640,5760,-1008],[71,5760,5911.5,-1008],[9,1740,1800,-1032],[22,1800,2370,-1032],[67,2880,3012,-1032],[35,1230,1392,-1056],[71,5911.5,6420,-1092],[24,6420,6900,-1092],[76,6900,7320,-1092],[53,7320,7680,-1092],[35,1080,1230,-1104],[9,1620,1740,-1116],[49,5520,
+5640,-1152],[63,0,840,-1156],[35,960,1080,-1176],[40,1470,1536,-1176],[9,1536,1620,-1176],[38,7680,7920,-1200],[67,2160,2880,-1218],[84,2880,2940,-1218],[35,870,960,-1224],[40,1380,1470,-1224],[63,0,660,-1236],[12,2160,2220,-1260],[84,2940,3042,-1272],[40,1260,1380,-1276],[32,1380,1440,-1276],[63,0,570,-1284],[35,780,870,-1296],[64,1620,1800,-1296],[49,5418,5520,-1296],[84,3042,3180,-1308],[12,2220,2340,-1320],[14,4260,4620,-1320],[49,5100,5418,-1320],[56,5418,5520,-1320],[32,1440,1560,-1356],[84,
+3180,3960,-1356],[14,3960,4050,-1356],[5,6300,6480,-1368],[78,6480,7320,-1368],[38,7920,8400,-1368],[40,1152,1260,-1380],[64,1800,1980,-1380],[12,2340,2460,-1392],[63,0,480,-1404],[35,480,780,-1404],[63,8400,8640,-1404],[32,1560,1650,-1416],[56,5520,5911.5,-1440],[43,7320,7680,-1440],[64,1980,2160,-1464],[18,5460,5520,-1464],[5,5911.5,5970,-1464],[18,5370,5460,-1526],[5,5970,6030,-1526],[64,2160,2460,-1536],[12,2460,3252,-1536],[14,4050,4260,-1536],[27,4260,4620,-1536],[14,4620,5232,-1536],[18,4860,
+4920,-1560],[5,6030,6060,-1560],[40,780,1152,-1620],[69,1152,1650,-1620],[18,5310,5370,-1620],[5,6060,6300,-1620],[60,6300,6480,-1620],[81,7920,8400,-1620],[32,1650,2370,-1680],[18,4920,5310,-1680],[79,5310,6120,-1680],[81,0,480,-1800],[42,1260,1650,-1800],[86,2370,3252,-1800],[12,3252,4050,-1800],[55,4050,4920,-1800],[60,6480,7680,-1800],[43,7680,8400,-1800],[81,8400,8640,-1800],[81,270,480,-1824],[42,0,1260,-1980],[17,2760,4920,-1980],[2,4920,6480,-1980],[52,1260,2760,-2040],[57,0,8640,-2160]],
+wb,Ac,Bc=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};e.ConstellationInfo=Bc;e.Constellation=function(a,b){v(a);v(b);if(-90>b||90<b)throw"Invalid declination angle. Must be -90..+90.";a%=24;0>a&&(a+=24);wb||(wb=pb(new N(-45655.74141261017)),Ac=new N(0));a=new Va(b,15*a,1);a=mb(a,Ac);a=Ea(wb,a);a=ac(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Uc),f=d.next();!f.done;f=d.next()){f=f.value;var h=f[1]*c,l=f[2]*c;if(f[3]*b<=a.dec&&h<=a.ra&&a.ra<l)return b=Tc[f[0]],new Bc(b[0],
+b[1],a.ra,a.dec)}throw"Unable to find constellation for given coordinates.";};var mc=function(a,b,c,d,f){this.kind=a;this.peak=b;this.sd_penum=c;this.sd_partial=d;this.sd_total=f};e.LunarEclipseInfo=mc;var Jc=function(a,b,c,d,f,h,l){this.time=a;this.u=b;this.r=c;this.k=d;this.p=f;this.target=h;this.dir=l};e.SearchLunarEclipse=lc;var oc=function(a,b,c,d,f){this.kind=a;this.peak=b;this.distance=c;this.latitude=d;this.longitude=f};e.GlobalSolarEclipseInfo=oc;e.NextLunarEclipse=function(a){a=a.AddDays(10);
+return lc(a)};e.SearchGlobalSolarEclipse=nc;e.NextGlobalSolarEclipse=function(a){a=a.AddDays(10);return nc(a)};var sc=function(a,b){this.time=a;this.altitude=b};e.EclipseEvent=sc;var uc=function(a,b,c,d,f,h){this.kind=a;this.partial_begin=b;this.total_begin=c;this.peak=d;this.total_end=f;this.partial_end=h};e.LocalSolarEclipseInfo=uc;e.SearchLocalSolarEclipse=tc;e.NextLocalSolarEclipse=function(a,b){a=a.AddDays(10);return tc(a,b)};var xc=function(a,b,c,d){this.start=a;this.peak=b;this.finish=c;this.separation=
+d};e.TransitInfo=xc;e.SearchTransit=wc;e.NextTransit=function(a,b){b=b.AddDays(100);return wc(a,b)}},{}]},{},[1])(1)});
diff --git a/source/js/astronomy.d.ts b/source/js/astronomy.d.ts
index fcc9dd0b..bc2cd996 100644
--- a/source/js/astronomy.d.ts
+++ b/source/js/astronomy.d.ts
@@ -32,13 +32,21 @@ export declare type FlexibleDateTime = Date | number | AstroTime;
  */
 export declare const KM_PER_AU = 149597870.69098932;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 export declare const DEG2RAD = 0.017453292519943295;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+export declare const HOUR2RAD = 0.26179938779914946;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 export declare const RAD2DEG = 57.29577951308232;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+export declare const RAD2HOUR = 3.819718634205488;
 /**
  * @brief The equatorial radius of Jupiter, expressed in kilometers.
  */
diff --git a/source/js/astronomy.js b/source/js/astronomy.js
index f11e9f8f..2c7dafa0 100644
--- a/source/js/astronomy.js
+++ b/source/js/astronomy.js
@@ -33,21 +33,29 @@
  */
 'use strict';
 Object.defineProperty(exports, "__esModule", { value: true });
-exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2DEG = exports.DEG2RAD = exports.KM_PER_AU = void 0;
-exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = void 0;
+exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.LongitudeFromSun = exports.SearchSunLongitude = exports.Search = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = void 0;
+exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = void 0;
 /**
  * @brief The number of kilometers per astronomical unit.
  */
 exports.KM_PER_AU = 1.4959787069098932e+8;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 exports.DEG2RAD = 0.017453292519943296;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+exports.HOUR2RAD = 0.2617993877991494365;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 exports.RAD2DEG = 57.295779513082321;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+exports.RAD2HOUR = 3.819718634205488;
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1971,10 +1979,10 @@ function vector2radec(pos, time) {
             return new EquatorialCoordinates(0, -90, dist, vec);
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
-    let ra = Math.atan2(vec.y, vec.x) / (exports.DEG2RAD * 15);
+    let ra = exports.RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / exports.DEG2RAD;
+    const dec = exports.RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 function spin(angle, pos) {
@@ -2035,8 +2043,8 @@ function Horizon(date, observer, ra, dec, refraction) {
     const coslon = Math.cos(observer.longitude * exports.DEG2RAD);
     const sindc = Math.sin(dec * exports.DEG2RAD);
     const cosdc = Math.cos(dec * exports.DEG2RAD);
-    const sinra = Math.sin(ra * 15 * exports.DEG2RAD);
-    const cosra = Math.cos(ra * 15 * exports.DEG2RAD);
+    const sinra = Math.sin(ra * exports.HOUR2RAD);
+    const cosra = Math.cos(ra * exports.HOUR2RAD);
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
     //
@@ -2082,7 +2090,7 @@ function Horizon(date, observer, ra, dec, refraction) {
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * exports.RAD2DEG;
+        az = -exports.RAD2DEG * Math.atan2(pw, pn);
         if (az < 0)
             az += 360;
     }
@@ -2092,7 +2100,7 @@ function Horizon(date, observer, ra, dec, refraction) {
         az = 0;
     }
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * exports.RAD2DEG;
+    let zd = exports.RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
     if (refraction) {
@@ -2110,7 +2118,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             }
             proj = Math.sqrt(pr[0] * pr[0] + pr[1] * pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * exports.RAD2DEG / 15;
+                out_ra = exports.RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
@@ -2118,7 +2126,7 @@ function Horizon(date, observer, ra, dec, refraction) {
             else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * exports.RAD2DEG;
+            out_dec = exports.RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
     return new HorizontalCoordinates(az, 90 - zd, out_ra, out_dec);
@@ -2372,7 +2380,7 @@ function GeoMoon(date) {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 exports.GeoMoon = GeoMoon;
-function VsopFormula(formula, t) {
+function VsopFormula(formula, t, clamp_angle) {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2380,7 +2388,10 @@ function VsopFormula(formula, t) {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2; // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2418,26 +2429,28 @@ function VsopRotate(eclip) {
 function VsopSphereToRect(lon, lat, radius) {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 function CalcVsop(model, time) {
     const t = time.tt / DAYS_PER_MILLENNIUM; // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
 function CalcVsopPosVel(model, tt) {
     const t = tt / DAYS_PER_MILLENNIUM;
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
     const drad_dt = VsopDeriv(model[RAD_INDEX], t);
@@ -3086,7 +3099,7 @@ exports.HelioVector = HelioVector;
 function HelioDistance(body, date) {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
diff --git a/source/js/astronomy.min.js b/source/js/astronomy.min.js
index 438e6e27..0df9ef3f 100644
--- a/source/js/astronomy.min.js
+++ b/source/js/astronomy.min.js
@@ -35,13 +35,13 @@ $jscomp.polyfillUnisolated=function(a,b,c,d){c=$jscomp.global;a=a.split(".");for
 $jscomp.polyfillIsolated=function(a,b,c,d){var e=a.split(".");a=1===e.length;d=e[0];d=!a&&d in $jscomp.polyfills?$jscomp.polyfills:$jscomp.global;for(var f=0;f<e.length-1;f++){var g=e[f];if(!(g in d))return;d=d[g]}e=e[e.length-1];c=$jscomp.IS_SYMBOL_NATIVE&&"es6"===c?d[e]:null;b=b(c);null!=b&&(a?$jscomp.defineProperty($jscomp.polyfills,e,{configurable:!0,writable:!0,value:b}):b!==c&&(void 0===$jscomp.propertyToPolyfillSymbol[e]&&($jscomp.propertyToPolyfillSymbol[e]=$jscomp.IS_SYMBOL_NATIVE?$jscomp.global.Symbol(e):
 $jscomp.POLYFILL_PREFIX+e),$jscomp.defineProperty(d,$jscomp.propertyToPolyfillSymbol[e],{configurable:!0,writable:!0,value:b})))};$jscomp.polyfill("Math.log10",function(a){return a?a:function(b){return Math.log(b)/Math.LN10}},"es6","es3");$jscomp.polyfill("Number.isFinite",function(a){return a?a:function(b){return"number"!==typeof b?!1:!isNaN(b)&&Infinity!==b&&-Infinity!==b}},"es6","es3");$jscomp.polyfill("Number.MAX_SAFE_INTEGER",function(){return 9007199254740991},"es6","es3");
 $jscomp.polyfill("Number.isInteger",function(a){return a?a:function(b){return Number.isFinite(b)?b===Math.floor(b):!1}},"es6","es3");$jscomp.polyfill("Number.isSafeInteger",function(a){return a?a:function(b){return Number.isInteger(b)&&Math.abs(b)<=Number.MAX_SAFE_INTEGER}},"es6","es3");Object.defineProperty(exports,"__esModule",{value:!0});
-exports.SearchMoonQuarter=exports.MoonQuarter=exports.SearchMoonPhase=exports.MoonPhase=exports.SearchRelativeLongitude=exports.Illumination=exports.IlluminationInfo=exports.EclipticLongitude=exports.AngleFromSun=exports.LongitudeFromSun=exports.SearchSunLongitude=exports.Search=exports.GeoVector=exports.HelioDistance=exports.HelioVector=exports.JupiterMoons=exports.JupiterMoonsInfo=exports.GeoMoon=exports.Ecliptic=exports.ObserverVector=exports.Equator=exports.SunPosition=exports.Observer=exports.Horizon=
-exports.EclipticCoordinates=exports.HorizontalCoordinates=exports.MakeRotation=exports.RotationMatrix=exports.EquatorialCoordinates=exports.Spherical=exports.StateVector=exports.Vector=exports.CalcMoonCount=exports.MakeTime=exports.AstroTime=exports.SetDeltaTFunction=exports.DeltaT_JplHorizons=exports.DeltaT_EspenakMeeus=exports.Body=exports.AngleBetween=exports.CALLISTO_RADIUS_KM=exports.GANYMEDE_RADIUS_KM=exports.EUROPA_RADIUS_KM=exports.IO_RADIUS_KM=exports.JUPITER_MEAN_RADIUS_KM=exports.JUPITER_POLAR_RADIUS_KM=
-exports.JUPITER_EQUATORIAL_RADIUS_KM=exports.RAD2DEG=exports.DEG2RAD=exports.KM_PER_AU=void 0;
-exports.LocalSolarEclipseInfo=exports.EclipseEvent=exports.NextGlobalSolarEclipse=exports.SearchGlobalSolarEclipse=exports.NextLunarEclipse=exports.GlobalSolarEclipseInfo=exports.SearchLunarEclipse=exports.LunarEclipseInfo=exports.Constellation=exports.ConstellationInfo=exports.Rotation_HOR_ECL=exports.Rotation_ECL_HOR=exports.Rotation_ECL_EQD=exports.Rotation_EQD_ECL=exports.Rotation_EQJ_HOR=exports.Rotation_HOR_EQJ=exports.Rotation_HOR_EQD=exports.Rotation_EQD_HOR=exports.Rotation_EQD_EQJ=exports.Rotation_EQJ_EQD=
-exports.Rotation_ECL_EQJ=exports.Rotation_EQJ_ECL=exports.RotateState=exports.RotateVector=exports.InverseRefraction=exports.Refraction=exports.VectorFromHorizon=exports.HorizonFromVector=exports.SphereFromVector=exports.EquatorFromVector=exports.VectorFromSphere=exports.Pivot=exports.IdentityMatrix=exports.CombineRotation=exports.InverseRotation=exports.NextPlanetApsis=exports.SearchPlanetApsis=exports.NextLunarApsis=exports.SearchLunarApsis=exports.Apsis=exports.SearchPeakMagnitude=exports.SearchMaxElongation=
-exports.Elongation=exports.ElongationEvent=exports.Seasons=exports.SeasonInfo=exports.SearchHourAngle=exports.HourAngleEvent=exports.SearchRiseSet=exports.NextMoonQuarter=void 0;exports.NextTransit=exports.SearchTransit=exports.TransitInfo=exports.NextLocalSolarEclipse=exports.SearchLocalSolarEclipse=void 0;exports.KM_PER_AU=1.4959787069098932E8;exports.DEG2RAD=.017453292519943295;exports.RAD2DEG=57.29577951308232;exports.JUPITER_EQUATORIAL_RADIUS_KM=71492;exports.JUPITER_POLAR_RADIUS_KM=66854;
-exports.JUPITER_MEAN_RADIUS_KM=69911;exports.IO_RADIUS_KM=1821.6;exports.EUROPA_RADIUS_KM=1560.8;exports.GANYMEDE_RADIUS_KM=2631.2;exports.CALLISTO_RADIUS_KM=2410.3;
+exports.SearchMoonPhase=exports.MoonPhase=exports.SearchRelativeLongitude=exports.Illumination=exports.IlluminationInfo=exports.EclipticLongitude=exports.AngleFromSun=exports.LongitudeFromSun=exports.SearchSunLongitude=exports.Search=exports.GeoVector=exports.HelioDistance=exports.HelioVector=exports.JupiterMoons=exports.JupiterMoonsInfo=exports.GeoMoon=exports.Ecliptic=exports.ObserverVector=exports.Equator=exports.SunPosition=exports.Observer=exports.Horizon=exports.EclipticCoordinates=exports.HorizontalCoordinates=
+exports.MakeRotation=exports.RotationMatrix=exports.EquatorialCoordinates=exports.Spherical=exports.StateVector=exports.Vector=exports.CalcMoonCount=exports.MakeTime=exports.AstroTime=exports.SetDeltaTFunction=exports.DeltaT_JplHorizons=exports.DeltaT_EspenakMeeus=exports.Body=exports.AngleBetween=exports.CALLISTO_RADIUS_KM=exports.GANYMEDE_RADIUS_KM=exports.EUROPA_RADIUS_KM=exports.IO_RADIUS_KM=exports.JUPITER_MEAN_RADIUS_KM=exports.JUPITER_POLAR_RADIUS_KM=exports.JUPITER_EQUATORIAL_RADIUS_KM=exports.RAD2HOUR=
+exports.RAD2DEG=exports.HOUR2RAD=exports.DEG2RAD=exports.KM_PER_AU=void 0;
+exports.NextGlobalSolarEclipse=exports.SearchGlobalSolarEclipse=exports.NextLunarEclipse=exports.GlobalSolarEclipseInfo=exports.SearchLunarEclipse=exports.LunarEclipseInfo=exports.Constellation=exports.ConstellationInfo=exports.Rotation_HOR_ECL=exports.Rotation_ECL_HOR=exports.Rotation_ECL_EQD=exports.Rotation_EQD_ECL=exports.Rotation_EQJ_HOR=exports.Rotation_HOR_EQJ=exports.Rotation_HOR_EQD=exports.Rotation_EQD_HOR=exports.Rotation_EQD_EQJ=exports.Rotation_EQJ_EQD=exports.Rotation_ECL_EQJ=exports.Rotation_EQJ_ECL=
+exports.RotateState=exports.RotateVector=exports.InverseRefraction=exports.Refraction=exports.VectorFromHorizon=exports.HorizonFromVector=exports.SphereFromVector=exports.EquatorFromVector=exports.VectorFromSphere=exports.Pivot=exports.IdentityMatrix=exports.CombineRotation=exports.InverseRotation=exports.NextPlanetApsis=exports.SearchPlanetApsis=exports.NextLunarApsis=exports.SearchLunarApsis=exports.Apsis=exports.SearchPeakMagnitude=exports.SearchMaxElongation=exports.Elongation=exports.ElongationEvent=
+exports.Seasons=exports.SeasonInfo=exports.SearchHourAngle=exports.HourAngleEvent=exports.SearchRiseSet=exports.NextMoonQuarter=exports.SearchMoonQuarter=exports.MoonQuarter=void 0;exports.NextTransit=exports.SearchTransit=exports.TransitInfo=exports.NextLocalSolarEclipse=exports.SearchLocalSolarEclipse=exports.LocalSolarEclipseInfo=exports.EclipseEvent=void 0;exports.KM_PER_AU=1.4959787069098932E8;exports.DEG2RAD=.017453292519943295;exports.HOUR2RAD=.26179938779914946;exports.RAD2DEG=57.29577951308232;
+exports.RAD2HOUR=3.819718634205488;exports.JUPITER_EQUATORIAL_RADIUS_KM=71492;exports.JUPITER_POLAR_RADIUS_KM=66854;exports.JUPITER_MEAN_RADIUS_KM=69911;exports.IO_RADIUS_KM=1821.6;exports.EUROPA_RADIUS_KM=1560.8;exports.GANYMEDE_RADIUS_KM=2631.2;exports.CALLISTO_RADIUS_KM=2410.3;
 var DAYS_PER_TROPICAL_YEAR=365.24217,J2000=new Date("2000-01-01T12:00:00Z"),PI2=2*Math.PI,ARC=180/Math.PI*3600,C_AUDAY=173.1446326846693,ASEC2RAD=4.84813681109536E-6,ASEC180=648E3,ASEC360=2*ASEC180,ANGVEL=7.292115E-5,AU_PER_PARSEC=ASEC180/Math.PI,SUN_MAG_1AU=-.17-5*Math.log10(AU_PER_PARSEC),MEAN_SYNODIC_MONTH=29.530588,SECONDS_PER_DAY=86400,MILLIS_PER_DAY=1E3*SECONDS_PER_DAY,SOLAR_DAYS_PER_SIDEREAL_DAY=.9972695717592592,SUN_RADIUS_KM=695700,SUN_RADIUS_AU=SUN_RADIUS_KM/exports.KM_PER_AU,EARTH_FLATTENING=
 .996647180302104,EARTH_EQUATORIAL_RADIUS_KM=6378.1366,EARTH_EQUATORIAL_RADIUS_AU=EARTH_EQUATORIAL_RADIUS_KM/exports.KM_PER_AU,EARTH_MEAN_RADIUS_KM=6371,EARTH_ATMOSPHERE_KM=88,EARTH_ECLIPSE_RADIUS_KM=EARTH_MEAN_RADIUS_KM+EARTH_ATMOSPHERE_KM,MOON_EQUATORIAL_RADIUS_KM=1738.1,MOON_MEAN_RADIUS_KM=1737.4,MOON_POLAR_RADIUS_KM=1736,MOON_EQUATORIAL_RADIUS_AU=MOON_EQUATORIAL_RADIUS_KM/exports.KM_PER_AU,REFRACTION_NEAR_HORIZON=34/60,EARTH_MOON_MASS_RATIO=81.30056,SUN_GM=2.959122082855911E-4,JUPITER_GM=2.825345909524226E-7,
 SATURN_GM=8.459715185680659E-8,URANUS_GM=1.292024916781969E-8,NEPTUNE_GM=1.524358900784276E-8,ob2000,cos_ob2000,sin_ob2000;function VerifyBoolean(a){if(!0!==a&&!1!==a)throw console.trace(),"Value is not boolean: "+a;return a}function VerifyNumber(a){if(!Number.isFinite(a))throw console.trace(),"Value is not a finite number: "+a;return a}function Frac(a){return a-Math.floor(a)}
@@ -126,18 +126,18 @@ function gyration(a,b,c){return c===PrecessDirection.Into2000?precession(nutatio
 var StateVector=function(a,b,c,d,e,f,g){this.x=a;this.y=b;this.z=c;this.vx=d;this.vy=e;this.vz=f;this.t=g};exports.StateVector=StateVector;var Spherical=function(a,b,c){this.lat=VerifyNumber(a);this.lon=VerifyNumber(b);this.dist=VerifyNumber(c)};exports.Spherical=Spherical;var EquatorialCoordinates=function(a,b,c,d){this.ra=VerifyNumber(a);this.dec=VerifyNumber(b);this.dist=VerifyNumber(c);this.vec=d};exports.EquatorialCoordinates=EquatorialCoordinates;
 function IsValidRotationArray(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}var RotationMatrix=function(a){this.rot=a};exports.RotationMatrix=RotationMatrix;function MakeRotation(a){if(!IsValidRotationArray(a))throw"Argument must be a [3][3] array of numbers";return new RotationMatrix(a)}exports.MakeRotation=MakeRotation;
 var HorizontalCoordinates=function(a,b,c,d){this.azimuth=VerifyNumber(a);this.altitude=VerifyNumber(b);this.ra=VerifyNumber(c);this.dec=VerifyNumber(d)};exports.HorizontalCoordinates=HorizontalCoordinates;var EclipticCoordinates=function(a,b,c){this.vec=a;this.elat=VerifyNumber(b);this.elon=VerifyNumber(c)};exports.EclipticCoordinates=EclipticCoordinates;function VectorFromArray(a,b){return new Vector(a[0],a[1],a[2],b)}
-function vector2radec(a,b){b=VectorFromArray(a,b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return 0>b.z?new EquatorialCoordinates(0,-90,d,b):new EquatorialCoordinates(0,90,d,b)}var e=Math.atan2(b.y,b.x)/(15*exports.DEG2RAD);0>e&&(e+=24);return new EquatorialCoordinates(e,Math.atan2(a[2],Math.sqrt(c))/exports.DEG2RAD,d,b)}function spin(a,b){var c=a*exports.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}
-function Horizon(a,b,c,d,e){a=MakeTime(a);VerifyObserver(b);VerifyNumber(c);VerifyNumber(d);var f=Math.sin(b.latitude*exports.DEG2RAD),g=Math.cos(b.latitude*exports.DEG2RAD),k=Math.sin(b.longitude*exports.DEG2RAD),h=Math.cos(b.longitude*exports.DEG2RAD);b=Math.sin(d*exports.DEG2RAD);var l=Math.cos(d*exports.DEG2RAD),m=Math.sin(15*c*exports.DEG2RAD),n=Math.cos(15*c*exports.DEG2RAD),p=[g*h,g*k,f];f=[-f*h,-f*k,g];k=[k,-h,0];g=-15*sidereal_time(a);a=spin(g,p);p=spin(g,f);k=spin(g,k);b=[l*n,l*m,b];m=b[0]*
-a[0]+b[1]*a[1]+b[2]*a[2];l=b[0]*p[0]+b[1]*p[1]+b[2]*p[2];p=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];n=Math.sqrt(l*l+p*p);0<n?(l=-Math.atan2(p,l)*exports.RAD2DEG,0>l&&(l+=360)):l=0;m=Math.atan2(n,m)*exports.RAD2DEG;n=d;if(e&&(d=m,e=Refraction(e,90-m),m-=e,0<e&&3E-4<m)){c=Math.sin(m*exports.DEG2RAD);n=Math.cos(m*exports.DEG2RAD);p=Math.sin(d*exports.DEG2RAD);d=Math.cos(d*exports.DEG2RAD);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/p*c+a[k]*n);n=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<n?(c=Math.atan2(e[1],e[0])*exports.RAD2DEG/
-15,0>c&&(c+=24)):c=0;n=Math.atan2(e[2],n)*exports.RAD2DEG}return new HorizontalCoordinates(l,90-m,c,n)}exports.Horizon=Horizon;function VerifyObserver(a){if(!(a instanceof Observer))throw"Not an instance of the Observer class: "+a;VerifyNumber(a.latitude);VerifyNumber(a.longitude);VerifyNumber(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}var Observer=function(a,b,c){this.latitude=a;this.longitude=b;this.height=c;VerifyObserver(this)};
+function vector2radec(a,b){b=VectorFromArray(a,b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return 0>b.z?new EquatorialCoordinates(0,-90,d,b):new EquatorialCoordinates(0,90,d,b)}var e=exports.RAD2HOUR*Math.atan2(b.y,b.x);0>e&&(e+=24);return new EquatorialCoordinates(e,exports.RAD2DEG*Math.atan2(a[2],Math.sqrt(c)),d,b)}function spin(a,b){var c=a*exports.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}
+function Horizon(a,b,c,d,e){a=MakeTime(a);VerifyObserver(b);VerifyNumber(c);VerifyNumber(d);var f=Math.sin(b.latitude*exports.DEG2RAD),g=Math.cos(b.latitude*exports.DEG2RAD),k=Math.sin(b.longitude*exports.DEG2RAD),h=Math.cos(b.longitude*exports.DEG2RAD);b=Math.sin(d*exports.DEG2RAD);var l=Math.cos(d*exports.DEG2RAD),m=Math.sin(c*exports.HOUR2RAD),n=Math.cos(c*exports.HOUR2RAD),p=[g*h,g*k,f];f=[-f*h,-f*k,g];k=[k,-h,0];g=-15*sidereal_time(a);a=spin(g,p);p=spin(g,f);k=spin(g,k);b=[l*n,l*m,b];m=b[0]*
+a[0]+b[1]*a[1]+b[2]*a[2];l=b[0]*p[0]+b[1]*p[1]+b[2]*p[2];p=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];n=Math.sqrt(l*l+p*p);0<n?(l=-exports.RAD2DEG*Math.atan2(p,l),0>l&&(l+=360)):l=0;m=exports.RAD2DEG*Math.atan2(n,m);n=d;if(e&&(d=m,e=Refraction(e,90-m),m-=e,0<e&&3E-4<m)){c=Math.sin(m*exports.DEG2RAD);n=Math.cos(m*exports.DEG2RAD);p=Math.sin(d*exports.DEG2RAD);d=Math.cos(d*exports.DEG2RAD);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/p*c+a[k]*n);n=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<n?(c=exports.RAD2HOUR*Math.atan2(e[1],
+e[0]),0>c&&(c+=24)):c=0;n=exports.RAD2DEG*Math.atan2(e[2],n)}return new HorizontalCoordinates(l,90-m,c,n)}exports.Horizon=Horizon;function VerifyObserver(a){if(!(a instanceof Observer))throw"Not an instance of the Observer class: "+a;VerifyNumber(a.latitude);VerifyNumber(a.longitude);VerifyNumber(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}var Observer=function(a,b,c){this.latitude=a;this.longitude=b;this.height=c;VerifyObserver(this)};
 exports.Observer=Observer;function SunPosition(a){a=MakeTime(a).AddDays(-1/C_AUDAY);var b=CalcVsop(vsop.Earth,a),c=$jscomp.makeIterator(gyration([-b.x,-b.y,-b.z],a,PrecessDirection.From2000));b=c.next().value;var d=c.next().value,e=c.next().value,f=exports.DEG2RAD*e_tilt(a).tobl;c=Math.cos(f);f=Math.sin(f);a=new Vector(b,d,e,a);return RotateEquatorialToEcliptic(a,c,f)}exports.SunPosition=SunPosition;
 function Equator(a,b,c,d,e){VerifyObserver(c);VerifyBoolean(d);VerifyBoolean(e);b=MakeTime(b);c=geo_pos(b,c);a=GeoVector(a,b,e);a=[a.x-c[0],a.y-c[1],a.z-c[2]];if(!d)return vector2radec(a,b);d=gyration(a,b,PrecessDirection.From2000);return vector2radec(d,b)}exports.Equator=Equator;function ObserverVector(a,b,c){a=MakeTime(a);var d=sidereal_time(a);b=terra(b,d).pos;c||(b=gyration(b,a,PrecessDirection.Into2000));return VectorFromArray(b,a)}exports.ObserverVector=ObserverVector;
 function RotateEquatorialToEcliptic(a,b,c){var d=a.x,e=a.y*b+a.z*c;c=-a.y*c+a.z*b;var f=Math.sqrt(d*d+e*e);b=0;0<f&&(b=exports.RAD2DEG*Math.atan2(e,d),0>b&&(b+=360));f=exports.RAD2DEG*Math.atan2(c,f);a=new Vector(d,e,c,a.t);return new EclipticCoordinates(a,f,b)}function Ecliptic(a){void 0===ob2000&&(ob2000=exports.DEG2RAD*e_tilt(MakeTime(J2000)).mobl,cos_ob2000=Math.cos(ob2000),sin_ob2000=Math.sin(ob2000));return RotateEquatorialToEcliptic(a,cos_ob2000,sin_ob2000)}exports.Ecliptic=Ecliptic;
 function GeoMoon(a){a=MakeTime(a);var b=CalcMoon(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=ecl2equ_vec(a,[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)]);b=precession(b,a,PrecessDirection.Into2000);return new Vector(b[0],b[1],b[2],a)}exports.GeoMoon=GeoMoon;
-function VsopFormula(a,b){var c=1,d=0;a=$jscomp.makeIterator(a);for(var e=a.next();!e.done;e=a.next()){var f=0;e=$jscomp.makeIterator(e.value);for(var g=e.next();!g.done;g=e.next()){var k=$jscomp.makeIterator(g.value);g=k.next().value;var h=k.next().value;k=k.next().value;f+=g*Math.cos(h+b*k)}d+=c*f;c*=b}return d}
+function VsopFormula(a,b,c){var d=1,e=0;a=$jscomp.makeIterator(a);for(var f=a.next();!f.done;f=a.next()){var g=0;f=$jscomp.makeIterator(f.value);for(var k=f.next();!k.done;k=f.next()){var h=$jscomp.makeIterator(k.value);k=h.next().value;var l=h.next().value;h=h.next().value;g+=k*Math.cos(l+b*h)}g*=d;c&&(g%=PI2);e+=g;d*=b}return e}
 function VsopDeriv(a,b){var c=1,d=0,e=0,f=0;a=$jscomp.makeIterator(a);for(var g=a.next();!g.done;g=a.next()){var k=0,h=0;g=$jscomp.makeIterator(g.value);for(var l=g.next();!l.done;l=g.next()){var m=$jscomp.makeIterator(l.value);l=m.next().value;var n=m.next().value;m=m.next().value;n+=b*m;k+=l*m*Math.sin(n);0<f&&(h+=l*Math.cos(n))}e+=f*d*h-c*k;d=c;c*=b;++f}return e}var DAYS_PER_MILLENNIUM=365250,LON_INDEX=0,LAT_INDEX=1,RAD_INDEX=2;
-function VsopRotate(a){return new TerseVector(a[0]+4.4036E-7*a[1]-1.90919E-7*a[2],-4.79966E-7*a[0]+.917482137087*a[1]-.397776982902*a[2],.397776982902*a[1]+.917482137087*a[2])}function VsopSphereToRect(a,b,c){var d=c*Math.cos(b);return[d*Math.cos(a),d*Math.sin(a),c*Math.sin(b)]}function CalcVsop(a,b){var c=b.tt/DAYS_PER_MILLENNIUM,d=VsopFormula(a[LON_INDEX],c),e=VsopFormula(a[LAT_INDEX],c);a=VsopFormula(a[RAD_INDEX],c);d=VsopSphereToRect(d,e,a);return VsopRotate(d).ToAstroVector(b)}
-function CalcVsopPosVel(a,b){var c=b/DAYS_PER_MILLENNIUM,d=VsopFormula(a[LON_INDEX],c),e=VsopFormula(a[LAT_INDEX],c),f=VsopFormula(a[RAD_INDEX],c),g=VsopDeriv(a[LON_INDEX],c),k=VsopDeriv(a[LAT_INDEX],c);c=VsopDeriv(a[RAD_INDEX],c);var h=Math.cos(d),l=Math.sin(d),m=Math.cos(e),n=Math.sin(e);a=+(c*m*h)-f*n*h*k-f*m*l*g;g=+(c*m*l)-f*n*l*k+f*m*h*g;k=+(c*n)+f*m*k;d=VsopSphereToRect(d,e,f);e=[a/DAYS_PER_MILLENNIUM,g/DAYS_PER_MILLENNIUM,k/DAYS_PER_MILLENNIUM];d=VsopRotate(d);e=VsopRotate(e);return new body_state_t(b,
+function VsopRotate(a){return new TerseVector(a[0]+4.4036E-7*a[1]-1.90919E-7*a[2],-4.79966E-7*a[0]+.917482137087*a[1]-.397776982902*a[2],.397776982902*a[1]+.917482137087*a[2])}function VsopSphereToRect(a,b,c){var d=c*Math.cos(b);return[d*Math.cos(a),d*Math.sin(a),c*Math.sin(b)]}function CalcVsop(a,b){var c=b.tt/DAYS_PER_MILLENNIUM,d=VsopFormula(a[LON_INDEX],c,!0),e=VsopFormula(a[LAT_INDEX],c,!1);a=VsopFormula(a[RAD_INDEX],c,!1);d=VsopSphereToRect(d,e,a);return VsopRotate(d).ToAstroVector(b)}
+function CalcVsopPosVel(a,b){var c=b/DAYS_PER_MILLENNIUM,d=VsopFormula(a[LON_INDEX],c,!0),e=VsopFormula(a[LAT_INDEX],c,!1),f=VsopFormula(a[RAD_INDEX],c,!1),g=VsopDeriv(a[LON_INDEX],c),k=VsopDeriv(a[LAT_INDEX],c);c=VsopDeriv(a[RAD_INDEX],c);var h=Math.cos(d),l=Math.sin(d),m=Math.cos(e),n=Math.sin(e);a=+(c*m*h)-f*n*h*k-f*m*l*g;g=+(c*m*l)-f*n*l*k+f*m*h*g;k=+(c*n)+f*m*k;d=VsopSphereToRect(d,e,f);e=[a/DAYS_PER_MILLENNIUM,g/DAYS_PER_MILLENNIUM,k/DAYS_PER_MILLENNIUM];d=VsopRotate(d);e=VsopRotate(e);return new body_state_t(b,
 d,e)}function AdjustBarycenter(a,b,c,d){d/=d+SUN_GM;b=CalcVsop(vsop[c],b);a.x+=d*b.x;a.y+=d*b.y;a.z+=d*b.z}function CalcSolarSystemBarycenter(a){var b=new Vector(0,0,0,a);AdjustBarycenter(b,a,Body.Jupiter,JUPITER_GM);AdjustBarycenter(b,a,Body.Saturn,SATURN_GM);AdjustBarycenter(b,a,Body.Uranus,URANUS_GM);AdjustBarycenter(b,a,Body.Neptune,NEPTUNE_GM);return b}
 var PLUTO_NUM_STATES=41,PLUTO_TIME_STEP=36500,PlutoStateTable=[[-73E4,[-26.1182072321076,-14.376168177825,3.3844025152995],[.0016339372163656,-.0027861699588508,-.0013585880229445]],[-693500,[43.6599275018261,15.7782921408811,-8.2269833881374],[-2.504304629586E-4,.0021163039457238,7.3466073583102E-4]],[-657E3,[-17.0086014985033,33.059074387642,15.4080189624259],[-.0019676551946049,-.001833770776677,2.0125441459959E-5]],[-620500,[26.9005106893171,-21.5285596810214,-14.7987712668075],[.0022939261196998,
 .0017431871970059,-1.4585639832643E-4]],[-584E3,[20.2303809506997,43.2669666571891,7.3829660919234],[-.0019754081700585,5.3457141292226E-4,7.5929169129793E-4]],[-547500,[-22.5571440338751,-19.2958112538447,.7806423603826],[.0021494578646505,-.0024266772630044,-.0014013084013574]],[-511E3,[43.023623681036,19.6179542007347,-6.8406553041565],[-4.7729923671058E-4,.0020208979483877,7.7191815992131E-4]],[-474500,[-20.4245105862934,29.5157679318005,15.3408675727018],[-.0018003167284198,-.0021025226687937,
@@ -175,7 +175,7 @@ function CalcJupiterMoon(a,b){for(var c=a.tt+18262.5,d=[0,b.al[0]+c*b.al[1],0,0,
 e.next())g=$jscomp.makeIterator(f.value),f=g.next().value,k=g.next().value,g=g.next().value,k+=c*g,d[2]+=f*Math.cos(k),d[3]+=f*Math.sin(k);e=$jscomp.makeIterator(b.zeta);for(f=e.next();!f.done;f=e.next())g=$jscomp.makeIterator(f.value),f=g.next().value,k=g.next().value,g=g.next().value,k+=c*g,d[4]+=f*Math.cos(k),d[5]+=f*Math.sin(k);a=JupiterMoon_elem2pv(a,b.mu,d);return RotateState(Rotation_JUP_EQJ,a)}
 function JupiterMoons(a){a=new AstroTime(a);for(var b=[],c=$jscomp.makeIterator(JupiterMoonModel),d=c.next();!d.done;d=c.next())b.push(CalcJupiterMoon(a,d.value));return new JupiterMoonsInfo(b)}exports.JupiterMoons=JupiterMoons;
 function HelioVector(a,b){b=MakeTime(b);if(a in vsop)return CalcVsop(vsop[a],b);if(a===Body.Pluto)return CalcPluto(b);if(a===Body.Sun)return new Vector(0,0,0,b);if(a===Body.Moon){a=CalcVsop(vsop.Earth,b);var c=GeoMoon(b);return new Vector(a.x+c.x,a.y+c.y,a.z+c.z,b)}if(a===Body.EMB){a=CalcVsop(vsop.Earth,b);c=GeoMoon(b);var d=1+EARTH_MOON_MASS_RATIO;return new Vector(a.x+c.x/d,a.y+c.y/d,a.z+c.z/d,b)}if(a===Body.SSB)return CalcSolarSystemBarycenter(b);throw'HelioVector: Unknown body "'+a+'"';}
-exports.HelioVector=HelioVector;function HelioDistance(a,b){b=MakeTime(b);return a in vsop?VsopFormula(vsop[a][RAD_INDEX],b.tt/DAYS_PER_MILLENNIUM):HelioVector(a,b).Length()}exports.HelioDistance=HelioDistance;
+exports.HelioVector=HelioVector;function HelioDistance(a,b){b=MakeTime(b);return a in vsop?VsopFormula(vsop[a][RAD_INDEX],b.tt/DAYS_PER_MILLENNIUM,!1):HelioVector(a,b).Length()}exports.HelioDistance=HelioDistance;
 function GeoVector(a,b,c){VerifyBoolean(c);b=MakeTime(b);if(a===Body.Moon)return GeoMoon(b);if(a===Body.Earth)return new Vector(0,0,0,b);for(var d=null,e,f=0,g=b,k=0;10>k;++k){e=HelioVector(a,g);c?d=CalcVsop(vsop.Earth,g):d||(d=CalcVsop(vsop.Earth,b));e=new Vector(e.x-d.x,e.y-d.y,e.z-d.z,b);var h=b.AddDays(-e.Length()/C_AUDAY);f=Math.abs(h.tt-g.tt);if(1E-9>f)return e;g=h}throw"Light-travel time solver did not converge: dt="+f;}exports.GeoVector=GeoVector;
 function QuadInterp(a,b,c,d,e){var f=(e+c)/2-d;c=(e-c)/2;if(0==f){if(0==c)return null;d=-d/c;if(-1>d||1<d)return null}else{d=c*c-4*f*d;if(0>=d)return null;e=Math.sqrt(d);d=(-c+e)/(2*f);e=(-c-e)/(2*f);if(-1<=d&&1>=d){if(-1<=e&&1>=e)return null}else if(-1<=e&&1>=e)d=e;else return null}return{x:d,t:a+d*b,df_dt:(2*f*d+c)/b}}
 function Search(a,b,c,d){var e=VerifyNumber(d&&d.dt_tolerance_seconds||1);e=Math.abs(e/SECONDS_PER_DAY);var f=d&&d.init_f1||a(b),g=d&&d.init_f2||a(c),k=NaN,h=0;d=d&&d.iter_limit||20;for(var l=!0;;){if(++h>d)throw"Excessive iteration in Search()";var m=InterpolateTime(b,c,.5),n=m.ut-b.ut;if(Math.abs(n)<e)return m;l?k=a(m):l=!0;var p=QuadInterp(m.ut,c.ut-m.ut,f,k,g);if(p){var r=MakeTime(p.t),x=a(r);if(0!==p.df_dt){if(Math.abs(x/p.df_dt)<e)return r;p=1.2*Math.abs(x/p.df_dt);if(p<n/10&&(n=r.AddDays(-p),
diff --git a/source/js/astronomy.ts b/source/js/astronomy.ts
index 7b365993..022a5ff1 100644
--- a/source/js/astronomy.ts
+++ b/source/js/astronomy.ts
@@ -42,15 +42,26 @@ export type FlexibleDateTime = Date | number | AstroTime;
 export const KM_PER_AU = 1.4959787069098932e+8;
 
