From 296f23af768318103cf1dcfd844ca4f2bda9fb3a Mon Sep 17 00:00:00 2001
From: Don Cross <cosinekitty@gmail.com>
Date: Fri, 5 Nov 2021 16:02:14 -0400
Subject: [PATCH] Libration functions now calculate apparent angular diameter
 of the Moon.

All 4 languages have added a `diam_deg` field to the
structure returned by the Libration function.
It is the apparent angular diameter of the Moon as
seen from the center of the Earth, expressed in degrees.
---
 README.md                                  |     2 +-
 demo/browser/astronomy.browser.js          |    13 +-
 demo/nodejs/astronomy.js                   |    13 +-
 demo/nodejs/calendar/astronomy.ts          |    13 +-
 demo/python/astronomy.py                   |    13 +-
 generate/ctest.c                           |    12 +-
 generate/dotnet/csharp_test/csharp_test.cs |     8 +-
 generate/template/astronomy.c              |     6 +-
 generate/template/astronomy.cs             |     9 +-
 generate/template/astronomy.py             |    13 +-
 generate/template/astronomy.ts             |    13 +-
 generate/test.js                           |     8 +-
 generate/test.py                           |    10 +-
 source/c/README.md                         |     3 +-
 source/c/astronomy.c                       |     6 +-
 source/c/astronomy.h                       |     1 +
 source/csharp/README.md                    |     6 +-
 source/csharp/astronomy.cs                 |     9 +-
 source/js/README.md                        |     6 +-
 source/js/astronomy.browser.js             |    13 +-
 source/js/astronomy.browser.min.js         |   132 +-
 source/js/astronomy.d.ts                   |    10 +-
 source/js/astronomy.js                     |    13 +-
 source/js/astronomy.min.js                 |     4 +-
 source/js/astronomy.ts                     |    13 +-
 source/js/esm/astronomy.js                 |    13 +-
 source/python/README.md                    |     6 +-
 source/python/astronomy.py                 |    13 +-
 website/src/assets/documentation.json      | 14124 ++++++++++---------
 29 files changed, 7340 insertions(+), 7165 deletions(-)

diff --git a/README.md b/README.md
index 1f96ec90..cd9bc1b0 100644
--- a/README.md
+++ b/README.md
@@ -151,7 +151,7 @@ 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-->98453 bytes.)
+- Minified JavaScript code less than 100K. (The current size is <!--MINIFIED_SIZE-->98530 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 5160d867..f1acb1dd 100644
--- a/demo/browser/astronomy.browser.js
+++ b/demo/browser/astronomy.browser.js
@@ -1584,14 +1584,17 @@ function CalcMoon(time) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 class LibrationInfo {
-    constructor(elat, elon, mlat, mlon, dist_km) {
+    constructor(elat, elon, mlat, mlon, dist_km, diam_deg) {
         this.elat = elat;
         this.elon = elon;
         this.mlat = mlat;
         this.mlon = mlon;
         this.dist_km = dist_km;
+        this.diam_deg = diam_deg;
     }
 }
 exports.LibrationInfo = LibrationInfo;
@@ -1608,8 +1611,9 @@ exports.LibrationInfo = LibrationInfo;
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1693,7 +1697,8 @@ function Libration(date) {
         +0.00011 * Math.sin(2 * mdash - 2 * m - 2 * d));
     const ldash2 = -tau + (rho * Math.cos(a) + sigma * Math.sin(a)) * Math.tan(bdash);
     const bdash2 = sigma * Math.cos(a) - rho * Math.sin(a);
-    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * exports.RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km * dist_km - MOON_MEAN_RADIUS_KM * MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 exports.Libration = Libration;
 function precession(pos, time, dir) {
diff --git a/demo/nodejs/astronomy.js b/demo/nodejs/astronomy.js
index 118b05f9..22e9dbb9 100644
--- a/demo/nodejs/astronomy.js
+++ b/demo/nodejs/astronomy.js
@@ -1583,14 +1583,17 @@ function CalcMoon(time) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 class LibrationInfo {
-    constructor(elat, elon, mlat, mlon, dist_km) {
+    constructor(elat, elon, mlat, mlon, dist_km, diam_deg) {
         this.elat = elat;
         this.elon = elon;
         this.mlat = mlat;
         this.mlon = mlon;
         this.dist_km = dist_km;
+        this.diam_deg = diam_deg;
     }
 }
 exports.LibrationInfo = LibrationInfo;
@@ -1607,8 +1610,9 @@ exports.LibrationInfo = LibrationInfo;
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1692,7 +1696,8 @@ function Libration(date) {
         +0.00011 * Math.sin(2 * mdash - 2 * m - 2 * d));
     const ldash2 = -tau + (rho * Math.cos(a) + sigma * Math.sin(a)) * Math.tan(bdash);
     const bdash2 = sigma * Math.cos(a) - rho * Math.sin(a);
-    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * exports.RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km * dist_km - MOON_MEAN_RADIUS_KM * MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 exports.Libration = Libration;
 function precession(pos, time, dir) {
diff --git a/demo/nodejs/calendar/astronomy.ts b/demo/nodejs/calendar/astronomy.ts
index 0f61a5f3..055425a1 100644
--- a/demo/nodejs/calendar/astronomy.ts
+++ b/demo/nodejs/calendar/astronomy.ts
@@ -1688,6 +1688,8 @@ function CalcMoon(time: AstroTime) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 export class LibrationInfo {
     constructor(
@@ -1695,7 +1697,8 @@ export class LibrationInfo {
         public elon: number,
         public mlat: number,
         public mlon: number,
-        public dist_km: number
+        public dist_km: number,
+        public diam_deg: number
     ) {}
 }
 
@@ -1712,8 +1715,9 @@ export class LibrationInfo {
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1816,7 +1820,8 @@ export function Libration(date: FlexibleDateTime): LibrationInfo {
 
     const ldash2 = -tau + (rho*Math.cos(a) + sigma*Math.sin(a))*Math.tan(bdash);
     const bdash2 = sigma*Math.cos(a) - rho*Math.sin(a);
-    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km*dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 
 function precession(pos: ArrayVector, time: AstroTime, dir: PrecessDirection): ArrayVector {
diff --git a/demo/python/astronomy.py b/demo/python/astronomy.py
index a9dfc8e9..bccba31f 100644
--- a/demo/python/astronomy.py
+++ b/demo/python/astronomy.py
@@ -8554,13 +8554,16 @@ class LibrationInfo:
         Moon's geocentric ecliptic longitude.
     dist_km : float
         Distance between the centers of the Earth and Moon in kilometers.
+    diam_deg : float
+        The apparent angular diameter of the Moon as seen from the center of the Earth.
     """
-    def __init__(self, elat, elon, mlat, mlon, dist_km):
+    def __init__(self, elat, elon, mlat, mlon, dist_km, diam_deg):
         self.elat = elat
         self.elon = elon
         self.mlat = mlat
         self.mlon = mlon
         self.dist_km = dist_km
+        self.diam_deg = diam_deg
 
 
 def Libration(time):
@@ -8576,8 +8579,9 @@ def Libration(time):
     in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
     This function also returns the geocentric position of the Moon
-    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+    and the apparent angular diameter of the Moon `diam_deg`.
 
     Parameters
     ----------
@@ -8596,6 +8600,7 @@ def Libration(time):
     mlon = moon.geo_eclip_lon
     mlat = moon.geo_eclip_lat
     dist_km = moon.distance_au * KM_PER_AU
+    diam_deg = 2.0 * math.degrees(math.atan(_MOON_MEAN_RADIUS_KM / math.sqrt(dist_km*dist_km - _MOON_MEAN_RADIUS_KM*_MOON_MEAN_RADIUS_KM)))
 
     # Inclination angle
     I = math.radians(1.54242)
@@ -8682,4 +8687,4 @@ def Libration(time):
     ldash2 = -tau + (rho*math.cos(a) + sigma*math.sin(a))*math.tan(bdash)
     bdash = math.degrees(bdash)
     bdash2 = sigma*math.cos(a) - rho*math.sin(a)
-    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km)
+    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg)
diff --git a/generate/ctest.c b/generate/ctest.c
index 29606900..719da0c7 100644
--- a/generate/ctest.c
+++ b/generate/ctest.c
@@ -4626,8 +4626,8 @@ static int Libration(const char *filename, int *ndata, double *var_lon, double *
     double phase, age, diam, dist, ra, dec, slon, slat, elon, elat, axisa;
     astro_time_t time;
     astro_libration_t lib;
-    double diff_elon, diff_elat, diff_distance;
-    double max_diff_elon = 0.0, max_diff_elat = 0.0, max_diff_distance = 0.0;
+    double diff_elon, diff_elat, diff_distance, diff_diam;
+    double max_diff_elon = 0.0, max_diff_elat = 0.0, max_diff_distance = 0.0, max_diff_diam = 0.0;
 
     infile = fopen(filename, "rt");
     if (infile == NULL)
@@ -4673,6 +4673,10 @@ static int Libration(const char *filename, int *ndata, double *var_lon, double *
             if (diff_distance > max_diff_distance)
                 max_diff_distance = diff_distance;
 
+            diff_diam = ABS(lib.diam_deg - diam/3600.0);
+            if (diff_diam > max_diff_diam)
+                max_diff_diam = diff_diam;
+
             if (diff_elon > 0.130)
                 FAIL("C Libration(%s line %d): EXCESSIVE diff_elon = %0.4lf arcmin\n", filename, lnum, diff_elon);
 
@@ -4690,8 +4694,8 @@ static int Libration(const char *filename, int *ndata, double *var_lon, double *
         }
     }
 
-    printf("C Libration(%s): PASS (%d test cases, max_diff_elon = %0.4lf arcmin, max_diff_elat = %0.4lf arcmin, max_diff_distance = %0.3lf km)\n", 
-        filename, count, max_diff_elon, max_diff_elat, max_diff_distance);
+    printf("C Libration(%s): PASS (%d test cases, max_diff_elon = %0.4lf arcmin, max_diff_elat = %0.4lf arcmin, max_diff_distance = %0.3lf km, max_diff_diam = %0.12lf deg)\n",
+        filename, count, max_diff_elon, max_diff_elat, max_diff_distance, max_diff_diam);
 
     *ndata += count;
     error = 0;
diff --git a/generate/dotnet/csharp_test/csharp_test.cs b/generate/dotnet/csharp_test/csharp_test.cs
index 11764dc5..f7857527 100644
--- a/generate/dotnet/csharp_test/csharp_test.cs
+++ b/generate/dotnet/csharp_test/csharp_test.cs
@@ -3009,6 +3009,7 @@ namespace csharp_test
             double max_diff_elon = 0.0;
             double max_diff_elat = 0.0;
             double max_diff_distance = 0.0;
+            double max_diff_diam = 0.0;
             string line;
             while (null != (line = infile.ReadLine()))
             {
@@ -3046,6 +3047,7 @@ namespace csharp_test
                     int minute = int.Parse(hmtoken[1]);
                     var time = new AstroTime(year, month, day, hour, minute, 0);
 
+                    double diam = double.Parse(token[7]) / 3600.0;
                     double dist = double.Parse(token[8]);
                     double elon = double.Parse(token[13]);
                     double elat = double.Parse(token[14]);
@@ -3064,6 +3066,10 @@ namespace csharp_test
                     if (diff_distance > max_diff_distance)
                         max_diff_distance = diff_distance;
 
+                    double diff_diam = abs(lib.diam_deg - diam);
+                    if (diff_diam > max_diff_diam)
+                        max_diff_diam = diff_diam;
+
                     if (diff_elon > 0.130)
                     {
                         Console.WriteLine($"C# Libration({filename} line {lnum}): EXCESSIVE diff_elon = {diff_elon} arcmin");
@@ -3085,7 +3091,7 @@ namespace csharp_test
                 }
             }
 
-            Console.WriteLine($"C# Libration({filename}): PASS ({count} test cases, max_diff_elon = {max_diff_elon} arcmin, max_diff_elat = {max_diff_elat} arcmin, max_diff_distance = {max_diff_distance})");
+            Console.WriteLine($"C# Libration({filename}): PASS ({count} test cases, max_diff_elon = {max_diff_elon} arcmin, max_diff_elat = {max_diff_elat} arcmin, max_diff_distance = {max_diff_distance} km, max_diff_diam = {max_diff_diam} deg)");
             return 0;
         }
 
diff --git a/generate/template/astronomy.c b/generate/template/astronomy.c
index 0570e3f4..03236173 100644
--- a/generate/template/astronomy.c
+++ b/generate/template/astronomy.c
@@ -1882,8 +1882,9 @@ astro_vector_t Astronomy_GeoMoon(astro_time_t time)
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param time  The date and time for which to calculate libration angles.
  * @return The Moon's ecliptic position and libration angles as seen from the Earth.
@@ -1903,6 +1904,7 @@ astro_libration_t Astronomy_Libration(astro_time_t time)
 
     CalcMoon(t, &lib.mlon, &lib.mlat, &lib.dist_km);
     lib.dist_km *= KM_PER_AU;
+    lib.diam_deg = (2.0 * RAD2DEG) * atan(MOON_MEAN_RADIUS_KM / sqrt(lib.dist_km*lib.dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
 
     /* Moon's argument of latitude in radians. */
     f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
diff --git a/generate/template/astronomy.cs b/generate/template/astronomy.cs
index 280a7814..d82fc27a 100644
--- a/generate/template/astronomy.cs
+++ b/generate/template/astronomy.cs
@@ -974,6 +974,9 @@ namespace CosineKitty
 
         /// <summary>Distance between the centers of the Earth and Moon in kilometers.</summary>
         public double dist_km;
+
+        /// <summary>The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.</summary>
+        public double diam_deg;
     }
 
     /// <summary>
@@ -3355,8 +3358,9 @@ $ASTRO_IAU_DATA()
         /// in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
         ///
         /// This function also returns the geocentric position of the Moon
-        /// expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-        /// distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+        /// expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+        /// distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+        /// and the apparent angular diameter of the Moon `diam_deg`.
         /// </remarks>
         /// <param name="time">The date and time for which to calculate lunar libration.</param>
         /// <returns>The Moon's ecliptic position and libration angles as seen from the Earth.</returns>
@@ -3374,6 +3378,7 @@ $ASTRO_IAU_DATA()
             lib.mlon = moon.geo_eclip_lon;
             lib.mlat = moon.geo_eclip_lat;
             lib.dist_km = moon.distance_au * KM_PER_AU;
+            lib.diam_deg = (2.0 * RAD2DEG) * Math.Atan(MOON_MEAN_RADIUS_KM / Math.Sqrt(lib.dist_km*lib.dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
 
             // Inclination angle
             const double I = DEG2RAD * 1.54242;
diff --git a/generate/template/astronomy.py b/generate/template/astronomy.py
index fa1596e3..4993d194 100644
--- a/generate/template/astronomy.py
+++ b/generate/template/astronomy.py
@@ -6073,13 +6073,16 @@ class LibrationInfo:
         Moon's geocentric ecliptic longitude.
     dist_km : float
         Distance between the centers of the Earth and Moon in kilometers.
+    diam_deg : float
+        The apparent angular diameter of the Moon as seen from the center of the Earth.
     """
-    def __init__(self, elat, elon, mlat, mlon, dist_km):
+    def __init__(self, elat, elon, mlat, mlon, dist_km, diam_deg):
         self.elat = elat
         self.elon = elon
         self.mlat = mlat
         self.mlon = mlon
         self.dist_km = dist_km
+        self.diam_deg = diam_deg
 
 
 def Libration(time):
@@ -6095,8 +6098,9 @@ def Libration(time):
     in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
     This function also returns the geocentric position of the Moon
-    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+    and the apparent angular diameter of the Moon `diam_deg`.
 
     Parameters
     ----------
@@ -6115,6 +6119,7 @@ def Libration(time):
     mlon = moon.geo_eclip_lon
     mlat = moon.geo_eclip_lat
     dist_km = moon.distance_au * KM_PER_AU
+    diam_deg = 2.0 * math.degrees(math.atan(_MOON_MEAN_RADIUS_KM / math.sqrt(dist_km*dist_km - _MOON_MEAN_RADIUS_KM*_MOON_MEAN_RADIUS_KM)))
 
     # Inclination angle
     I = math.radians(1.54242)
@@ -6201,4 +6206,4 @@ def Libration(time):
     ldash2 = -tau + (rho*math.cos(a) + sigma*math.sin(a))*math.tan(bdash)
     bdash = math.degrees(bdash)
     bdash2 = sigma*math.cos(a) - rho*math.sin(a)
-    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km)
+    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg)
diff --git a/generate/template/astronomy.ts b/generate/template/astronomy.ts
index 850d9f1b..fd0beaf6 100644
--- a/generate/template/astronomy.ts
+++ b/generate/template/astronomy.ts
@@ -877,6 +877,8 @@ $ASTRO_ADDSOL()
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 export class LibrationInfo {
     constructor(
@@ -884,7 +886,8 @@ export class LibrationInfo {
         public elon: number,
         public mlat: number,
         public mlon: number,
-        public dist_km: number
+        public dist_km: number,
+        public diam_deg: number
     ) {}
 }
 
@@ -901,8 +904,9 @@ export class LibrationInfo {
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1005,7 +1009,8 @@ export function Libration(date: FlexibleDateTime): LibrationInfo {
 
     const ldash2 = -tau + (rho*Math.cos(a) + sigma*Math.sin(a))*Math.tan(bdash);
     const bdash2 = sigma*Math.cos(a) - rho*Math.sin(a);
-    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km*dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 
 function precession(pos: ArrayVector, time: AstroTime, dir: PrecessDirection): ArrayVector {
diff --git a/generate/test.js b/generate/test.js
index 8d0b347f..b4da4d74 100644
--- a/generate/test.js
+++ b/generate/test.js
@@ -2345,6 +2345,7 @@ function Libration(filename) {
     let max_diff_elon = 0.0;
     let max_diff_elat = 0.0;
     let max_diff_distance = 0.0;
+    let max_diff_diam = 0.0;
     let count = 0;
     let lnum = 0;
     for (let line of lines) {
@@ -2373,6 +2374,7 @@ function Libration(filename) {
             const minute = int(hmtoken[1]);
             const time = Astronomy.MakeTime(new Date(Date.UTC(year, month-1, day, hour, minute)));
 
+            const diam = float(token[7]) / 3600.0;
             const dist = float(token[8]);
             const elon = float(token[13]);
             const elat = float(token[14]);
@@ -2391,6 +2393,10 @@ function Libration(filename) {
             if (diff_distance > max_diff_distance)
                 max_diff_distance = diff_distance;
 
+            const diff_diam = abs(lib.diam_deg - diam);
+            if (diff_diam > max_diff_diam)
+                max_diff_diam = diff_diam;
+
             if (diff_elon > 0.130) {
                 console.error(`JS Libration(${filename} line ${lnum}): EXCESSIVE diff_elon = ${diff_elon} arcmin`);
                 return 1;
@@ -2408,7 +2414,7 @@ function Libration(filename) {
             ++count;
         }
     }
-    console.log(`JS Libration(${filename}): PASS (${count} test cases, max_diff_elon = ${max_diff_elon} arcmin, max_diff_elat = ${max_diff_elat} arcmin, max_diff_distance = ${max_diff_distance} km)`);
+    console.log(`JS Libration(${filename}): PASS (${count} test cases, max_diff_elon = ${max_diff_elon} arcmin, max_diff_elat = ${max_diff_elat} arcmin, max_diff_distance = ${max_diff_distance} km, max_diff_diam = ${max_diff_diam} deg)`);
     return 0;
 }
 
diff --git a/generate/test.py b/generate/test.py
index 355672e4..50c161f3 100755
--- a/generate/test.py
+++ b/generate/test.py
@@ -2096,6 +2096,7 @@ def LibrationFile(filename):
     max_diff_elon = 0.0
     max_diff_elat = 0.0
     max_diff_distance = 0.0
+    max_diff_diam = 0.0
     count = 0
     with open(filename, 'rt') as infile:
         lnum = 0
@@ -2120,6 +2121,7 @@ def LibrationFile(filename):
                 hour = int(hmtoken[0])
                 minute = int(hmtoken[1])
                 time = astronomy.Time.Make(year, month, day, hour, minute, 0.0)
+                diam = float(token[7]) / 3600.0
                 dist = float(token[8])
                 elon = float(token[13])
                 elat = float(token[14])
@@ -2137,6 +2139,10 @@ def LibrationFile(filename):
                 if diff_distance > max_diff_distance:
                     max_diff_distance = diff_distance
 
+                diff_diam = vabs(lib.diam_deg - diam)
+                if diff_diam > max_diff_diam:
+                    max_diff_diam = diff_diam
+
                 if diff_elon > 0.130:
                     print('PY LibrationFile({} line {}): EXCESSIVE diff_elon = {}'.format(filename, lnum, diff_elon))
                     return 1
@@ -2151,8 +2157,8 @@ def LibrationFile(filename):
 
                 count += 1
 
-    print('PY Libration({}): PASS ({} test cases, max_diff_elon = {} arcmin, max_diff_elat = {} arcmin, max_diff_distance = {} km)'.format(
-        filename, count, max_diff_elon, max_diff_elat, max_diff_distance
+    print('PY Libration({}): PASS ({} test cases, max_diff_elon = {} arcmin, max_diff_elat = {} arcmin, max_diff_distance = {} km, max_diff_diam = {} deg)'.format(
+        filename, count, max_diff_elon, max_diff_elat, max_diff_distance, max_diff_diam
     ))
     return 0
 
diff --git a/source/c/README.md b/source/c/README.md
index 0e5c4b7e..c2aba08e 100644
--- a/source/c/README.md
+++ b/source/c/README.md
@@ -918,7 +918,7 @@ Libration is an observed back-and-forth wobble of the portion of the Moon visibl
 
 This function calculates a pair of perpendicular libration angles, one representing rotation of the Moon in eclitpic longitude `elon`, the other in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
-This function also returns the geocentric position of the Moon expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+This function also returns the geocentric position of the Moon expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the distance `dist_km` between the centers of the Earth and Moon expressed in kilometers, and the apparent angular diameter of the Moon `diam_deg`.
 