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 export const DEG2RAD = 0.017453292519943296;
 
+/**
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+export const HOUR2RAD = 0.2617993877991494365;
+
  /**
-  * @brief The factor to convert degrees to radians = 180/pi.
+  * @brief The factor to convert radians to degrees = 180/pi.
   */
 export const RAD2DEG = 57.295779513082321;
 
+ /**
+  * @brief The factor to convert radians to sidereal hours = 12/pi.
+  */
+export const RAD2HOUR = 3.819718634205488;
+
+
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -2125,10 +2136,10 @@ function vector2radec(pos: ArrayVector, time: AstroTime): EquatorialCoordinates
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
 
-    let ra = Math.atan2(vec.y, vec.x) / (DEG2RAD * 15);
+    let ra = RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / DEG2RAD;
+    const dec = RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 
@@ -2192,8 +2203,8 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     const coslon = Math.cos(observer.longitude * DEG2RAD);
     const sindc  = Math.sin(dec * DEG2RAD);
     const cosdc  = Math.cos(dec * DEG2RAD);
-    const sinra  = Math.sin(ra * 15 * DEG2RAD);
-    const cosra  = Math.cos(ra * 15 * DEG2RAD);
+    const sinra  = Math.sin(ra * HOUR2RAD);
+    const cosra  = Math.cos(ra * HOUR2RAD);
 
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
@@ -2249,7 +2260,7 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * RAD2DEG;
+        az = -RAD2DEG * Math.atan2(pw, pn);
         if (az < 0) az += 360;
     } else {
         // The body is straight up/down, so it does not have an azimuth.
@@ -2258,7 +2269,7 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     }
 
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * RAD2DEG;
+    let zd = RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
 
@@ -2277,14 +2288,14 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
             }
             proj = Math.sqrt(pr[0]*pr[0] + pr[1]*pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * RAD2DEG / 15;
+                out_ra = RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
             } else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * RAD2DEG;
+            out_dec = RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
 
@@ -2557,7 +2568,7 @@ export function GeoMoon(date: FlexibleDateTime): Vector {
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
 
-function VsopFormula(formula: any, t: number): number {
+function VsopFormula(formula: any, t: number, clamp_angle: boolean): number {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2565,7 +2576,10 @@ function VsopFormula(formula: any, t: number): number {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2;    // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2611,18 +2625,20 @@ function VsopRotate(eclip: ArrayVector): TerseVector {
 function VsopSphereToRect(lon: number, lat: number, radius: number): ArrayVector {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 
 function CalcVsop(model: any[], time: AstroTime): Vector {
     const t = time.tt / DAYS_PER_MILLENNIUM;   // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
@@ -2631,9 +2647,9 @@ function CalcVsopPosVel(model: any[], tt: number): body_state_t {
     const t = tt / DAYS_PER_MILLENNIUM;
 
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
 
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
@@ -3416,7 +3432,7 @@ export function HelioVector(body: Body, date: FlexibleDateTime): Vector {
 export function HelioDistance(body: Body, date: FlexibleDateTime): number {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
@@ -7108,7 +7124,7 @@ function GeoidIntersect(shadow: ShadowInfo): GlobalSolarEclipseInfo {
 