 
 
@@ -3290,6 +3290,7 @@ The following integer constants may be useful for indexing into the `moon` array
 | `double` | `mlat` |  Moon's geocentric ecliptic latitude.  |
 | `double` | `mlon` |  Moon's geocentric ecliptic longitude.  |
 | `double` | `dist_km` |  Distance between the centers of the Earth and Moon in kilometers.  |
+| `double` | `diam_deg` |  The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.  |
 
 
 ---
diff --git a/source/c/astronomy.c b/source/c/astronomy.c
index f3351e0b..0fba4197 100644
--- a/source/c/astronomy.c
+++ b/source/c/astronomy.c
@@ -2065,8 +2065,9 @@ astro_vector_t Astronomy_GeoMoon(astro_time_t time)
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param time  The date and time for which to calculate libration angles.
  * @return The Moon's ecliptic position and libration angles as seen from the Earth.
@@ -2086,6 +2087,7 @@ astro_libration_t Astronomy_Libration(astro_time_t time)
 
     CalcMoon(t, &lib.mlon, &lib.mlat, &lib.dist_km);
     lib.dist_km *= KM_PER_AU;
+    lib.diam_deg = (2.0 * RAD2DEG) * atan(MOON_MEAN_RADIUS_KM / sqrt(lib.dist_km*lib.dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
 
     /* Moon's argument of latitude in radians. */
     f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
diff --git a/source/c/astronomy.h b/source/c/astronomy.h
index b24bdc63..06f3175b 100644
--- a/source/c/astronomy.h
+++ b/source/c/astronomy.h
@@ -902,6 +902,7 @@ typedef struct
     double mlat;                /**< Moon's geocentric ecliptic latitude. */
     double mlon;                /**< Moon's geocentric ecliptic longitude. */
     double dist_km;             /**< Distance between the centers of the Earth and Moon in kilometers. */
+    double diam_deg;            /**< The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth. */
 }
 astro_libration_t;
 
diff --git a/source/csharp/README.md b/source/csharp/README.md
index cab50089..00dd443e 100644
--- a/source/csharp/README.md
+++ b/source/csharp/README.md
@@ -711,8 +711,9 @@ one representing rotation of the Moon in eclitpic longitude `elon`, the other
 in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
 This function also returns the geocentric position of the Moon
-expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+and the apparent angular diameter of the Moon `diam_deg`.
 
 | Type | Parameter | Description |
 | --- | --- | --- |
@@ -2224,6 +2225,7 @@ and the velocities in AU/day.
 | `double` | `mlat` | Moon's geocentric ecliptic latitude. |
 | `double` | `mlon` | Moon's geocentric ecliptic longitude. |
 | `double` | `dist_km` | Distance between the centers of the Earth and Moon in kilometers. |
+| `double` | `diam_deg` | The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth. |
 
 ---
 
diff --git a/source/csharp/astronomy.cs b/source/csharp/astronomy.cs
index 638a4266..d79bf2ae 100644
--- a/source/csharp/astronomy.cs
+++ b/source/csharp/astronomy.cs
@@ -974,6 +974,9 @@ namespace CosineKitty
 
         /// <summary>Distance between the centers of the Earth and Moon in kilometers.</summary>
         public double dist_km;
+
+        /// <summary>The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.</summary>
+        public double diam_deg;
     }
 
     /// <summary>
@@ -4555,8 +4558,9 @@ namespace CosineKitty
         /// in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
         ///
         /// This function also returns the geocentric position of the Moon
-        /// expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-        /// distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+        /// expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+        /// distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+        /// and the apparent angular diameter of the Moon `diam_deg`.
         /// </remarks>
         /// <param name="time">The date and time for which to calculate lunar libration.</param>
         /// <returns>The Moon's ecliptic position and libration angles as seen from the Earth.</returns>
@@ -4574,6 +4578,7 @@ namespace CosineKitty
             lib.mlon = moon.geo_eclip_lon;
             lib.mlat = moon.geo_eclip_lat;
             lib.dist_km = moon.distance_au * KM_PER_AU;
+            lib.diam_deg = (2.0 * RAD2DEG) * Math.Atan(MOON_MEAN_RADIUS_KM / Math.Sqrt(lib.dist_km*lib.dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
 
             // Inclination angle
             const double I = DEG2RAD * 1.54242;
diff --git a/source/js/README.md b/source/js/README.md
index cdcc17a1..0fc50f9c 100644
--- a/source/js/README.md
+++ b/source/js/README.md
@@ -243,6 +243,7 @@ an `AstroTime` value that can be passed to Astronomy Engine functions.
 | mlat | <code>number</code> | Moon's geocentric ecliptic latitude. |
 | mlon | <code>number</code> | Moon's geocentric ecliptic longitude. |
 | dist_km | <code>number</code> | Distance between the centers of the Earth and Moon in kilometers. |
+| diam_deg | <code>number</code> | The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth. |
 
 
 * * *
@@ -927,8 +928,9 @@ one representing rotation of the Moon in eclitpic longitude `elon`, the other
 in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
 This function also returns the geocentric position of the Moon
-expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.  
+expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+and the apparent angular diameter of the Moon `diam_deg`.  
 