         // Adjust longitude for Earth's rotation at the given UT.
         const gast = sidereal_time(peak);
-        longitude = (RAD2DEG * Math.atan2(py, px) - (15*gast)) % 360.0;
+        longitude = (RAD2DEG*Math.atan2(py, px) - (15*gast)) % 360.0;
         if (longitude <= -180.0) {
             longitude += 360.0;
         } else if (longitude > +180.0) {
diff --git a/source/js/esm/astronomy.js b/source/js/esm/astronomy.js
index e4a99380..8c96cb74 100644
--- a/source/js/esm/astronomy.js
+++ b/source/js/esm/astronomy.js
@@ -37,13 +37,21 @@
  */
 export const KM_PER_AU = 1.4959787069098932e+8;
 /**
- * @brief The factor to convert radians to degrees = pi/180.
+ * @brief The factor to convert degrees to radians = pi/180.
  */
 export const DEG2RAD = 0.017453292519943296;
 /**
- * @brief The factor to convert degrees to radians = 180/pi.
+ * @brief The factor to convert sidereal hours to radians = pi/12.
+ */
+export const HOUR2RAD = 0.2617993877991494365;
+/**
+ * @brief The factor to convert radians to degrees = 180/pi.
  */
 export const RAD2DEG = 57.295779513082321;
+/**
+ * @brief The factor to convert radians to sidereal hours = 12/pi.
+ */
+export const RAD2HOUR = 3.819718634205488;
 // Jupiter radius data are nominal values obtained from:
 // https://www.iau.org/static/resolutions/IAU2015_English.pdf
 // https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
@@ -1953,10 +1961,10 @@ function vector2radec(pos, time) {
             return new EquatorialCoordinates(0, -90, dist, vec);
         return new EquatorialCoordinates(0, +90, dist, vec);
     }
-    let ra = Math.atan2(vec.y, vec.x) / (DEG2RAD * 15);
+    let ra = RAD2HOUR * Math.atan2(vec.y, vec.x);
     if (ra < 0)
         ra += 24;
-    const dec = Math.atan2(pos[2], Math.sqrt(xyproj)) / DEG2RAD;
+    const dec = RAD2DEG * Math.atan2(pos[2], Math.sqrt(xyproj));
     return new EquatorialCoordinates(ra, dec, dist, vec);
 }
 function spin(angle, pos) {
@@ -2017,8 +2025,8 @@ export function Horizon(date, observer, ra, dec, refraction) {
     const coslon = Math.cos(observer.longitude * DEG2RAD);
     const sindc = Math.sin(dec * DEG2RAD);
     const cosdc = Math.cos(dec * DEG2RAD);
-    const sinra = Math.sin(ra * 15 * DEG2RAD);
-    const cosra = Math.cos(ra * 15 * DEG2RAD);
+    const sinra = Math.sin(ra * HOUR2RAD);
+    const cosra = Math.cos(ra * HOUR2RAD);
     // Calculate three mutually perpendicular unit vectors
     // in equatorial coordinates: uze, une, uwe.
     //
@@ -2064,7 +2072,7 @@ export function Horizon(date, observer, ra, dec, refraction) {
     if (proj > 0) {
         // If the body is not exactly straight up/down, it has an azimuth.
         // Invert the angle to produce degrees eastward from north.
-        az = -Math.atan2(pw, pn) * RAD2DEG;
+        az = -RAD2DEG * Math.atan2(pw, pn);
         if (az < 0)
             az += 360;
     }
@@ -2074,7 +2082,7 @@ export function Horizon(date, observer, ra, dec, refraction) {
         az = 0;
     }
     // zd = the angle of the body away from the observer's zenith, in degrees.
-    let zd = Math.atan2(proj, pz) * RAD2DEG;
+    let zd = RAD2DEG * Math.atan2(proj, pz);
     let out_ra = ra;
     let out_dec = dec;
     if (refraction) {
@@ -2092,7 +2100,7 @@ export function Horizon(date, observer, ra, dec, refraction) {
             }
             proj = Math.sqrt(pr[0] * pr[0] + pr[1] * pr[1]);
             if (proj > 0) {
-                out_ra = Math.atan2(pr[1], pr[0]) * RAD2DEG / 15;
+                out_ra = RAD2HOUR * Math.atan2(pr[1], pr[0]);
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
@@ -2100,7 +2108,7 @@ export function Horizon(date, observer, ra, dec, refraction) {
             else {
                 out_ra = 0;
             }
-            out_dec = Math.atan2(pr[2], proj) * RAD2DEG;
+            out_dec = RAD2DEG * Math.atan2(pr[2], proj);
         }
     }
     return new HorizontalCoordinates(az, 90 - zd, out_ra, out_dec);
@@ -2347,7 +2355,7 @@ export function GeoMoon(date) {
     var mpos2 = precession(mpos1, time, PrecessDirection.Into2000);
     return new Vector(mpos2[0], mpos2[1], mpos2[2], time);
 }
-function VsopFormula(formula, t) {
+function VsopFormula(formula, t, clamp_angle) {
     let tpower = 1;
     let coord = 0;
     for (let series of formula) {
@@ -2355,7 +2363,10 @@ function VsopFormula(formula, t) {
         for (let [ampl, phas, freq] of series) {
             sum += ampl * Math.cos(phas + (t * freq));
         }
-        coord += tpower * sum;
+        let incr = tpower * sum;
+        if (clamp_angle)
+            incr %= PI2; // improve precision for longitudes: they can be hundreds of radians
+        coord += incr;
         tpower *= t;
     }
     return coord;
@@ -2393,26 +2404,28 @@ function VsopRotate(eclip) {
 function VsopSphereToRect(lon, lat, radius) {
     // Convert spherical coordinates to ecliptic cartesian coordinates.
     const r_coslat = radius * Math.cos(lat);
+    const coslon = Math.cos(lon);
+    const sinlon = Math.sin(lon);
     return [
-        r_coslat * Math.cos(lon),
-        r_coslat * Math.sin(lon),
+        r_coslat * coslon,
+        r_coslat * sinlon,
         radius * Math.sin(lat)
     ];
 }
 function CalcVsop(model, time) {
     const t = time.tt / DAYS_PER_MILLENNIUM; // millennia since 2000
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const eclip = VsopSphereToRect(lon, lat, rad);
     return VsopRotate(eclip).ToAstroVector(time);
 }
 function CalcVsopPosVel(model, tt) {
     const t = tt / DAYS_PER_MILLENNIUM;
     // Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates.
-    const lon = VsopFormula(model[LON_INDEX], t);
-    const lat = VsopFormula(model[LAT_INDEX], t);
-    const rad = VsopFormula(model[RAD_INDEX], t);
+    const lon = VsopFormula(model[LON_INDEX], t, true);
+    const lat = VsopFormula(model[LAT_INDEX], t, false);
+    const rad = VsopFormula(model[RAD_INDEX], t, false);
     const dlon_dt = VsopDeriv(model[LON_INDEX], t);
     const dlat_dt = VsopDeriv(model[LAT_INDEX], t);
     const drad_dt = VsopDeriv(model[RAD_INDEX], t);
@@ -3058,7 +3071,7 @@ export function HelioVector(body, date) {
 export function HelioDistance(body, date) {
     const time = MakeTime(date);
     if (body in vsop) {
-        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM);
+        return VsopFormula(vsop[body][RAD_INDEX], time.tt / DAYS_PER_MILLENNIUM, false);
     }
     return HelioVector(body, time).Length();
 }
diff --git a/source/python/astronomy.py b/source/python/astronomy.py
index 374daee1..d0d810da 100644
--- a/source/python/astronomy.py
+++ b/source/python/astronomy.py
@@ -56,6 +56,8 @@ CALLISTO_RADIUS_KM = 2410.3     #<const> The mean radius of Jupiter's moon Calli
 
 _CalcMoonCount = 0
 
+_RAD2HOUR  =  3.819718634205488         # 12/pi = factor to convert radians to sidereal hours
+_HOUR2RAD  =  0.2617993877991494365     # pi/12 = factor to convert sidereal hours to radians
 _DAYS_PER_TROPICAL_YEAR = 365.24217
 _PI2 = 2.0 * math.pi
 _EPOCH = datetime.datetime(2000, 1, 1, 12)
@@ -1465,7 +1467,7 @@ def _vector2radec(pos, time):
         else:
             dec = +90.0
     else:
-        ra = math.degrees(math.atan2(pos[1], pos[0])) / 15.0
+        ra = _RAD2HOUR * math.atan2(pos[1], pos[0])
         if ra < 0:
             ra += 24
         dec = math.degrees(math.atan2(pos[2], math.sqrt(xyproj)))
@@ -3085,11 +3087,16 @@ _vsop = [
 ],
 ]
 
-def _VsopFormula(formula, t):
+def _VsopFormula(formula, t, clamp_angle):
     tpower = 1.0
     coord = 0.0
     for series in formula:
-        coord += tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        incr = tpower * sum(A * math.cos(B + C*t) for (A, B, C) in series)
+        if clamp_angle:
+            # Longitude angles can be hundreds of radians.
+            # Improve precision by keeping each increment within [-2*pi, +2*pi].
+            incr = math.fmod(incr, _PI2)
+        coord += incr
         tpower *= t
     return coord
 
@@ -3136,7 +3143,9 @@ def _VsopSphereToRect(lon, lat, rad):
 
 def _CalcVsop(model, time):
     t = time.tt / _DAYS_PER_MILLENNIUM
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
     eclip = _VsopSphereToRect(lon, lat, rad)
     return _VsopRotate(eclip).ToAstroVector(time)
 
@@ -3149,7 +3158,10 @@ class _body_state_t:
 def _CalcVsopPosVel(model, tt):
     t = tt / _DAYS_PER_MILLENNIUM
 
-    (lon, lat, rad) = [_VsopFormula(formula, t) for formula in model]
+    lon = _VsopFormula(model[0], t, True)
+    lat = _VsopFormula(model[1], t, False)
+    rad = _VsopFormula(model[2], t, False)
+
     (dlon_dt, dlat_dt, drad_dt) = [_VsopDeriv(formula, t) for formula in model]
 
     # Use spherical coords and spherical derivatives to calculate
@@ -3209,7 +3221,7 @@ def _VsopHelioDistance(model, time):
     # The caller only wants to know the distance between the planet and the Sun.
     # So we only need to calculate the radial component of the spherical coordinates.
     # There is no need to translate coordinates.
-    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM)
+    return _VsopFormula(model[2], time.tt / _DAYS_PER_MILLENNIUM, False)
 
 def _CalcEarth(time):
     return _CalcVsop(_vsop[Body.Earth.value], time)
@@ -4314,7 +4326,7 @@ def Horizon(time, observer, ra, dec, refraction):
     latrad = math.radians(observer.latitude)
     lonrad = math.radians(observer.longitude)
     decrad = math.radians(dec)
-    rarad = math.radians(ra * 15.0)
+    rarad = ra * _HOUR2RAD
 