 | Param | Type | Description |
 | --- | --- | --- |
diff --git a/source/js/astronomy.browser.js b/source/js/astronomy.browser.js
index 5160d867..f1acb1dd 100644
--- a/source/js/astronomy.browser.js
+++ b/source/js/astronomy.browser.js
@@ -1584,14 +1584,17 @@ function CalcMoon(time) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 class LibrationInfo {
-    constructor(elat, elon, mlat, mlon, dist_km) {
+    constructor(elat, elon, mlat, mlon, dist_km, diam_deg) {
         this.elat = elat;
         this.elon = elon;
         this.mlat = mlat;
         this.mlon = mlon;
         this.dist_km = dist_km;
+        this.diam_deg = diam_deg;
     }
 }
 exports.LibrationInfo = LibrationInfo;
@@ -1608,8 +1611,9 @@ exports.LibrationInfo = LibrationInfo;
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1693,7 +1697,8 @@ function Libration(date) {
         +0.00011 * Math.sin(2 * mdash - 2 * m - 2 * d));
     const ldash2 = -tau + (rho * Math.cos(a) + sigma * Math.sin(a)) * Math.tan(bdash);
     const bdash2 = sigma * Math.cos(a) - rho * Math.sin(a);
-    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * exports.RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km * dist_km - MOON_MEAN_RADIUS_KM * MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 exports.Libration = Libration;
 function precession(pos, time, dir) {
diff --git a/source/js/astronomy.browser.min.js b/source/js/astronomy.browser.min.js
index 4d2cba7c..182aea09 100644
--- a/source/js/astronomy.browser.min.js
+++ b/source/js/astronomy.browser.min.js
@@ -154,69 +154,69 @@ a.SSB="SSB";a.EMB="EMB"})(r=e.Body||(e.Body={}));var F;(function(a){a[a.From2000
 0,-14,104,0,2]],[[0,1,2,0,2],[7566,-21,-11,-3250,0,-5]],[[0,0,2,2,1],[-6637,-11,25,3353,0,14]],[[0,-1,2,0,2],[-7141,21,8,3070,0,4]],[[0,0,0,2,1],[-6302,-11,2,3272,0,4]],[[1,0,2,-2,1],[5800,10,2,-3045,0,-1]],[[2,0,2,-2,2],[6443,0,-7,-2768,0,-4]],[[-2,0,0,2,1],[-5774,-11,-15,3041,0,-5]],[[2,0,2,0,1],[-5350,0,21,2695,0,12]],[[0,-1,2,-2,1],[-4752,-11,-3,2719,0,-3]],[[0,0,0,-2,1],[-4940,-11,-21,2720,0,-9]],[[-1,-1,0,2,0],[7350,0,-8,-51,0,4]],[[2,0,0,-2,1],[4065,0,6,-2206,0,1]],[[1,0,0,2,0],[6579,0,-24,
 -199,0,2]],[[0,1,2,-2,1],[3579,0,5,-1900,0,1]],[[1,-1,0,0,0],[4725,0,-6,-41,0,3]],[[-2,0,2,0,2],[-3075,0,-2,1313,0,-1]],[[3,0,2,0,2],[-2904,0,15,1233,0,7]],[[0,-1,0,2,0],[4348,0,-10,-81,0,2]],[[1,-1,2,0,2],[-2878,0,8,1232,0,4]],[[0,0,0,1,0],[-4230,0,5,-20,0,-2]],[[-1,-1,2,2,2],[-2819,0,7,1207,0,3]],[[-1,0,2,0,0],[-4056,0,5,40,0,-2]],[[0,-1,2,2,2],[-2647,0,11,1129,0,5]],[[-2,0,0,0,1],[-2294,0,-10,1266,0,-4]],[[1,1,2,0,2],[2481,0,-7,-1062,0,-3]],[[2,0,0,0,1],[2179,0,-2,-1129,0,-2]],[[-1,1,0,1,0],[3276,
 0,1,-9,0,0]],[[1,1,0,0,0],[-3389,0,5,35,0,-2]],[[1,0,2,0,0],[3339,0,-13,-107,0,1]],[[-1,0,2,-2,1],[-1987,0,-6,1073,0,-2]],[[1,0,0,0,2],[-1981,0,0,854,0,0]],[[-1,0,0,1,0],[4026,0,-353,-553,0,-139]],[[0,0,2,1,2],[1660,0,-5,-710,0,-2]],[[-1,0,2,4,2],[-1521,0,9,647,0,4]],[[-1,1,0,1,1],[1314,0,0,-700,0,0]],[[0,-2,2,-2,1],[-1283,0,0,672,0,0]],[[1,0,2,2,1],[-1331,0,8,663,0,4]],[[-2,0,2,2,2],[1383,0,-2,-594,0,-2]],[[-1,0,0,0,2],[1405,0,4,-610,0,2]],[[1,1,2,-2,2],[1290,0,0,-556,0,0]]],Ma;e.CalcMoonCount=0;
-var Cc=function(a,b,c,d,f){this.elat=a;this.elon=b;this.mlat=c;this.mlon=d;this.dist_km=f};e.LibrationInfo=Cc;e.Libration=function(a){var b=x(a);a=b.tt/36525;var c=a*a,d=c*a,f=c*c,h=aa(b);b=h.geo_eclip_lon;var l=h.geo_eclip_lat;h=h.distance_au*e.KM_PER_AU;var k=1.54242*e.DEG2RAD,g=e.DEG2RAD*pa(93.272095+483202.0175233*a-.0036539*c-d/3526E3+f/86331E4),m=e.DEG2RAD*pa(125.0445479-1934.1362891*a+.0020754*c+d/467441-f/60616E3),n=e.DEG2RAD*pa(357.5291092+35999.0502909*a-1.536E-4*c+d/2449E4),p=e.DEG2RAD*
-pa(134.9633964+477198.8675055*a+.0087414*c+d/69699-f/14712E3);d=e.DEG2RAD*pa(297.8501921+445267.1114034*a-.0018819*c+d/545868-f/113065E3);c=1-.002516*a-7.4E-6*c;var u=b-m;f=Math.atan2(Math.sin(u)*Math.cos(l)*Math.cos(k)-Math.sin(l)*Math.sin(k),Math.cos(u)*Math.cos(l));var w=oa(e.RAD2DEG*(f-g));k=Math.asin(-Math.sin(u)*Math.cos(l)*Math.sin(k)-Math.sin(l)*Math.cos(k));u=-.02752*Math.cos(p)+-.02245*Math.sin(g)+.00684*Math.cos(p-2*g)+-.00293*Math.cos(2*g)+-8.5E-4*Math.cos(2*g-2*d)+-5.4E-4*Math.cos(p-
-2*d)+-2E-4*Math.sin(p+g)+-2E-4*Math.cos(p+2*g)+-2E-4*Math.cos(p-g)+1.4E-4*Math.cos(p+2*g-2*d);var B=-.02816*Math.sin(p)+.02244*Math.cos(g)+-.00682*Math.sin(p-2*g)+-.00279*Math.sin(2*g)+-8.3E-4*Math.sin(2*g-2*d)+6.9E-4*Math.sin(p-2*d)+4E-4*Math.cos(p+g)+-2.5E-4*Math.sin(2*p)+-2.3E-4*Math.sin(p+2*g)+2E-4*Math.cos(p-g)+1.9E-4*Math.sin(p-g)+1.3E-4*Math.sin(p+2*g-2*d)+-1E-4*Math.cos(p-3*g);return new Cc(e.RAD2DEG*k+(B*Math.cos(f)-u*Math.sin(f)),w+(-(.0252*c*Math.sin(n)+.00473*Math.sin(2*p-2*g)+-.00467*
-Math.sin(p)+.00396*Math.sin(e.DEG2RAD*(119.75+131.849*a))+.00276*Math.sin(2*p-2*d)+.00196*Math.sin(m)+-.00183*Math.cos(p-g)+.00115*Math.sin(p-2*d)+-9.6E-4*Math.sin(p-d)+4.6E-4*Math.sin(2*g-2*d)+-3.9E-4*Math.sin(p-g)+-3.2E-4*Math.sin(p-n-d)+2.7E-4*Math.sin(2*p-n-2*d)+2.3E-4*Math.sin(e.DEG2RAD*(72.56+20.186*a))+-1.4E-4*Math.sin(2*d)+1.4E-4*Math.cos(2*p-2*g)+-1.2E-4*Math.sin(p-2*g)+-1.2E-4*Math.sin(2*p)+1.1E-4*Math.sin(2*p-2*n-2*d))+(u*Math.cos(f)+B*Math.sin(f))*Math.tan(k)),l,b,h)};var D=function(a,
-b,c,d){this.x=a;this.y=b;this.z=c;this.t=d};D.prototype.Length=function(){return Math.sqrt(this.x*this.x+this.y*this.y+this.z*this.z)};e.Vector=D;var na=function(a,b,c,d,f,h,l){this.x=a;this.y=b;this.z=c;this.vx=d;this.vy=f;this.vz=h;this.t=l};e.StateVector=na;var Za=function(a,b,c){this.lat=v(a);this.lon=v(b);this.dist=v(c)};e.Spherical=Za;var Sa=function(a,b,c,d){this.ra=v(a);this.dec=v(b);this.dist=v(c);this.vec=d};e.EquatorialCoordinates=Sa;var J=function(a){this.rot=a};e.RotationMatrix=J;e.MakeRotation=
-function(a){if(!Kc(a))throw"Argument must be a [3][3] array of numbers";return new J(a)};var Ib=function(a,b,c,d){this.azimuth=v(a);this.altitude=v(b);this.ra=v(c);this.dec=v(d)};e.HorizontalCoordinates=Ib;var Lb=function(a,b,c){this.vec=a;this.elat=v(b);this.elon=v(c)};e.EclipticCoordinates=Lb;e.Horizon=xa;var ib=function(a,b,c){this.latitude=a;this.longitude=b;this.height=c;ma(this)};e.Observer=ib;e.SunPosition=Jb;e.Equator=za;e.ObserverVector=function(a,b,c){a=x(a);var d=da(a);b=Fb(b,d).pos;c||
-(b=Ra(b,a,F.Into2000));return new D(b[0],b[1],b[2],a)};e.VectorObserver=function(a,b){var c=da(a.t),d=[a.x,a.y,a.z];b||(d=Qa(d,a.t,F.From2000),d=gb(d,a.t,F.From2000));b=d[0]*e.KM_PER_AU;var f=d[1]*e.KM_PER_AU;d=d[2]*e.KM_PER_AU;a=Math.sqrt(b*b+f*f);if(1E-6>a){c=0;var h=0<d?90:-90;d=Math.abs(d)-6356.751857971648}else{for(c=e.RAD2DEG*Math.atan2(f,b)-15*c;-180>=c;)c+=360;for(;180<c;)c-=360;h=Math.atan2(d,a);for(var l;;){b=Math.cos(h);f=Math.sin(h);var k=b*b,g=f*f,m=k+.9933056020041345*g;l=Math.sqrt(m);
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-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 u=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,va=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=u*va*g*(-B-ba*p*z);g=u*va*g*(+w+ba*m*z);m=2*Math.sqrt(1-l*l-k*k);u=1-2*
-k*k;w=1-2*l*l;B=2*k*l;d=new na(d*u+n*B,d*B+n*w,(l*n-d*k)*m,p*u+g*B,p*B+g*w,(l*g-p*k)*m,a);d=hc(Wc,d);h.call(f,d)}return new Dc(b)};e.HelioVector=Da;e.HelioDistance=ha;e.GeoVector=X;e.BaryState=function(a,b){b=x(b);if(a==r.SSB)return new na(0,0,0,0,0,0,b);var c=new Ca(b.tt);switch(a){case r.Sun:return Ea(c.Sun,b);case r.Jupiter:return Ea(c.Jupiter,b);case r.Saturn:return Ea(c.Saturn,b);case r.Uranus:return Ea(c.Uranus,b);case r.Neptune:return Ea(c.Neptune,b)}if(a in H)return a=Pb(H[a],b.tt),new na(c.Sun.r.x+
-a.r.x,c.Sun.r.y+a.r.y,c.Sun.r.z+a.r.z,c.Sun.v.x+a.v.x,c.Sun.v.y+a.v.y,c.Sun.v.z+a.v.z,b);throw'BaryState: Unsupported body "'+a+'"';};e.Search=I;e.SearchSunLongitude=Ub;e.PairLongitude=pb;e.AngleFromSun=qa;e.EclipticLongitude=ia;var Vb=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=Vb;e.Illumination=Ya;e.SearchRelativeLongitude=ra;e.MoonPhase=
-qb;e.SearchMoonPhase=Ga;var Xb=function(a,b){this.quarter=a;this.time=b};e.MoonQuarter=Xb;e.SearchMoonQuarter=Wb;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Wb(a)};e.SearchRiseSet=function(a,b,c,d,f){a:switch(a){case r.Sun:var h=Tc;break a;case r.Moon:h=Uc;break a;default:h=0}return Yb(a,b,c,d,f,function(l){var k=za(a,l,b,!0,!0);l=xa(l,b,k.ra,k.dec).altitude+h/k.dist*e.RAD2DEG+Vc;return c*l})};e.SearchAltitude=function(a,b,c,d,f,h){if(!Number.isFinite(h)||-90>h||
-90<h)throw"Invalid altitude angle: "+h;return Yb(a,b,c,d,f,function(l){var k=za(a,l,b,!0,!0);l=xa(l,b,k.ra,k.dec);return c*(l.altitude-h)})};var Zb=function(a,b){this.time=a;this.hor=b};e.HourAngleEvent=Zb;e.SearchHourAngle=Ha;var Ec=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=Ec;e.Seasons=function(a){function b(l,k,g){k=new Date(Date.UTC(a,k-1,g));l=Ub(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 Ec(c,d,f,h)};var ac=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=ac;e.Elongation=$b;e.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);m=m.AddDays(.005);n=qa(a,
-n);m=qa(a,m);return(n-m)/.01}b=x(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=ia(a,b),l=ia(r.Earth,b),k=oa(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=-Fa(a)/4,l=+d.s1,h=+d.s2):(g=-Fa(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(g);l=ra(a,l,k);h=ra(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=I(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 $b(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=Ya(a,m).mag;return(Ya(a,g).mag-m)/.01}if(a!==r.Venus)throw"SearchPeakMagnitude currently works for Venus only.";b=x(b);for(var d=0;2>=++d;){var f=
-ia(a,b),h=ia(r.Earth,b),l=oa(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=-Fa(a)/4,h=10,f=30):(k=-Fa(a)/4,h=-30,f=-10);l=b.AddDays(k);h=ra(a,h,l);f=ra(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=I(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 Ya(a,l);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Ia=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Ia;e.SearchLunarApsis=bc;e.NextLunarApsis=function(a){var b=bc(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=dc;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=dc(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=sa;e.CombineRotation=ta;e.IdentityMatrix=function(){return new J([[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 J(l)};e.VectorFromSphere=rb;e.EquatorFromVector=ec;e.SphereFromVector=sb;e.HorizonFromVector=function(a,b){a=sb(a);a.lon=fc(a.lon);a.lat+=ya(b,a.lat);return a};e.VectorFromHorizon=
-function(a,b,c){var d=fc(a.lon);c=a.lat+gc(c,a.lat);a=new Za(c,d,a.dist);return rb(a,b)};e.Refraction=ya;e.InverseRefraction=gc;e.RotateVector=Ja;e.RotateState=hc;e.Rotation_EQJ_ECL=ic;e.Rotation_ECL_EQJ=function(){return new J([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=tb;e.Rotation_EQD_EQJ=ub;e.Rotation_EQD_HOR=vb;e.Rotation_HOR_EQD=jc;e.Rotation_HOR_EQJ=kc;e.Rotation_EQJ_HOR=function(a,b){a=kc(a,b);return sa(a)};e.Rotation_EQD_ECL=
-lc;e.Rotation_ECL_EQD=mc;e.Rotation_ECL_HOR=nc;e.Rotation_HOR_ECL=function(a,b){a=nc(a,b);return sa(a)};e.Rotation_EQJ_GAL=function(){return new J([[-.0548624779711344,.4941095946388765,-.8676668813529025],[-.8734572784246782,-.4447938112296831,-.1980677870294097],[-.483800052994852,.7470034631630423,.4559861124470794]])};e.Rotation_GAL_EQJ=function(){return new J([[-.0548624779711344,-.8734572784246782,-.483800052994852],[.4941095946388765,-.4447938112296831,.7470034631630423],[-.8676668813529025,
--.1980677870294097,.4559861124470794]])};var Yc=[["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",
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-"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"]],Zc=[[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,
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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],
+[5.925911780766E-4,4.0899396636448,-.01290686414666],[2.045597496146E-4,5.2713683670372,-.12523544076106],[1.785118648258E-4,.28743156721063,.8782079244252],[1.131999784893E-4,1.4462127277818,3.5515522949802],[-6.5877816921E-5,2.2702423990985,-1.7951364394537],[4.97058888328E-5,5.9096792204858,1.7693227129285]],zeta:[[.0015932721570848,3.3368862796665,-1.2491307058E-4],[8.533093128905E-4,2.4133881688166,0],[3.513347911037E-4,5.9720789850127,-3.056101771E-5],[-1.441929255483E-4,1.0477061764435,-5.6920632124E-4]]},
+{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]]}],Dc=function(a){this.moon=a};e.JupiterMoonsInfo=Dc;e.JupiterMoons=function(a){a=new N(a);for(var b=[],c=$jscomp.makeIterator(Xc),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 u=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,va=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=u*va*g*(-B-ba*p*z);g=u*va*g*(+w+
+ba*m*z);m=2*Math.sqrt(1-l*l-k*k);u=1-2*k*k;w=1-2*l*l;B=2*k*l;d=new na(d*u+n*B,d*B+n*w,(l*n-d*k)*m,p*u+g*B,p*B+g*w,(l*g-p*k)*m,a);d=hc(Wc,d);h.call(f,d)}return new Dc(b)};e.HelioVector=Da;e.HelioDistance=ha;e.GeoVector=X;e.BaryState=function(a,b){b=x(b);if(a==r.SSB)return new na(0,0,0,0,0,0,b);var c=new Ca(b.tt);switch(a){case r.Sun:return Ea(c.Sun,b);case r.Jupiter:return Ea(c.Jupiter,b);case r.Saturn:return Ea(c.Saturn,b);case r.Uranus:return Ea(c.Uranus,b);case r.Neptune:return Ea(c.Neptune,b)}if(a in
+H)return a=Pb(H[a],b.tt),new na(c.Sun.r.x+a.r.x,c.Sun.r.y+a.r.y,c.Sun.r.z+a.r.z,c.Sun.v.x+a.v.x,c.Sun.v.y+a.v.y,c.Sun.v.z+a.v.z,b);throw'BaryState: Unsupported body "'+a+'"';};e.Search=I;e.SearchSunLongitude=Ub;e.PairLongitude=pb;e.AngleFromSun=qa;e.EclipticLongitude=ia;var Vb=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=Vb;e.Illumination=
+Ya;e.SearchRelativeLongitude=ra;e.MoonPhase=qb;e.SearchMoonPhase=Ga;var Xb=function(a,b){this.quarter=a;this.time=b};e.MoonQuarter=Xb;e.SearchMoonQuarter=Wb;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Wb(a)};e.SearchRiseSet=function(a,b,c,d,f){a:switch(a){case r.Sun:var h=Tc;break a;case r.Moon:h=Uc;break a;default:h=0}return Yb(a,b,c,d,f,function(l){var k=za(a,l,b,!0,!0);l=xa(l,b,k.ra,k.dec).altitude+h/k.dist*e.RAD2DEG+Vc;return c*l})};e.SearchAltitude=function(a,
+b,c,d,f,h){if(!Number.isFinite(h)||-90>h||90<h)throw"Invalid altitude angle: "+h;return Yb(a,b,c,d,f,function(l){var k=za(a,l,b,!0,!0);l=xa(l,b,k.ra,k.dec);return c*(l.altitude-h)})};var Zb=function(a,b){this.time=a;this.hor=b};e.HourAngleEvent=Zb;e.SearchHourAngle=Ha;var Ec=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=Ec;e.Seasons=function(a){function b(l,k,g){k=new Date(Date.UTC(a,k-1,g));l=Ub(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 Ec(c,d,f,h)};var ac=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=ac;e.Elongation=$b;e.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);
+m=m.AddDays(.005);n=qa(a,n);m=qa(a,m);return(n-m)/.01}b=x(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=ia(a,b),l=ia(r.Earth,b),k=oa(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=-Fa(a)/4,l=+d.s1,h=+d.s2):(g=-Fa(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(g);l=ra(a,l,k);h=ra(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=I(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 $b(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=Ya(a,m).mag;return(Ya(a,g).mag-m)/.01}if(a!==r.Venus)throw"SearchPeakMagnitude currently works for Venus only.";
+b=x(b);for(var d=0;2>=++d;){var f=ia(a,b),h=ia(r.Earth,b),l=oa(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=-Fa(a)/4,h=10,f=30):(k=-Fa(a)/4,h=-30,f=-10);l=b.AddDays(k);h=ra(a,h,l);f=ra(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=I(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 Ya(a,l);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Ia=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Ia;e.SearchLunarApsis=bc;e.NextLunarApsis=function(a){var b=bc(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=dc;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=dc(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=sa;e.CombineRotation=ta;e.IdentityMatrix=function(){return new J([[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 J(l)};e.VectorFromSphere=rb;e.EquatorFromVector=ec;e.SphereFromVector=sb;e.HorizonFromVector=function(a,b){a=sb(a);a.lon=
+fc(a.lon);a.lat+=ya(b,a.lat);return a};e.VectorFromHorizon=function(a,b,c){var d=fc(a.lon);c=a.lat+gc(c,a.lat);a=new Za(c,d,a.dist);return rb(a,b)};e.Refraction=ya;e.InverseRefraction=gc;e.RotateVector=Ja;e.RotateState=hc;e.Rotation_EQJ_ECL=ic;e.Rotation_ECL_EQJ=function(){return new J([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=tb;e.Rotation_EQD_EQJ=ub;e.Rotation_EQD_HOR=vb;e.Rotation_HOR_EQD=jc;e.Rotation_HOR_EQJ=kc;e.Rotation_EQJ_HOR=
+function(a,b){a=kc(a,b);return sa(a)};e.Rotation_EQD_ECL=lc;e.Rotation_ECL_EQD=mc;e.Rotation_ECL_HOR=nc;e.Rotation_HOR_ECL=function(a,b){a=nc(a,b);return sa(a)};e.Rotation_EQJ_GAL=function(){return new J([[-.0548624779711344,.4941095946388765,-.8676668813529025],[-.8734572784246782,-.4447938112296831,-.1980677870294097],[-.483800052994852,.7470034631630423,.4559861124470794]])};e.Rotation_GAL_EQJ=function(){return new J([[-.0548624779711344,-.8734572784246782,-.483800052994852],[.4941095946388765,
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+["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"]],Zc=[[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,
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+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]],Ab,Fc,Gc=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};e.ConstellationInfo=Gc;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);Ab||(Ab=tb(new N(-45655.74141261017)),Fc=new N(0));a=new Za(b,15*a,1);a=rb(a,Fc);a=Ja(Ab,a);a=ec(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Zc),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=Yc[f[0]],new Gc(b[0],b[1],a.ra,a.dec)}throw"Unable to find constellation for given coordinates.";};var qc=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=qc;var Oc=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=pc;var sc=function(a,b,c,d,f){this.kind=a;this.peak=b;this.distance=
+c;this.latitude=d;this.longitude=f};e.GlobalSolarEclipseInfo=sc;e.NextLunarEclipse=function(a){a=a.AddDays(10);return pc(a)};e.SearchGlobalSolarEclipse=rc;e.NextGlobalSolarEclipse=function(a){a=a.AddDays(10);return rc(a)};var wc=function(a,b){this.time=a;this.altitude=b};e.EclipseEvent=wc;var yc=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=yc;e.SearchLocalSolarEclipse=xc;e.NextLocalSolarEclipse=function(a,
+b){a=a.AddDays(10);return xc(a,b)};var Bc=function(a,b,c,d){this.start=a;this.peak=b;this.finish=c;this.separation=d};e.TransitInfo=Bc;e.SearchTransit=Ac;e.NextTransit=function(a,b){b=b.AddDays(100);return Ac(a,b)}},{}]},{},[1])(1)});
diff --git a/source/js/astronomy.d.ts b/source/js/astronomy.d.ts
index bec73480..919ee182 100644
--- a/source/js/astronomy.d.ts
+++ b/source/js/astronomy.d.ts
@@ -255,6 +255,8 @@ export declare let CalcMoonCount: number;
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 export declare class LibrationInfo {
     elat: number;
@@ -262,7 +264,8 @@ export declare class LibrationInfo {
     mlat: number;
     mlon: number;
     dist_km: number;
-    constructor(elat: number, elon: number, mlat: number, mlon: number, dist_km: number);
+    diam_deg: number;
+    constructor(elat: number, elon: number, mlat: number, mlon: number, dist_km: number, diam_deg: number);
 }
 /**
  * @brief Calculates the Moon's libration angles at a given moment in time.
@@ -277,8 +280,9 @@ export declare class LibrationInfo {
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
diff --git a/source/js/astronomy.js b/source/js/astronomy.js
index 118b05f9..22e9dbb9 100644
--- a/source/js/astronomy.js
+++ b/source/js/astronomy.js
@@ -1583,14 +1583,17 @@ function CalcMoon(time) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 class LibrationInfo {
-    constructor(elat, elon, mlat, mlon, dist_km) {
+    constructor(elat, elon, mlat, mlon, dist_km, diam_deg) {
         this.elat = elat;
         this.elon = elon;
         this.mlat = mlat;
         this.mlon = mlon;
         this.dist_km = dist_km;
+        this.diam_deg = diam_deg;
     }
 }
 exports.LibrationInfo = LibrationInfo;
@@ -1607,8 +1610,9 @@ exports.LibrationInfo = LibrationInfo;
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1692,7 +1696,8 @@ function Libration(date) {
         +0.00011 * Math.sin(2 * mdash - 2 * m - 2 * d));
     const ldash2 = -tau + (rho * Math.cos(a) + sigma * Math.sin(a)) * Math.tan(bdash);
     const bdash2 = sigma * Math.cos(a) - rho * Math.sin(a);
-    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * exports.RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km * dist_km - MOON_MEAN_RADIUS_KM * MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(exports.RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 exports.Libration = Libration;
 function precession(pos, time, dir) {
diff --git a/source/js/astronomy.min.js b/source/js/astronomy.min.js
index a284f02f..946dab4f 100644
--- a/source/js/astronomy.min.js
+++ b/source/js/astronomy.min.js
@@ -115,12 +115,12 @@ L;t=4;z=1.000002208;break;case 2:y=I;t=3;z=.997504612-.002495388*a;break;case 3:
 2,2);h(-45.099,-.02,0,-.001,1,0,2,0);h(-.179,-9.52,0,-.0833,1,0,2,-2);h(-.301,-.33,0,.0014,1,0,2,-4);h(-6.382,-3.37,0,-.0481,1,0,-2,2);h(39.528,85.13,0,-.7136,1,0,-2,0);h(9.366,.71,0,-.0112,1,0,-2,-2);h(.202,.02,0,0,1,0,-2,-4);h(.415,.1,0,.0013,0,1,2,0);h(-2.152,-2.26,0,-.0066,0,1,2,-2);h(-1.44,-1.3,0,.0014,0,1,-2,2);h(.384,-.04,0,0,0,1,-2,-2);h(1.938,3.6,-.145,.0401,4,0,0,0);h(-.952,-1.58,.052,-.013,4,0,0,-2);h(-.551,-.94,.032,-.0097,3,1,0,0);h(-.482,-.57,.005,-.0045,3,1,0,-2);h(.681,.96,-.026,.0115,
 3,-1,0,0);h(-.297,-.27,.002,-9E-4,2,2,0,-2);h(.254,.21,-.003,0,2,-2,0,-2);h(-.25,-.22,.004,.0014,1,3,0,-2);h(-3.996,0,0,4E-4,2,0,2,0);h(.557,-.75,0,-.009,2,0,2,-2);h(-.459,-.38,0,-.0053,2,0,-2,2);h(-1.298,.74,0,4E-4,2,0,-2,0);h(.538,1.14,0,-.0141,2,0,-2,-2);h(.263,.02,0,0,1,1,2,0);h(.426,.07,0,-6E-4,1,1,-2,-2);h(-.304,.03,0,3E-4,1,-1,2,0);h(-.372,-.19,0,-.0027,1,-1,-2,2);h(.418,0,0,0,0,0,4,0);h(-.33,-.04,0,0,3,0,2,0);t=-526.069*k(0,0,1,-2).y;t+=-3.352*k(0,0,1,-4).y;t+=44.297*k(1,0,1,-2).y;t+=-6*k(1,
 0,1,-4).y;t+=20.599*k(-1,0,1,0).y;t+=-30.598*k(-1,0,1,-2).y;t+=-24.649*k(-2,0,1,0).y;t+=-2*k(-2,0,1,-2).y;t+=-22.571*k(0,1,1,-2).y;t+=10.985*k(0,-1,1,-2).y;n+=.82*g(.7736-62.5512*a)+.31*g(.0466-125.1025*a)+.35*g(.5785-25.1042*a)+.66*g(.4591+1335.8075*a)+.64*g(.313-91.568*a)+1.14*g(.148+1331.2898*a)+.21*g(.5918+1056.5859*a)+.44*g(.5784+1322.8595*a)+.24*g(.2275-5.7374*a)+.28*g(.2965+2.6929*a)+.33*g(.3132+6.3368*a);a=B+p/ARC;a=(1.000002708+139.978*C)*(18518.511+1.189+O)*Math.sin(a)-6.24*Math.sin(3*a)+
-t;return{geo_eclip_lon:PI2*Frac((H+n/ARC)/PI2),geo_eclip_lat:Math.PI/648E3*a,distance_au:ARC*EARTH_EQUATORIAL_RADIUS_AU/(.999953253*P)}}var LibrationInfo=function(a,b,c,d,e){this.elat=a;this.elon=b;this.mlat=c;this.mlon=d;this.dist_km=e};exports.LibrationInfo=LibrationInfo;
+t;return{geo_eclip_lon:PI2*Frac((H+n/ARC)/PI2),geo_eclip_lat:Math.PI/648E3*a,distance_au:ARC*EARTH_EQUATORIAL_RADIUS_AU/(.999953253*P)}}var LibrationInfo=function(a,b,c,d,e,f){this.elat=a;this.elon=b;this.mlat=c;this.mlon=d;this.dist_km=e;this.diam_deg=f};exports.LibrationInfo=LibrationInfo;
 function Libration(a){var b=MakeTime(a);a=b.tt/36525;var c=a*a,d=c*a,e=c*c,f=CalcMoon(b);b=f.geo_eclip_lon;var g=f.geo_eclip_lat;f=f.distance_au*exports.KM_PER_AU;var k=1.54242*exports.DEG2RAD,h=exports.DEG2RAD*NormalizeLongitude(93.272095+483202.0175233*a-.0036539*c-d/3526E3+e/86331E4),l=exports.DEG2RAD*NormalizeLongitude(125.0445479-1934.1362891*a+.0020754*c+d/467441-e/60616E3),m=exports.DEG2RAD*NormalizeLongitude(357.5291092+35999.0502909*a-1.536E-4*c+d/2449E4),n=exports.DEG2RAD*NormalizeLongitude(134.9633964+
 477198.8675055*a+.0087414*c+d/69699-e/14712E3);d=exports.DEG2RAD*NormalizeLongitude(297.8501921+445267.1114034*a-.0018819*c+d/545868-e/113065E3);c=1-.002516*a-7.4E-6*c;var p=b-l;e=Math.atan2(Math.sin(p)*Math.cos(g)*Math.cos(k)-Math.sin(g)*Math.sin(k),Math.cos(p)*Math.cos(g));var r=LongitudeOffset(exports.RAD2DEG*(e-h));k=Math.asin(-Math.sin(p)*Math.cos(g)*Math.sin(k)-Math.sin(g)*Math.cos(k));p=-.02752*Math.cos(n)+-.02245*Math.sin(h)+.00684*Math.cos(n-2*h)+-.00293*Math.cos(2*h)+-8.5E-4*Math.cos(2*
 h-2*d)+-5.4E-4*Math.cos(n-2*d)+-2E-4*Math.sin(n+h)+-2E-4*Math.cos(n+2*h)+-2E-4*Math.cos(n-h)+1.4E-4*Math.cos(n+2*h-2*d);var x=-.02816*Math.sin(n)+.02244*Math.cos(h)+-.00682*Math.sin(n-2*h)+-.00279*Math.sin(2*h)+-8.3E-4*Math.sin(2*h-2*d)+6.9E-4*Math.sin(n-2*d)+4E-4*Math.cos(n+h)+-2.5E-4*Math.sin(2*n)+-2.3E-4*Math.sin(n+2*h)+2E-4*Math.cos(n-h)+1.9E-4*Math.sin(n-h)+1.3E-4*Math.sin(n+2*h-2*d)+-1E-4*Math.cos(n-3*h);return new LibrationInfo(exports.RAD2DEG*k+(x*Math.cos(e)-p*Math.sin(e)),r+(-(.0252*c*Math.sin(m)+
 .00473*Math.sin(2*n-2*h)+-.00467*Math.sin(n)+.00396*Math.sin(exports.DEG2RAD*(119.75+131.849*a))+.00276*Math.sin(2*n-2*d)+.00196*Math.sin(l)+-.00183*Math.cos(n-h)+.00115*Math.sin(n-2*d)+-9.6E-4*Math.sin(n-d)+4.6E-4*Math.sin(2*h-2*d)+-3.9E-4*Math.sin(n-h)+-3.2E-4*Math.sin(n-m-d)+2.7E-4*Math.sin(2*n-m-2*d)+2.3E-4*Math.sin(exports.DEG2RAD*(72.56+20.186*a))+-1.4E-4*Math.sin(2*d)+1.4E-4*Math.cos(2*n-2*h)+-1.2E-4*Math.sin(n-2*h)+-1.2E-4*Math.sin(2*n)+1.1E-4*Math.sin(2*n-2*m-2*d))+(p*Math.cos(e)+x*Math.sin(e))*
-Math.tan(k)),g,b,f)}exports.Libration=Libration;function precession(a,b,c){b=precession_rot(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]]}
+Math.tan(k)),g,b,f,2*exports.RAD2DEG*Math.atan(MOON_MEAN_RADIUS_KM/Math.sqrt(f*f-MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM)))}exports.Libration=Libration;function precession(a,b,c){b=precession_rot(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 precession_rot(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*=ASEC2RAD;var e=((((-9.51E-8*a+1.32851E-4)*a-.00114045)*a-1.0790069)*a+5038.481507)*a*ASEC2RAD;d*=ASEC2RAD;var f=((((-5.6E-8*a+1.70663E-4)*a-.00121197)*a-2.3814292)*a+10.556403)*a*ASEC2RAD;a=Math.sin(c);c=Math.cos(c);var g=Math.sin(-e);e=Math.cos(-e);var k=Math.sin(-d);d=Math.cos(-d);var h=Math.sin(f),l=Math.cos(f);f=l*e-g*h*d;var m=l*g*c+h*d*e*c-a*h*k,n=l*g*a+h*d*e*a+c*h*
 k,p=-h*e-g*l*d,r=-h*g*c+l*d*e*c-a*l*k;h=-h*g*a+l*d*e*a+c*l*k;g*=k;l=-k*e*c-a*d;a=-k*e*a+d*c;if(b===PrecessDirection.Into2000)return new RotationMatrix([[f,m,n],[p,r,h],[g,l,a]]);if(b===PrecessDirection.From2000)return new RotationMatrix([[f,p,g],[m,r,l],[n,h,a]]);throw"Invalid precess direction";}function era(a){a=(.779057273264+.00273781191135448*a.ut+a.ut%1)%1*360;0>a&&(a+=360);return a}
 function sidereal_time(a){var b=a.tt/36525,c=15*e_tilt(a).ee;a=era(a);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}
diff --git a/source/js/astronomy.ts b/source/js/astronomy.ts
index 0f61a5f3..055425a1 100644
--- a/source/js/astronomy.ts
+++ b/source/js/astronomy.ts
@@ -1688,6 +1688,8 @@ function CalcMoon(time: AstroTime) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 export class LibrationInfo {
     constructor(
@@ -1695,7 +1697,8 @@ export class LibrationInfo {
         public elon: number,
         public mlat: number,
         public mlon: number,
-        public dist_km: number
+        public dist_km: number,
+        public diam_deg: number
     ) {}
 }
 