     sinlat = math.sin(latrad)
     coslat = math.cos(latrad)
@@ -4407,7 +4419,7 @@ def Horizon(time, observer, ra, dec, refraction):
             pr = [(((p[j] - coszd0 * uz[j]) / sinzd0)*sinzd + uz[j]*coszd) for j in range(3)]
             proj = math.sqrt(pr[0]*pr[0] + pr[1]*pr[1])
             if proj > 0:
-                hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
+                hor_ra = _RAD2HOUR * math.atan2(pr[1], pr[0])
                 if hor_ra < 0:
                     hor_ra += 24
             else:
diff --git a/website/src/assets/documentation.json b/website/src/assets/documentation.json
index fcedb841..712c48fd 100644
--- a/website/src/assets/documentation.json
+++ b/website/src/assets/documentation.json
@@ -46,61 +46,13 @@
         "meta": {
             "range": [
                 1519,
-                2743
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
             "columnno": 0,
             "code": {
                 "id": "astnode100000015",
-                "name": "exports.SearchMoonQuarter",
-                "type": "AssignmentExpression",
-                "value": "exports.MoonQuarter",
-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "SearchMoonQuarter",
-        "longname": "SearchMoonQuarter",
-        "kind": "member",
-        "scope": "global"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                1547,
-                2743
-            ],
-            "filename": "astronomy.js",
-            "lineno": 36,
-            "columnno": 28,
-            "code": {
-                "id": "astnode100000019",
-                "name": "exports.MoonQuarter",
-                "type": "AssignmentExpression",
-                "value": "exports.SearchMoonPhase",
-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "MoonQuarter",
-        "longname": "MoonQuarter",
-        "kind": "member",
-        "scope": "global"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                1569,
-                2743
-            ],
-            "filename": "astronomy.js",
-            "lineno": 36,
-            "columnno": 50,
-            "code": {
-                "id": "astnode100000023",
                 "name": "exports.SearchMoonPhase",
                 "type": "AssignmentExpression",
                 "value": "exports.MoonPhase",
@@ -109,23 +61,22 @@
         },
         "undocumented": true,
         "name": "SearchMoonPhase",
-        "longname": "SearchMoonQuarter#SearchMoonPhase",
+        "longname": "SearchMoonPhase",
         "kind": "member",
-        "memberof": "SearchMoonQuarter",
-        "scope": "instance"
+        "scope": "global"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1595,
-                2743
+                1545,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 76,
+            "columnno": 26,
             "code": {
-                "id": "astnode100000027",
+                "id": "astnode100000019",
                 "name": "exports.MoonPhase",
                 "type": "AssignmentExpression",
                 "value": "exports.SearchRelativeLongitude",
@@ -134,23 +85,22 @@
         },
         "undocumented": true,
         "name": "MoonPhase",
-        "longname": "MoonQuarter#MoonPhase",
+        "longname": "MoonPhase",
         "kind": "member",
-        "memberof": "MoonQuarter",
-        "scope": "instance"
+        "scope": "global"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1615,
-                2743
+                1565,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 96,
+            "columnno": 46,
             "code": {
-                "id": "astnode100000031",
+                "id": "astnode100000023",
                 "name": "exports.SearchRelativeLongitude",
                 "type": "AssignmentExpression",
                 "value": "exports.Illumination",
@@ -159,23 +109,23 @@
         },
         "undocumented": true,
         "name": "SearchRelativeLongitude",
-        "longname": "SearchMoonQuarter#SearchMoonPhase#SearchRelativeLongitude",
+        "longname": "SearchMoonPhase#SearchRelativeLongitude",
         "kind": "member",
-        "memberof": "SearchMoonQuarter#SearchMoonPhase",
+        "memberof": "SearchMoonPhase",
         "scope": "instance"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1649,
-                2743
+                1599,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 130,
+            "columnno": 80,
             "code": {
-                "id": "astnode100000035",
+                "id": "astnode100000027",
                 "name": "exports.Illumination",
                 "type": "AssignmentExpression",
                 "value": "exports.IlluminationInfo",
@@ -184,23 +134,23 @@
         },
         "undocumented": true,
         "name": "Illumination",
-        "longname": "MoonQuarter#MoonPhase#Illumination",
+        "longname": "MoonPhase#Illumination",
         "kind": "member",
-        "memberof": "MoonQuarter#MoonPhase",
+        "memberof": "MoonPhase",
         "scope": "instance"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1672,
-                2743
+                1622,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 153,
+            "columnno": 103,
             "code": {
-                "id": "astnode100000039",
+                "id": "astnode100000031",
                 "name": "exports.IlluminationInfo",
                 "type": "AssignmentExpression",
                 "value": "exports.EclipticLongitude",
@@ -209,23 +159,23 @@
         },
         "undocumented": true,
         "name": "IlluminationInfo",
-        "longname": "SearchMoonQuarter#SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo",
+        "longname": "SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo",
         "kind": "member",
-        "memberof": "SearchMoonQuarter#SearchMoonPhase#SearchRelativeLongitude",
+        "memberof": "SearchMoonPhase#SearchRelativeLongitude",
         "scope": "instance"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1699,
-                2743
+                1649,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 180,
+            "columnno": 130,
             "code": {
-                "id": "astnode100000043",
+                "id": "astnode100000035",
                 "name": "exports.EclipticLongitude",
                 "type": "AssignmentExpression",
                 "value": "exports.AngleFromSun",
@@ -234,23 +184,23 @@
         },
         "undocumented": true,
         "name": "EclipticLongitude",
-        "longname": "MoonQuarter#MoonPhase#Illumination#EclipticLongitude",
+        "longname": "MoonPhase#Illumination#EclipticLongitude",
         "kind": "member",
-        "memberof": "MoonQuarter#MoonPhase#Illumination",
+        "memberof": "MoonPhase#Illumination",
         "scope": "instance"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1727,
-                2743
+                1677,
+                2731
             ],
             "filename": "astronomy.js",
             "lineno": 36,
-            "columnno": 208,
+            "columnno": 158,
             "code": {
-                "id": "astnode100000047",
+                "id": "astnode100000039",
                 "name": "exports.AngleFromSun",
                 "type": "AssignmentExpression",
                 "value": "exports.LongitudeFromSun",
@@ -259,23 +209,23 @@
         },
         "undocumented": true,
         "name": "AngleFromSun",
-        "longname": "SearchMoonQuarter#SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo#AngleFromSun",
+        "longname": "SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo#AngleFromSun",
         "kind": "member",
-        "memberof": "SearchMoonQuarter#SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo",
+        "memberof": "SearchMoonPhase#SearchRelativeLongitude#IlluminationInfo",
         "scope": "instance"
     },
     {
         "comment": "",
         "meta": {
             "range": [
-                1750,
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@@ -1382,23 +1333,22 @@
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@@ -2482,23 +2432,23 @@
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@@ -2507,42 +2457,92 @@
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@@ -2639,8 +2639,8 @@
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@@ -2648,8 +2648,8 @@
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-                "type": "UnaryExpression",
-                "value": "void0",
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+                "value": "exports.LocalSolarEclipseInfo",
                 "paramnames": []
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@@ -2660,18 +2660,68 @@
         "memberof": "NextTransit#TransitInfo",
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+                "value": "exports.EclipseEvent",
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+        "name": "LocalSolarEclipseInfo",
+        "longname": "SearchTransit#NextLocalSolarEclipse#LocalSolarEclipseInfo",
+        "kind": "member",
+        "memberof": "SearchTransit#NextLocalSolarEclipse",
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+        "kind": "member",
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     {
         "comment": "/**\n * @brief The number of kilometers per astronomical unit.\n */",
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                 "name": "exports.KM_PER_AU",
                 "type": "Literal",
                 "value": 149597870.69098932,
@@ -2692,17 +2742,17 @@
         "scope": "global"
     },
     {
-        "comment": "/**\n * @brief The factor to convert radians to degrees = pi/180.\n */",
+        "comment": "/**\n * @brief The factor to convert degrees to radians = pi/180.\n */",
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@@ -2713,8 +2763,8 @@
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                 "originalTitle": "brief",
                 "title": "brief",
-                "text": "The factor to convert radians to degrees = pi/180.",
-                "value": "The factor to convert radians to degrees = pi/180."
+                "text": "The factor to convert degrees to radians = pi/180.",
+                "value": "The factor to convert degrees to radians = pi/180."
             }
         ],
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@@ -2723,17 +2773,48 @@
         "scope": "global"
     },
     {
-        "comment": "/**\n * @brief The factor to convert degrees to radians = 180/pi.\n */",
+        "comment": "/**\n * @brief The factor to convert sidereal hours to radians = pi/12.\n */",
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+                "name": "exports.HOUR2RAD",
+                "type": "Literal",
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+                "paramnames": []
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+        },
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+                "title": "brief",
+                "text": "The factor to convert sidereal hours to radians = pi/12.",
+                "value": "The factor to convert sidereal hours to radians = pi/12."
+            }
+        ],
+        "name": "HOUR2RAD",
+        "longname": "HOUR2RAD",
+        "kind": "member",
+        "scope": "global"
+    },
+    {
+        "comment": "/**\n * @brief The factor to convert radians to degrees = 180/pi.\n */",
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@@ -2744,8 +2825,8 @@
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                 "title": "brief",
-                "text": "The factor to convert degrees to radians = 180/pi.",
-                "value": "The factor to convert degrees to radians = 180/pi."
+                "text": "The factor to convert radians to degrees = 180/pi.",
+                "value": "The factor to convert radians to degrees = 180/pi."
             }
         ],
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@@ -2753,18 +2834,49 @@
         "kind": "member",
         "scope": "global"
     },
+    {
+        "comment": "/**\n * @brief The factor to convert radians to sidereal hours = 12/pi.\n */",
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+                "name": "exports.RAD2HOUR",
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+                "paramnames": []
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+                "originalTitle": "brief",
+                "title": "brief",
+                "text": "The factor to convert radians to sidereal hours = 12/pi.",
+                "value": "The factor to convert radians to sidereal hours = 12/pi."
+            }
+        ],
+        "name": "RAD2HOUR",
+        "longname": "RAD2HOUR",
+        "kind": "member",
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+    },
     {
         "comment": "/**\n * @brief The equatorial radius of Jupiter, expressed in kilometers.\n */",
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                 "name": "exports.JUPITER_EQUATORIAL_RADIUS_KM",
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@@ -2788,14 +2900,14 @@
         "comment": "/**\n * @brief The polar radius of Jupiter, expressed in kilometers.\n */",
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@@ -2819,14 +2931,14 @@
         "comment": "/**\n * @brief The volumetric mean radius of Jupiter, expressed in kilometers.\n */",
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@@ -2850,14 +2962,14 @@
         "comment": "/**\n * @brief The mean radius of Jupiter's moon Io, expressed in kilometers.\n */",
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                 "name": "exports.IO_RADIUS_KM",
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@@ -2881,14 +2993,14 @@
         "comment": "/**\n * @brief The mean radius of Jupiter's moon Europa, expressed in kilometers.\n */",
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                 "name": "exports.EUROPA_RADIUS_KM",
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@@ -2912,14 +3024,14 @@
         "comment": "/**\n * @brief The mean radius of Jupiter's moon Ganymede, expressed in kilometers.\n */",
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                 "name": "exports.GANYMEDE_RADIUS_KM",
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@@ -2943,14 +3055,14 @@
         "comment": "/**\n * @brief The mean radius of Jupiter's moon Callisto, expressed in kilometers.\n */",
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@@ -2974,14 +3086,14 @@
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                 "name": "DAYS_PER_TROPICAL_YEAR",
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@@ -2998,14 +3110,14 @@
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@@ -7079,14 +7191,14 @@
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             "columnno": 4,
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@@ -7105,14 +7217,14 @@
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                 "value": "SetDeltaTFunction",
@@ -7129,14 +7241,14 @@
         "comment": "/**\n * @ignore\n *\n * @brief Calculates Terrestrial Time (TT) from Universal Time (UT).\n *\n * @param {number} ut\n *      The Universal Time expressed as a floating point number of days since the 2000.0 epoch.\n *\n * @returns {number}\n *      A Terrestrial Time expressed as a floating point number of days since the 2000.0 epoch.\n */",
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             "columnno": 0,
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                 "name": "TerrestrialTime",
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@@ -7183,14 +7295,14 @@
         "comment": "/**\n * @brief The date and time of an astronomical observation.\n *\n * Objects of type `AstroTime` are used throughout the internals\n * of the Astronomy library, and are included in certain return objects.\n * Use the constructor or the {@link MakeTime} function to create an `AstroTime` object.\n *\n * @property {Date} date\n *      The JavaScript Date object for the given date and time.\n *      This Date corresponds to the numeric day value stored in the `ut` property.\n *\n * @property {number} ut\n *      Universal Time (UT1/UTC) in fractional days since the J2000 epoch.\n *      Universal Time represents time measured with respect to the Earth's rotation,\n *      tracking mean solar days.\n *      The Astronomy library approximates UT1 and UTC as being the same thing.\n *      This gives sufficient accuracy for the precision requirements of this project.\n *\n * @property {number} tt\n *      Terrestrial Time in fractional days since the J2000 epoch.\n *      TT represents a continuously flowing ephemeris timescale independent of\n *      any variations of the Earth's rotation, and is adjusted from UT\n *      using a best-fit piecewise polynomial model devised by\n *      [Espenak and Meeus](https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html).\n */",
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@@ -7245,14 +7357,14 @@
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             "columnno": 4,
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                 "name": "AstroTime",
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@@ -7284,14 +7396,14 @@
         "comment": "/**\n * @brief The date and time of an astronomical observation.\n *\n * Objects of type `AstroTime` are used throughout the internals\n * of the Astronomy library, and are included in certain return objects.\n * Use the constructor or the {@link MakeTime} function to create an `AstroTime` object.\n *\n * @property {Date} date\n *      The JavaScript Date object for the given date and time.\n *      This Date corresponds to the numeric day value stored in the `ut` property.\n *\n * @property {number} ut\n *      Universal Time (UT1/UTC) in fractional days since the J2000 epoch.\n *      Universal Time represents time measured with respect to the Earth's rotation,\n *      tracking mean solar days.\n *      The Astronomy library approximates UT1 and UTC as being the same thing.\n *      This gives sufficient accuracy for the precision requirements of this project.\n *\n * @property {number} tt\n *      Terrestrial Time in fractional days since the J2000 epoch.\n *      TT represents a continuously flowing ephemeris timescale independent of\n *      any variations of the Earth's rotation, and is adjusted from UT\n *      using a best-fit piecewise polynomial model devised by\n *      [Espenak and Meeus](https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html).\n */",
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             "columnno": 0,
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-                "id": "astnode100003785",
+                "id": "astnode100003805",
                 "name": "AstroTime",
                 "type": "ClassDeclaration",
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@@ -7356,14 +7468,14 @@
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             "columnno": 12,
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                 "name": "this.date",
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@@ -7381,14 +7493,14 @@
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@@ -7406,14 +7518,14 @@
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             "columnno": 12,
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                 "type": "MemberExpression",
                 "value": "date.tt",
@@ -7431,14 +7543,14 @@
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             "columnno": 14,
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                 "type": "BinaryExpression",
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@@ -7456,14 +7568,14 @@
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             "columnno": 12,
             "code": {
-                "id": "astnode100003846",
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                 "name": "this.date",
                 "type": "Identifier",
                 "value": "date",
@@ -7481,14 +7593,14 @@
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             "columnno": 12,
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@@ -7506,14 +7618,14 @@
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             "columnno": 12,
             "code": {
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                 "name": "this.tt",
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@@ -7531,14 +7643,14 @@
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             "columnno": 12,
             "code": {
-                "id": "astnode100003886",
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                 "name": "this.date",
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                 "value": "",
@@ -7556,14 +7668,14 @@
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100003901",
+                "id": "astnode100003921",
                 "name": "this.ut",
                 "type": "Identifier",
                 "value": "date",
@@ -7581,14 +7693,14 @@
         "comment": "",
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             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 12,
             "code": {
-                "id": "astnode100003907",
+                "id": "astnode100003927",
                 "name": "this.tt",
                 "type": "CallExpression",
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@@ -7606,14 +7718,14 @@
         "comment": "/**\n     * @brief Creates an `AstroTime` value from a Terrestrial Time (TT) day value.\n     *\n     * This function can be used in rare cases where a time must be based\n     * on Terrestrial Time (TT) rather than Universal Time (UT).\n     * Most developers will want to invoke `new AstroTime(ut)` with a universal time\n     * instead of this function, because usually time is based on civil time adjusted\n     * by leap seconds to match the Earth's rotation, rather than the uniformly\n     * flowing TT used to calculate solar system dynamics. In rare cases\n     * where the caller already knows TT, this function is provided to create\n     * an `AstroTime` value that can be passed to Astronomy Engine functions.\n     *\n     * @param {number} tt\n     *      The number of days since the J2000 epoch as expressed in Terrestrial Time.\n     *\n     * @returns {AstroTime}\n     *      An `AstroTime` object for the specified terrestrial time.\n     */",
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             ],
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             "columnno": 4,
             "code": {
-                "id": "astnode100003919",
+                "id": "astnode100003939",
                 "name": "AstroTime.FromTerrestrialTime",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -7663,14 +7775,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100003925",
+                "id": "astnode100003945",
                 "name": "time",
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@@ -7688,14 +7800,14 @@
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             ],
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             "columnno": 18,
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@@ -7713,14 +7825,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100003951",
+                "id": "astnode100003971",
                 "name": "time",
                 "type": "CallExpression",
                 "funcscope": "<anonymous>",
@@ -7739,14 +7851,14 @@
         "comment": "/**\n     * Formats an `AstroTime` object as an [ISO 8601](https://en.wikipedia.org/wiki/ISO_8601)\n     * date/time string in UTC, to millisecond resolution.\n     * Example: `2018-08-17T17:22:04.050Z`\n     * @returns {string}\n     */",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100003958",
+                "id": "astnode100003978",
                 "name": "AstroTime#toString",
                 "type": "MethodDefinition",
                 "paramnames": []
@@ -7776,14 +7888,14 @@
         "comment": "/**\n     * Returns a new `AstroTime` object adjusted by the floating point number of days.\n     * Does NOT modify the original `AstroTime` object.\n     *\n     * @param {number} days\n     *      The floating point number of days by which to adjust the given date and time.\n     *      Positive values adjust the date toward the future, and\n     *      negative values adjust the date toward the past.\n     *\n     * @returns {AstroTime}\n     */",
         "meta": {
             "range": [
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             ],
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             "columnno": 4,
             "code": {
-                "id": "astnode100003969",
+                "id": "astnode100003989",
                 "name": "AstroTime#AddDays",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -7825,14 +7937,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100003983",
+                "id": "astnode100004003",
                 "name": "exports.AstroTime",
                 "type": "Identifier",
                 "value": "AstroTime",
@@ -7849,14 +7961,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 0,
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-                "id": "astnode100003988",
+                "id": "astnode100004008",
                 "name": "InterpolateTime",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -7877,7 +7989,7 @@
         "comment": "/**\n * @brief A `Date`, `number`, or `AstroTime` value that specifies the date and time of an astronomical event.\n *\n * `FlexibleDateTime` is a placeholder type that represents three different types\n * that may be passed to many Astronomy Engine functions: a JavaScript `Date` object,\n * a number representing the real-valued number of UT days since the J2000 epoch,\n * or an {@link AstroTime} object.\n *\n * This flexibility is for convenience of outside callers.\n * Internally, Astronomy Engine always converts a `FlexibleTime` parameter\n * to an `AstroTime` object by calling {@link MakeTime}.\n *\n * @typedef {Date | number | AstroTime} FlexibleDateTime\n */",
         "meta": {
             "filename": "astronomy.js",
-            "lineno": 1121,
+            "lineno": 1129,
             "columnno": 0,
             "code": {}
         },
@@ -7905,14 +8017,14 @@
         "comment": "/**\n * @brief Converts multiple date/time formats to `AstroTime` format.\n *\n * Given a Date object or a number days since noon (12:00) on January 1, 2000 (UTC),\n * this function creates an {@link AstroTime} object.\n *\n * Given an {@link AstroTime} object, returns the same object unmodified.\n * Use of this function is not required for any of the other exposed functions in this library,\n * because they all guarantee converting date/time parameters to `AstroTime`\n * as needed. However, it may be convenient for callers who need to understand\n * the difference between UTC and TT (Terrestrial Time). In some use cases,\n * converting once to `AstroTime` format and passing the result into multiple\n * function calls may be more efficient than passing in native JavaScript Date objects.\n *\n * @param {FlexibleDateTime} date\n *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),\n *      or an AstroTime object. See remarks above.\n *\n * @returns {AstroTime}\n */",
         "meta": {
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             "columnno": 0,
             "code": {
-                "id": "astnode100004010",
+                "id": "astnode100004030",
                 "name": "MakeTime",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -7957,14 +8069,14 @@
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         "meta": {
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             "columnno": 0,
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                 "name": "exports.MakeTime",
                 "type": "Identifier",
                 "value": "MakeTime",
@@ -7981,14 +8093,14 @@
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             "columnno": 6,
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@@ -18793,14 +18905,14 @@
         "comment": "/**\n * @brief A combination of a position vector, a velocity vector, and a time.\n *\n * Holds the state vector of a body at a given time, including its position,\n * velocity, and the time they are valid.\n *\n * @property {number} x        The position x-coordinate expressed in astronomical units (AU).\n * @property {number} y        The position y-coordinate expressed in astronomical units (AU).\n * @property {number} z        The position z-coordinate expressed in astronomical units (AU).\n * @property {number} vx       The velocity x-coordinate expressed in AU/day.\n * @property {number} vy       The velocity y-coordinate expressed in AU/day.\n * @property {number} vz       The velocity z-coordinate expressed in AU/day.\n * @property {AstroTime} t     The time at which the vector is valid.\n */",
         "meta": {
             "range": [
-                81932,
-                82147
+                82200,
+                82415
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100009917",
+                "id": "astnode100009937",
                 "name": "StateVector",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -18896,14 +19008,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82002,
-                82012
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009932",
+                "id": "astnode100009952",
                 "name": "this.x",
                 "type": "Identifier",
                 "value": "x",
@@ -18921,14 +19033,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82022,
-                82032
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009938",
+                "id": "astnode100009958",
                 "name": "this.y",
                 "type": "Identifier",
                 "value": "y",
@@ -18946,14 +19058,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82042,
-                82052
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009944",
+                "id": "astnode100009964",
                 "name": "this.z",
                 "type": "Identifier",
                 "value": "z",
@@ -18971,14 +19083,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82062,
-                82074
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009950",
+                "id": "astnode100009970",
                 "name": "this.vx",
                 "type": "Identifier",
                 "value": "vx",
@@ -18996,14 +19108,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                82096
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009956",
+                "id": "astnode100009976",
                 "name": "this.vy",
                 "type": "Identifier",
                 "value": "vy",
@@ -19021,14 +19133,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82106,
-                82118
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009962",
+                "id": "astnode100009982",
                 "name": "this.vz",
                 "type": "Identifier",
                 "value": "vz",
@@ -19046,14 +19158,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82128,
-                82138
+                82396,
+                82406
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009968",
+                "id": "astnode100009988",
                 "name": "this.t",
                 "type": "Identifier",
                 "value": "t",
@@ -19071,14 +19183,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82148,
-                82181
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+                82449
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100009974",
+                "id": "astnode100009994",
                 "name": "exports.StateVector",
                 "type": "Identifier",
                 "value": "StateVector",
@@ -19095,14 +19207,14 @@
         "comment": "/**\n * @brief Holds spherical coordinates: latitude, longitude, distance.\n *\n * Spherical coordinates represent the location of\n * a point using two angles and a distance.\n *\n * @property {number} lat       The latitude angle: -90..+90 degrees.\n * @property {number} lon       The longitude angle: 0..360 degrees.\n * @property {number} dist      Distance in AU.\n */",
         "meta": {
             "range": [
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+                82992
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100009979",
+                "id": "astnode100009999",
                 "name": "Spherical",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19159,14 +19271,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                82722
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100009982",
+                "id": "astnode100010002",
                 "name": "Spherical",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -19190,14 +19302,14 @@
         "comment": "/**\n * @brief Holds spherical coordinates: latitude, longitude, distance.\n *\n * Spherical coordinates represent the location of\n * a point using two angles and a distance.\n *\n * @property {number} lat       The latitude angle: -90..+90 degrees.\n * @property {number} lon       The longitude angle: 0..360 degrees.\n * @property {number} dist      Distance in AU.\n */",
         "meta": {
             "range": [
-                82549,
-                82724
+                82817,
+                82992
             ],
             "filename": "astronomy.js",
-            "lineno": 1797,
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             "columnno": 0,
             "code": {
-                "id": "astnode100009979",
+                "id": "astnode100009999",
                 "name": "Spherical",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19253,14 +19365,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82609,
-                82637
+                82877,
+                82905
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100009990",
+                "id": "astnode100010010",
                 "name": "this.lat",
                 "type": "CallExpression",
                 "value": "",
@@ -19278,14 +19390,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82647,
-                82675
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+                82943
             ],
             "filename": "astronomy.js",
-            "lineno": 1800,
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             "columnno": 8,
             "code": {
-                "id": "astnode100009998",
+                "id": "astnode100010018",
                 "name": "this.lon",
                 "type": "CallExpression",
                 "value": "",
@@ -19303,14 +19415,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82685,
-                82715
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+                82983
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100010006",
+                "id": "astnode100010026",
                 "name": "this.dist",
                 "type": "CallExpression",
                 "value": "",
@@ -19328,14 +19440,14 @@
         "comment": "",
         "meta": {
             "range": [
-                82725,
-                82754
+                82993,
+                83022
             ],
             "filename": "astronomy.js",
-            "lineno": 1804,
+            "lineno": 1812,
             "columnno": 0,
             "code": {
-                "id": "astnode100010014",
+                "id": "astnode100010034",
                 "name": "exports.Spherical",
                 "type": "Identifier",
                 "value": "Spherical",
@@ -19352,14 +19464,14 @@
         "comment": "/**\n * @brief Holds right ascension, declination, and distance of a celestial object.\n *\n * @property {number} ra\n *      Right ascension in sidereal hours: [0, 24).\n *\n * @property {number} dec\n *      Declination in degrees: [-90, +90].\n *\n * @property {number} dist\n *      Distance to the celestial object expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n *\n * @property {Vector} vec\n *      The equatorial coordinates in cartesian form, using AU distance units.\n *      x = direction of the March equinox,\n *      y = direction of the June solstice,\n *      z = north.\n */",
         "meta": {
             "range": [
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+                83874
             ],
             "filename": "astronomy.js",
-            "lineno": 1824,
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             "columnno": 0,
             "code": {
-                "id": "astnode100010019",
+                "id": "astnode100010039",
                 "name": "EquatorialCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19426,14 +19538,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83427,
-                83604
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+                83872
             ],
             "filename": "astronomy.js",
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+            "lineno": 1833,
             "columnno": 4,
             "code": {
-                "id": "astnode100010022",
+                "id": "astnode100010042",
                 "name": "EquatorialCoordinates",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -19458,14 +19570,14 @@
         "comment": "/**\n * @brief Holds right ascension, declination, and distance of a celestial object.\n *\n * @property {number} ra\n *      Right ascension in sidereal hours: [0, 24).\n *\n * @property {number} dec\n *      Declination in degrees: [-90, +90].\n *\n * @property {number} dist\n *      Distance to the celestial object expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n *\n * @property {Vector} vec\n *      The equatorial coordinates in cartesian form, using AU distance units.\n *      x = direction of the March equinox,\n *      y = direction of the June solstice,\n *      z = north.\n */",