@@ -1712,8 +1715,9 @@ export class LibrationInfo {
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1816,7 +1820,8 @@ export function Libration(date: FlexibleDateTime): LibrationInfo {
 
     const ldash2 = -tau + (rho*Math.cos(a) + sigma*Math.sin(a))*Math.tan(bdash);
     const bdash2 = sigma*Math.cos(a) - rho*Math.sin(a);
-    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km*dist_km - MOON_MEAN_RADIUS_KM*MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(RAD2DEG*bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 
 function precession(pos: ArrayVector, time: AstroTime, dir: PrecessDirection): ArrayVector {
diff --git a/source/js/esm/astronomy.js b/source/js/esm/astronomy.js
index 0e11d386..1bbb9fb1 100644
--- a/source/js/esm/astronomy.js
+++ b/source/js/esm/astronomy.js
@@ -1573,14 +1573,17 @@ function CalcMoon(time) {
  *      Moon's geocentric ecliptic longitude.
  * @property {number} dist_km
  *      Distance between the centers of the Earth and Moon in kilometers.
+ * @property {number} diam_deg
+ *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
  */
 export class LibrationInfo {
-    constructor(elat, elon, mlat, mlon, dist_km) {
+    constructor(elat, elon, mlat, mlon, dist_km, diam_deg) {
         this.elat = elat;
         this.elon = elon;
         this.mlat = mlat;
         this.mlon = mlon;
         this.dist_km = dist_km;
+        this.diam_deg = diam_deg;
     }
 }
 /**
@@ -1596,8 +1599,9 @@ export class LibrationInfo {
  * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
  *
  * This function also returns the geocentric position of the Moon
- * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
- * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+ * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+ * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+ * and the apparent angular diameter of the Moon `diam_deg`.
  *
  * @param {FlexibleDateTime} date
  *      A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),
@@ -1681,7 +1685,8 @@ export function Libration(date) {
         +0.00011 * Math.sin(2 * mdash - 2 * m - 2 * d));
     const ldash2 = -tau + (rho * Math.cos(a) + sigma * Math.sin(a)) * Math.tan(bdash);
     const bdash2 = sigma * Math.cos(a) - rho * Math.sin(a);
-    return new LibrationInfo(RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km);
+    const diam_deg = 2.0 * RAD2DEG * Math.atan(MOON_MEAN_RADIUS_KM / Math.sqrt(dist_km * dist_km - MOON_MEAN_RADIUS_KM * MOON_MEAN_RADIUS_KM));
+    return new LibrationInfo(RAD2DEG * bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg);
 }
 function precession(pos, time, dir) {
     const r = precession_rot(time, dir);
diff --git a/source/python/README.md b/source/python/README.md
index 368c5f09..4c7bb090 100644
--- a/source/python/README.md
+++ b/source/python/README.md
@@ -476,6 +476,7 @@ for a given moment in time. See [`Libration`](#Libration) for more details.
 | `float` | `mlat` | Moon's geocentric ecliptic latitude. |
 | `float` | `mlon` | Moon's geocentric ecliptic longitude. |
 | `float` | `dist_km` | Distance between the centers of the Earth and Moon in kilometers. |
+| `float` | `diam_deg` | The apparent angular diameter of the Moon as seen from the center of the Earth. |
 
 ---
 
@@ -1516,8 +1517,9 @@ This function calculates a pair of perpendicular libration angles,
 one representing rotation of the Moon in eclitpic longitude `elon`, the other
 in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 This function also returns the geocentric position of the Moon
-expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+and the apparent angular diameter of the Moon `diam_deg`.
 
 | Type | Parameter | Description |
 | --- | --- | --- |
diff --git a/source/python/astronomy.py b/source/python/astronomy.py
index a9dfc8e9..bccba31f 100644
--- a/source/python/astronomy.py
+++ b/source/python/astronomy.py
@@ -8554,13 +8554,16 @@ class LibrationInfo:
         Moon's geocentric ecliptic longitude.
     dist_km : float
         Distance between the centers of the Earth and Moon in kilometers.
+    diam_deg : float
+        The apparent angular diameter of the Moon as seen from the center of the Earth.
     """
-    def __init__(self, elat, elon, mlat, mlon, dist_km):
+    def __init__(self, elat, elon, mlat, mlon, dist_km, diam_deg):
         self.elat = elat
         self.elon = elon
         self.mlat = mlat
         self.mlon = mlon
         self.dist_km = dist_km
+        self.diam_deg = diam_deg
 
 
 def Libration(time):
@@ -8576,8 +8579,9 @@ def Libration(time):
     in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
 
     This function also returns the geocentric position of the Moon
-    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and
-    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.
+    expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
+    distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
+    and the apparent angular diameter of the Moon `diam_deg`.
 
     Parameters
     ----------
@@ -8596,6 +8600,7 @@ def Libration(time):
     mlon = moon.geo_eclip_lon
     mlat = moon.geo_eclip_lat
     dist_km = moon.distance_au * KM_PER_AU
+    diam_deg = 2.0 * math.degrees(math.atan(_MOON_MEAN_RADIUS_KM / math.sqrt(dist_km*dist_km - _MOON_MEAN_RADIUS_KM*_MOON_MEAN_RADIUS_KM)))
 
     # Inclination angle
     I = math.radians(1.54242)
@@ -8682,4 +8687,4 @@ def Libration(time):
     ldash2 = -tau + (rho*math.cos(a) + sigma*math.sin(a))*math.tan(bdash)
     bdash = math.degrees(bdash)
     bdash2 = sigma*math.cos(a) - rho*math.sin(a)
-    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km)
+    return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg)
diff --git a/website/src/assets/documentation.json b/website/src/assets/documentation.json
index 947ddf99..4c04c224 100644
--- a/website/src/assets/documentation.json
+++ b/website/src/assets/documentation.json
@@ -12835,14 +12835,14 @@
         "scope": "global"
     },
     {
-        "comment": "/**\n * @brief Lunar libration angles, returned by {@link Libration}.\n *\n * @property {number} elat\n *      Sub-Earth libration ecliptic latitude angle, in degrees.\n * @property {number} elon\n *      Sub-Earth libration ecliptic longitude angle, in degrees.\n * @property {number} mlat\n *      Moon's geocentric ecliptic latitude.\n * @property {number} mlon\n *      Moon's geocentric ecliptic longitude.\n * @property {number} dist_km\n *      Distance between the centers of the Earth and Moon in kilometers.\n */",
+        "comment": "/**\n * @brief Lunar libration angles, returned by {@link Libration}.\n *\n * @property {number} elat\n *      Sub-Earth libration ecliptic latitude angle, in degrees.\n * @property {number} elon\n *      Sub-Earth libration ecliptic longitude angle, in degrees.\n * @property {number} mlat\n *      Moon's geocentric ecliptic latitude.\n * @property {number} mlon\n *      Moon's geocentric ecliptic longitude.\n * @property {number} dist_km\n *      Distance between the centers of the Earth and Moon in kilometers.\n * @property {number} diam_deg\n *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.\n */",
         "meta": {
             "range": [
-                74227,
-                74443
+                74359,
+                74619
             ],
             "filename": "astronomy.js",
-            "lineno": 1587,
+            "lineno": 1589,
             "columnno": 0,
             "code": {
                 "id": "astnode100008548",
@@ -12853,7 +12853,8 @@
                     "elon",
                     "mlat",
                     "mlon",
-                    "dist_km"
+                    "dist_km",
+                    "diam_deg"
                 ]
             }
         },
@@ -12910,6 +12911,15 @@
                 },
                 "description": "Distance between the centers of the Earth and Moon in kilometers.",
                 "name": "dist_km"
+            },
+            {
+                "type": {
+                    "names": [
+                        "number"
+                    ]
+                },
+                "description": "The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.",
+                "name": "diam_deg"
             }
         ],
         "name": "LibrationInfo",
@@ -12922,11 +12932,11 @@
         "comment": "",
         "meta": {
             "range": [
-                74253,
-                74441
+                74385,
+                74617
             ],
             "filename": "astronomy.js",
-            "lineno": 1588,
+            "lineno": 1590,
             "columnno": 4,
             "code": {
                 "id": "astnode100008551",
@@ -12937,7 +12947,8 @@
                     "elon",
                     "mlat",
                     "mlon",
-                    "dist_km"
+                    "dist_km",
+                    "diam_deg"
                 ]
             },
             "vars": {
@@ -12952,14 +12963,14 @@
         "params": []
     },
     {
-        "comment": "/**\n * @brief Lunar libration angles, returned by {@link Libration}.\n *\n * @property {number} elat\n *      Sub-Earth libration ecliptic latitude angle, in degrees.\n * @property {number} elon\n *      Sub-Earth libration ecliptic longitude angle, in degrees.\n * @property {number} mlat\n *      Moon's geocentric ecliptic latitude.\n * @property {number} mlon\n *      Moon's geocentric ecliptic longitude.\n * @property {number} dist_km\n *      Distance between the centers of the Earth and Moon in kilometers.\n */",
+        "comment": "/**\n * @brief Lunar libration angles, returned by {@link Libration}.\n *\n * @property {number} elat\n *      Sub-Earth libration ecliptic latitude angle, in degrees.\n * @property {number} elon\n *      Sub-Earth libration ecliptic longitude angle, in degrees.\n * @property {number} mlat\n *      Moon's geocentric ecliptic latitude.\n * @property {number} mlon\n *      Moon's geocentric ecliptic longitude.\n * @property {number} dist_km\n *      Distance between the centers of the Earth and Moon in kilometers.\n * @property {number} diam_deg\n *      The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.\n */",
         "meta": {
             "range": [
-                74227,
-                74443
+                74359,
+                74619
             ],
             "filename": "astronomy.js",
-            "lineno": 1587,
+            "lineno": 1589,
             "columnno": 0,
             "code": {
                 "id": "astnode100008548",
@@ -12970,7 +12981,8 @@
                     "elon",
                     "mlat",
                     "mlon",
-                    "dist_km"
+                    "dist_km",
+                    "diam_deg"
                 ]
             }
         },
@@ -13031,6 +13043,15 @@
                 },
                 "description": "Distance between the centers of the Earth and Moon in kilometers.",
                 "name": "dist_km"
+            },
+            {
+                "type": {
+                    "names": [
+                        "number"
+                    ]
+                },
+                "description": "The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.",
+                "name": "diam_deg"
             }
         ]
     },
@@ -13038,14 +13059,14 @@
         "comment": "",
         "meta": {
             "range": [
-                74308,
-                74324
+                74450,
+                74466
             ],
             "filename": "astronomy.js",
-            "lineno": 1589,
+            "lineno": 1591,
             "columnno": 8,
             "code": {
-                "id": "astnode100008561",
+                "id": "astnode100008562",
                 "name": "this.elat",
                 "type": "Identifier",
                 "value": "elat",
@@ -13063,14 +13084,14 @@
         "comment": "",
         "meta": {
             "range": [
-                74334,
-                74350
+                74476,
+                74492
             ],
             "filename": "astronomy.js",
-            "lineno": 1590,
+            "lineno": 1592,
             "columnno": 8,
             "code": {
-                "id": "astnode100008567",
+                "id": "astnode100008568",
                 "name": "this.elon",
                 "type": "Identifier",
                 "value": "elon",
@@ -13088,14 +13109,14 @@
         "comment": "",
         "meta": {
             "range": [
-                74360,
-                74376
+                74502,
+                74518
             ],
             "filename": "astronomy.js",
-            "lineno": 1591,
+            "lineno": 1593,
             "columnno": 8,
             "code": {
-                "id": "astnode100008573",
+                "id": "astnode100008574",
                 "name": "this.mlat",
                 "type": "Identifier",
                 "value": "mlat",
@@ -13113,14 +13134,14 @@
         "comment": "",
         "meta": {
             "range": [
-                74386,
-                74402
+                74528,
+                74544
             ],
             "filename": "astronomy.js",
-            "lineno": 1592,
+            "lineno": 1594,
             "columnno": 8,
             "code": {
-                "id": "astnode100008579",
+                "id": "astnode100008580",
                 "name": "this.mlon",
                 "type": "Identifier",
                 "value": "mlon",
@@ -13138,14 +13159,14 @@
         "comment": "",
         "meta": {
             "range": [
-                74412,
-                74434
+                74554,
+                74576
             ],
             "filename": "astronomy.js",
-            "lineno": 1593,
+            "lineno": 1595,
             "columnno": 8,
             "code": {
-                "id": "astnode100008585",
+                "id": "astnode100008586",
                 "name": "this.dist_km",
                 "type": "Identifier",
                 "value": "dist_km",
@@ -13163,14 +13184,39 @@
         "comment": "",
         "meta": {
             "range": [
-                74444,
-                74481
+                74586,
+                74610
             ],
             "filename": "astronomy.js",
             "lineno": 1596,
+            "columnno": 8,
+            "code": {
+                "id": "astnode100008592",
+                "name": "this.diam_deg",
+                "type": "Identifier",
+                "value": "diam_deg",
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "diam_deg",
+        "longname": "LibrationInfo#diam_deg",
+        "kind": "member",
+        "memberof": "LibrationInfo",
+        "scope": "instance"
+    },
+    {
+        "comment": "",
+        "meta": {
+            "range": [
+                74620,
+                74657
+            ],
+            "filename": "astronomy.js",
+            "lineno": 1599,
             "columnno": 0,
             "code": {
-                "id": "astnode100008591",
+                "id": "astnode100008598",
                 "name": "exports.LibrationInfo",
                 "type": "Identifier",
                 "value": "LibrationInfo",
@@ -13184,17 +13230,17 @@
         "scope": "global"
     },
     {
-        "comment": "/**\n * @brief Calculates the Moon's libration angles at a given moment in time.\n *\n * Libration is an observed back-and-forth wobble of the portion of the\n * Moon visible from the Earth. It is caused by the imperfect tidal locking\n * of the Moon's fixed rotation rate, compared to its variable angular speed\n * of orbit around the Earth.\n *\n * This function calculates a pair of perpendicular libration angles,\n * one representing rotation of the Moon in eclitpic longitude `elon`, the other\n * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n *\n * This function also returns the geocentric position of the Moon\n * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and\n * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers.\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.\n *\n * @returns {LibrationInfo}\n */",
+        "comment": "/**\n * @brief Calculates the Moon's libration angles at a given moment in time.\n *\n * Libration is an observed back-and-forth wobble of the portion of the\n * Moon visible from the Earth. It is caused by the imperfect tidal locking\n * of the Moon's fixed rotation rate, compared to its variable angular speed\n * of orbit around the Earth.\n *\n * This function calculates a pair of perpendicular libration angles,\n * one representing rotation of the Moon in eclitpic longitude `elon`, the other\n * in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n *\n * This function also returns the geocentric position of the Moon\n * expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the\n * distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,\n * and the apparent angular diameter of the Moon `diam_deg`.\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.\n *\n * @returns {LibrationInfo}\n */",
         "meta": {
             "range": [
-                75491,
-                79382
+                75728,
+                79781
             ],
             "filename": "astronomy.js",
-            "lineno": 1619,
+            "lineno": 1623,
             "columnno": 0,
             "code": {
-                "id": "astnode100008596",
+                "id": "astnode100008603",
                 "name": "Libration",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -13228,15 +13274,16 @@
                 "sigma": "Libration~sigma",
                 "tau": "Libration~tau",
                 "ldash2": "Libration~ldash2",
-                "bdash2": "Libration~bdash2"
+                "bdash2": "Libration~bdash2",
+                "diam_deg": "Libration~diam_deg"
             }
         },
         "tags": [
             {
                 "originalTitle": "brief",
                 "title": "brief",
-                "text": "Calculates the Moon's libration angles at a given moment in time.\n\nLibration is an observed back-and-forth wobble of the portion of the\nMoon visible from the Earth. It is caused by the imperfect tidal locking\nof the Moon's fixed rotation rate, compared to its variable angular speed\nof orbit around the Earth.\n\nThis function calculates a pair of perpendicular libration angles,\none representing rotation of the Moon in eclitpic longitude `elon`, the other\nin ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n\nThis function also returns the geocentric position of the Moon\nexpressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and\ndistance `dist_km` between the centers of the Earth and Moon expressed in kilometers.",
-                "value": "Calculates the Moon's libration angles at a given moment in time.\n\nLibration is an observed back-and-forth wobble of the portion of the\nMoon visible from the Earth. It is caused by the imperfect tidal locking\nof the Moon's fixed rotation rate, compared to its variable angular speed\nof orbit around the Earth.\n\nThis function calculates a pair of perpendicular libration angles,\none representing rotation of the Moon in eclitpic longitude `elon`, the other\nin ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n\nThis function also returns the geocentric position of the Moon\nexpressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, and\ndistance `dist_km` between the centers of the Earth and Moon expressed in kilometers."
+                "text": "Calculates the Moon's libration angles at a given moment in time.\n\nLibration is an observed back-and-forth wobble of the portion of the\nMoon visible from the Earth. It is caused by the imperfect tidal locking\nof the Moon's fixed rotation rate, compared to its variable angular speed\nof orbit around the Earth.\n\nThis function calculates a pair of perpendicular libration angles,\none representing rotation of the Moon in eclitpic longitude `elon`, the other\nin ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n\nThis function also returns the geocentric position of the Moon\nexpressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the\ndistance `dist_km` between the centers of the Earth and Moon expressed in kilometers,\nand the apparent angular diameter of the Moon `diam_deg`.",
+                "value": "Calculates the Moon's libration angles at a given moment in time.\n\nLibration is an observed back-and-forth wobble of the portion of the\nMoon visible from the Earth. It is caused by the imperfect tidal locking\nof the Moon's fixed rotation rate, compared to its variable angular speed\nof orbit around the Earth.\n\nThis function calculates a pair of perpendicular libration angles,\none representing rotation of the Moon in eclitpic longitude `elon`, the other\nin ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.\n\nThis function also returns the geocentric position of the Moon\nexpressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the\ndistance `dist_km` between the centers of the Earth and Moon expressed in kilometers,\nand the apparent angular diameter of the Moon `diam_deg`."
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                 "type": "BinaryExpression",
                 "value": ""
@@ -16786,14 +16858,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86671,
-                86708
+                87070,
+                87107
             ],
             "filename": "astronomy.js",
-            "lineno": 1889,
+            "lineno": 1894,
             "columnno": 10,
             "code": {
-                "id": "astnode100010850",
+                "id": "astnode100010884",
                 "name": "yy",
                 "type": "BinaryExpression",
                 "value": ""
@@ -16811,14 +16883,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86720,
-                86757
+                87119,
+                87156
             ],
             "filename": "astronomy.js",
-            "lineno": 1890,
+            "lineno": 1895,
             "columnno": 10,
             "code": {
-                "id": "astnode100010862",
+                "id": "astnode100010896",
                 "name": "zy",
                 "type": "BinaryExpression",
                 "value": ""
@@ -16836,14 +16908,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86769,
-                86785
+                87168,
+                87184
             ],
             "filename": "astronomy.js",
-            "lineno": 1891,
+            "lineno": 1896,
             "columnno": 10,
             "code": {
-                "id": "astnode100010874",
+                "id": "astnode100010908",
                 "name": "xz",
                 "type": "BinaryExpression",
                 "value": ""
@@ -16861,14 +16933,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86797,
-                86834
+                87196,
+                87233
             ],
             "filename": "astronomy.js",
-            "lineno": 1892,
+            "lineno": 1897,
             "columnno": 10,
             "code": {
-                "id": "astnode100010880",
+                "id": "astnode100010914",
                 "name": "yz",
                 "type": "BinaryExpression",
                 "value": ""
@@ -16886,14 +16958,14 @@
         "comment": "",
         "meta": {
             "range": [
-                86846,
-                86883
+                87245,
+                87282
             ],
             "filename": "astronomy.js",
-            "lineno": 1893,
+            "lineno": 1898,
             "columnno": 10,
             "code": {
-                "id": "astnode100010892",
+                "id": "astnode100010926",
                 "name": "zz",
                 "type": "BinaryExpression",
                 "value": ""
@@ -16911,14 +16983,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87350,
-                87755
+                87749,
+                88154
             ],
             "filename": "astronomy.js",
-            "lineno": 1912,
+            "lineno": 1917,
             "columnno": 0,
             "code": {
-                "id": "astnode100010951",
+                "id": "astnode100010985",
                 "name": "gyration",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -16939,14 +17011,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87756,
-                87932
+                88155,
+                88331
             ],
             "filename": "astronomy.js",
-            "lineno": 1920,
+            "lineno": 1925,
             "columnno": 0,
             "code": {
-                "id": "astnode100010982",
+                "id": "astnode100011016",
                 "name": "geo_pos",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -16970,14 +17042,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87801,
-                87827
+                88200,
+                88226
             ],
             "filename": "astronomy.js",
-            "lineno": 1921,
+            "lineno": 1926,
             "columnno": 10,
             "code": {
-                "id": "astnode100010988",
+                "id": "astnode100011022",
                 "name": "gast",
                 "type": "CallExpression",
                 "value": ""
@@ -16995,14 +17067,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87839,
-                87870
+                88238,
+                88269
             ],
             "filename": "astronomy.js",
-            "lineno": 1922,
+            "lineno": 1927,
             "columnno": 10,
             "code": {
-                "id": "astnode100010994",
+                "id": "astnode100011028",
                 "name": "pos",
                 "type": "MemberExpression",
                 "value": ".pos"
@@ -17020,14 +17092,14 @@
         "comment": "/**\n * @brief A 3D Cartesian vector with a time attached to it.\n *\n * Holds the Cartesian coordinates of a vector in 3D space,\n * along with the time at which the vector is valid.\n *\n * @property {number} x        The x-coordinate expressed in astronomical units (AU).\n * @property {number} y        The y-coordinate expressed in astronomical units (AU).\n * @property {number} z        The z-coordinate expressed in astronomical units (AU).\n * @property {AstroTime} t     The time at which the vector is valid.\n */",
         "meta": {
             "range": [
-                88448,
-                88789
+                88847,
+                89188
             ],
             "filename": "astronomy.js",
-            "lineno": 1936,
+            "lineno": 1941,
             "columnno": 0,
             "code": {
-                "id": "astnode100011010",
+                "id": "astnode100011044",
                 "name": "Vector",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17094,14 +17166,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88467,
-                88578
+                88866,
+                88977
             ],
             "filename": "astronomy.js",
-            "lineno": 1937,
+            "lineno": 1942,
             "columnno": 4,
             "code": {
-                "id": "astnode100011013",
+                "id": "astnode100011047",
                 "name": "Vector",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -17126,14 +17198,14 @@
         "comment": "/**\n * @brief A 3D Cartesian vector with a time attached to it.\n *\n * Holds the Cartesian coordinates of a vector in 3D space,\n * along with the time at which the vector is valid.\n *\n * @property {number} x        The x-coordinate expressed in astronomical units (AU).\n * @property {number} y        The y-coordinate expressed in astronomical units (AU).\n * @property {number} z        The z-coordinate expressed in astronomical units (AU).\n * @property {AstroTime} t     The time at which the vector is valid.\n */",
         "meta": {
             "range": [
-                88448,
-                88789
+                88847,
+                89188
             ],
             "filename": "astronomy.js",
-            "lineno": 1936,
+            "lineno": 1941,
             "columnno": 0,
             "code": {
-                "id": "astnode100011010",
+                "id": "astnode100011044",
                 "name": "Vector",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17199,14 +17271,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88501,
-                88511
+                88900,
+                88910
             ],
             "filename": "astronomy.js",
-            "lineno": 1938,
+            "lineno": 1943,
             "columnno": 8,
             "code": {
-                "id": "astnode100011022",
+                "id": "astnode100011056",
                 "name": "this.x",
                 "type": "Identifier",
                 "value": "x",
@@ -17224,14 +17296,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88521,
-                88531
+                88920,
+                88930
             ],
             "filename": "astronomy.js",
-            "lineno": 1939,
+            "lineno": 1944,
             "columnno": 8,
             "code": {
-                "id": "astnode100011028",
+                "id": "astnode100011062",
                 "name": "this.y",
                 "type": "Identifier",
                 "value": "y",
@@ -17249,14 +17321,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88541,
-                88551
+                88940,
+                88950
             ],
             "filename": "astronomy.js",
-            "lineno": 1940,
+            "lineno": 1945,
             "columnno": 8,
             "code": {
-                "id": "astnode100011034",
+                "id": "astnode100011068",
                 "name": "this.z",
                 "type": "Identifier",
                 "value": "z",
@@ -17274,14 +17346,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88561,
-                88571
+                88960,
+                88970
             ],
             "filename": "astronomy.js",
-            "lineno": 1941,
+            "lineno": 1946,
             "columnno": 8,
             "code": {
-                "id": "astnode100011040",
+                "id": "astnode100011074",
                 "name": "this.t",
                 "type": "Identifier",
                 "value": "t",
@@ -17299,14 +17371,14 @@
         "comment": "/**\n     * Returns the length of the vector in astronomical units (AU).\n     * @returns {number}\n     */",
         "meta": {
             "range": [
-                88692,
-                88787
+                89091,
+                89186
             ],
             "filename": "astronomy.js",
-            "lineno": 1947,
+            "lineno": 1952,
             "columnno": 4,
             "code": {
-                "id": "astnode100011045",
+                "id": "astnode100011079",
                 "name": "Vector#Length",
                 "type": "MethodDefinition",
                 "paramnames": []
@@ -17336,14 +17408,14 @@
         "comment": "",
         "meta": {
             "range": [
-                88790,
-                88813
+                89189,
+                89212
             ],
             "filename": "astronomy.js",
-            "lineno": 1951,
+            "lineno": 1956,
             "columnno": 0,
             "code": {
-                "id": "astnode100011078",
+                "id": "astnode100011112",
                 "name": "exports.Vector",
                 "type": "Identifier",
                 "value": "Vector",
@@ -17360,14 +17432,14 @@
         "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": [
-                89614,
-                89829
+                90013,
+                90228
             ],
             "filename": "astronomy.js",
-            "lineno": 1966,
+            "lineno": 1971,
             "columnno": 0,
             "code": {
-                "id": "astnode100011083",
+                "id": "astnode100011117",
                 "name": "StateVector",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17464,14 +17536,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89638,
-                89827
+                90037,
+                90226
             ],
             "filename": "astronomy.js",
-            "lineno": 1967,
+            "lineno": 1972,
             "columnno": 4,
             "code": {
-                "id": "astnode100011086",
+                "id": "astnode100011120",
                 "name": "StateVector",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -17499,14 +17571,14 @@
         "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": [
-                89614,
-                89829
+                90013,
+                90228
             ],
             "filename": "astronomy.js",
-            "lineno": 1966,
+            "lineno": 1971,
             "columnno": 0,
             "code": {
-                "id": "astnode100011083",
+                "id": "astnode100011117",
                 "name": "StateVector",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17602,14 +17674,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89684,
-                89694
+                90083,
+                90093
             ],
             "filename": "astronomy.js",
-            "lineno": 1968,
+            "lineno": 1973,
             "columnno": 8,
             "code": {
-                "id": "astnode100011098",
+                "id": "astnode100011132",
                 "name": "this.x",
                 "type": "Identifier",
                 "value": "x",
@@ -17627,14 +17699,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89704,
-                89714
+                90103,
+                90113
             ],
             "filename": "astronomy.js",
-            "lineno": 1969,
+            "lineno": 1974,
             "columnno": 8,
             "code": {
-                "id": "astnode100011104",
+                "id": "astnode100011138",
                 "name": "this.y",
                 "type": "Identifier",
                 "value": "y",
@@ -17652,14 +17724,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89724,
-                89734
+                90123,
+                90133
             ],
             "filename": "astronomy.js",
-            "lineno": 1970,
+            "lineno": 1975,
             "columnno": 8,
             "code": {
-                "id": "astnode100011110",
+                "id": "astnode100011144",
                 "name": "this.z",
                 "type": "Identifier",
                 "value": "z",
@@ -17677,14 +17749,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89744,
-                89756
+                90143,
+                90155
             ],
             "filename": "astronomy.js",
-            "lineno": 1971,
+            "lineno": 1976,
             "columnno": 8,
             "code": {
-                "id": "astnode100011116",
+                "id": "astnode100011150",
                 "name": "this.vx",
                 "type": "Identifier",
                 "value": "vx",
@@ -17702,14 +17774,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89766,
-                89778
+                90165,
+                90177
             ],
             "filename": "astronomy.js",
-            "lineno": 1972,
+            "lineno": 1977,
             "columnno": 8,
             "code": {
-                "id": "astnode100011122",
+                "id": "astnode100011156",
                 "name": "this.vy",
                 "type": "Identifier",
                 "value": "vy",
@@ -17727,14 +17799,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89788,
-                89800
+                90187,
+                90199
             ],
             "filename": "astronomy.js",
-            "lineno": 1973,
+            "lineno": 1978,
             "columnno": 8,
             "code": {
-                "id": "astnode100011128",
+                "id": "astnode100011162",
                 "name": "this.vz",
                 "type": "Identifier",
                 "value": "vz",
@@ -17752,14 +17824,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89810,
-                89820
+                90209,
+                90219
             ],
             "filename": "astronomy.js",
-            "lineno": 1974,
+            "lineno": 1979,
             "columnno": 8,
             "code": {
-                "id": "astnode100011134",
+                "id": "astnode100011168",
                 "name": "this.t",
                 "type": "Identifier",
                 "value": "t",
@@ -17777,14 +17849,14 @@
         "comment": "",
         "meta": {
             "range": [
-                89830,
-                89863
+                90229,
+                90262
             ],
             "filename": "astronomy.js",
-            "lineno": 1977,
+            "lineno": 1982,
             "columnno": 0,
             "code": {
-                "id": "astnode100011140",
+                "id": "astnode100011174",
                 "name": "exports.StateVector",
                 "type": "Identifier",