         "meta": {
             "range": [
-                83393,
-                83606
+                83661,
+                83874
             ],
             "filename": "astronomy.js",
-            "lineno": 1824,
+            "lineno": 1832,
             "columnno": 0,
             "code": {
-                "id": "astnode100010019",
+                "id": "astnode100010039",
                 "name": "EquatorialCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19531,14 +19643,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83469,
-                83495
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             ],
             "filename": "astronomy.js",
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+            "lineno": 1834,
             "columnno": 8,
             "code": {
-                "id": "astnode100010031",
+                "id": "astnode100010051",
                 "name": "this.ra",
                 "type": "CallExpression",
                 "value": "",
@@ -19556,14 +19668,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83505,
-                83533
+                83773,
+                83801
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100010039",
+                "id": "astnode100010059",
                 "name": "this.dec",
                 "type": "CallExpression",
                 "value": "",
@@ -19581,14 +19693,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83543,
-                83573
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+                83841
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100010047",
+                "id": "astnode100010067",
                 "name": "this.dist",
                 "type": "CallExpression",
                 "value": "",
@@ -19606,14 +19718,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83583,
-                83597
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+                83865
             ],
             "filename": "astronomy.js",
-            "lineno": 1829,
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             "columnno": 8,
             "code": {
-                "id": "astnode100010055",
+                "id": "astnode100010075",
                 "name": "this.vec",
                 "type": "Identifier",
                 "value": "vec",
@@ -19631,14 +19743,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83607,
-                83660
+                83875,
+                83928
             ],
             "filename": "astronomy.js",
-            "lineno": 1832,
+            "lineno": 1840,
             "columnno": 0,
             "code": {
-                "id": "astnode100010061",
+                "id": "astnode100010081",
                 "name": "exports.EquatorialCoordinates",
                 "type": "Identifier",
                 "value": "EquatorialCoordinates",
@@ -19655,14 +19767,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83662,
-                84036
+                83930,
+                84304
             ],
             "filename": "astronomy.js",
-            "lineno": 1833,
+            "lineno": 1841,
             "columnno": 0,
             "code": {
-                "id": "astnode100010066",
+                "id": "astnode100010086",
                 "name": "IsValidRotationArray",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -19685,14 +19797,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83789,
-                83794
+                84057,
+                84062
             ],
             "filename": "astronomy.js",
-            "lineno": 1836,
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             "columnno": 13,
             "code": {
-                "id": "astnode100010085",
+                "id": "astnode100010105",
                 "name": "i",
                 "type": "Literal",
                 "value": 0
@@ -19710,14 +19822,14 @@
         "comment": "",
         "meta": {
             "range": [
-                83918,
-                83923
+                84186,
+                84191
             ],
             "filename": "astronomy.js",
-            "lineno": 1839,
+            "lineno": 1847,
             "columnno": 17,
             "code": {
-                "id": "astnode100010113",
+                "id": "astnode100010133",
                 "name": "j",
                 "type": "Literal",
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@@ -19735,14 +19847,14 @@
         "comment": "/**\n * @brief Contains a rotation matrix that can be used to transform one coordinate system to another.\n *\n * @property {number[][]} rot\n *      A normalized 3x3 rotation matrix. For example, the identity matrix is represented\n *      as `[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`.\n */",
         "meta": {
             "range": [
-                84317,
-                84394
+                84585,
+                84662
             ],
             "filename": "astronomy.js",
-            "lineno": 1852,
+            "lineno": 1860,
             "columnno": 0,
             "code": {
-                "id": "astnode100010136",
+                "id": "astnode100010156",
                 "name": "RotationMatrix",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19779,14 +19891,14 @@
         "comment": "",
         "meta": {
             "range": [
-                84344,
-                84392
+                84612,
+                84660
             ],
             "filename": "astronomy.js",
-            "lineno": 1853,
+            "lineno": 1861,
             "columnno": 4,
             "code": {
-                "id": "astnode100010139",
+                "id": "astnode100010159",
                 "name": "RotationMatrix",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -19808,14 +19920,14 @@
         "comment": "/**\n * @brief Contains a rotation matrix that can be used to transform one coordinate system to another.\n *\n * @property {number[][]} rot\n *      A normalized 3x3 rotation matrix. For example, the identity matrix is represented\n *      as `[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`.\n */",
         "meta": {
             "range": [
-                84317,
-                84394
+                84585,
+                84662
             ],
             "filename": "astronomy.js",
-            "lineno": 1852,
+            "lineno": 1860,
             "columnno": 0,
             "code": {
-                "id": "astnode100010136",
+                "id": "astnode100010156",
                 "name": "RotationMatrix",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -19851,14 +19963,14 @@
         "comment": "",
         "meta": {
             "range": [
-                84371,
-                84385
+                84639,
+                84653
             ],
             "filename": "astronomy.js",
-            "lineno": 1854,
+            "lineno": 1862,
             "columnno": 8,
             "code": {
-                "id": "astnode100010145",
+                "id": "astnode100010165",
                 "name": "this.rot",
                 "type": "Identifier",
                 "value": "rot",
@@ -19876,14 +19988,14 @@
         "comment": "",
         "meta": {
             "range": [
-                84395,
-                84434
+                84663,
+                84702
             ],
             "filename": "astronomy.js",
-            "lineno": 1857,
+            "lineno": 1865,
             "columnno": 0,
             "code": {
-                "id": "astnode100010151",
+                "id": "astnode100010171",
                 "name": "exports.RotationMatrix",
                 "type": "Identifier",
                 "value": "RotationMatrix",
@@ -19900,14 +20012,14 @@
         "comment": "/**\n * @brief Creates a rotation matrix that can be used to transform one coordinate system to another.\n *\n * This function verifies that the `rot` parameter is of the correct format:\n * a number[3][3] array. It throws an exception if `rot` is not of that shape.\n * Otherwise it creates a new {@link RotationMatrix} object based on `rot`.\n *\n * @param {number[][]} rot\n *      An array [3][3] of numbers. Defines a rotation matrix used to premultiply\n *      a 3D vector to reorient it into another coordinate system.\n *\n * @returns {RotationMatrix}\n */",
         "meta": {
             "range": [
-                84990,
-                85152
+                85258,
+                85420
             ],
             "filename": "astronomy.js",
-            "lineno": 1871,
+            "lineno": 1879,
             "columnno": 0,
             "code": {
-                "id": "astnode100010156",
+                "id": "astnode100010176",
                 "name": "MakeRotation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -19952,14 +20064,14 @@
         "comment": "",
         "meta": {
             "range": [
-                85153,
-                85188
+                85421,
+                85456
             ],
             "filename": "astronomy.js",
-            "lineno": 1876,
+            "lineno": 1884,
             "columnno": 0,
             "code": {
-                "id": "astnode100010172",
+                "id": "astnode100010192",
                 "name": "exports.MakeRotation",
                 "type": "Identifier",
                 "value": "MakeRotation",
@@ -19976,14 +20088,14 @@
         "comment": "/**\n * @brief Represents the location of an object seen by an observer on the Earth.\n *\n * Holds azimuth (compass direction) and altitude (angle above/below the horizon)\n * of a celestial object as seen by an observer at a particular location on the Earth's surface.\n * Also holds right ascension and declination of the same object.\n * All of these coordinates are optionally adjusted for atmospheric refraction;\n * therefore the right ascension and declination values may not exactly match\n * those found inside a corresponding {@link EquatorialCoordinates} object.\n *\n * @property {number} azimuth\n *      A horizontal compass direction angle in degrees measured starting at north\n *      and increasing positively toward the east.\n *      The value is in the range [0, 360).\n *      North = 0, east = 90, south = 180, west = 270.\n *\n * @property {number} altitude\n *      A vertical angle in degrees above (positive) or below (negative) the horizon.\n *      The value is in the range [-90, +90].\n *      The altitude angle is optionally adjusted upward due to atmospheric refraction.\n *\n * @property {number} ra\n *      The right ascension of the celestial body in sidereal hours.\n *      The value is in the reange [0, 24).\n *      If `altitude` was adjusted for atmospheric reaction, `ra`\n *      is likewise adjusted.\n *\n * @property {number} dec\n *      The declination of of the celestial body in degrees.\n *      The value in the range [-90, +90].\n *      If `altitude` was adjusted for atmospheric reaction, `dec`\n *      is likewise adjusted.\n */",
         "meta": {
             "range": [
-                86748,
-                86999
+                87016,
+                87267
             ],
             "filename": "astronomy.js",
-            "lineno": 1910,
+            "lineno": 1918,
             "columnno": 0,
             "code": {
-                "id": "astnode100010177",
+                "id": "astnode100010197",
                 "name": "HorizontalCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -20050,14 +20162,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86782,
-                86997
+                87050,
+                87265
             ],
             "filename": "astronomy.js",
-            "lineno": 1911,
+            "lineno": 1919,
             "columnno": 4,
             "code": {
-                "id": "astnode100010180",
+                "id": "astnode100010200",
                 "name": "HorizontalCoordinates",
                 "type": "MethodDefinition",
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@@ -20082,14 +20194,14 @@
         "comment": "/**\n * @brief Represents the location of an object seen by an observer on the Earth.\n *\n * Holds azimuth (compass direction) and altitude (angle above/below the horizon)\n * of a celestial object as seen by an observer at a particular location on the Earth's surface.\n * Also holds right ascension and declination of the same object.\n * All of these coordinates are optionally adjusted for atmospheric refraction;\n * therefore the right ascension and declination values may not exactly match\n * those found inside a corresponding {@link EquatorialCoordinates} object.\n *\n * @property {number} azimuth\n *      A horizontal compass direction angle in degrees measured starting at north\n *      and increasing positively toward the east.\n *      The value is in the range [0, 360).\n *      North = 0, east = 90, south = 180, west = 270.\n *\n * @property {number} altitude\n *      A vertical angle in degrees above (positive) or below (negative) the horizon.\n *      The value is in the range [-90, +90].\n *      The altitude angle is optionally adjusted upward due to atmospheric refraction.\n *\n * @property {number} ra\n *      The right ascension of the celestial body in sidereal hours.\n *      The value is in the reange [0, 24).\n *      If `altitude` was adjusted for atmospheric reaction, `ra`\n *      is likewise adjusted.\n *\n * @property {number} dec\n *      The declination of of the celestial body in degrees.\n *      The value in the range [-90, +90].\n *      If `altitude` was adjusted for atmospheric reaction, `dec`\n *      is likewise adjusted.\n */",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
-            "lineno": 1910,
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             "columnno": 0,
             "code": {
-                "id": "astnode100010177",
+                "id": "astnode100010197",
                 "name": "HorizontalCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -20155,14 +20267,14 @@
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         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "name": "this.azimuth",
                 "type": "CallExpression",
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@@ -20180,14 +20292,14 @@
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         "meta": {
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             ],
             "filename": "astronomy.js",
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+            "lineno": 1921,
             "columnno": 8,
             "code": {
-                "id": "astnode100010197",
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                 "name": "this.altitude",
                 "type": "CallExpression",
                 "value": "",
@@ -20205,14 +20317,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
-            "lineno": 1914,
+            "lineno": 1922,
             "columnno": 8,
             "code": {
-                "id": "astnode100010205",
+                "id": "astnode100010225",
                 "name": "this.ra",
                 "type": "CallExpression",
                 "value": "",
@@ -20230,14 +20342,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86962,
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             ],
             "filename": "astronomy.js",
-            "lineno": 1915,
+            "lineno": 1923,
             "columnno": 8,
             "code": {
-                "id": "astnode100010213",
+                "id": "astnode100010233",
                 "name": "this.dec",
                 "type": "CallExpression",
                 "value": "",
@@ -20255,14 +20367,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87000,
-                87053
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+                87321
             ],
             "filename": "astronomy.js",
-            "lineno": 1918,
+            "lineno": 1926,
             "columnno": 0,
             "code": {
-                "id": "astnode100010221",
+                "id": "astnode100010241",
                 "name": "exports.HorizontalCoordinates",
                 "type": "Identifier",
                 "value": "HorizontalCoordinates",
@@ -20279,14 +20391,14 @@
         "comment": "/**\n * @brief Ecliptic coordinates of a celestial body.\n *\n * The origin and date of the coordinate system may vary depending on the caller's usage.\n * In general, ecliptic coordinates are measured with respect to the mean plane of the Earth's\n * orbit around the Sun.\n * Includes Cartesian coordinates `(ex, ey, ez)` measured in\n * <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU)\n * and spherical coordinates `(elon, elat)` measured in degrees.\n *\n * @property {Vector} vec\n *      Ecliptic cartesian vector with components measured in astronomical units (AU).\n *      The x-axis is within the ecliptic plane and is oriented in the direction of the\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>.\n *      The y-axis is within the ecliptic plane and is oriented 90 degrees\n *      counterclockwise from the equinox, as seen from above the Sun's north pole.\n *      The z-axis is oriented perpendicular to the ecliptic plane,\n *      along the direction of the Sun's north pole.\n *\n * @property {number} elat\n *      The ecliptic latitude of the body in degrees.\n *      This is the angle north or south of the ecliptic plane.\n *      The value is in the range [-90, +90].\n *      Positive values are north and negative values are south.\n *\n * @property {number} elon\n *      The ecliptic longitude of the body in degrees.\n *      This is the angle measured counterclockwise around the ecliptic plane,\n *      as seen from above the Sun's north pole.\n *      This is the same direction that the Earth orbits around the Sun.\n *      The angle is measured starting at 0 from the equinox and increases\n *      up to 360 degrees.\n */",
         "meta": {
             "range": [
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+                89035,
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             ],
             "filename": "astronomy.js",
-            "lineno": 1952,
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             "columnno": 0,
             "code": {
-                "id": "astnode100010226",
+                "id": "astnode100010246",
                 "name": "EclipticCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -20343,14 +20455,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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+            "lineno": 1961,
             "columnno": 4,
             "code": {
-                "id": "astnode100010229",
+                "id": "astnode100010249",
                 "name": "EclipticCoordinates",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -20374,14 +20486,14 @@
         "comment": "/**\n * @brief Ecliptic coordinates of a celestial body.\n *\n * The origin and date of the coordinate system may vary depending on the caller's usage.\n * In general, ecliptic coordinates are measured with respect to the mean plane of the Earth's\n * orbit around the Sun.\n * Includes Cartesian coordinates `(ex, ey, ez)` measured in\n * <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU)\n * and spherical coordinates `(elon, elat)` measured in degrees.\n *\n * @property {Vector} vec\n *      Ecliptic cartesian vector with components measured in astronomical units (AU).\n *      The x-axis is within the ecliptic plane and is oriented in the direction of the\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>.\n *      The y-axis is within the ecliptic plane and is oriented 90 degrees\n *      counterclockwise from the equinox, as seen from above the Sun's north pole.\n *      The z-axis is oriented perpendicular to the ecliptic plane,\n *      along the direction of the Sun's north pole.\n *\n * @property {number} elat\n *      The ecliptic latitude of the body in degrees.\n *      This is the angle north or south of the ecliptic plane.\n *      The value is in the range [-90, +90].\n *      Positive values are north and negative values are south.\n *\n * @property {number} elon\n *      The ecliptic longitude of the body in degrees.\n *      This is the angle measured counterclockwise around the ecliptic plane,\n *      as seen from above the Sun's north pole.\n *      This is the same direction that the Earth orbits around the Sun.\n *      The angle is measured starting at 0 from the equinox and increases\n *      up to 360 degrees.\n */",
         "meta": {
             "range": [
-                88767,
-                88941
+                89035,
+                89209
             ],
             "filename": "astronomy.js",
-            "lineno": 1952,
+            "lineno": 1960,
             "columnno": 0,
             "code": {
-                "id": "astnode100010226",
+                "id": "astnode100010246",
                 "name": "EclipticCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -20437,14 +20549,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88838,
-                88852
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+                89120
             ],
             "filename": "astronomy.js",
-            "lineno": 1954,
+            "lineno": 1962,
             "columnno": 8,
             "code": {
-                "id": "astnode100010237",
+                "id": "astnode100010257",
                 "name": "this.vec",
                 "type": "Identifier",
                 "value": "vec",
@@ -20462,14 +20574,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88862,
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             ],
             "filename": "astronomy.js",
-            "lineno": 1955,
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             "columnno": 8,
             "code": {
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                 "name": "this.elat",
                 "type": "CallExpression",
                 "value": "",
@@ -20487,14 +20599,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
-            "lineno": 1956,
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             "columnno": 8,
             "code": {
-                "id": "astnode100010251",
+                "id": "astnode100010271",
                 "name": "this.elon",
                 "type": "CallExpression",
                 "value": "",
@@ -20512,14 +20624,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
-            "lineno": 1959,
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             "columnno": 0,
             "code": {
-                "id": "astnode100010259",
+                "id": "astnode100010279",
                 "name": "exports.EclipticCoordinates",
                 "type": "Identifier",
                 "value": "EclipticCoordinates",
@@ -20536,14 +20648,14 @@
         "comment": "",
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@@ -20563,14 +20675,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
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                 "name": "vector2radec",
                 "type": "FunctionDeclaration",
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@@ -20597,14 +20709,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
-            "lineno": 1964,
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             "columnno": 10,
             "code": {
-                "id": "astnode100010288",
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                 "name": "vec",
                 "type": "CallExpression",
                 "value": ""
@@ -20622,14 +20734,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89171,
-                89209
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+                89477
             ],
             "filename": "astronomy.js",
-            "lineno": 1965,
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             "columnno": 10,
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@@ -20647,14 +20759,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                89529
             ],
             "filename": "astronomy.js",
-            "lineno": 1966,
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             "columnno": 10,
             "code": {
-                "id": "astnode100010313",
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                 "value": ""
@@ -20672,14 +20784,14 @@
         "comment": "",
         "meta": {
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-                89526,
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+                89842
             ],
             "filename": "astronomy.js",
-            "lineno": 1974,
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             "columnno": 8,
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-                "id": "astnode100010364",
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@@ -20697,14 +20809,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89606,
-                89614
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+                89876
             ],
             "filename": "astronomy.js",
-            "lineno": 1976,
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             "columnno": 8,
             "code": {
-                "id": "astnode100010387",
+                "id": "astnode100010405",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "vector2radec",
@@ -20723,14 +20835,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89626,
-                89687
+                89888,
+                89949
             ],
             "filename": "astronomy.js",
-            "lineno": 1977,
+            "lineno": 1985,
             "columnno": 10,
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-                "id": "astnode100010391",
+                "id": "astnode100010409",
                 "name": "dec",
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@@ -20748,14 +20860,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89749,
-                89951
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+                90213
             ],
             "filename": "astronomy.js",
-            "lineno": 1980,
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             "columnno": 0,
             "code": {
-                "id": "astnode100010416",
+                "id": "astnode100010434",
                 "name": "spin",
                 "type": "FunctionDeclaration",
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@@ -20780,14 +20892,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89787,
-                89817
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+                90079
             ],
             "filename": "astronomy.js",
-            "lineno": 1981,
+            "lineno": 1989,
             "columnno": 10,
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@@ -20805,14 +20917,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89829,
-                89847
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+                90109
             ],
             "filename": "astronomy.js",
-            "lineno": 1982,
+            "lineno": 1990,
             "columnno": 10,
             "code": {
-                "id": "astnode100010430",
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                 "type": "CallExpression",
                 "value": ""
@@ -20830,14 +20942,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89859,
-                89877
+                90121,
+                90139
             ],
             "filename": "astronomy.js",
-            "lineno": 1983,
+            "lineno": 1991,
             "columnno": 10,
             "code": {
-                "id": "astnode100010438",
+                "id": "astnode100010456",
                 "name": "s",
                 "type": "CallExpression",
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@@ -20855,14 +20967,14 @@
         "comment": "/**\n * @brief Converts equatorial coordinates to horizontal coordinates.\n *\n * Given a date and time, a geographic location of an observer on the Earth, and\n * equatorial coordinates (right ascension and declination) of a celestial body,\n * returns horizontal coordinates (azimuth and altitude angles) for that body\n * as seen by that observer. Allows optional correction for atmospheric refraction.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to find horizontal coordinates.\n *\n * @param {Observer} observer\n *      The location of the observer for which to find horizontal coordinates.\n *\n * @param {number} ra\n *      Right ascension in sidereal hours of the celestial object,\n *      referred to the mean equinox of date for the J2000 epoch.\n *\n * @param {number} dec\n *      Declination in degrees of the celestial object,\n *      referred to the mean equator of date for the J2000 epoch.\n *      Positive values are north of the celestial equator and negative values are south.\n *\n * @param {string} refraction\n *      If omitted or has a false-like value (false, null, undefined, etc.)\n *      the calculations are performed without any correction for atmospheric\n *      refraction. If the value is the string `\"normal\"`,\n *      uses the recommended refraction correction based on Meeus \"Astronomical Algorithms\"\n *      with a linear taper more than 1 degree below the horizon. The linear\n *      taper causes the refraction to linearly approach 0 as the altitude of the\n *      body approaches the nadir (-90 degrees).\n *      If the value is the string `\"jplhor\"`, uses a JPL Horizons\n *      compatible formula. This is the same algorithm as `\"normal\"`,\n *      only without linear tapering; this can result in physically impossible\n *      altitudes of less than -90 degrees, which may cause problems for some applications.\n *      (The `\"jplhor\"` option was created for unit testing against data\n *      generated by JPL Horizons, and is otherwise not recommended for use.)\n *\n * @returns {HorizontalCoordinates}\n */",
         "meta": {
             "range": [
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-                96653
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+                96903
             ],
             "filename": "astronomy.js",
-            "lineno": 2026,
+            "lineno": 2034,
             "columnno": 0,
             "code": {
-                "id": "astnode100010472",
+                "id": "astnode100010490",
                 "name": "Horizon",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -20982,14 +21094,14 @@
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-                92130
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             "columnno": 8,
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@@ -21007,14 +21119,14 @@
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@@ -21032,14 +21144,14 @@
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             "columnno": 10,
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@@ -21057,14 +21169,14 @@
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             "columnno": 10,
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@@ -21082,14 +21194,14 @@
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@@ -21107,14 +21219,14 @@
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@@ -21132,14 +21244,14 @@
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             "columnno": 10,
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@@ -21157,14 +21269,14 @@
         "comment": "",
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             "columnno": 10,
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@@ -21182,14 +21294,14 @@
         "comment": "",
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             "columnno": 10,
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@@ -21207,14 +21319,14 @@
         "comment": "",
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                 "value": "[\"\",\"\",\"sinlat\"]"
@@ -21232,14 +21344,14 @@
         "comment": "",
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@@ -22609,14 +22721,14 @@
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                 "value": "SunPosition",
@@ -22633,14 +22745,14 @@
         "comment": "/**\n * @brief Calculates equatorial coordinates of a Solar System body at a given time.\n *\n * Returns topocentric equatorial coordinates (right ascension and declination)\n * in one of two different systems: J2000 or true-equator-of-date.\n * Allows optional correction for aberration.\n * Always corrects for light travel time (represents the object as seen by the observer\n * with light traveling to the Earth at finite speed, not where the object is right now).\n * <i>Topocentric</i> refers to a position as seen by an observer on the surface of the Earth.\n * This function corrects for\n * <a href=\"https://en.wikipedia.org/wiki/Parallax\">parallax</a>\n * of the object between a geocentric observer and a topocentric observer.\n * This is most significant for the Moon, because it is so close to the Earth.\n * However, it can have a small effect on the apparent positions of other bodies.\n *\n * @param {Body} body\n *      The body for which to find equatorial coordinates.\n *      Not allowed to be `\"Earth\"`.\n *\n * @param {FlexibleDateTime} date\n *      Specifies the date and time at which the body is to be observed.\n *\n * @param {Observer} observer\n *      The location on the Earth of the observer.\n *\n * @param {bool} ofdate\n *      Pass `true` to return equatorial coordinates of date,\n *      i.e. corrected for precession and nutation at the given date.\n *      This is needed to get correct horizontal coordinates when you call\n *      {@link Horizon}.\n *      Pass `false` to return equatorial coordinates in the J2000 system.\n *\n * @param {bool} aberration\n *      Pass `true` to correct for\n *      <a href=\"https://en.wikipedia.org/wiki/Aberration_of_light\">aberration</a>,\n *      or `false` to leave uncorrected.\n *\n * @returns {EquatorialCoordinates}\n *      The topocentric coordinates of the body as adjusted for the given observer.\n */",
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@@ -22733,14 +22845,14 @@
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                 "name": "exports.Equator",
                 "type": "Identifier",
                 "value": "Equator",
@@ -22882,14 +22994,14 @@
         "comment": "/**\n * @brief Calculates geocentric equatorial coordinates of an observer on the surface of the Earth.\n *\n * This function calculates a vector from the center of the Earth to\n * a point on or near the surface of the Earth, expressed in equatorial\n * coordinates. It takes into account the rotation of the Earth at the given\n * time, along with the given latitude, longitude, and elevation of the observer.\n *\n * The caller may pass `ofdate` as `true` to return coordinates relative to the Earth's\n * equator at the specified time, or `false` to use the J2000 equator.\n *\n * The returned vector has components expressed in astronomical units (AU).\n * To convert to kilometers, multiply the `x`, `y`, and `z` values by\n * the constant value {@link KM_PER_AU}.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the observer's position vector.\n *\n * @param {Observer} observer\n *      The geographic location of a point on or near the surface of the Earth.\n *\n * @param {boolean} ofdate\n *      Selects the date of the Earth's equator in which to express the equatorial coordinates.\n *      The caller may pass `false` to use the orientation of the Earth's equator\n *      at noon UTC on January 1, 2000, in which case this function corrects for precession\n *      and nutation of the Earth as it was at the moment specified by the `time` parameter.\n *      Or the caller may pass `true` to use the Earth's equator at `time`\n *      as the orientation.\n *\n * @returns {Vector}\n *      An equatorial vector from the center of the Earth to the specified location\n *      on (or near) the Earth's surface.\n */",
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@@ -22960,14 +23072,14 @@
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@@ -23035,14 +23147,14 @@
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                 "type": "CallExpression",
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@@ -23061,14 +23173,14 @@
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             "columnno": 0,
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                 "name": "exports.ObserverVector",
                 "type": "Identifier",
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@@ -23085,14 +23197,14 @@
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@@ -23122,14 +23234,14 @@
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@@ -23147,14 +23259,14 @@
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@@ -23172,14 +23284,14 @@
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@@ -23197,14 +23309,14 @@
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@@ -23222,14 +23334,14 @@
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@@ -23247,14 +23359,14 @@
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@@ -23273,14 +23385,14 @@
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             "columnno": 12,
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@@ -23299,14 +23411,14 @@
         "comment": "",
         "meta": {
             "range": [
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@@ -23324,14 +23436,14 @@
         "comment": "",
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@@ -23349,14 +23461,14 @@
         "comment": "/**\n * @brief Converts equatorial Cartesian coordinates to ecliptic Cartesian and angular coordinates.\n *\n * Given J2000 equatorial Cartesian coordinates,\n * returns J2000 ecliptic latitude, longitude, and cartesian coordinates.\n * You can call {@link GeoVector} and pass the resulting vector to this function.\n *\n * @param {Vector} equ\n *      A vector in the J2000 equatorial coordinate system.\n *\n * @returns {EclipticCoordinates}\n */",