                 "value": "StateVector",
@@ -17801,14 +17873,14 @@
         "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": [
-                90231,
-                90406
+                90630,
+                90805
             ],
             "filename": "astronomy.js",
-            "lineno": 1988,
+            "lineno": 1993,
             "columnno": 0,
             "code": {
-                "id": "astnode100011145",
+                "id": "astnode100011179",
                 "name": "Spherical",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17865,14 +17937,14 @@
         "comment": "",
         "meta": {
             "range": [
-                90253,
-                90404
+                90652,
+                90803
             ],
             "filename": "astronomy.js",
-            "lineno": 1989,
+            "lineno": 1994,
             "columnno": 4,
             "code": {
-                "id": "astnode100011148",
+                "id": "astnode100011182",
                 "name": "Spherical",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -17896,14 +17968,14 @@
         "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": [
-                90231,
-                90406
+                90630,
+                90805
             ],
             "filename": "astronomy.js",
-            "lineno": 1988,
+            "lineno": 1993,
             "columnno": 0,
             "code": {
-                "id": "astnode100011145",
+                "id": "astnode100011179",
                 "name": "Spherical",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -17959,14 +18031,14 @@
         "comment": "",
         "meta": {
             "range": [
-                90291,
-                90319
+                90690,
+                90718
             ],
             "filename": "astronomy.js",
-            "lineno": 1990,
+            "lineno": 1995,
             "columnno": 8,
             "code": {
-                "id": "astnode100011156",
+                "id": "astnode100011190",
                 "name": "this.lat",
                 "type": "CallExpression",
                 "value": "",
@@ -17984,14 +18056,14 @@
         "comment": "",
         "meta": {
             "range": [
-                90329,
-                90357
+                90728,
+                90756
             ],
             "filename": "astronomy.js",
-            "lineno": 1991,
+            "lineno": 1996,
             "columnno": 8,
             "code": {
-                "id": "astnode100011164",
+                "id": "astnode100011198",
                 "name": "this.lon",
                 "type": "CallExpression",
                 "value": "",
@@ -18009,14 +18081,14 @@
         "comment": "",
         "meta": {
             "range": [
-                90367,
-                90397
+                90766,
+                90796
             ],
             "filename": "astronomy.js",
-            "lineno": 1992,
+            "lineno": 1997,
             "columnno": 8,
             "code": {
-                "id": "astnode100011172",
+                "id": "astnode100011206",
                 "name": "this.dist",
                 "type": "CallExpression",
                 "value": "",
@@ -18034,14 +18106,14 @@
         "comment": "",
         "meta": {
             "range": [
-                90407,
-                90436
+                90806,
+                90835
             ],
             "filename": "astronomy.js",
-            "lineno": 1995,
+            "lineno": 2000,
             "columnno": 0,
             "code": {
-                "id": "astnode100011180",
+                "id": "astnode100011214",
                 "name": "exports.Spherical",
                 "type": "Identifier",
                 "value": "Spherical",
@@ -18058,14 +18130,14 @@
         "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": [
-                91075,
-                91288
+                91474,
+                91687
             ],
             "filename": "astronomy.js",
-            "lineno": 2015,
+            "lineno": 2020,
             "columnno": 0,
             "code": {
-                "id": "astnode100011185",
+                "id": "astnode100011219",
                 "name": "EquatorialCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -18132,14 +18204,14 @@
         "comment": "",
         "meta": {
             "range": [
-                91109,
-                91286
+                91508,
+                91685
             ],
             "filename": "astronomy.js",
-            "lineno": 2016,
+            "lineno": 2021,
             "columnno": 4,
             "code": {
-                "id": "astnode100011188",
+                "id": "astnode100011222",
                 "name": "EquatorialCoordinates",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -18164,14 +18236,14 @@
         "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": [
-                91075,
-                91288
+                91474,
+                91687
             ],
             "filename": "astronomy.js",
-            "lineno": 2015,
+            "lineno": 2020,
             "columnno": 0,
             "code": {
-                "id": "astnode100011185",
+                "id": "astnode100011219",
                 "name": "EquatorialCoordinates",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -18237,14 +18309,14 @@
         "comment": "",
         "meta": {
             "range": [
-                91151,
-                91177
+                91550,
+                91576
             ],
             "filename": "astronomy.js",
-            "lineno": 2017,
+            "lineno": 2022,
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@@ -18262,14 +18334,14 @@
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             "columnno": 8,
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@@ -18312,14 +18384,14 @@
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             "columnno": 8,
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-                "id": "astnode100011221",
+                "id": "astnode100011255",
                 "name": "this.vec",
                 "type": "Identifier",
                 "value": "vec",
@@ -18337,14 +18409,14 @@
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             "columnno": 0,
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                 "name": "exports.EquatorialCoordinates",
                 "type": "Identifier",
                 "value": "EquatorialCoordinates",
@@ -18361,14 +18433,14 @@
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             "columnno": 0,
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                 "name": "IsValidRotationArray",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -18391,14 +18463,14 @@
         "comment": "",
         "meta": {
             "range": [
-                91471,
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             ],
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             "columnno": 13,
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@@ -18416,14 +18488,14 @@
         "comment": "",
         "meta": {
             "range": [
-                91600,
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             ],
             "filename": "astronomy.js",
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             "columnno": 17,
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@@ -18441,14 +18513,14 @@
         "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": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100011302",
+                "id": "astnode100011336",
                 "name": "RotationMatrix",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -18485,14 +18557,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 4,
             "code": {
-                "id": "astnode100011305",
+                "id": "astnode100011339",
                 "name": "RotationMatrix",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -18514,14 +18586,14 @@
         "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 */",
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             "columnno": 0,
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-                "id": "astnode100011302",
+                "id": "astnode100011336",
                 "name": "RotationMatrix",
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@@ -18557,14 +18629,14 @@
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100011311",
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                 "name": "this.rot",
                 "type": "Identifier",
                 "value": "rot",
@@ -18582,14 +18654,14 @@
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         "meta": {
             "range": [
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             ],
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             "columnno": 0,
             "code": {
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                 "name": "exports.RotationMatrix",
                 "type": "Identifier",
                 "value": "RotationMatrix",
@@ -18606,14 +18678,14 @@
         "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 */",
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             ],
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@@ -18658,14 +18730,14 @@
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                 "name": "exports.MakeRotation",
                 "type": "Identifier",
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@@ -18682,14 +18754,14 @@
         "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 */",
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             "columnno": 0,
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-                "id": "astnode100011343",
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@@ -18756,14 +18828,14 @@
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             "columnno": 4,
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@@ -18788,14 +18860,14 @@
         "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 */",
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             "columnno": 0,
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@@ -18861,14 +18933,14 @@
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             "columnno": 8,
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             "columnno": 8,
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@@ -18911,14 +18983,14 @@
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@@ -18936,14 +19008,14 @@
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             "columnno": 8,
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@@ -18961,14 +19033,14 @@
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         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100011387",
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                 "name": "exports.HorizontalCoordinates",
                 "type": "Identifier",
                 "value": "HorizontalCoordinates",
@@ -18985,14 +19057,14 @@
         "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 */",
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             "columnno": 0,
             "code": {
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                 "name": "EclipticCoordinates",
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@@ -19049,14 +19121,14 @@
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             "columnno": 4,
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                 "name": "EclipticCoordinates",
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@@ -19080,14 +19152,14 @@
         "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 */",
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             ],
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             "columnno": 0,
             "code": {
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                 "type": "ClassDeclaration",
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@@ -19143,14 +19215,14 @@
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         "meta": {
             "range": [
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             "columnno": 8,
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                 "name": "this.vec",
                 "type": "Identifier",
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@@ -19168,14 +19240,14 @@
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             "columnno": 8,
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@@ -19193,14 +19265,14 @@
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             "columnno": 8,
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                 "name": "this.elon",
                 "type": "CallExpression",
                 "value": "",
@@ -19218,14 +19290,14 @@
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             "columnno": 0,
             "code": {
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                 "name": "exports.EclipticCoordinates",
                 "type": "Identifier",
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@@ -19242,14 +19314,14 @@
         "comment": "",
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             "range": [
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             "columnno": 0,
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                 "name": "VectorFromArray",
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@@ -19269,14 +19341,14 @@
         "comment": "",
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             "columnno": 0,
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                 "name": "vector2radec",
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@@ -19303,14 +19375,14 @@
         "comment": "",
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             "columnno": 10,
             "code": {
-                "id": "astnode100011454",
+                "id": "astnode100011488",
                 "name": "vec",
                 "type": "CallExpression",
                 "value": ""
@@ -19328,14 +19400,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                96891
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
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@@ -19353,14 +19425,14 @@
         "comment": "",
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             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
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@@ -20590,14 +20662,14 @@
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@@ -20615,14 +20687,14 @@
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@@ -20641,14 +20713,14 @@
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@@ -20667,14 +20739,14 @@
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             "filename": "astronomy.js",
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             "columnno": 20,
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@@ -20693,14 +20765,14 @@
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             "filename": "astronomy.js",
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             "columnno": 16,
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@@ -20719,14 +20791,14 @@
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         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 12,
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@@ -20745,14 +20817,14 @@
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         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
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-                "id": "astnode100012180",
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                 "name": "exports.Horizon",
                 "type": "Identifier",
                 "value": "Horizon",
@@ -20769,14 +20841,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                104712
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             ],
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             "columnno": 0,
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@@ -20795,14 +20867,14 @@
         "comment": "/**\n * @brief Represents the geographic location of an observer on the surface of the Earth.\n *\n * @property {number} latitude\n *      The observer's geographic latitude in degrees north of the Earth's equator.\n *      The value is negative for observers south of the equator.\n *      Must be in the range -90 to +90.\n *\n * @property {number} longitude\n *      The observer's geographic longitude in degrees east of the prime meridian\n *      passing through Greenwich, England.\n *      The value is negative for observers west of the prime meridian.\n *      The value should be kept in the range -180 to +180 to minimize floating point errors.\n *\n * @property {number} height\n *      The observer's elevation above mean sea level, expressed in meters.\n */",
         "meta": {
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@@ -20859,14 +20931,14 @@
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@@ -20890,14 +20962,14 @@
         "comment": "/**\n * @brief Represents the geographic location of an observer on the surface of the Earth.\n *\n * @property {number} latitude\n *      The observer's geographic latitude in degrees north of the Earth's equator.\n *      The value is negative for observers south of the equator.\n *      Must be in the range -90 to +90.\n *\n * @property {number} longitude\n *      The observer's geographic longitude in degrees east of the prime meridian\n *      passing through Greenwich, England.\n *      The value is negative for observers west of the prime meridian.\n *      The value should be kept in the range -180 to +180 to minimize floating point errors.\n *\n * @property {number} height\n *      The observer's elevation above mean sea level, expressed in meters.\n */",
         "meta": {
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             "columnno": 0,
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@@ -20953,14 +21025,14 @@
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         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100012253",
+                "id": "astnode100012287",
                 "name": "this.latitude",
                 "type": "Identifier",
                 "value": "latitude",
@@ -20978,14 +21050,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100012259",
+                "id": "astnode100012293",
                 "name": "this.longitude",
                 "type": "Identifier",
                 "value": "longitude",
@@ -21003,14 +21075,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100012265",
+                "id": "astnode100012299",
                 "name": "this.height",
                 "type": "Identifier",
                 "value": "height",
@@ -21028,14 +21100,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
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-                "id": "astnode100012275",
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                 "name": "exports.Observer",
                 "type": "Identifier",
                 "value": "Observer",
@@ -21052,14 +21124,14 @@
         "comment": "/**\n * @brief Returns apparent geocentric true ecliptic coordinates of date for the Sun.\n *\n * This function is used for calculating the times of equinoxes and solstices.\n *\n * <i>Geocentric</i> means coordinates as the Sun would appear to a hypothetical observer\n * at the center of the Earth.\n * <i>Ecliptic coordinates of date</i> are measured along the plane of the Earth's mean\n * orbit around the Sun, using the\n * <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>\n * of the Earth as adjusted for precession and nutation of the Earth's\n * axis of rotation on the given date.\n *\n * @param {FlexibleDateTime} date\n *      The date and time at which to calculate the Sun's apparent location as seen from\n *      the center of the Earth.\n *\n * @returns {EclipticCoordinates}\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100012280",
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                 "name": "SunPosition",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -21115,14 +21187,14 @@
         "comment": "",
         "meta": {
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@@ -21140,14 +21212,14 @@
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             "columnno": 10,
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@@ -21165,14 +21237,14 @@
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         "meta": {
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             "columnno": 10,
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                 "type": "ArrayExpression",
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@@ -21190,14 +21262,14 @@
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         "meta": {
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             ],
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             "columnno": 10,
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@@ -21215,14 +21287,14 @@
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             ],
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             "columnno": 10,
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@@ -21240,14 +21312,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
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@@ -21265,14 +21337,14 @@
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         "meta": {
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             ],
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@@ -21290,14 +21362,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
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@@ -21315,14 +21387,14 @@
         "comment": "",
         "meta": {
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+                107958
             ],
             "filename": "astronomy.js",
-            "lineno": 2392,
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             "columnno": 0,
             "code": {
-                "id": "astnode100012382",
+                "id": "astnode100012416",
                 "name": "exports.SunPosition",
                 "type": "Identifier",
                 "value": "SunPosition",
@@ -21339,14 +21411,14 @@
         "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 */",
         "meta": {
             "range": [
-                109416,
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+                110387
             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100012387",
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                 "name": "Equator",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -21439,14 +21511,14 @@
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         "meta": {
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             "columnno": 10,
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@@ -21464,14 +21536,14 @@
         "comment": "",
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             ],
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             "columnno": 10,
             "code": {
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                 "type": "CallExpression",
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@@ -21489,14 +21561,14 @@
         "comment": "",
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@@ -21514,14 +21586,14 @@
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                 "type": "ArrayExpression",
                 "value": "[\"\",\"\",\"\"]"
@@ -21539,14 +21611,14 @@
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@@ -21564,14 +21636,14 @@
         "comment": "",
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100012477",
+                "id": "astnode100012511",
                 "name": "exports.Equator",
                 "type": "Identifier",
                 "value": "Equator",
@@ -21588,14 +21660,14 @@
         "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 * The inverse of this function is also available: {@link VectorObserver}.\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 */",
         "meta": {
             "range": [
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+                112417
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100012482",
+                "id": "astnode100012516",
                 "name": "ObserverVector",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -21666,14 +21738,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 10,
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@@ -21691,14 +21763,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 10,
             "code": {
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@@ -21716,14 +21788,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 8,
             "code": {
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                 "type": "MemberExpression",
                 "value": ".pos"
@@ -21741,14 +21813,14 @@
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             "range": [
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             "columnno": 8,
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@@ -21767,14 +21839,14 @@
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             "columnno": 0,
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                 "name": "exports.ObserverVector",
                 "type": "Identifier",
                 "value": "ObserverVector",
@@ -21791,14 +21863,14 @@
         "comment": "/**\n * @brief Calculates the geographic location corresponding to an equatorial vector.\n *\n * This is the inverse function of {@link ObserverVector}.\n * Given a geocentric equatorial vector, it returns the geographic\n * latitude, longitude, and elevation for that vector.\n *\n * @param {Vector} vector\n *      The geocentric equatorial position vector for which to find geographic coordinates.\n *      The components are expressed in Astronomical Units (AU).\n *      You can calculate AU by dividing kilometers by the constant {@link KM_PER_AU}.\n *      The time `vector.t` determines the Earth's rotation.\n *\n * @param {boolean} ofdate\n *      Selects the date of the Earth's equator in which `vector` is expressed.\n *      The caller may select `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 `vector.t`.\n *      Or the caller may select `true` to use the Earth's equator at `vector.t`\n *      as the orientation.\n *\n * @returns {Observer}\n *      The geographic latitude, longitude, and elevation above sea level\n *      that corresponds to the given equatorial vector.\n */",
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@@ -21883,14 +21955,14 @@
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                 "value": "[\"vector.x\",\"vector.y\",\"vector.z\"]"
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             "filename": "astronomy.js",
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+        "longname": "VectorObserver~ovec",
+        "kind": "member",
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+        "scope": "inner"
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+        "comment": "",
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+            "code": {
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+        "name": "ovec",
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+    },
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             "columnno": 0,
             "code": {
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                 "name": "exports.VectorObserver",
                 "type": "Identifier",
                 "value": "VectorObserver",
@@ -21984,14 +22056,14 @@
         "comment": "/**\n * @brief Calculates the gravitational acceleration experienced by an observer on the Earth.\n *\n * This function implements the WGS 84 Ellipsoidal Gravity Formula.\n * The result is a combination of inward gravitational acceleration\n * with outward centrifugal acceleration, as experienced by an observer\n * in the Earth's rotating frame of reference.\n * The resulting value increases toward the Earth's poles and decreases\n * toward the equator, consistent with changes of the weight measured\n * by a spring scale of a fixed mass moved to different latitudes and heights\n * on the Earth.\n *\n * @param {number} latitude\n *      The latitude of the observer in degrees north or south of the equator.\n *      By formula symmetry, positive latitudes give the same answer as negative\n *      latitudes, so the sign does not matter.\n *\n * @param {number} height\n *      The height above the sea level geoid in meters.\n *      No range checking is done; however, accuracy is only valid in the\n *      range 0 to 100000 meters.\n *\n * @returns {number}\n *      The effective gravitational acceleration expressed in meters per second squared [m/s^2].\n */",
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                 "name": "ObserverGravity",
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@@ -22052,14 +22124,14 @@
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@@ -22127,14 +22199,14 @@
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             "columnno": 0,
             "code": {
-                "id": "astnode100012660",
+                "id": "astnode100012694",
                 "name": "exports.ObserverGravity",
                 "type": "Identifier",
                 "value": "ObserverGravity",
@@ -22151,14 +22223,14 @@
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                 "name": "RotateEquatorialToEcliptic",
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@@ -22188,14 +22260,14 @@
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@@ -22213,14 +22285,14 @@
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@@ -22288,14 +22360,14 @@
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@@ -22313,14 +22385,14 @@
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@@ -22339,14 +22411,14 @@
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@@ -22365,14 +22437,14 @@
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@@ -22390,14 +22462,14 @@
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@@ -22415,14 +22487,14 @@
         "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 */",
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             "columnno": 0,
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@@ -22498,14 +22570,14 @@
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             "columnno": 8,
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                 "type": "CallExpression",
                 "funcscope": "Ecliptic",
@@ -22524,14 +22596,14 @@
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             "columnno": 8,
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@@ -22550,14 +22622,14 @@
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             "columnno": 0,
             "code": {
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                 "type": "Identifier",
                 "value": "Ecliptic",
@@ -22574,14 +22646,14 @@
         "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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             "columnno": 0,
             "code": {
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+                "id": "astnode100012865",
                 "name": "GeoMoon",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -22634,14 +22706,14 @@
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@@ -22659,14 +22731,14 @@
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@@ -22684,14 +22756,14 @@
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@@ -22709,14 +22781,14 @@
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@@ -22734,14 +22806,14 @@
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@@ -22759,14 +22831,14 @@
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@@ -22784,14 +22856,14 @@
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                 "type": "Identifier",
                 "value": "GeoMoon",
@@ -22808,14 +22880,14 @@
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@@ -22844,14 +22916,14 @@
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@@ -22869,14 +22941,14 @@
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@@ -30327,14 +30399,14 @@
         "comment": "/**\n * @brief Calculates a vector from the center of the Earth to the given body at the given time.\n *\n * Calculates geocentric (i.e., with respect to the center of the Earth)\n * Cartesian coordinates in the J2000 equatorial system of a celestial\n * body at a specified time. The position is always corrected for light travel time:\n * this means the position of the body is \"back-dated\" based on how long it\n * takes light to travel from the body to an observer on the Earth.\n * Also, the position can optionally be corrected for aberration, an effect\n * causing the apparent direction of the body to be shifted based on\n * transverse movement of the Earth with respect to the rays of light\n * coming from that body.\n *\n * @param {Body} body\n *      One of the strings\n *      `\"Sun\"`, `\"Moon\"`, `\"Mercury\"`, `\"Venus\"`,\n *      `\"Earth\"`, `\"Mars\"`, `\"Jupiter\"`, `\"Saturn\"`,\n *      `\"Uranus\"`, `\"Neptune\"`, or `\"Pluto\"`.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which the body's position is to be calculated.\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 {Vector}\n */",
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             "columnno": 0,
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@@ -30505,14 +30577,14 @@
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                 "value": "time"
@@ -30555,14 +30627,14 @@
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             "code": {
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-        "kind": "member",
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+        "name": "earth",
+        "longname": "GeoVector~earth",
+        "kind": "member",
+        "memberof": "GeoVector",
+        "scope": "inner"
+    },
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@@ -30812,14 +30884,14 @@
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         "comment": "/**\n * @brief Searches for when the Sun reaches a given ecliptic longitude.\n *\n * Searches for the moment in time when the center of the Sun reaches a given apparent\n * ecliptic longitude, as seen from the center of the Earth, within a given range of dates.\n * This function can be used to determine equinoxes and solstices.\n * However, it is usually more convenient and efficient to call {@link Seasons}\n * to calculate equinoxes and solstices for a given calendar year.\n * `SearchSunLongitude` is more general in that it allows searching for arbitrary longitude values.\n *\n * @param {number} targetLon\n *      The desired ecliptic longitude of date in degrees.\n *      This may be any value in the range [0, 360), although certain\n *      values have conventional meanings:\n *\n *      When `targetLon` is 0, finds the March equinox,\n *      which is the moment spring begins in the northern hemisphere\n *      and the beginning of autumn in the southern hemisphere.\n *\n *      When `targetLon` is 180, finds the September equinox,\n *      which is the moment autumn begins in the northern hemisphere and\n *      spring begins in the southern hemisphere.\n *\n *      When `targetLon` is 90, finds the northern solstice, which is the\n *      moment summer begins in the northern hemisphere and winter\n *      begins in the southern hemisphere.\n *\n *      When `targetLon` is 270, finds the southern solstice, which is the\n *      moment winter begins in the northern hemisphere and summer\n *      begins in the southern hemisphere.\n *\n * @param {FlexibleDateTime} dateStart\n *      A date and time known to be earlier than the desired longitude event.\n *\n * @param {number} limitDays\n *      A floating point number of days, which when added to `dateStart`,\n *      yields a date and time known to be after the desired longitude event.\n *\n * @returns {AstroTime | null}\n *      The date and time when the Sun reaches the apparent ecliptic longitude `targetLon`\n *      within the range of times specified by `dateStart` and `limitDays`.\n *      If the Sun does not reach the target longitude within the specified time range, or the\n *      time range is excessively wide, the return value is `null`.\n *      To avoid a `null` return value, the caller must pick a time window around\n *      the event that is within a few days but not so small that the event might fall outside the window.\n */",
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                 "name": "exports.SearchSunLongitude",
                 "type": "Identifier",
                 "value": "SearchSunLongitude",
@@ -32771,14 +32843,14 @@
         "comment": "/**\n * @brief Returns one body's ecliptic longitude with respect to another, as seen from the Earth.\n *\n * This function determines where one body appears around the ecliptic plane\n * (the plane of the Earth's orbit around the Sun) as seen from the Earth,\n * relative to the another body's apparent position.\n * The function returns an angle in the half-open range [0, 360) degrees.\n * The value is the ecliptic longitude of `body1` relative to the ecliptic\n * longitude of `body2`.\n *\n * The angle is 0 when the two bodies are at the same ecliptic longitude\n * as seen from the Earth. The angle increases in the prograde direction\n * (the direction that the planets orbit the Sun and the Moon orbits the Earth).\n *\n * When the angle is 180 degrees, it means the two bodies appear on opposite sides\n * of the sky for an Earthly observer.\n *\n * Neither `body1` nor `body2` is allowed to be `Body.Earth`.\n * If this happens, the function throws an exception.\n *\n * @param {Body} body1\n *      The first body, whose longitude is to be found relative to the second body.\n *\n * @param {Body} body2\n *      The second body, relative to which the longitude of the first body is to be found.\n *\n * @param {FlexibleDateTime} date\n *      The date and time of the observation.\n *\n * @returns {number}\n *      An angle in the range [0, 360), expressed in degrees.\n */",
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                 "name": "exports.PairLongitude",
                 "type": "Identifier",
                 "value": "PairLongitude",
@@ -33000,14 +33072,14 @@
         "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 PairLongitude}, 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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                 "name": "exports.AngleFromSun",
                 "type": "Identifier",
                 "value": "AngleFromSun",
@@ -33193,14 +33265,14 @@
         "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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                 "name": "EclipticLongitude",
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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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@@ -34922,14 +34994,14 @@
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                 "name": "this.phase_angle",
                 "type": "Identifier",
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@@ -34947,14 +35019,14 @@
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                 "name": "this.helio_dist",
                 "type": "Identifier",
                 "value": "helio_dist",
@@ -34972,14 +35044,14 @@
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             "columnno": 8,
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-                "id": "astnode100018649",
+                "id": "astnode100018683",
                 "name": "this.geo_dist",
                 "type": "Identifier",
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@@ -34997,14 +35069,14 @@
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+                "id": "astnode100018689",
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@@ -35022,14 +35094,14 @@
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             "columnno": 8,
             "code": {
-                "id": "astnode100018661",
+                "id": "astnode100018695",
                 "name": "this.hc",
                 "type": "Identifier",
                 "value": "hc",
@@ -35047,14 +35119,14 @@
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018667",
+                "id": "astnode100018701",
                 "name": "this.ring_tilt",
                 "type": "Identifier",
                 "value": "ring_tilt",
@@ -35072,14 +35144,14 @@
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018673",
+                "id": "astnode100018707",
                 "name": "this.phase_fraction",
                 "type": "BinaryExpression",
                 "value": "",
@@ -35097,14 +35169,14 @@
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             ],
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+            "lineno": 3960,
             "columnno": 0,
             "code": {
-                "id": "astnode100018691",
+                "id": "astnode100018725",
                 "name": "exports.IlluminationInfo",
                 "type": "Identifier",
                 "value": "IlluminationInfo",
@@ -35121,14 +35193,14 @@
         "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 */",
         "meta": {
             "range": [
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-                180556
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             ],
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+            "lineno": 3977,
             "columnno": 0,
             "code": {
-                "id": "astnode100018696",
+                "id": "astnode100018730",
                 "name": "Illumination",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -35195,14 +35267,14 @@
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             "range": [
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             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100018711",
+                "id": "astnode100018745",
                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -35220,14 +35292,14 @@
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             "range": [
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-                178824
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             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100018717",
+                "id": "astnode100018751",
                 "name": "earth",
                 "type": "CallExpression",
                 "value": ""
@@ -35245,14 +35317,14 @@
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018726",
+                "id": "astnode100018760",
                 "name": "phase"
             }
         },
@@ -35268,14 +35340,14 @@
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             ],
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             "columnno": 8,
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+                "id": "astnode100018763",
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         },
@@ -35291,14 +35363,14 @@
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             ],
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+                "id": "astnode100018766",
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@@ -35314,14 +35386,14 @@
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             ],
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+                "id": "astnode100018769",
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@@ -35337,14 +35409,14 @@
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             ],
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@@ -35363,14 +35435,14 @@
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             "columnno": 8,
             "code": {
-                "id": "astnode100018763",
+                "id": "astnode100018797",
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                 "type": "NewExpression",
                 "funcscope": "Illumination",
@@ -35389,14 +35461,14 @@
         "comment": "",
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             "range": [
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             ],
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+            "lineno": 3989,
             "columnno": 8,
             "code": {
-                "id": "astnode100018772",
+                "id": "astnode100018806",
                 "name": "phase",
                 "type": "Literal",
                 "funcscope": "Illumination",
@@ -35415,66 +35487,66 @@
         "comment": "",
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-            ],
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-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "gc",
-        "longname": "Illumination~gc",
-        "kind": "member",
-        "memberof": "Illumination",
-        "scope": "inner"
-    },
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-        "scope": "inner"
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             ],
             "filename": "astronomy.js",
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             "columnno": 12,
             "code": {
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+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "gc",
+        "longname": "Illumination~gc",
+        "kind": "member",
+        "memberof": "Illumination",
+        "scope": "inner"
+    },
+    {
+        "comment": "",
+        "meta": {
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+            ],
+            "filename": "astronomy.js",
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+            "code": {
+                "id": "astnode100018824",
+                "name": "hc",
+                "type": "NewExpression",
+                "funcscope": "Illumination",
+                "value": "",
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "hc",
+        "longname": "Illumination~hc",
+        "kind": "member",
+        "memberof": "Illumination",
+        "scope": "inner"
+    },
+    {
+        "comment": "",
+        "meta": {
+            "range": [
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+            ],
+            "filename": "astronomy.js",
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+            "columnno": 12,
+            "code": {
+                "id": "astnode100018852",
                 "name": "hc",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -35493,14 +35565,14 @@
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100018825",
+                "id": "astnode100018859",
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                 "type": "NewExpression",
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@@ -35519,14 +35591,14 @@
         "comment": "",
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018852",
+                "id": "astnode100018886",
                 "name": "phase",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -35545,14 +35617,14 @@
         "comment": "",
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             "range": [
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+                180242
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100018859",
+                "id": "astnode100018893",
                 "name": "geo_dist",
                 "type": "CallExpression",
                 "value": ""
@@ -35570,14 +35642,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018866",
+                "id": "astnode100018900",
                 "name": "helio_dist",
                 "type": "CallExpression",
                 "value": ""
@@ -35595,14 +35667,14 @@
         "comment": "",
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018873",
+                "id": "astnode100018907",
                 "name": "ring_tilt"
             }
         },
@@ -35618,14 +35690,14 @@
         "comment": "",
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             "range": [
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+                180486
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018883",
+                "id": "astnode100018917",
                 "name": "mag",
                 "type": "BinaryExpression",
                 "funcscope": "Illumination",
@@ -35644,14 +35716,14 @@
         "comment": "",
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+                180585
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018902",
+                "id": "astnode100018936",
                 "name": "mag",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -35670,14 +35742,14 @@
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             "range": [
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+                180707
             ],
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             "columnno": 14,
             "code": {
-                "id": "astnode100018917",
+                "id": "astnode100018951",
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                 "value": ""
@@ -35695,14 +35767,14 @@
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+                180733
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018927",
+                "id": "astnode100018961",
                 "name": "mag",
                 "type": "MemberExpression",
                 "funcscope": "Illumination",
@@ -35721,14 +35793,14 @@
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             "range": [
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+                180771
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018933",
+                "id": "astnode100018967",
                 "name": "ring_tilt",
                 "type": "MemberExpression",
                 "funcscope": "Illumination",
@@ -35747,14 +35819,14 @@
         "comment": "",
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             "range": [
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+                180854
             ],
             "filename": "astronomy.js",
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+            "lineno": 4019,
             "columnno": 8,
             "code": {
-                "id": "astnode100018940",
+                "id": "astnode100018974",
                 "name": "mag",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -35773,14 +35845,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                180991
             ],
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+            "lineno": 4023,
             "columnno": 0,
             "code": {
-                "id": "astnode100018960",
+                "id": "astnode100018994",
                 "name": "exports.Illumination",
                 "type": "Identifier",
                 "value": "Illumination",
@@ -35797,14 +35869,14 @@
         "comment": "",
         "meta": {
             "range": [
-                180594,
-                181505
+                180993,
+                181904
             ],
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+            "lineno": 4024,
             "columnno": 0,
             "code": {
-                "id": "astnode100018965",
+                "id": "astnode100018999",
                 "name": "SynodicPeriod",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -35829,14 +35901,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                181147
+                181525,
+                181546
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100018986",
+                "id": "astnode100019020",
                 "name": "planet",
                 "type": "MemberExpression",
                 "value": "Planet[undefined]"
@@ -35854,14 +35926,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                181383
+                181751,
+                181782
             ],
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+            "lineno": 4038,
             "columnno": 10,
             "code": {
-                "id": "astnode100019000",
+                "id": "astnode100019034",
                 "name": "Te",
                 "type": "MemberExpression",
                 "value": "Planet.Earth.OrbitalPeriod"
@@ -35879,14 +35951,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                181420
+                181794,
+                181819
             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100019008",
+                "id": "astnode100019042",
                 "name": "Tp",
                 "type": "MemberExpression",
                 "value": "planet.OrbitalPeriod"
@@ -35904,14 +35976,14 @@
         "comment": "",
         "meta": {
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+                181875
             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100019014",
+                "id": "astnode100019048",
                 "name": "synodicPeriod",
                 "type": "CallExpression",
                 "value": ""
@@ -35929,14 +36001,14 @@
         "comment": "/**\n * @brief Searches for when the Earth and a given body reach a relative ecliptic longitude separation.\n *\n * Searches for the date and time the relative ecliptic longitudes of\n * the specified body and the Earth, as seen from the Sun, reach a certain\n * difference. This function is useful for finding conjunctions and oppositions\n * of the planets. For the opposition of a superior planet (Mars, Jupiter, ..., Pluto),\n * or the inferior conjunction of an inferior planet (Mercury, Venus),\n * call with `targetRelLon` = 0. The 0 value indicates that both\n * planets are on the same ecliptic longitude line, ignoring the other planet's\n * distance above or below the plane of the Earth's orbit.\n * For superior conjunctions, call with `targetRelLon` = 180.\n * This means the Earth and the other planet are on opposite sides of the Sun.\n *\n * @param {Body} body\n *      The name of a planet other than the Earth.\n *\n * @param {number} targetRelLon\n *      The desired angular difference in degrees between the ecliptic longitudes\n *      of `body` and the Earth. Must be in the range (-180, +180].\n *\n * @param {FlexibleDateTime} startDate\n *      The date and time after which to find the next occurrence of the\n *      body and the Earth reaching the desired relative longitude.\n *\n * @returns {AstroTime}\n *      The time when the Earth and the body next reach the specified relative longitudes.\n */",
         "meta": {
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+                185552
             ],
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+            "lineno": 4071,
             "columnno": 0,
             "code": {
-                "id": "astnode100019029",
+                "id": "astnode100019063",
                 "name": "SearchRelativeLongitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -36014,14 +36086,14 @@
         "comment": "",
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         "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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@@ -36551,14 +36623,14 @@
         "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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@@ -36941,14 +37013,14 @@
         "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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@@ -37025,14 +37097,14 @@
         "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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                 "name": "exports.MoonQuarter",
                 "type": "Identifier",
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@@ -37152,14 +37224,14 @@
         "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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             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100019412",
+                "id": "astnode100019446",
                 "name": "quarterStart",
                 "type": "CallExpression",
                 "value": ""
@@ -37260,14 +37332,14 @@
         "comment": "",
         "meta": {
             "range": [
-                190167,
-                190199
+                190566,
+                190598
             ],
             "filename": "astronomy.js",
-            "lineno": 4238,
+            "lineno": 4243,
             "columnno": 8,
             "code": {
-                "id": "astnode100019422",
+                "id": "astnode100019456",
                 "name": "quarter",
                 "type": "BinaryExpression",
                 "value": ""
@@ -37285,14 +37357,14 @@
         "comment": "",
         "meta": {
             "range": [
-                190209,
-                190260
+                190608,
+                190659
             ],
             "filename": "astronomy.js",
-            "lineno": 4239,
+            "lineno": 4244,
             "columnno": 8,
             "code": {
-                "id": "astnode100019430",
+                "id": "astnode100019464",
                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -37310,14 +37382,14 @@
         "comment": "",
         "meta": {
             "range": [
-                190364,
-                190409
+                190763,
+                190808
             ],
             "filename": "astronomy.js",
-            "lineno": 4244,
+            "lineno": 4249,
             "columnno": 0,
             "code": {
-                "id": "astnode100019450",
+                "id": "astnode100019484",
                 "name": "exports.SearchMoonQuarter",
                 "type": "Identifier",
                 "value": "SearchMoonQuarter",
@@ -37334,14 +37406,14 @@
         "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 */",
         "meta": {
             "range": [
-                190756,
-                191113
+                191155,
+                191512
             ],
             "filename": "astronomy.js",
-            "lineno": 4255,
+            "lineno": 4260,
             "columnno": 0,
             "code": {
-                "id": "astnode100019455",
+                "id": "astnode100019489",
                 "name": "NextMoonQuarter",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37380,14 +37452,14 @@
         "comment": "",
         "meta": {
             "range": [
-                191014,
-                191074
+                191413,
+                191473
             ],
             "filename": "astronomy.js",
-            "lineno": 4259,
+            "lineno": 4264,
             "columnno": 8,
             "code": {
-                "id": "astnode100019460",
+                "id": "astnode100019494",
                 "name": "date",
                 "type": "NewExpression",
                 "value": ""
@@ -37405,14 +37477,14 @@
         "comment": "",
         "meta": {
             "range": [
-                191114,
-                191155
+                191513,
+                191554
             ],
             "filename": "astronomy.js",
-            "lineno": 4262,
+            "lineno": 4267,
             "columnno": 0,
             "code": {
-                "id": "astnode100019481",
+                "id": "astnode100019515",
                 "name": "exports.NextMoonQuarter",
                 "type": "Identifier",
                 "value": "NextMoonQuarter",
@@ -37429,14 +37501,14 @@
         "comment": "",
         "meta": {
             "range": [
-                191157,
-                191558
+                191556,
+                191957
             ],
             "filename": "astronomy.js",
-            "lineno": 4263,
+            "lineno": 4268,
             "columnno": 0,
             "code": {
-                "id": "astnode100019486",
+                "id": "astnode100019520",
                 "name": "BodyRadiusAu",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37455,14 +37527,14 @@
         "comment": "/**\n * @brief Finds the next rise or set time for a body.\n *\n * Finds a rise or set time for the given body as\n * seen by an observer at the specified location on the Earth.\n * Rise time is defined as the moment when the top of the body\n * is observed to first appear above the horizon in the east.\n * Set time is defined as the moment the top of the body\n * is observed to sink below the horizon in the west.\n * The times are adjusted for typical atmospheric refraction conditions.\n *\n * @param {Body} body\n *      The name of the body to find the rise or set time for.\n *\n * @param {Observer} observer\n *      Specifies the geographic coordinates and elevation above sea level of the observer.\n *\n * @param {number} direction\n *      Either +1 to find rise time or -1 to find set time.\n *      Any other value will cause an exception to be thrown.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which the specified rise or set time is to be found.\n *\n * @param {number} limitDays\n *      The fractional number of days after `dateStart` that limits\n *      when the rise or set time is to be found.\n *\n * @returns {AstroTime | null}\n *      The date and time of the rise or set event, or null if no such event\n *      occurs within the specified time window.\n */",
         "meta": {
             "range": [
-                192850,
-                193897
+                193249,
+                194296
             ],
             "filename": "astronomy.js",
-            "lineno": 4306,
+            "lineno": 4311,
             "columnno": 0,
             "code": {
-                "id": "astnode100019507",
+                "id": "astnode100019541",
                 "name": "SearchRiseSet",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37553,14 +37625,14 @@
         "comment": "",
         "meta": {
             "range": [
-                192932,
-                192967
+                193331,
+                193366
             ],
             "filename": "astronomy.js",
-            "lineno": 4307,
+            "lineno": 4312,
             "columnno": 8,
             "code": {
-                "id": "astnode100019516",
+                "id": "astnode100019550",
                 "name": "body_radius_au",
                 "type": "CallExpression",
                 "value": ""
@@ -37578,14 +37650,14 @@
         "comment": "",
         "meta": {
             "range": [
-                192973,
-                193796
+                193372,
+                194195
             ],
             "filename": "astronomy.js",
-            "lineno": 4308,
+            "lineno": 4313,
             "columnno": 4,
             "code": {
-                "id": "astnode100019521",
+                "id": "astnode100019555",
                 "name": "peak_altitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37610,14 +37682,14 @@
         "comment": "",
         "meta": {
             "range": [
-                193534,
-                193581
+                193933,