         "meta": {
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             "columnno": 0,
             "code": {
-                "id": "astnode100011494",
+                "id": "astnode100011506",
                 "name": "Ecliptic",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -23406,14 +23518,14 @@
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             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "type": "BinaryExpression",
                 "funcscope": "Ecliptic",
@@ -23432,14 +23544,14 @@
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                 "type": "CallExpression",
                 "funcscope": "Ecliptic",
@@ -23458,14 +23570,14 @@
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             "columnno": 8,
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                 "type": "CallExpression",
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@@ -23484,14 +23596,14 @@
         "comment": "",
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             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100011540",
+                "id": "astnode100011552",
                 "name": "exports.Ecliptic",
                 "type": "Identifier",
                 "value": "Ecliptic",
@@ -23508,14 +23620,14 @@
         "comment": "/**\n * @brief Calculates the geocentric Cartesian coordinates for the Moon in the J2000 equatorial system.\n *\n * Based on the Nautical Almanac Office's <i>Improved Lunar Ephemeris</i> of 1954,\n * which in turn derives from E. W. Brown's lunar theories.\n * Adapted from Turbo Pascal code from the book\n * <a href=\"https://www.springer.com/us/book/9783540672210\">Astronomy on the Personal Computer</a>\n * by Montenbruck and Pfleger.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the Moon's geocentric position.\n *\n * @returns {Vector}\n */",
         "meta": {
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+                107484
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100011545",
+                "id": "astnode100011557",
                 "name": "GeoMoon",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -23568,14 +23680,14 @@
         "comment": "",
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@@ -23593,14 +23705,14 @@
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@@ -23618,14 +23730,14 @@
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         "comment": "/**\n * @brief Calculates the angular separation between the Sun and the given body.\n *\n * Returns the full angle seen from\n * the Earth, between the given body and the Sun.\n * Unlike {@link LongitudeFromSun}, this function does not\n * project the body's \"shadow\" onto the ecliptic;\n * the angle is measured in 3D space around the plane that\n * contains the centers of the Earth, the Sun, and `body`.\n *\n * @param {Body} body\n *      The name of a supported celestial body other than the Earth.\n *\n * @param {FlexibleDateTime} date\n *      The time at which the angle from the Sun is to be found.\n *\n * @returns {number}\n *      An angle in degrees in the range [0, 180].\n */",
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         "comment": "/**\n * @brief Calculates heliocentric ecliptic longitude based on the J2000 equinox.\n *\n * @param {Body} body\n *      The name of a celestial body other than the Sun.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the ecliptic longitude.\n *\n * @returns {number}\n *      The ecliptic longitude angle of the body in degrees measured counterclockwise around the mean\n *      plane of the Earth's orbit, as seen from above the Sun's north pole.\n *      Ecliptic longitude starts at 0 at the J2000\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a> and\n *      increases in the same direction the Earth orbits the Sun.\n *      The returned value is always in the range [0, 360).\n */",
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         "comment": "/**\n * @brief Information about the apparent brightness and sunlit phase of a celestial object.\n *\n * @property {AstroTime} time\n *      The date and time pertaining to the other calculated values in this object.\n *\n * @property {number} mag\n *      The <a href=\"https://en.wikipedia.org/wiki/Apparent_magnitude\">apparent visual magnitude</a> of the celestial body.\n *\n * @property {number} phase_angle\n *      The angle in degrees as seen from the center of the celestial body between the Sun and the Earth.\n *      The value is always in the range 0 to 180.\n *      The phase angle provides a measure of what fraction of the body's face appears\n *      illuminated by the Sun as seen from the Earth.\n *      When the observed body is the Sun, the `phase` property is set to 0,\n *      although this has no physical meaning because the Sun emits, rather than reflects, light.\n *      When the phase is near 0 degrees, the body appears \"full\".\n *      When it is 90 degrees, the body appears \"half full\".\n *      And when it is 180 degrees, the body appears \"new\" and is very difficult to see\n *      because it is both dim and lost in the Sun's glare as seen from the Earth.\n *\n * @property {number} phase_fraction\n *      The fraction of the body's face that is illuminated by the Sun, as seen from the Earth.\n *      Calculated from `phase_angle` for convenience.\n *      This value ranges from 0 to 1.\n *\n * @property {number} helio_dist\n *      The distance between the center of the Sun and the center of the body in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n *\n * @property {number} geo_dist\n *      The distance between the center of the Earth and the center of the body in AU.\n *\n * @property {Vector} gc\n *      Geocentric coordinates: the 3D vector from the center of the Earth to the center of the body.\n *      The components are in expressed in AU and are oriented with respect to the J2000 equatorial plane.\n *\n * @property {Vector} hc\n *      Heliocentric coordinates: The 3D vector from the center of the Sun to the center of the body.\n *      Like `gc`, `hc` is expressed in AU and oriented with respect\n *      to the J2000 equatorial plane.\n *\n * @property {number | undefined} ring_tilt\n *      For Saturn, this is the angular tilt of the planet's rings in degrees away\n *      from the line of sight from the Earth. When the value is near 0, the rings\n *      appear edge-on from the Earth and are therefore difficult to see.\n *      When `ring_tilt` approaches its maximum value (about 27 degrees),\n *      the rings appear widest and brightest from the Earth.\n *      Unlike the <a href=\"https://ssd.jpl.nasa.gov/horizons.cgi\">JPL Horizons</a> online tool,\n *      this library includes the effect of the ring tilt angle in the calculated value\n *      for Saturn's visual magnitude.\n *      For all bodies other than Saturn, the value of `ring_tilt` is `undefined`.\n */",
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@@ -35348,14 +35565,14 @@
         "comment": "/**\n * @brief Information about the apparent brightness and sunlit phase of a celestial object.\n *\n * @property {AstroTime} time\n *      The date and time pertaining to the other calculated values in this object.\n *\n * @property {number} mag\n *      The <a href=\"https://en.wikipedia.org/wiki/Apparent_magnitude\">apparent visual magnitude</a> of the celestial body.\n *\n * @property {number} phase_angle\n *      The angle in degrees as seen from the center of the celestial body between the Sun and the Earth.\n *      The value is always in the range 0 to 180.\n *      The phase angle provides a measure of what fraction of the body's face appears\n *      illuminated by the Sun as seen from the Earth.\n *      When the observed body is the Sun, the `phase` property is set to 0,\n *      although this has no physical meaning because the Sun emits, rather than reflects, light.\n *      When the phase is near 0 degrees, the body appears \"full\".\n *      When it is 90 degrees, the body appears \"half full\".\n *      And when it is 180 degrees, the body appears \"new\" and is very difficult to see\n *      because it is both dim and lost in the Sun's glare as seen from the Earth.\n *\n * @property {number} phase_fraction\n *      The fraction of the body's face that is illuminated by the Sun, as seen from the Earth.\n *      Calculated from `phase_angle` for convenience.\n *      This value ranges from 0 to 1.\n *\n * @property {number} helio_dist\n *      The distance between the center of the Sun and the center of the body in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n *\n * @property {number} geo_dist\n *      The distance between the center of the Earth and the center of the body in AU.\n *\n * @property {Vector} gc\n *      Geocentric coordinates: the 3D vector from the center of the Earth to the center of the body.\n *      The components are in expressed in AU and are oriented with respect to the J2000 equatorial plane.\n *\n * @property {Vector} hc\n *      Heliocentric coordinates: The 3D vector from the center of the Sun to the center of the body.\n *      Like `gc`, `hc` is expressed in AU and oriented with respect\n *      to the J2000 equatorial plane.\n *\n * @property {number | undefined} ring_tilt\n *      For Saturn, this is the angular tilt of the planet's rings in degrees away\n *      from the line of sight from the Earth. When the value is near 0, the rings\n *      appear edge-on from the Earth and are therefore difficult to see.\n *      When `ring_tilt` approaches its maximum value (about 27 degrees),\n *      the rings appear widest and brightest from the Earth.\n *      Unlike the <a href=\"https://ssd.jpl.nasa.gov/horizons.cgi\">JPL Horizons</a> online tool,\n *      this library includes the effect of the ring tilt angle in the calculated value\n *      for Saturn's visual magnitude.\n *      For all bodies other than Saturn, the value of `ring_tilt` is `undefined`.\n */",
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@@ -35471,14 +35688,14 @@
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@@ -35571,14 +35788,14 @@
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                 "type": "Identifier",
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@@ -35596,14 +35813,14 @@
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@@ -35646,14 +35863,14 @@
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@@ -35671,14 +35888,14 @@
         "comment": "",
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                 "name": "this.phase_fraction",
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@@ -35696,14 +35913,14 @@
         "comment": "",
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             "columnno": 0,
             "code": {
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                 "name": "exports.IlluminationInfo",
                 "type": "Identifier",
                 "value": "IlluminationInfo",
@@ -35720,14 +35937,14 @@
         "comment": "/**\n * @brief Calculates visual magnitude and related information about a body.\n *\n * Calculates the phase angle, visual magnitude,\n * and other values relating to the body's illumination\n * at the given date and time, as seen from the Earth.\n *\n * @param {Body} body\n *      The name of the celestial body being observed.\n *      Not allowed to be `\"Earth\"`.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the illumination data for the given body.\n *\n * @returns {IlluminationInfo}\n */",
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             "columnno": 0,
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@@ -35819,14 +36036,14 @@
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             "columnno": 10,
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@@ -35844,14 +36061,14 @@
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@@ -36092,14 +36309,14 @@
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@@ -36144,14 +36361,14 @@
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@@ -36372,14 +36486,117 @@
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             ],
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+        "kind": "constant",
+        "memberof": "Illumination",
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+    },
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+        "longname": "Illumination~mag",
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+                "paramnames": []
+            }
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+        "undocumented": true,
+        "name": "mag",
+        "longname": "Illumination~mag",
+        "kind": "member",
+        "memberof": "Illumination",
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             "code": {
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                 "name": "exports.Illumination",
                 "type": "Identifier",
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             "columnno": 0,
             "code": {
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+                "id": "astnode100017451",
                 "name": "SynodicPeriod",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -36428,14 +36645,14 @@
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             ],
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                 "type": "MemberExpression",
                 "value": "Planet.Earth.OrbitalPeriod"
@@ -36478,14 +36695,14 @@
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                 "type": "MemberExpression",
                 "value": "planet.OrbitalPeriod"
@@ -36503,14 +36720,14 @@
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@@ -36528,14 +36745,14 @@
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             "columnno": 0,
             "code": {
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+                "id": "astnode100017515",
                 "name": "SearchRelativeLongitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
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                 "type": "MemberExpression",
                 "value": "Planet[undefined]"
@@ -36638,14 +36855,14 @@
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@@ -36663,14 +36880,14 @@
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@@ -36695,14 +36912,14 @@
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                 "name": "plon",
                 "type": "CallExpression",
                 "value": ""
@@ -36720,14 +36937,14 @@
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             "code": {
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+                "id": "astnode100017576",
                 "name": "elon",
                 "type": "CallExpression",
                 "value": ""
@@ -36745,14 +36962,14 @@
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             ],
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@@ -36770,14 +36987,14 @@
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@@ -36795,14 +37012,14 @@
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@@ -37073,14 +37290,14 @@
         "comment": "/**\n * @brief Determines the moon's phase expressed as an ecliptic longitude.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the moon's phase.\n *\n * @returns {number}\n *      A value in the range [0, 360) indicating the difference\n *      in ecliptic longitude between the center of the Sun and the\n *      center of the Moon, as seen from the center of the Earth.\n *      Certain longitude values have conventional meanings:\n *\n * * 0 = new moon\n * * 90 = first quarter\n * * 180 = full moon\n * * 270 = third quarter\n */",
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@@ -37126,14 +37343,14 @@
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                 "name": "exports.MoonPhase",
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@@ -37150,14 +37367,14 @@
         "comment": "/**\n * @brief Searches for the date and time that the Moon reaches a specified phase.\n *\n * Lunar phases are defined in terms of geocentric ecliptic longitudes\n * with respect to the Sun.  When the Moon and the Sun have the same ecliptic\n * longitude, that is defined as a new moon. When the two ecliptic longitudes\n * are 180 degrees apart, that is defined as a full moon.\n * To enumerate quarter lunar phases, it is simpler to call\n * {@link SearchMoonQuarter} once, followed by repeatedly calling\n * {@link NextMoonQuarter}. `SearchMoonPhase` is only\n * necessary for finding other lunar phases than the usual quarter phases.\n *\n * @param {number} targetLon\n *      The difference in geocentric ecliptic longitude between the Sun and Moon\n *      that specifies the lunar phase being sought. This can be any value\n *      in the range [0, 360). Here are some helpful examples:\n *      0 = new moon,\n *      90 = first quarter,\n *      180 = full moon,\n *      270 = third quarter.\n *\n * @param {FlexibleDateTime} dateStart\n *      The beginning of the window of time in which to search.\n *\n * @param {number} limitDays\n *      The floating point number of days after `dateStart`\n *      that limits the window of time in which to search.\n *\n * @returns {AstroTime | null}\n *      If the specified lunar phase occurs after `dateStart`\n *      and before `limitDays` days after `dateStart`,\n *      this function returns the date and time of the first such occurrence.\n *      Otherwise, it returns `null`.\n */",
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                 "name": "exports.SearchMoonPhase",
                 "type": "Identifier",
                 "value": "SearchMoonPhase",
@@ -37540,14 +37757,14 @@
         "comment": "/**\n * @brief A quarter lunar phase, along with when it occurs.\n *\n * @property {number} quarter\n *      An integer as follows:\n *      0 = new moon,\n *      1 = first quarter,\n *      2 = full moon,\n *      3 = third quarter.\n *\n * @property {AstroTime} time\n *      The date and time of the quarter lunar phase.\n */",
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             "columnno": 0,
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@@ -37594,14 +37811,14 @@
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             "columnno": 4,
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                 "name": "MoonQuarter",
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@@ -37624,14 +37841,14 @@
         "comment": "/**\n * @brief A quarter lunar phase, along with when it occurs.\n *\n * @property {number} quarter\n *      An integer as follows:\n *      0 = new moon,\n *      1 = first quarter,\n *      2 = full moon,\n *      3 = third quarter.\n *\n * @property {AstroTime} time\n *      The date and time of the quarter lunar phase.\n */",
         "meta": {
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@@ -37677,14 +37894,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "this.quarter",
                 "type": "Identifier",
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@@ -37702,14 +37919,14 @@
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@@ -37727,14 +37944,14 @@
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             "columnno": 0,
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                 "name": "exports.MoonQuarter",
                 "type": "Identifier",
                 "value": "MoonQuarter",
@@ -37751,14 +37968,14 @@
         "comment": "/**\n * @brief Finds the first quarter lunar phase after the specified date and time.\n *\n * The quarter lunar phases are: new moon, first quarter, full moon, and third quarter.\n * To enumerate quarter lunar phases, call `SearchMoonQuarter` once,\n * then pass its return value to {@link NextMoonQuarter} to find the next\n * `MoonQuarter`. Keep calling `NextMoonQuarter` in a loop,\n * passing the previous return value as the argument to the next call.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which to find the first quarter lunar phase.\n *\n * @returns {MoonQuarter}\n */",
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             "columnno": 0,
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                 "name": "SearchMoonQuarter",
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@@ -37809,14 +38026,14 @@
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@@ -37834,14 +38051,14 @@
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             "columnno": 8,
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                 "name": "quarterStart",
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@@ -37859,14 +38076,14 @@
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             "columnno": 8,
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@@ -37884,14 +38101,14 @@
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@@ -37909,14 +38126,14 @@
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             "columnno": 0,
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                 "name": "exports.SearchMoonQuarter",
                 "type": "Identifier",
                 "value": "SearchMoonQuarter",
@@ -37933,14 +38150,14 @@
         "comment": "/**\n * @brief Finds the next quarter lunar phase in a series.\n *\n * Given a {@link MoonQuarter} object, finds the next consecutive\n * quarter lunar phase. See remarks in {@link SearchMoonQuarter}\n * for explanation of usage.\n *\n * @param {MoonQuarter} mq\n *      The return value of a prior call to {@link MoonQuarter} or `NextMoonQuarter`.\n */",
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             "columnno": 0,
             "code": {
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                 "name": "NextMoonQuarter",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37979,14 +38196,14 @@
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@@ -38004,14 +38221,14 @@
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         "comment": "/**\n * @brief Finds when a body will reach a given hour angle.\n *\n * Finds the next time the given body is seen to reach the specified\n * <a href=\"https://en.wikipedia.org/wiki/Hour_angle\">hour angle</a>\n * by the given observer.\n * Providing `hourAngle` = 0 finds the next maximum altitude event (culmination).\n * Providing `hourAngle` = 12 finds the next minimum altitude event.\n * Note that, especially close to the Earth's poles, a body as seen on a given day\n * may always be above the horizon or always below the horizon, so the caller cannot\n * assume that a culminating object is visible nor that an object is below the horizon\n * at its minimum altitude.\n *\n * @param {Body} body\n *      The name of a celestial body other than the Earth.\n *\n * @param {Observer} observer\n *      Specifies the geographic coordinates and elevation above sea level of the observer.\n *\n * @param {number} hourAngle\n *      The hour angle expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Sidereal_time\">sidereal</a>\n *      hours for which the caller seeks to find the body attain.\n *      The value must be in the range [0, 24).\n *      The hour angle represents the number of sidereal hours that have\n *      elapsed since the most recent time the body crossed the observer's local\n *      <a href=\"https://en.wikipedia.org/wiki/Meridian_(astronomy)\">meridian</a>.\n *      This specifying `hourAngle` = 0 finds the moment in time\n *      the body reaches the highest angular altitude in a given sidereal day.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which the desired hour angle crossing event\n *      is to be found.\n *\n * @returns {HourAngleEvent}\n */",
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             "columnno": 0,
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                 "name": "SearchHourAngle",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -39268,14 +39485,14 @@
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             "columnno": 8,
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                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -39293,14 +39510,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 8,
             "code": {
-                "id": "astnode100018282",
+                "id": "astnode100018320",
                 "name": "iter",
                 "type": "Literal",
                 "value": 0
@@ -39318,14 +39535,14 @@
         "comment": "",
         "meta": {
             "range": [
-                185877,
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             "filename": "astronomy.js",
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             "columnno": 12,
             "code": {
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                 "name": "gast",
                 "type": "CallExpression",
                 "value": ""
@@ -39343,14 +39560,14 @@
         "comment": "",
         "meta": {
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             "columnno": 12,
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                 "name": "ofdate",
                 "type": "CallExpression",
                 "value": ""
@@ -39368,14 +39585,14 @@
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             "columnno": 12,
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                 "name": "delta_sidereal_hours",
                 "type": "BinaryExpression",
                 "value": ""
@@ -39393,14 +39610,14 @@
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             "code": {
-                "id": "astnode100018360",
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                 "name": "delta_sidereal_hours",
                 "type": "Literal",
                 "funcscope": "SearchHourAngle",
@@ -39419,14 +39636,14 @@
         "comment": "",
         "meta": {
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             "columnno": 16,
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                 "name": "delta_sidereal_hours",
                 "type": "Literal",
                 "funcscope": "SearchHourAngle",
@@ -39445,14 +39662,14 @@
         "comment": "",
         "meta": {
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                 "name": "delta_sidereal_hours",
                 "type": "Literal",
                 "funcscope": "SearchHourAngle",
@@ -39471,14 +39688,14 @@
         "comment": "",
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@@ -39496,14 +39713,14 @@
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@@ -39521,14 +39738,14 @@
         "comment": "",
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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-                "id": "astnode100018421",
+                "id": "astnode100018459",
                 "name": "time",
                 "type": "CallExpression",
                 "funcscope": "SearchHourAngle",
@@ -39547,14 +39764,14 @@
         "comment": "",
         "meta": {
             "range": [
-                187259,
-                187300
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             ],
             "filename": "astronomy.js",
-            "lineno": 4179,
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             "columnno": 0,
             "code": {
-                "id": "astnode100018429",
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                 "name": "exports.SearchHourAngle",
                 "type": "Identifier",
                 "value": "SearchHourAngle",
@@ -39571,14 +39788,14 @@
         "comment": "/**\n * @brief When the seasons change for a given calendar year.\n *\n * Represents the dates and times of the two solstices\n * and the two equinoxes in a given calendar year.\n * These four events define the changing of the seasons on the Earth.\n *\n * @property {AstroTime} mar_equinox\n *      The date and time of the March equinox in the given calendar year.\n *      This is the moment in March that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a negative number to a positive number.\n *      The March equinox defines\n *      the beginning of spring in the northern hemisphere and\n *      the beginning of autumn in the southern hemisphere.\n *\n * @property {AstroTime} jun_solstice\n *      The date and time of the June solstice in the given calendar year.\n *      This is the moment in June that the Sun reaches its most positive\n *      declination value.\n *      At this moment the Earth's north pole is most tilted most toward the Sun.\n *      The June solstice defines\n *      the beginning of summer in the northern hemisphere and\n *      the beginning of winter in the southern hemisphere.\n *\n * @property {AstroTime} sep_equinox\n *      The date and time of the September equinox in the given calendar year.\n *      This is the moment in September that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a positive number to a negative number.\n *      The September equinox defines\n *      the beginning of autumn in the northern hemisphere and\n *      the beginning of spring in the southern hemisphere.\n *\n * @property {AstroTime} dec_solstice\n *      The date and time of the December solstice in the given calendar year.\n *      This is the moment in December that the Sun reaches its most negative\n *      declination value.\n *      At this moment the Earth's south pole is tilted most toward the Sun.\n *      The December solstice defines\n *      the beginning of winter in the northern hemisphere and\n *      the beginning of summer in the southern hemisphere.\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100018434",
+                "id": "astnode100018472",
                 "name": "SeasonInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -39645,14 +39862,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 4,
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                 "name": "SeasonInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -39677,14 +39894,14 @@
         "comment": "/**\n * @brief When the seasons change for a given calendar year.\n *\n * Represents the dates and times of the two solstices\n * and the two equinoxes in a given calendar year.\n * These four events define the changing of the seasons on the Earth.\n *\n * @property {AstroTime} mar_equinox\n *      The date and time of the March equinox in the given calendar year.\n *      This is the moment in March that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a negative number to a positive number.\n *      The March equinox defines\n *      the beginning of spring in the northern hemisphere and\n *      the beginning of autumn in the southern hemisphere.\n *\n * @property {AstroTime} jun_solstice\n *      The date and time of the June solstice in the given calendar year.\n *      This is the moment in June that the Sun reaches its most positive\n *      declination value.\n *      At this moment the Earth's north pole is most tilted most toward the Sun.\n *      The June solstice defines\n *      the beginning of summer in the northern hemisphere and\n *      the beginning of winter in the southern hemisphere.\n *\n * @property {AstroTime} sep_equinox\n *      The date and time of the September equinox in the given calendar year.\n *      This is the moment in September that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a positive number to a negative number.\n *      The September equinox defines\n *      the beginning of autumn in the northern hemisphere and\n *      the beginning of spring in the southern hemisphere.\n *\n * @property {AstroTime} dec_solstice\n *      The date and time of the December solstice in the given calendar year.\n *      This is the moment in December that the Sun reaches its most negative\n *      declination value.\n *      At this moment the Earth's south pole is tilted most toward the Sun.\n *      The December solstice defines\n *      the beginning of winter in the northern hemisphere and\n *      the beginning of summer in the southern hemisphere.\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
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+                "id": "astnode100018472",
                 "name": "SeasonInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -39750,14 +39967,14 @@
         "comment": "",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018446",
+                "id": "astnode100018484",
                 "name": "this.mar_equinox",
                 "type": "Identifier",
                 "value": "mar_equinox",
@@ -39775,14 +39992,14 @@
         "comment": "",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018452",
+                "id": "astnode100018490",
                 "name": "this.jun_solstice",
                 "type": "Identifier",
                 "value": "jun_solstice",
@@ -39800,14 +40017,14 @@
         "comment": "",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018458",
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                 "name": "this.sep_equinox",
                 "type": "Identifier",
                 "value": "sep_equinox",
@@ -39825,14 +40042,14 @@
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             "columnno": 8,
             "code": {
-                "id": "astnode100018464",
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                 "name": "this.dec_solstice",
                 "type": "Identifier",
                 "value": "dec_solstice",
@@ -39850,14 +40067,14 @@
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             "columnno": 0,
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                 "name": "exports.SeasonInfo",
                 "type": "Identifier",
                 "value": "SeasonInfo",
@@ -39874,14 +40091,14 @@
         "comment": "/**\n * @brief Finds the equinoxes and solstices for a given calendar year.\n *\n * @param {number | AstroTime} year\n *      The integer value or `AstroTime` object that specifies\n *      the UTC calendar year for which to find equinoxes and solstices.\n *\n * @returns {SeasonInfo}\n */",
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             "columnno": 0,
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+                "id": "astnode100018513",
                 "name": "Seasons",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -39935,14 +40152,14 @@
         "comment": "",
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                 "name": "find",
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@@ -39968,14 +40185,14 @@
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             "filename": "astronomy.js",
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                 "name": "startDate",
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@@ -39993,14 +40210,14 @@
         "comment": "",
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             "columnno": 12,
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                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -40018,14 +40235,14 @@
         "comment": "",
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             "columnno": 8,
             "code": {
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+                "id": "astnode100018573",
                 "name": "year",
                 "type": "CallExpression",
                 "funcscope": "Seasons",
@@ -40044,14 +40261,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 8,
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                 "name": "mar_equinox",
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@@ -40069,14 +40286,14 @@
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             "columnno": 8,
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                 "name": "jun_solstice",
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                 "value": ""
@@ -40094,14 +40311,14 @@
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@@ -40119,14 +40336,14 @@
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             "columnno": 8,
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@@ -40144,14 +40361,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100018594",
+                "id": "astnode100018632",
                 "name": "exports.Seasons",
                 "type": "Identifier",
                 "value": "Seasons",
@@ -40168,14 +40385,14 @@
         "comment": "/**\n * @brief The viewing conditions of a body relative to the Sun.\n *\n * Represents the angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n *\n * @property {AstroTime} time\n *      The date and time of the observation.\n *\n * @property {string}  visibility\n *      Either `\"morning\"` or `\"evening\"`,\n *      indicating when the body is most easily seen.\n *\n * @property {number}  elongation\n *      The angle in degrees, as seen from the center of the Earth,\n *      of the apparent separation between the body and the Sun.\n *      This angle is measured in 3D space and is not projected onto the ecliptic plane.\n *      When `elongation` is less than a few degrees, the body is very\n *      difficult to see from the Earth because it is lost in the Sun's glare.\n *      The elongation is always in the range [0, 180].\n *\n * @property {number}  ecliptic_separation\n *      The absolute value of the difference between the body's ecliptic longitude\n *      and the Sun's ecliptic longitude, both as seen from the center of the Earth.\n *      This angle measures around the plane of the Earth's orbit (the ecliptic),\n *      and ignores how far above or below that plane the body is.\n *      The ecliptic separation is measured in degrees and is always in the range [0, 180].\n *\n * @see {@link Elongation}\n */",
         "meta": {
             "range": [
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+                193061
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100018599",
+                "id": "astnode100018637",
                 "name": "ElongationEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -40245,14 +40462,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 4,
             "code": {
-                "id": "astnode100018602",
+                "id": "astnode100018640",
                 "name": "ElongationEvent",
                 "type": "MethodDefinition",
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@@ -40277,14 +40494,14 @@
         "comment": "/**\n * @brief The viewing conditions of a body relative to the Sun.\n *\n * Represents the angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n *\n * @property {AstroTime} time\n *      The date and time of the observation.\n *\n * @property {string}  visibility\n *      Either `\"morning\"` or `\"evening\"`,\n *      indicating when the body is most easily seen.\n *\n * @property {number}  elongation\n *      The angle in degrees, as seen from the center of the Earth,\n *      of the apparent separation between the body and the Sun.\n *      This angle is measured in 3D space and is not projected onto the ecliptic plane.\n *      When `elongation` is less than a few degrees, the body is very\n *      difficult to see from the Earth because it is lost in the Sun's glare.\n *      The elongation is always in the range [0, 180].\n *\n * @property {number}  ecliptic_separation\n *      The absolute value of the difference between the body's ecliptic longitude\n *      and the Sun's ecliptic longitude, both as seen from the center of the Earth.\n *      This angle measures around the plane of the Earth's orbit (the ecliptic),\n *      and ignores how far above or below that plane the body is.\n *      The ecliptic separation is measured in degrees and is always in the range [0, 180].\n *\n * @see {@link Elongation}\n */",
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             "columnno": 0,
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                 "name": "ElongationEvent",
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@@ -40353,14 +40570,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -40378,14 +40595,14 @@
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         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100018617",
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                 "name": "this.visibility",
                 "type": "Identifier",
                 "value": "visibility",
@@ -40403,14 +40620,14 @@
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         "meta": {
             "range": [
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-                192488
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018623",
+                "id": "astnode100018661",
                 "name": "this.elongation",
                 "type": "Identifier",
                 "value": "elongation",
@@ -40428,14 +40645,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
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                 "name": "this.ecliptic_separation",
                 "type": "Identifier",
                 "value": "ecliptic_separation",
@@ -40453,14 +40670,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100018635",
+                "id": "astnode100018673",
                 "name": "exports.ElongationEvent",
                 "type": "Identifier",
                 "value": "ElongationEvent",
@@ -40477,14 +40694,14 @@
         "comment": "/**\n * @brief Calculates the viewing conditions of a body relative to the Sun.\n *\n * Calculates angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n * See the return type {@link ElongationEvent} for details.\n *\n * This function is helpful for determining how easy\n * it is to view a planet away from the Sun's glare on a given date.\n * It also determines whether the object is visible in the morning or evening;\n * this is more important the smaller the elongation is.\n * It is also used to determine how far a planet is from opposition, conjunction, or quadrature.\n *\n * @param {Body} body\n *      The name of the observed body. Not allowed to be `\"Earth\"`.\n *\n * @returns {ElongationEvent}\n */",
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             "columnno": 0,
             "code": {
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+                "id": "astnode100018678",
                 "name": "Elongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -40536,14 +40753,14 @@
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             "filename": "astronomy.js",
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             "columnno": 8,
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@@ -40561,14 +40778,14 @@
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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@@ -40586,14 +40803,14 @@
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018659",
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                 "name": "vis"
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@@ -40609,14 +40826,14 @@
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018667",
+                "id": "astnode100018705",
                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -40635,14 +40852,14 @@
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         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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                 "funcscope": "Elongation",
@@ -40661,14 +40878,14 @@
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018678",
+                "id": "astnode100018716",
                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -40687,14 +40904,14 @@
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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@@ -40712,14 +40929,14 @@
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         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100018696",
+                "id": "astnode100018734",
                 "name": "exports.Elongation",
                 "type": "Identifier",
                 "value": "Elongation",
@@ -40736,14 +40953,14 @@
         "comment": "/**\n * @brief Finds the next time Mercury or Venus reaches maximum elongation.\n *\n * Searches for the next maximum elongation event for Mercury or Venus\n * that occurs after the given start date. Calling with other values\n * of `body` will result in an exception.\n * Maximum elongation occurs when the body has the greatest\n * angular separation from the Sun, as seen from the Earth.\n * Returns an `ElongationEvent` object containing the date and time of the next\n * maximum elongation, the elongation in degrees, and whether\n * the body is visible in the morning or evening.\n *\n * @param {Body} body     Either `\"Mercury\"` or `\"Venus\"`.\n * @param {FlexibleDateTime} startDate  The date and time after which to search for the next maximum elongation event.\n *\n * @returns {ElongationEvent}\n */",
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             ],
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             "columnno": 0,
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                 "name": "SearchMaxElongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -40818,14 +41035,14 @@
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             "columnno": 10,
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@@ -40843,14 +41060,14 @@
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@@ -40877,14 +41094,14 @@
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@@ -40902,14 +41119,14 @@
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             "columnno": 14,
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@@ -40927,14 +41144,14 @@
         "comment": "",
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             ],
             "filename": "astronomy.js",
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             "columnno": 12,
             "code": {
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@@ -40952,14 +41169,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                195045
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             ],
             "filename": "astronomy.js",
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             "columnno": 12,
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@@ -40977,14 +41194,14 @@
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             "range": [
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@@ -41002,14 +41219,14 @@
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@@ -41027,14 +41244,14 @@
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@@ -41052,14 +41269,14 @@
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             "columnno": 8,
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@@ -41076,14 +41293,14 @@
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@@ -41100,14 +41317,14 @@
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@@ -41124,14 +41341,14 @@
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@@ -41148,14 +41365,14 @@
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@@ -41172,14 +41389,14 @@
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@@ -41196,14 +41413,14 @@
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@@ -41221,14 +41438,14 @@
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@@ -41246,14 +41463,14 @@
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@@ -41271,14 +41488,14 @@
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@@ -41296,14 +41513,14 @@
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@@ -41321,14 +41538,14 @@
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@@ -41367,14 +41584,14 @@
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             "columnno": 30,
             "code": {
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+                "id": "astnode100018870",
                 "name": "adjust_days"
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@@ -41390,14 +41607,14 @@
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             "columnno": 12,
             "code": {
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+                "id": "astnode100018888",
                 "name": "adjust_days",
                 "type": "Literal",
                 "funcscope": "SearchMaxElongation",
@@ -41416,14 +41633,14 @@
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@@ -41442,170 +41659,14 @@
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                 "type": "Identifier",
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@@ -46935,14 +47152,14 @@
         "comment": "/**\n * @brief Given an equatorial vector, calculates equatorial angular coordinates.\n *\n * @param {Vector} vec\n *      A vector in an equatorial coordinate system.\n *\n * @returns {EquatorialCoordinates}\n *      Angular coordinates expressed in the same equatorial system as `vec`.\n */",
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@@ -46991,14 +47208,14 @@
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@@ -47016,14 +47233,14 @@
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@@ -47040,14 +47257,14 @@
         "comment": "/**\n * @brief Converts Cartesian coordinates to spherical coordinates.\n *\n * Given a Cartesian vector, returns latitude, longitude, and distance.\n *\n * @param {Vector} vector\n *      Cartesian vector to be converted to spherical coordinates.\n *\n * @returns {Spherical}\n *      Spherical coordinates that are equivalent to the given vector.\n */",
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@@ -47456,14 +47673,14 @@
         "comment": "/**\n * @brief Converts Cartesian coordinates to horizontal coordinates.\n *\n * Given a horizontal Cartesian vector, returns horizontal azimuth and altitude.\n *\n * *IMPORTANT:* This function differs from {@link SphereFromVector} in two ways:\n * - `SphereFromVector` returns a `lon` value that represents azimuth defined counterclockwise\n *   from north (e.g., west = +90), but this function represents a clockwise rotation\n *   (e.g., east = +90). The difference is because `SphereFromVector` is intended\n *   to preserve the vector \"right-hand rule\", while this function defines azimuth in a more\n *   traditional way as used in navigation and cartography.\n * - This function optionally corrects for atmospheric refraction, while `SphereFromVector` does not.\n *\n * The returned object contains the azimuth in `lon`.\n * It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees.\n *\n * The altitude is stored in `lat`.\n *\n * The distance to the observed object is stored in `dist`,\n * and is expressed in astronomical units (AU).\n *\n * @param {Vector} vector\n *      Cartesian vector to be converted to horizontal coordinates.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @returns {Spherical}\n */",
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                 "type": "Identifier",
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@@ -47624,14 +47841,14 @@
         "comment": "/**\n * @brief Given apparent angular horizontal coordinates in `sphere`, calculate horizontal vector.\n *\n * @param {Spherical} sphere\n *      A structure that contains apparent horizontal coordinates:\n *      `lat` holds the refracted azimuth angle,\n *      `lon` holds the azimuth in degrees clockwise from north,\n *      and `dist` holds the distance from the observer to the object in AU.\n *\n * @param {AstroTime} time\n *      The date and time of the observation. This is needed because the returned\n *      vector object requires a valid time value when passed to certain other functions.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @returns {Vector}\n *      A vector in the horizontal system: `x` = north, `y` = west, and `z` = zenith (up).\n */",
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@@ -47801,14 +48018,14 @@
         "comment": "/**\n * @brief Calculates the amount of \"lift\" to an altitude angle caused by atmospheric refraction.\n *\n * Given an altitude angle and a refraction option, calculates\n * the amount of \"lift\" caused by atmospheric refraction.\n * This is the number of degrees higher in the sky an object appears\n * due to the lensing of the Earth's atmosphere.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @param {number} altitude\n *      An altitude angle in a horizontal coordinate system. Must be a value between -90 and +90.\n *\n * @returns {number}\n *      The angular adjustment in degrees to be added to the altitude angle to correct for atmospheric lensing.\n */",
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                 "name": "exports.Refraction",
                 "type": "Identifier",
                 "value": "Refraction",
@@ -48044,14 +48261,14 @@
         "comment": "/**\n * @brief Calculates the inverse of an atmospheric refraction angle.\n *\n * Given an observed altitude angle that includes atmospheric refraction,\n * calculate the negative angular correction to obtain the unrefracted\n * altitude. This is useful for cases where observed horizontal\n * coordinates are to be converted to another orientation system,\n * but refraction first must be removed from the observed position.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @param {number} bent_altitude\n *      The apparent altitude that includes atmospheric refraction.\n *\n * @returns {number}\n *      The angular adjustment in degrees to be added to the\n *      altitude angle to correct for atmospheric lensing.\n *      This will be less than or equal to zero.\n */",
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             "columnno": 0,
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                 "name": "InverseRefraction",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -48111,14 +48328,14 @@
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@@ -48136,14 +48353,14 @@
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@@ -48187,14 +48404,14 @@
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             "columnno": 0,
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@@ -48211,14 +48428,14 @@
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@@ -48274,14 +48491,14 @@
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@@ -48298,14 +48515,14 @@
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@@ -48361,14 +48578,14 @@
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         "meta": {
             "range": [
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             "filename": "astronomy.js",
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                 "name": "exports.RotateState",
                 "type": "Identifier",
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@@ -48385,14 +48602,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using equator at J2000 epoch.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQJ to ECL.\n */",
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@@ -48430,14 +48647,14 @@
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@@ -48455,14 +48672,14 @@
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@@ -48480,14 +48697,14 @@
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             "columnno": 0,
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                 "type": "Identifier",
                 "value": "Rotation_EQJ_ECL",
@@ -48504,14 +48721,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts ECL to EQJ.\n */",
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             "columnno": 0,
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@@ -48599,14 +48816,14 @@
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@@ -48623,14 +48840,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using equator at J2000 epoch.\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {FlexibleDateTime} time\n *      The date and time at which the Earth's equator defines the target orientation.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQJ to EQD at `time`.\n */",
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             ],
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             "columnno": 0,
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@@ -48681,14 +48898,14 @@
         "comment": "",
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@@ -48707,14 +48924,14 @@
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@@ -48757,14 +48974,14 @@
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             ],
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             "columnno": 0,
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                 "type": "Identifier",
                 "value": "Rotation_EQJ_EQD",
@@ -48781,14 +48998,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @param {FlexibleDateTime} time\n *      The date and time at which the Earth's equator defines the source orientation.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD at `time` to EQJ.\n */",
         "meta": {
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             ],
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             "columnno": 0,
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                 "name": "Rotation_EQD_EQJ",
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@@ -48839,14 +49056,14 @@
         "comment": "",
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@@ -48890,14 +49107,14 @@
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@@ -48915,14 +49132,14 @@
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             "range": [
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             ],
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             "columnno": 0,
             "code": {
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                 "type": "Identifier",
                 "value": "Rotation_EQD_EQJ",
@@ -48939,14 +49156,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: HOR = horizontal system.\n *\n * Use `HorizonFromVector` to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param {FlexibleDateTime} time\n *      The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD to HOR at `time` and for `observer`.\n *      The components of the horizontal vector are:\n *      x = north, y = west, z = zenith (straight up from the observer).\n *      These components are chosen so that the \"right-hand rule\" works for the vector\n *      and so that north represents the direction where azimuth = 0.\n */",
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             ],
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             "columnno": 0,
             "code": {
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@@ -49016,14 +49233,14 @@
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             ],
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@@ -49042,14 +49259,14 @@
         "comment": "",
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             ],
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             "columnno": 10,
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@@ -49067,14 +49284,14 @@
         "comment": "",
         "meta": {
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             "columnno": 10,
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@@ -49092,14 +49309,14 @@
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@@ -49117,14 +49334,14 @@
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@@ -49142,14 +49359,14 @@
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@@ -49167,14 +49384,14 @@
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             "columnno": 10,
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@@ -49192,14 +49409,14 @@
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             "columnno": 10,
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@@ -49217,14 +49434,14 @@
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             "range": [
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@@ -49242,14 +49459,14 @@
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@@ -49267,14 +49484,14 @@
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@@ -49292,14 +49509,14 @@
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@@ -49317,14 +49534,14 @@
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             "columnno": 0,
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                 "name": "exports.Rotation_EQD_HOR",
                 "type": "Identifier",
                 "value": "Rotation_EQD_HOR",
@@ -49341,14 +49558,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: HOR = horizontal system (x=North, y=West, z=Zenith).\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {FlexibleDateTime} time\n *      The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts HOR to EQD at `time` and for `observer`.\n */",
         "meta": {
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@@ -50301,14 +50518,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
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                 "name": "ConstelRot"
             }
         },
@@ -50323,14 +50540,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100024842",
+                "id": "astnode100024880",
                 "name": "Epoch2000"
             }
         },
@@ -50345,14 +50562,14 @@
         "comment": "/**\n * @brief Reports the constellation that a given celestial point lies within.\n *\n * @property {string} symbol\n *      3-character mnemonic symbol for the constellation, e.g. \"Ori\".\n *\n * @property {string} name\n *      Full name of constellation, e.g. \"Orion\".\n *\n * @property {number} ra1875\n *      Right ascension expressed in B1875 coordinates.\n *\n * @property {number} dec1875\n *      Declination expressed in B1875 coordinates.\n */",
         "meta": {
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             "columnno": 0,
             "code": {
-                "id": "astnode100024844",
+                "id": "astnode100024882",
                 "name": "ConstellationInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -50419,14 +50636,14 @@
         "comment": "",
         "meta": {
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             "columnno": 4,
             "code": {
-                "id": "astnode100024847",
+                "id": "astnode100024885",
                 "name": "ConstellationInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -50451,14 +50668,14 @@
         "comment": "/**\n * @brief Reports the constellation that a given celestial point lies within.\n *\n * @property {string} symbol\n *      3-character mnemonic symbol for the constellation, e.g. \"Ori\".\n *\n * @property {string} name\n *      Full name of constellation, e.g. \"Orion\".\n *\n * @property {number} ra1875\n *      Right ascension expressed in B1875 coordinates.\n *\n * @property {number} dec1875\n *      Declination expressed in B1875 coordinates.\n */",
         "meta": {
             "range": [
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             "code": {
-                "id": "astnode100024844",
+                "id": "astnode100024882",
                 "name": "ConstellationInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -50524,14 +50741,14 @@
         "comment": "",
         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100024856",
+                "id": "astnode100024894",
                 "name": "this.symbol",
                 "type": "Identifier",
                 "value": "symbol",
@@ -50549,14 +50766,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100024862",
+                "id": "astnode100024900",
                 "name": "this.name",
                 "type": "Identifier",
                 "value": "name",
@@ -50574,14 +50791,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100024868",
+                "id": "astnode100024906",
                 "name": "this.ra1875",
                 "type": "Identifier",
                 "value": "ra1875",
@@ -50599,14 +50816,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100024874",
+                "id": "astnode100024912",
                 "name": "this.dec1875",
                 "type": "Identifier",
                 "value": "dec1875",
@@ -50624,14 +50841,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100024880",
+                "id": "astnode100024918",
                 "name": "exports.ConstellationInfo",
                 "type": "Identifier",
                 "value": "ConstellationInfo",
@@ -50648,14 +50865,14 @@
         "comment": "/**\n * @brief Determines the constellation that contains the given point in the sky.\n *\n * Given J2000 equatorial (EQJ) coordinates of a point in the sky,\n * determines the constellation that contains that point.\n *\n * @param {number} ra\n *      The right ascension (RA) of a point in the sky, using the J2000 equatorial system.\n *\n * @param {number} dec\n *      The declination (DEC) of a point in the sky, using the J2000 equatorial system.\n *\n * @returns {ConstellationInfo}\n *      An object that contains the 3-letter abbreviation and full name\n *      of the constellation that contains the given (ra,dec), along with\n *      the converted B1875 (ra,dec) for that point.\n */",
         "meta": {
             "range": [
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+                268588
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100024885",
+                "id": "astnode100024923",
                 "name": "Constellation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -50727,14 +50944,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100024912",
+                "id": "astnode100024950",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -50753,14 +50970,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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+            "lineno": 6546,
             "columnno": 8,
             "code": {
-                "id": "astnode100024921",
+                "id": "astnode100024959",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -50779,14 +50996,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                267521
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100024929",
+                "id": "astnode100024967",
                 "name": "ConstelRot",
                 "type": "CallExpression",
                 "funcscope": "Constellation",
@@ -50805,14 +51022,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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+            "lineno": 6562,
             "columnno": 8,
             "code": {
-                "id": "astnode100024938",
+                "id": "astnode100024976",
                 "name": "Epoch2000",
                 "type": "NewExpression",
                 "funcscope": "Constellation",
@@ -50831,14 +51048,14 @@
         "comment": "",
         "meta": {
             "range": [
-                267117,
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+                267625,
+                267669
             ],
             "filename": "astronomy.js",
-            "lineno": 6552,
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             "columnno": 10,
             "code": {
-                "id": "astnode100024944",
+                "id": "astnode100024982",
                 "name": "sph2000",
                 "type": "NewExpression",
                 "value": ""
@@ -50856,14 +51073,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                267219
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+                267727
             ],
             "filename": "astronomy.js",
-            "lineno": 6553,
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             "columnno": 10,
             "code": {
-                "id": "astnode100024954",
+                "id": "astnode100024992",
                 "name": "vec2000",
                 "type": "CallExpression",
                 "value": ""
@@ -50881,14 +51098,14 @@
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             "code": {
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@@ -51128,14 +51345,14 @@
         "comment": "/**\n * @brief Returns information about a lunar eclipse.\n *\n * Returned by {@link SearchLunarEclipse} or {@link NextLunarEclipse}\n * to report information about a lunar eclipse event.\n * When a lunar eclipse is found, it is classified as penumbral, partial, or total.\n * Penumbral eclipses are difficult to observe, because the moon is only slightly dimmed\n * by the Earth's penumbra; no part of the Moon touches the Earth's umbra.\n * Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra.\n * Total eclipses occur when the entire Moon passes into the Earth's umbra.\n *\n * The `kind` field thus holds one of the strings `\"penumbral\"`, `\"partial\"`,\n * or `\"total\"`, depending on the kind of lunar eclipse found.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, when it is at its peak.\n *\n * Fields `sd_penum`, `sd_partial`, and `sd_total` hold the semi-duration of each phase\n * of the eclipse, which is half of the amount of time the eclipse spends in each\n * phase (expressed in minutes), or 0 if the eclipse never reaches that phase.\n * By converting from minutes to days, and subtracting/adding with `peak`, the caller\n * may determine the date and time of the beginning/end of each eclipse phase.\n *\n * @property {string} kind\n *      The type of lunar eclipse found.\n *\n * @property {AstroTime} peak\n *      The time of the eclipse at its peak.\n *\n * @property {number} sd_penum\n *      The semi-duration of the penumbral phase in minutes.\n *\n * @property {number} sd_partial\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n * @property {number} sd_total\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n */",
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             "columnno": 0,
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@@ -51212,14 +51429,14 @@
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             "columnno": 4,
             "code": {
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@@ -51245,14 +51462,14 @@
         "comment": "/**\n * @brief Returns information about a lunar eclipse.\n *\n * Returned by {@link SearchLunarEclipse} or {@link NextLunarEclipse}\n * to report information about a lunar eclipse event.\n * When a lunar eclipse is found, it is classified as penumbral, partial, or total.\n * Penumbral eclipses are difficult to observe, because the moon is only slightly dimmed\n * by the Earth's penumbra; no part of the Moon touches the Earth's umbra.\n * Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra.\n * Total eclipses occur when the entire Moon passes into the Earth's umbra.\n *\n * The `kind` field thus holds one of the strings `\"penumbral\"`, `\"partial\"`,\n * or `\"total\"`, depending on the kind of lunar eclipse found.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, when it is at its peak.\n *\n * Fields `sd_penum`, `sd_partial`, and `sd_total` hold the semi-duration of each phase\n * of the eclipse, which is half of the amount of time the eclipse spends in each\n * phase (expressed in minutes), or 0 if the eclipse never reaches that phase.\n * By converting from minutes to days, and subtracting/adding with `peak`, the caller\n * may determine the date and time of the beginning/end of each eclipse phase.\n *\n * @property {string} kind\n *      The type of lunar eclipse found.\n *\n * @property {AstroTime} peak\n *      The time of the eclipse at its peak.\n *\n * @property {number} sd_penum\n *      The semi-duration of the penumbral phase in minutes.\n *\n * @property {number} sd_partial\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n * @property {number} sd_total\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n */",
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@@ -51477,14 +51694,14 @@
         "comment": "/**\n * @ignore\n *\n * @brief Represents the relative alignment of the Earth and another body, and their respective shadows.\n *\n * This is an internal data structure used to assist calculation of\n * lunar eclipses, solar eclipses, and transits of Mercury and Venus.\n *\n * Definitions:\n *\n * casting body = A body that casts a shadow of interest, possibly striking another body.\n *\n * receiving body = A body on which the shadow of another body might land.\n *\n * shadow axis = The line passing through the center of the Sun and the center of the casting body.\n *\n * shadow plane = The plane passing through the center of a receiving body,\n * and perpendicular to the shadow axis.\n *\n * @property {AstroTime} time\n *      The time associated with the shadow calculation.\n *\n * @property {number} u\n *      The distance [au] between the center of the casting body and the shadow plane.\n *\n * @property {number} r\n *      The distance [km] between center of receiving body and the shadow axis.\n *\n * @property {number} k\n *      The umbra radius [km] at the shadow plane.\n *\n * @property {number} p\n *      The penumbra radius [km] at the shadow plane.\n *\n * @property {Vector} target\n *      The location in space where we are interested in determining how close a shadow falls.\n *      For example, when calculating lunar eclipses, `target` would be the center of the Moon\n *      expressed in geocentric coordinates. Then we can evaluate how far the center of the Earth's\n *      shadow cone approaches the center of the Moon.\n *      The vector components are expressed in [au].\n *\n * @property {Vector} dir\n *      The direction in space that the shadow points away from the center of a shadow-casting body.\n *      This vector lies on the shadow axis and points away from the Sun.\n *      In other words: the direction light from the Sun would be traveling,\n *      except that the center of a body (Earth, Moon, Mercury, or Venus) is blocking it.\n *      The distance units do not matter, because the vector will be normalized.\n */",
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@@ -51617,14 +51834,14 @@
         "comment": "/**\n * @ignore\n *\n * @brief Represents the relative alignment of the Earth and another body, and their respective shadows.\n *\n * This is an internal data structure used to assist calculation of\n * lunar eclipses, solar eclipses, and transits of Mercury and Venus.\n *\n * Definitions:\n *\n * casting body = A body that casts a shadow of interest, possibly striking another body.\n *\n * receiving body = A body on which the shadow of another body might land.\n *\n * shadow axis = The line passing through the center of the Sun and the center of the casting body.\n *\n * shadow plane = The plane passing through the center of a receiving body,\n * and perpendicular to the shadow axis.\n *\n * @property {AstroTime} time\n *      The time associated with the shadow calculation.\n *\n * @property {number} u\n *      The distance [au] between the center of the casting body and the shadow plane.\n *\n * @property {number} r\n *      The distance [km] between center of receiving body and the shadow axis.\n *\n * @property {number} k\n *      The umbra radius [km] at the shadow plane.\n *\n * @property {number} p\n *      The penumbra radius [km] at the shadow plane.\n *\n * @property {Vector} target\n *      The location in space where we are interested in determining how close a shadow falls.\n *      For example, when calculating lunar eclipses, `target` would be the center of the Moon\n *      expressed in geocentric coordinates. Then we can evaluate how far the center of the Earth's\n *      shadow cone approaches the center of the Moon.\n *      The vector components are expressed in [au].\n *\n * @property {Vector} dir\n *      The direction in space that the shadow points away from the center of a shadow-casting body.\n *      This vector lies on the shadow axis and points away from the Sun.\n *      In other words: the direction light from the Sun would be traveling,\n *      except that the center of a body (Earth, Moon, Mercury, or Venus) is blocking it.\n *      The distance units do not matter, because the vector will be normalized.\n */",
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@@ -51746,14 +51963,14 @@
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@@ -51934,14 +52151,14 @@
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         "comment": "/**\n    @brief Reports the time and geographic location of the peak of a solar eclipse.\n\n    Returned by {@link SearchGlobalSolarEclipse} or {@link NextGlobalSolarEclipse}\n    to report information about a solar eclipse event.\n\n    Field `peak` holds the date and time of the peak of the eclipse, defined as\n    the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.\n\n    The eclipse is classified as partial, annular, or total, depending on the\n    maximum amount of the Sun's disc obscured, as seen at the peak location\n    on the surface of the Earth.\n\n    The `kind` field thus holds one of the strings `\"partial\"`, `\"annular\"`, or `\"total\"`.\n    A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.\n    An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface\n    to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.\n    A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth\n    observes either a total or annular eclipse.\n\n    If `kind` is `\"total\"` or `\"annular\"`, the `latitude` and `longitude`\n    fields give the geographic coordinates of the center of the Moon's shadow projected\n    onto the daytime side of the Earth at the instant of the eclipse's peak.\n    If `kind` has any other value, `latitude` and `longitude` are undefined and should\n    not be used.\n\n    @property {string} kind\n        One of the following string values: `\"partial\"`, `\"annular\"`, `\"total\"`.\n\n    @property {AstroTime} peak\n        The date and time of the peak of the eclipse, defined as the instant\n        when the axis of the Moon's shadow cone passes closest to the Earth's center.\n\n    @property {number} distance\n        The distance in kilometers between the axis of the Moon's shadow cone\n        and the center of the Earth at the time indicated by `peak`.\n\n    @property {number | undefined} latitude\n        If `kind` holds `\"total\"`, the geographic latitude in degrees\n        where the center of the Moon's shadow falls on the Earth at the\n        time indicated by `peak`; otherwise, `latitude` holds `undefined`.\n\n    @property {number | undefined} longitude\n        If `kind` holds `\"total\"`, the geographic longitude in degrees\n        where the center of the Moon's shadow falls on the Earth at the\n        time indicated by `peak`; otherwise, `longitude` holds `undefined`.\n*/",
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                 "name": "o.x",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55589,14 +55806,14 @@
         "comment": "",
         "meta": {
             "range": [
-                288017,
-                288039
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+                288547
             ],
             "filename": "astronomy.js",
-            "lineno": 6996,
+            "lineno": 7009,
             "columnno": 8,
             "code": {
-                "id": "astnode100026647",
+                "id": "astnode100026685",
                 "name": "o.y",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55615,14 +55832,14 @@
         "comment": "",
         "meta": {
             "range": [
-                288049,
-                288071
+                288557,
+                288579
             ],
             "filename": "astronomy.js",
-            "lineno": 6997,
+            "lineno": 7010,
             "columnno": 8,
             "code": {
-                "id": "astnode100026657",
+                "id": "astnode100026695",
                 "name": "o.z",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55641,14 +55858,14 @@
         "comment": "",
         "meta": {
             "range": [
-                288180,
-                288250
+                288688,
+                288758
             ],
             "filename": "astronomy.js",
-            "lineno": 6999,
+            "lineno": 7012,
             "columnno": 14,
             "code": {
-                "id": "astnode100026667",
+                "id": "astnode100026705",
                 "name": "surface",
                 "type": "CallExpression",
                 "value": ""
@@ -55666,14 +55883,14 @@
         "comment": "",
         "meta": {
             "range": [
-                288587,
-                288625
+                289095,
+                289133
             ],
             "filename": "astronomy.js",
-            "lineno": 7005,
+            "lineno": 7018,
             "columnno": 8,
             "code": {
-                "id": "astnode100026700",
+                "id": "astnode100026738",
                 "name": "kind",
                 "type": "CallExpression",
                 "funcscope": "GeoidIntersect",
@@ -55692,14 +55909,14 @@
         "comment": "/**\n * @brief Searches for the next lunar eclipse in a series.\n *\n * After using {@link SearchLunarEclipse} to find the first lunar eclipse\n * in a series, you can call this function to find the next consecutive lunar eclipse.\n * Pass in the `center` value from the {@link LunarEclipseInfo} returned by the\n * previous call to `SearchLunarEclipse` or `NextLunarEclipse`\n * to find the next lunar eclipse.\n *\n * @param {AstroTime} prevEclipseTime\n *      A date and time near a full moon. Lunar eclipse search will start at the next full moon.\n *\n * @returns {LunarEclipseInfo}\n */",
         "meta": {
             "range": [
-                289298,
-                289437
+                289806,
+                289945
             ],
             "filename": "astronomy.js",
-            "lineno": 7023,
+            "lineno": 7036,
             "columnno": 0,
             "code": {
-                "id": "astnode100026715",
+                "id": "astnode100026753",
                 "name": "NextLunarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -55747,14 +55964,14 @@
         "comment": "",
         "meta": {
             "range": [
-                289353,
-                289392
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+                289900
             ],
             "filename": "astronomy.js",
-            "lineno": 7024,
+            "lineno": 7037,
             "columnno": 10,
             "code": {
-                "id": "astnode100026720",
+                "id": "astnode100026758",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -55772,14 +55989,14 @@
         "comment": "",
         "meta": {
             "range": [
-                289438,
-                289481
+                289946,
+                289989
             ],
             "filename": "astronomy.js",
-            "lineno": 7027,
+            "lineno": 7040,
             "columnno": 0,
             "code": {
-                "id": "astnode100026732",
+                "id": "astnode100026770",
                 "name": "exports.NextLunarEclipse",
                 "type": "Identifier",
                 "value": "NextLunarEclipse",
@@ -55796,14 +56013,14 @@
         "comment": "/**\n * @brief Searches for a solar eclipse visible anywhere on the Earth's surface.\n *\n * This function finds the first solar eclipse that occurs after `startTime`.\n * A solar eclipse may be partial, annular, or total.\n * See {@link GlobalSolarEclipseInfo} for more information.\n * To find a series of solar eclipses, call this function once,\n * then keep calling {@link NextGlobalSolarEclipse} as many times as desired,\n * passing in the `peak` value returned from the previous call.\n *\n * @param {AstroTime} startTime\n *      The date and time for starting the search for a solar eclipse.\n *\n * @returns {GlobalSolarEclipseInfo}\n */",
         "meta": {
             "range": [
-                290118,
-                291735
+                290626,
+                292243
             ],
             "filename": "astronomy.js",
-            "lineno": 7043,
+            "lineno": 7056,
             "columnno": 0,
             "code": {
-                "id": "astnode100026737",
+                "id": "astnode100026775",
                 "name": "SearchGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -55856,14 +56073,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290175,
-                290194
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+                290702
             ],
             "filename": "astronomy.js",
-            "lineno": 7044,
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             "columnno": 10,
             "code": {
-                "id": "astnode100026742",
+                "id": "astnode100026780",
                 "name": "PruneLatitude",
                 "type": "Literal",
                 "value": 1.8
@@ -55881,14 +56098,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290370,
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+                290896
             ],
             "filename": "astronomy.js",
-            "lineno": 7046,
+            "lineno": 7059,
             "columnno": 8,
             "code": {
-                "id": "astnode100026746",
+                "id": "astnode100026784",
                 "name": "nmtime",
                 "type": "Identifier",
                 "value": "startTime"
@@ -55906,14 +56123,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290398,
-                290405
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+                290913
             ],
             "filename": "astronomy.js",
-            "lineno": 7047,
+            "lineno": 7060,
             "columnno": 8,
             "code": {
-                "id": "astnode100026750",
+                "id": "astnode100026788",
                 "name": "nmcount"
             }
         },
@@ -55929,14 +56146,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290416,
-                290427
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+                290935
             ],
             "filename": "astronomy.js",
-            "lineno": 7048,
+            "lineno": 7061,
             "columnno": 9,
             "code": {
-                "id": "astnode100026753",
+                "id": "astnode100026791",
                 "name": "nmcount",
                 "type": "Literal",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -55955,14 +56172,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290540,
-                290584
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+                291092
             ],
             "filename": "astronomy.js",
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             "columnno": 14,
             "code": {
-                "id": "astnode100026763",
+                "id": "astnode100026801",
                 "name": "newmoon",
                 "type": "CallExpression",
                 "value": ""
@@ -55980,14 +56197,14 @@
         "comment": "",
         "meta": {
             "range": [
-                290767,
-                290815
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+                291323
             ],
             "filename": "astronomy.js",
-            "lineno": 7054,
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             "columnno": 14,
             "code": {
-                "id": "astnode100026776",
+                "id": "astnode100026814",
                 "name": "eclip_lat",
                 "type": "CallExpression",
                 "value": ""
@@ -56005,14 +56222,14 @@
         "comment": "",
         "meta": {
             "range": [
-                291055,
-                291087
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+                291595
             ],
             "filename": "astronomy.js",
-            "lineno": 7058,
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             "columnno": 18,
             "code": {
-                "id": "astnode100026791",
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                 "name": "shadow",
                 "type": "CallExpression",
                 "value": ""
@@ -56030,14 +56247,14 @@
         "comment": "",
         "meta": {
             "range": [
-                291502,
-                291532
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+                292040
             ],
             "filename": "astronomy.js",
-            "lineno": 7066,
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             "columnno": 8,
             "code": {
-                "id": "astnode100026812",
+                "id": "astnode100026850",
                 "name": "nmtime",
                 "type": "CallExpression",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -56056,14 +56273,14 @@
         "comment": "",
         "meta": {
             "range": [
-                291736,
-                291795
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+                292303
             ],
             "filename": "astronomy.js",
-            "lineno": 7072,
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             "columnno": 0,
             "code": {
-                "id": "astnode100026822",
+                "id": "astnode100026860",
                 "name": "exports.SearchGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "SearchGlobalSolarEclipse",
@@ -56080,14 +56297,14 @@
         "comment": "/**\n * @brief Searches for the next global solar eclipse in a series.\n *\n * After using {@link SearchGlobalSolarEclipse} to find the first solar eclipse\n * in a series, you can call this function to find the next consecutive solar eclipse.\n * Pass in the `peak` value from the {@link GlobalSolarEclipseInfo} returned by the\n * previous call to `SearchGlobalSolarEclipse` or `NextGlobalSolarEclipse`\n * to find the next solar eclipse.\n *\n * @param {AstroTime} prevEclipseTime\n *      A date and time near a new moon. Solar eclipse search will start at the next new moon.\n *\n * @returns {GlobalSolarEclipseInfo}\n */",
         "meta": {
             "range": [
-                292411,
-                292564
+                292919,
+                293072
             ],
             "filename": "astronomy.js",
-            "lineno": 7087,
+            "lineno": 7100,
             "columnno": 0,
             "code": {
-                "id": "astnode100026827",
+                "id": "astnode100026865",
                 "name": "NextGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -56135,14 +56352,14 @@
         "comment": "",
         "meta": {
             "range": [
-                292472,
-                292513
+                292980,
+                293021
             ],
             "filename": "astronomy.js",
-            "lineno": 7088,
+            "lineno": 7101,
             "columnno": 10,
             "code": {
-                "id": "astnode100026832",
+                "id": "astnode100026870",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -56160,14 +56377,14 @@
         "comment": "",
         "meta": {
             "range": [
-                292565,
-                292620
+                293073,
+                293128
             ],
             "filename": "astronomy.js",
-            "lineno": 7091,
+            "lineno": 7104,
             "columnno": 0,
             "code": {
-                "id": "astnode100026844",
+                "id": "astnode100026882",
                 "name": "exports.NextGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "NextGlobalSolarEclipse",
@@ -56184,14 +56401,14 @@
         "comment": "/**\n * @brief Holds a time and the observed altitude of the Sun at that time.\n *\n * When reporting a solar eclipse observed at a specific location on the Earth\n * (a \"local\" solar eclipse), a series of events occur. In addition\n * to the time of each event, it is important to know the altitude of the Sun,\n * because each event may be invisible to the observer if the Sun is below\n * the horizon (i.e. it at night).\n *\n * If `altitude` is negative, the event is theoretical only; it would be\n * visible if the Earth were transparent, but the observer cannot actually see it.\n * If `altitude` is positive but less than a few degrees, visibility will be impaired by\n * atmospheric interference (sunrise or sunset conditions).\n *\n * @property {AstroTime} time\n *      The date and time of the event.\n *\n * @property {number} altitude\n *      The angular altitude of the center of the Sun above/below the horizon, at `time`,\n *      corrected for atmospheric refraction and expressed in degrees.\n */",
         "meta": {
             "range": [
-                293619,
-                293741
+                294127,
+                294249
             ],
             "filename": "astronomy.js",
-            "lineno": 7113,
+            "lineno": 7126,
             "columnno": 0,
             "code": {
-                "id": "astnode100026849",
+                "id": "astnode100026887",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56238,14 +56455,14 @@
         "comment": "",
         "meta": {
             "range": [
-                293644,
-                293739
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+                294247
             ],
             "filename": "astronomy.js",
-            "lineno": 7114,
+            "lineno": 7127,
             "columnno": 4,
             "code": {
-                "id": "astnode100026852",
+                "id": "astnode100026890",
                 "name": "EclipseEvent",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -56268,14 +56485,14 @@
         "comment": "/**\n * @brief Holds a time and the observed altitude of the Sun at that time.\n *\n * When reporting a solar eclipse observed at a specific location on the Earth\n * (a \"local\" solar eclipse), a series of events occur. In addition\n * to the time of each event, it is important to know the altitude of the Sun,\n * because each event may be invisible to the observer if the Sun is below\n * the horizon (i.e. it at night).\n *\n * If `altitude` is negative, the event is theoretical only; it would be\n * visible if the Earth were transparent, but the observer cannot actually see it.\n * If `altitude` is positive but less than a few degrees, visibility will be impaired by\n * atmospheric interference (sunrise or sunset conditions).\n *\n * @property {AstroTime} time\n *      The date and time of the event.\n *\n * @property {number} altitude\n *      The angular altitude of the center of the Sun above/below the horizon, at `time`,\n *      corrected for atmospheric refraction and expressed in degrees.\n */",
         "meta": {
             "range": [
-                293619,
-                293741
+                294127,
+                294249
             ],
             "filename": "astronomy.js",
-            "lineno": 7113,
+            "lineno": 7126,
             "columnno": 0,
             "code": {
-                "id": "astnode100026849",
+                "id": "astnode100026887",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56321,14 +56538,14 @@
         "comment": "",
         "meta": {
             "range": [
-                293682,
-                293698
+                294190,
+                294206
             ],
             "filename": "astronomy.js",
-            "lineno": 7115,
+            "lineno": 7128,
             "columnno": 8,
             "code": {
-                "id": "astnode100026859",
+                "id": "astnode100026897",
                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -56346,14 +56563,14 @@
         "comment": "",
         "meta": {
             "range": [
-                293708,
-                293732
+                294216,
+                294240
             ],
             "filename": "astronomy.js",
-            "lineno": 7116,
+            "lineno": 7129,
             "columnno": 8,
             "code": {
-                "id": "astnode100026865",
+                "id": "astnode100026903",
                 "name": "this.altitude",
                 "type": "Identifier",
                 "value": "altitude",
@@ -56371,14 +56588,14 @@
         "comment": "",
         "meta": {
             "range": [
-                293742,
-                293777
+                294250,
+                294285
             ],
             "filename": "astronomy.js",
-            "lineno": 7119,
+            "lineno": 7132,
             "columnno": 0,
             "code": {
-                "id": "astnode100026871",
+                "id": "astnode100026909",
                 "name": "exports.EclipseEvent",
                 "type": "Identifier",
                 "value": "EclipseEvent",
@@ -56395,14 +56612,14 @@
         "comment": "/**\n * @brief Information about a solar eclipse as seen by an observer at a given time and geographic location.\n *\n * Returned by {@link SearchLocalSolarEclipse} or {@link NextLocalSolarEclipse}\n * to report information about a solar eclipse as seen at a given geographic location.\n *\n * When a solar eclipse is found, it is classified by setting `kind`\n * to `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A partial solar eclipse is when the Moon does not line up directly enough with the Sun\n * to completely block the Sun's light from reaching the observer.\n * An annular eclipse occurs when the Moon's disc is completely visible against the Sun\n * but the Moon is too far away to completely block the Sun's light; this leaves the\n * Sun with a ring-like appearance.\n * A total eclipse occurs when the Moon is close enough to the Earth and aligned with the\n * Sun just right to completely block all sunlight from reaching the observer.\n *\n * There are 5 \"event\" fields, each of which contains a time and a solar altitude.\n * Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.\n * The fields `partial_begin` and `partial_end` are always set, and indicate when\n * the eclipse begins/ends. If the eclipse reaches totality or becomes annular,\n * `total_begin` and `total_end` indicate when the total/annular phase begins/ends.\n * When an event field is valid, the caller must also check its `altitude` field to\n * see whether the Sun is above the horizon at the time indicated by the `time` field.\n * See {@link EclipseEvent} for more information.\n *\n * @property {string} kind\n *      The type of solar eclipse found: `\"partial\"`, `\"annular\"`, or `\"total\"`.\n *\n * @property {EclipseEvent} partial_begin\n *      The time and Sun altitude at the beginning of the eclipse.\n *\n * @property {EclipseEvent | undefined} total_begin\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise undefined.\n *\n * @property {EclipseEvent} peak\n *      The time and Sun altitude when the eclipse reaches its peak.\n *\n * @property {EclipseEvent | undefined} total_end\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise undefined.\n *\n * @property {EclipseEvent} partial_end\n *      The time and Sun altitude at the end of the eclipse.\n */",
         "meta": {
             "range": [
-                296163,
-                296494
+                296671,
+                297002
             ],
             "filename": "astronomy.js",
-            "lineno": 7163,
+            "lineno": 7176,
             "columnno": 0,
             "code": {
-                "id": "astnode100026876",
+                "id": "astnode100026914",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56491,14 +56708,14 @@
         "comment": "",
         "meta": {
             "range": [
-                296197,
-                296492
+                296705,
+                297000
             ],
             "filename": "astronomy.js",
-            "lineno": 7164,
+            "lineno": 7177,
             "columnno": 4,
             "code": {
-                "id": "astnode100026879",
+                "id": "astnode100026917",
                 "name": "LocalSolarEclipseInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -56525,14 +56742,14 @@
         "comment": "/**\n * @brief Information about a solar eclipse as seen by an observer at a given time and geographic location.\n *\n * Returned by {@link SearchLocalSolarEclipse} or {@link NextLocalSolarEclipse}\n * to report information about a solar eclipse as seen at a given geographic location.\n *\n * When a solar eclipse is found, it is classified by setting `kind`\n * to `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A partial solar eclipse is when the Moon does not line up directly enough with the Sun\n * to completely block the Sun's light from reaching the observer.\n * An annular eclipse occurs when the Moon's disc is completely visible against the Sun\n * but the Moon is too far away to completely block the Sun's light; this leaves the\n * Sun with a ring-like appearance.\n * A total eclipse occurs when the Moon is close enough to the Earth and aligned with the\n * Sun just right to completely block all sunlight from reaching the observer.\n *\n * There are 5 \"event\" fields, each of which contains a time and a solar altitude.\n * Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.\n * The fields `partial_begin` and `partial_end` are always set, and indicate when\n * the eclipse begins/ends. If the eclipse reaches totality or becomes annular,\n * `total_begin` and `total_end` indicate when the total/annular phase begins/ends.\n * When an event field is valid, the caller must also check its `altitude` field to\n * see whether the Sun is above the horizon at the time indicated by the `time` field.\n * See {@link EclipseEvent} for more information.\n *\n * @property {string} kind\n *      The type of solar eclipse found: `\"partial\"`, `\"annular\"`, or `\"total\"`.\n *\n * @property {EclipseEvent} partial_begin\n *      The time and Sun altitude at the beginning of the eclipse.\n *\n * @property {EclipseEvent | undefined} total_begin\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise undefined.\n *\n * @property {EclipseEvent} peak\n *      The time and Sun altitude when the eclipse reaches its peak.\n *\n * @property {EclipseEvent | undefined} total_end\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise undefined.\n *\n * @property {EclipseEvent} partial_end\n *      The time and Sun altitude at the end of the eclipse.\n */",
         "meta": {
             "range": [
-                296163,
-                296494
+                296671,
+                297002
             ],
             "filename": "astronomy.js",
-            "lineno": 7163,
+            "lineno": 7176,
             "columnno": 0,
             "code": {
-                "id": "astnode100026876",
+                "id": "astnode100026914",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56620,14 +56837,14 @@
         "comment": "",
         "meta": {
             "range": [
-                296283,
-                296299
+                296791,
+                296807
             ],
             "filename": "astronomy.js",
-            "lineno": 7165,
+            "lineno": 7178,
             "columnno": 8,
             "code": {
-                "id": "astnode100026890",
+                "id": "astnode100026928",
                 "name": "this.kind",
                 "type": "Identifier",
                 "value": "kind",
@@ -56645,14 +56862,14 @@
         "comment": "",
         "meta": {
             "range": [
-                296309,
-                296343
+                296817,
+                296851
             ],
             "filename": "astronomy.js",
-            "lineno": 7166,
+            "lineno": 7179,
             "columnno": 8,
             "code": {
-                "id": "astnode100026896",
+                "id": "astnode100026934",
                 "name": "this.partial_begin",
                 "type": "Identifier",
                 "value": "partial_begin",
@@ -56670,14 +56887,14 @@
         "comment": "",
         "meta": {
             "range": [
-                296353,
-                296383
+                296861,
+                296891
             ],
             "filename": "astronomy.js",
-            "lineno": 7167,
+            "lineno": 7180,
             "columnno": 8,
             "code": {
-                "id": "astnode100026902",
+                "id": "astnode100026940",
                 "name": "this.total_begin",
                 "type": "Identifier",
                 "value": "total_begin",
@@ -56695,14 +56912,14 @@
         "comment": "",
         "meta": {
             "range": [
-                296393,
-                296409
+                296901,
+                296917
             ],
             "filename": "astronomy.js",
-            "lineno": 7168,
+            "lineno": 7181,
             "columnno": 8,
             "code": {
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         "comment": "/**\n * @brief Information about a transit of Mercury or Venus, as seen from the Earth.\n *\n * Returned by {@link SearchTransit} or {@link NextTransit} to report\n * information about a transit of Mercury or Venus.\n * A transit is when Mercury or Venus passes between the Sun and Earth so that\n * the other planet is seen in silhouette against the Sun.\n *\n * The calculations are performed from the point of view of a geocentric observer.\n *\n * @property {AstroTime} start\n *      The date and time at the beginning of the transit.\n *      This is the moment the planet first becomes visible against the Sun in its background.\n *\n * @property {AstroTime} peak\n *      When the planet is most aligned with the Sun, as seen from the Earth.\n *\n * @property {AstroTime} finish\n *      The date and time at the end of the transit.\n *      This is the moment the planet is last seen against the Sun in its background.\n *\n * @property {number} separation\n *      The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.\n *      This angle pertains to the time stored in `peak`.\n */",
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             "columnno": 0,
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                 "paramnames": [
@@ -57993,14 +58210,14 @@
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             "columnno": 4,
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                 "name": "TransitInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -58025,14 +58242,14 @@
         "comment": "/**\n * @brief Information about a transit of Mercury or Venus, as seen from the Earth.\n *\n * Returned by {@link SearchTransit} or {@link NextTransit} to report\n * information about a transit of Mercury or Venus.\n * A transit is when Mercury or Venus passes between the Sun and Earth so that\n * the other planet is seen in silhouette against the Sun.\n *\n * The calculations are performed from the point of view of a geocentric observer.\n *\n * @property {AstroTime} start\n *      The date and time at the beginning of the transit.\n *      This is the moment the planet first becomes visible against the Sun in its background.\n *\n * @property {AstroTime} peak\n *      When the planet is most aligned with the Sun, as seen from the Earth.\n *\n * @property {AstroTime} finish\n *      The date and time at the end of the transit.\n *      This is the moment the planet is last seen against the Sun in its background.\n *\n * @property {number} separation\n *      The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.\n *      This angle pertains to the time stored in `peak`.\n */",
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             "columnno": 0,
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                 "name": "TransitInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -58098,14 +58315,14 @@
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             "columnno": 8,
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                 "value": "start",
@@ -58123,14 +58340,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "this.peak",
                 "type": "Identifier",
                 "value": "peak",
@@ -58148,14 +58365,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "this.finish",
                 "type": "Identifier",
                 "value": "finish",
@@ -58173,14 +58390,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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                 "name": "this.separation",
                 "type": "Identifier",
                 "value": "separation",
@@ -58198,14 +58415,14 @@
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             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100027378",
+                "id": "astnode100027416",
                 "name": "exports.TransitInfo",
                 "type": "Identifier",
                 "value": "TransitInfo",
@@ -58222,14 +58439,14 @@
         "comment": "",
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             "columnno": 0,
             "code": {
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                 "name": "PlanetShadowBoundary",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58254,14 +58471,14 @@
         "comment": "",
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             "columnno": 0,
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                 "name": "PlanetTransitBoundary",
                 "type": "FunctionDeclaration",
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@@ -58313,14 +58530,14 @@
         "comment": "",
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                 "name": "tx",
                 "type": "CallExpression",
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@@ -58338,14 +58555,14 @@
         "comment": "/**\n * @brief Searches for the first transit of Mercury or Venus after a given date.\n *\n * Finds the first transit of Mercury or Venus after a specified date.\n * A transit is when an inferior planet passes between the Sun and the Earth\n * so that the silhouette of the planet is visible against the Sun in the background.\n * To continue the search, pass the `finish` time in the returned structure to\n * {@link NextTransit}.\n *\n * @param {Body} body\n *      The planet whose transit is to be found. Must be `\"Mercury\"` or `\"Venus\"`.\n *\n * @param {AstroTime} startTime\n *      The date and time for starting the search for a transit.\n *\n * @returns {TransitInfo}\n */",
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             "columnno": 0,
             "code": {
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+                "id": "astnode100027476",
                 "name": "SearchTransit",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58414,14 +58631,14 @@
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             "columnno": 10,
             "code": {
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                 "name": "threshold_angle",
                 "type": "Literal",
                 "value": 0.4
@@ -58439,14 +58656,14 @@
         "comment": "",
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             "columnno": 10,
             "code": {
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                 "name": "dt_days",
                 "type": "Literal",
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@@ -58464,14 +58681,14 @@
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             "columnno": 8,
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                 "name": "planet_radius_km"
             }
         },
@@ -58487,14 +58704,14 @@
         "comment": "",
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                 "name": "planet_radius_km",
                 "type": "Literal",
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@@ -58513,14 +58730,14 @@
         "comment": "",
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                 "name": "planet_radius_km",
                 "type": "Literal",
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@@ -58539,14 +58756,14 @@
         "comment": "",
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             "columnno": 8,
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                 "name": "search_time",
                 "type": "Identifier",
                 "value": "startTime"
@@ -58564,14 +58781,14 @@
         "comment": "",
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@@ -58589,14 +58806,14 @@
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@@ -58614,14 +58831,14 @@
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@@ -58664,14 +58881,14 @@
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@@ -58689,14 +58906,14 @@
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@@ -58714,14 +58931,14 @@
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@@ -58764,14 +58981,14 @@
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                 "name": "exports.SearchTransit",
                 "type": "Identifier",
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@@ -58814,14 +59031,14 @@
         "comment": "/**\n * @brief Searches for the next transit of Mercury or Venus in a series.\n *\n * After calling {@link SearchTransit} to find a transit of Mercury or Venus,\n * this function finds the next transit after that.\n * Keep calling this function as many times as you want to keep finding more transits.\n *\n * @param {Body} body\n *      The planet whose transit is to be found. Must be `\"Mercury\"` or `\"Venus\"`.\n *\n * @param {AstroTime} prevTransitTime\n *      A date and time near the previous transit.\n *\n * @returns {TransitInfo}\n */",
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             "columnno": 0,
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@@ -58879,14 +59096,14 @@
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@@ -58904,14 +59121,14 @@
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             "columnno": 0,
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