+                193980
             ],
             "filename": "astronomy.js",
-            "lineno": 4317,
+            "lineno": 4322,
             "columnno": 14,
             "code": {
-                "id": "astnode100019526",
+                "id": "astnode100019560",
                 "name": "ofdate",
                 "type": "CallExpression",
                 "value": ""
@@ -37635,14 +37707,14 @@
         "comment": "",
         "meta": {
             "range": [
-                193597,
-                193646
+                193996,
+                194045
             ],
             "filename": "astronomy.js",
-            "lineno": 4318,
+            "lineno": 4323,
             "columnno": 14,
             "code": {
-                "id": "astnode100019536",
+                "id": "astnode100019570",
                 "name": "hor",
                 "type": "CallExpression",
                 "value": ""
@@ -37660,14 +37732,14 @@
         "comment": "",
         "meta": {
             "range": [
-                193662,
-                193757
+                194061,
+                194156
             ],
             "filename": "astronomy.js",
-            "lineno": 4319,
+            "lineno": 4324,
             "columnno": 14,
             "code": {
-                "id": "astnode100019549",
+                "id": "astnode100019583",
                 "name": "alt",
                 "type": "BinaryExpression",
                 "value": ""
@@ -37685,14 +37757,14 @@
         "comment": "",
         "meta": {
             "range": [
-                193898,
-                193935
+                194297,
+                194334
             ],
             "filename": "astronomy.js",
-            "lineno": 4324,
+            "lineno": 4329,
             "columnno": 0,
             "code": {
-                "id": "astnode100019580",
+                "id": "astnode100019614",
                 "name": "exports.SearchRiseSet",
                 "type": "Identifier",
                 "value": "SearchRiseSet",
@@ -37709,14 +37781,14 @@
         "comment": "/**\n * @brief Finds the next time a body reaches a given altitude.\n *\n * Finds when the given body ascends or descends through a given\n * altitude angle, as seen by an observer at the specified location on the Earth.\n * By using the appropriate combination of `direction` and `altitude` parameters,\n * this function can be used to find when civil, nautical, or astronomical twilight\n * begins (dawn) or ends (dusk).\n *\n * Civil dawn begins before sunrise when the Sun ascends through 6 degrees below\n * the horizon. To find civil dawn, pass +1 for `direction` and -6 for `altitude`.\n *\n * Civil dusk ends after sunset when the Sun descends through 6 degrees below the horizon.\n * To find civil dusk, pass -1 for `direction` and -6 for `altitude`.\n *\n * Nautical twilight is similar to civil twilight, only the `altitude` value should be -12 degrees.\n *\n * Astronomical twilight uses -18 degrees as the `altitude` value.\n *\n * @param {Body} body\n *      The name of the body for which to find the altitude event.\n *      Can be the Sun, Moon, or any planet 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} direction\n *      Either +1 to find when the body ascends through the altitude,\n *      or -1 for when the body descends through the altitude.\n *      Any other value will cause an exception to be thrown.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which the specified altitude event is to be found.\n *\n * @param {number} limitDays\n *      The fractional number of days after `dateStart` that limits\n *      when the altitude event is to be found. Must be a positive number.\n *\n * @param {number} altitude\n *      The desired altitude angle of the body's center above (positive)\n *      or below (negative) the observer's local horizon, expressed in degrees.\n *      Must be in the range [-90, +90].\n *\n * @returns {AstroTime | null}\n *      The date and time of the altitude event, or null if no such event\n *      occurs within the specified time window.\n */",
         "meta": {
             "range": [
-                196053,
-                196585
+                196452,
+                196984
             ],
             "filename": "astronomy.js",
-            "lineno": 4372,
+            "lineno": 4377,
             "columnno": 0,
             "code": {
-                "id": "astnode100019585",
+                "id": "astnode100019619",
                 "name": "SearchAltitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37816,14 +37888,14 @@
         "comment": "",
         "meta": {
             "range": [
-                196267,
-                196483
+                196666,
+                196882
             ],
             "filename": "astronomy.js",
-            "lineno": 4375,
+            "lineno": 4380,
             "columnno": 4,
             "code": {
-                "id": "astnode100019616",
+                "id": "astnode100019650",
                 "name": "altitude_error",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37847,14 +37919,14 @@
         "comment": "",
         "meta": {
             "range": [
-                196310,
-                196357
+                196709,
+                196756
             ],
             "filename": "astronomy.js",
-            "lineno": 4376,
+            "lineno": 4381,
             "columnno": 14,
             "code": {
-                "id": "astnode100019621",
+                "id": "astnode100019655",
                 "name": "ofdate",
                 "type": "CallExpression",
                 "value": ""
@@ -37872,14 +37944,14 @@
         "comment": "",
         "meta": {
             "range": [
-                196373,
-                196422
+                196772,
+                196821
             ],
             "filename": "astronomy.js",
-            "lineno": 4377,
+            "lineno": 4382,
             "columnno": 14,
             "code": {
-                "id": "astnode100019631",
+                "id": "astnode100019665",
                 "name": "hor",
                 "type": "CallExpression",
                 "value": ""
@@ -37897,14 +37969,14 @@
         "comment": "",
         "meta": {
             "range": [
-                196586,
-                196625
+                196985,
+                197024
             ],
             "filename": "astronomy.js",
-            "lineno": 4382,
+            "lineno": 4387,
             "columnno": 0,
             "code": {
-                "id": "astnode100019661",
+                "id": "astnode100019695",
                 "name": "exports.SearchAltitude",
                 "type": "Identifier",
                 "value": "SearchAltitude",
@@ -37921,14 +37993,14 @@
         "comment": "",
         "meta": {
             "range": [
-                196627,
-                199670
+                197026,
+                200069
             ],
             "filename": "astronomy.js",
-            "lineno": 4383,
+            "lineno": 4388,
             "columnno": 0,
             "code": {
-                "id": "astnode100019666",
+                "id": "astnode100019700",
                 "name": "InternalSearchAltitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37963,14 +38035,14 @@
         "comment": "",
         "meta": {
             "range": [
-                197546,
-                197555
+                197945,
+                197954
             ],
             "filename": "astronomy.js",
-            "lineno": 4398,
+            "lineno": 4403,
             "columnno": 8,
             "code": {
-                "id": "astnode100019701",
+                "id": "astnode100019735",
                 "name": "ha_before"
             }
         },
@@ -37986,14 +38058,14 @@
         "comment": "",
         "meta": {
             "range": [
-                197557,
-                197565
+                197956,
+                197964
             ],
             "filename": "astronomy.js",
-            "lineno": 4398,
+            "lineno": 4403,
             "columnno": 19,
             "code": {
-                "id": "astnode100019703",
+                "id": "astnode100019737",
                 "name": "ha_after"
             }
         },
@@ -38009,92 +38081,92 @@
         "comment": "",
         "meta": {
             "range": [
-                197603,
-                197617
-            ],
-            "filename": "astronomy.js",
-            "lineno": 4400,
-            "columnno": 8,
-            "code": {
-                "id": "astnode100019712",
-                "name": "ha_before",
-                "type": "Literal",
-                "funcscope": "InternalSearchAltitude",
-                "value": 12,
-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "ha_before",
-        "longname": "InternalSearchAltitude~ha_before",
-        "kind": "member",
-        "memberof": "InternalSearchAltitude",
-        "scope": "inner"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                197687,
-                197699
-            ],
-            "filename": "astronomy.js",
-            "lineno": 4401,
-            "columnno": 8,
-            "code": {
-                "id": "astnode100019716",
-                "name": "ha_after",
-                "type": "Literal",
-                "funcscope": "InternalSearchAltitude",
-                "value": 0,
-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "ha_after",
-        "longname": "InternalSearchAltitude~ha_after",
-        "kind": "member",
-        "memberof": "InternalSearchAltitude",
-        "scope": "inner"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                197812,
-                197825
-            ],
-            "filename": "astronomy.js",
-            "lineno": 4404,
-            "columnno": 8,
-            "code": {
-                "id": "astnode100019726",
-                "name": "ha_before",
-                "type": "Literal",
-                "funcscope": "InternalSearchAltitude",
-                "value": 0,
-                "paramnames": []
-            }
-        },
-        "undocumented": true,
-        "name": "ha_before",
-        "longname": "InternalSearchAltitude~ha_before",
-        "kind": "member",
-        "memberof": "InternalSearchAltitude",
-        "scope": "inner"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                197880,
-                197893
+                198002,
+                198016
             ],
             "filename": "astronomy.js",
             "lineno": 4405,
             "columnno": 8,
             "code": {
-                "id": "astnode100019730",
+                "id": "astnode100019746",
+                "name": "ha_before",
+                "type": "Literal",
+                "funcscope": "InternalSearchAltitude",
+                "value": 12,
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "ha_before",
+        "longname": "InternalSearchAltitude~ha_before",
+        "kind": "member",
+        "memberof": "InternalSearchAltitude",
+        "scope": "inner"
+    },
+    {
+        "comment": "",
+        "meta": {
+            "range": [
+                198086,
+                198098
+            ],
+            "filename": "astronomy.js",
+            "lineno": 4406,
+            "columnno": 8,
+            "code": {
+                "id": "astnode100019750",
+                "name": "ha_after",
+                "type": "Literal",
+                "funcscope": "InternalSearchAltitude",
+                "value": 0,
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "ha_after",
+        "longname": "InternalSearchAltitude~ha_after",
+        "kind": "member",
+        "memberof": "InternalSearchAltitude",
+        "scope": "inner"
+    },
+    {
+        "comment": "",
+        "meta": {
+            "range": [
+                198211,
+                198224
+            ],
+            "filename": "astronomy.js",
+            "lineno": 4409,
+            "columnno": 8,
+            "code": {
+                "id": "astnode100019760",
+                "name": "ha_before",
+                "type": "Literal",
+                "funcscope": "InternalSearchAltitude",
+                "value": 0,
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "ha_before",
+        "longname": "InternalSearchAltitude~ha_before",
+        "kind": "member",
+        "memberof": "InternalSearchAltitude",
+        "scope": "inner"
+    },
+    {
+        "comment": "",
+        "meta": {
+            "range": [
+                198279,
+                198292
+            ],
+            "filename": "astronomy.js",
+            "lineno": 4410,
+            "columnno": 8,
+            "code": {
+                "id": "astnode100019764",
                 "name": "ha_after",
                 "type": "Literal",
                 "funcscope": "InternalSearchAltitude",
@@ -38113,14 +38185,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198043,
-                198075
+                198442,
+                198474
             ],
             "filename": "astronomy.js",
-            "lineno": 4410,
+            "lineno": 4415,
             "columnno": 8,
             "code": {
-                "id": "astnode100019740",
+                "id": "astnode100019774",
                 "name": "time_start",
                 "type": "CallExpression",
                 "value": ""
@@ -38138,14 +38210,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198085,
-                198096
+                198484,
+                198495
             ],
             "filename": "astronomy.js",
-            "lineno": 4411,
+            "lineno": 4416,
             "columnno": 8,
             "code": {
-                "id": "astnode100019746",
+                "id": "astnode100019780",
                 "name": "time_before"
             }
         },
@@ -38161,14 +38233,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198106,
-                198116
+                198505,
+                198515
             ],
             "filename": "astronomy.js",
-            "lineno": 4412,
+            "lineno": 4417,
             "columnno": 8,
             "code": {
-                "id": "astnode100019749",
+                "id": "astnode100019783",
                 "name": "evt_before"
             }
         },
@@ -38184,14 +38256,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198126,
-                198135
+                198525,
+                198534
             ],
             "filename": "astronomy.js",
-            "lineno": 4413,
+            "lineno": 4418,
             "columnno": 8,
             "code": {
-                "id": "astnode100019752",
+                "id": "astnode100019786",
                 "name": "evt_after"
             }
         },
@@ -38207,14 +38279,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198145,
-                198186
+                198544,
+                198585
             ],
             "filename": "astronomy.js",
-            "lineno": 4414,
+            "lineno": 4419,
             "columnno": 8,
             "code": {
-                "id": "astnode100019755",
+                "id": "astnode100019789",
                 "name": "error_before",
                 "type": "CallExpression",
                 "value": ""
@@ -38232,14 +38304,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198196,
-                198207
+                198595,
+                198606
             ],
             "filename": "astronomy.js",
-            "lineno": 4415,
+            "lineno": 4420,
             "columnno": 8,
             "code": {
-                "id": "astnode100019761",
+                "id": "astnode100019795",
                 "name": "error_after"
             }
         },
@@ -38255,14 +38327,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198348,
-                198415
+                198747,
+                198814
             ],
             "filename": "astronomy.js",
-            "lineno": 4418,
+            "lineno": 4423,
             "columnno": 8,
             "code": {
-                "id": "astnode100019769",
+                "id": "astnode100019803",
                 "name": "evt_before",
                 "type": "CallExpression",
                 "funcscope": "InternalSearchAltitude",
@@ -38281,14 +38353,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198425,
-                198454
+                198824,
+                198853
             ],
             "filename": "astronomy.js",
-            "lineno": 4419,
+            "lineno": 4424,
             "columnno": 8,
             "code": {
-                "id": "astnode100019778",
+                "id": "astnode100019812",
                 "name": "time_before",
                 "type": "MemberExpression",
                 "funcscope": "InternalSearchAltitude",
@@ -38307,14 +38379,14 @@
         "comment": "",
         "meta": {
             "range": [
-                198464,
-                198506
+                198863,
+                198905
             ],
             "filename": "astronomy.js",
-            "lineno": 4420,
+            "lineno": 4425,
             "columnno": 8,
             "code": {
-                "id": "astnode100019784",
+                "id": "astnode100019818",
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@@ -38612,14 +38684,14 @@
         "comment": "/**\n * @brief Horizontal position of a body upon reaching an hour angle.\n *\n * Returns information about an occurrence of a celestial body\n * reaching a given hour angle as seen by an observer at a given\n * location on the surface of the Earth.\n *\n * @property {AstroTime} time\n *      The date and time of the celestial body reaching the hour angle.\n *\n * @property {HorizontalCoordinates} hor\n *      Topocentric horizontal coordinates for the body\n *      at the time indicated by the `time` property.\n */",
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@@ -38696,14 +38768,14 @@
         "comment": "/**\n * @brief Horizontal position of a body upon reaching an hour angle.\n *\n * Returns information about an occurrence of a celestial body\n * reaching a given hour angle as seen by an observer at a given\n * location on the surface of the Earth.\n *\n * @property {AstroTime} time\n *      The date and time of the celestial body reaching the hour angle.\n *\n * @property {HorizontalCoordinates} hor\n *      Topocentric horizontal coordinates for the body\n *      at the time indicated by the `time` property.\n */",
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@@ -38823,14 +38895,14 @@
         "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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+        },
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+        "name": "delta_sidereal_hours",
+        "longname": "SearchHourAngle~delta_sidereal_hours",
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                 "name": "exports.SearchHourAngle",
                 "type": "Identifier",
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@@ -39217,14 +39289,14 @@
         "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 */",
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                 "name": "SeasonInfo",
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@@ -39291,14 +39363,14 @@
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@@ -39323,14 +39395,14 @@
         "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": "astnode100020097",
+                "id": "astnode100020131",
                 "name": "SeasonInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -39396,14 +39468,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020109",
+                "id": "astnode100020143",
                 "name": "this.mar_equinox",
                 "type": "Identifier",
                 "value": "mar_equinox",
@@ -39421,14 +39493,14 @@
         "comment": "",
         "meta": {
             "range": [
-                206212,
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+                206643
             ],
             "filename": "astronomy.js",
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+            "lineno": 4596,
             "columnno": 8,
             "code": {
-                "id": "astnode100020115",
+                "id": "astnode100020149",
                 "name": "this.jun_solstice",
                 "type": "Identifier",
                 "value": "jun_solstice",
@@ -39446,14 +39518,14 @@
         "comment": "",
         "meta": {
             "range": [
-                206254,
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+                206683
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020121",
+                "id": "astnode100020155",
                 "name": "this.sep_equinox",
                 "type": "Identifier",
                 "value": "sep_equinox",
@@ -39471,14 +39543,14 @@
         "comment": "",
         "meta": {
             "range": [
-                206294,
-                206326
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+                206725
             ],
             "filename": "astronomy.js",
-            "lineno": 4593,
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             "columnno": 8,
             "code": {
-                "id": "astnode100020127",
+                "id": "astnode100020161",
                 "name": "this.dec_solstice",
                 "type": "Identifier",
                 "value": "dec_solstice",
@@ -39496,14 +39568,14 @@
         "comment": "",
         "meta": {
             "range": [
-                206336,
-                206367
+                206735,
+                206766
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020133",
+                "id": "astnode100020167",
                 "name": "exports.SeasonInfo",
                 "type": "Identifier",
                 "value": "SeasonInfo",
@@ -39520,14 +39592,14 @@
         "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 */",
         "meta": {
             "range": [
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100020138",
+                "id": "astnode100020172",
                 "name": "Seasons",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -39581,14 +39653,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 4,
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                 "name": "find",
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@@ -39614,14 +39686,14 @@
         "comment": "",
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             ],
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             "columnno": 12,
             "code": {
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                 "name": "startDate",
                 "type": "NewExpression",
                 "value": ""
@@ -39639,14 +39711,14 @@
         "comment": "",
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             "range": [
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             ],
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             "columnno": 12,
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                 "type": "CallExpression",
                 "value": ""
@@ -39664,14 +39736,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020197",
+                "id": "astnode100020231",
                 "name": "year",
                 "type": "CallExpression",
                 "funcscope": "Seasons",
@@ -39690,14 +39762,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
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                 "type": "CallExpression",
                 "value": ""
@@ -39715,14 +39787,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020224",
+                "id": "astnode100020258",
                 "name": "jun_solstice",
                 "type": "CallExpression",
                 "value": ""
@@ -39740,14 +39812,14 @@
         "comment": "",
         "meta": {
             "range": [
-                207312,
-                207342
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+                207741
             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020232",
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                 "name": "sep_equinox",
                 "type": "CallExpression",
                 "value": ""
@@ -39765,14 +39837,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                207384
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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-                "id": "astnode100020240",
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                 "name": "dec_solstice",
                 "type": "CallExpression",
                 "value": ""
@@ -39790,14 +39862,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020255",
+                "id": "astnode100020289",
                 "name": "exports.Seasons",
                 "type": "Identifier",
                 "value": "Seasons",
@@ -39814,14 +39886,14 @@
         "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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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100020260",
+                "id": "astnode100020294",
                 "name": "ElongationEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -39891,14 +39963,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100020263",
+                "id": "astnode100020297",
                 "name": "ElongationEvent",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -39923,14 +39995,14 @@
         "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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-                209169
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+                209568
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020260",
+                "id": "astnode100020294",
                 "name": "ElongationEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -39999,14 +40071,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020272",
+                "id": "astnode100020306",
                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -40024,14 +40096,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100020278",
+                "id": "astnode100020312",
                 "name": "this.visibility",
                 "type": "Identifier",
                 "value": "visibility",
@@ -40049,14 +40121,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                209503
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020284",
+                "id": "astnode100020318",
                 "name": "this.elongation",
                 "type": "Identifier",
                 "value": "elongation",
@@ -40074,14 +40146,14 @@
         "comment": "",
         "meta": {
             "range": [
-                209114,
-                209160
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+                209559
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020290",
+                "id": "astnode100020324",
                 "name": "this.ecliptic_separation",
                 "type": "Identifier",
                 "value": "ecliptic_separation",
@@ -40099,14 +40171,14 @@
         "comment": "",
         "meta": {
             "range": [
-                209170,
-                209211
+                209569,
+                209610
             ],
             "filename": "astronomy.js",
-            "lineno": 4663,
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             "columnno": 0,
             "code": {
-                "id": "astnode100020296",
+                "id": "astnode100020330",
                 "name": "exports.ElongationEvent",
                 "type": "Identifier",
                 "value": "ElongationEvent",
@@ -40123,14 +40195,14 @@
         "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 */",
         "meta": {
             "range": [
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+                210761
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020301",
+                "id": "astnode100020335",
                 "name": "Elongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -40182,14 +40254,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                210079
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -40207,14 +40279,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                210130
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+                210529
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020313",
+                "id": "astnode100020347",
                 "name": "lon",
                 "type": "CallExpression",
                 "value": ""
@@ -40232,14 +40304,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                210143
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+                210542
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020323",
+                "id": "astnode100020357",
                 "name": "vis"
             }
         },
@@ -40255,14 +40327,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                210588
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020331",
+                "id": "astnode100020365",
                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -40281,14 +40353,14 @@
         "comment": "",
         "meta": {
             "range": [
-                210199,
-                210214
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+                210613
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020335",
+                "id": "astnode100020369",
                 "name": "lon",
                 "type": "BinaryExpression",
                 "funcscope": "Elongation",
@@ -40307,14 +40379,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                210256
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+                210655
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020342",
+                "id": "astnode100020376",
                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -40333,14 +40405,14 @@
         "comment": "",
         "meta": {
             "range": [
-                210272,
-                210304
+                210671,
+                210703
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100020346",
+                "id": "astnode100020380",
                 "name": "angle",
                 "type": "CallExpression",
                 "value": ""
@@ -40358,14 +40430,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                210394
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+                210793
             ],
             "filename": "astronomy.js",
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+            "lineno": 4701,
             "columnno": 0,
             "code": {
-                "id": "astnode100020360",
+                "id": "astnode100020394",
                 "name": "exports.Elongation",
                 "type": "Identifier",
                 "value": "Elongation",
@@ -40382,14 +40454,14 @@
         "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 */",
         "meta": {
             "range": [
-                211190,
-                215316
+                211589,
+                215715
             ],
             "filename": "astronomy.js",
-            "lineno": 4714,
+            "lineno": 4719,
             "columnno": 0,
             "code": {
-                "id": "astnode100020365",
+                "id": "astnode100020399",
                 "name": "SearchMaxElongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -40464,14 +40536,14 @@
         "comment": "",
         "meta": {
             "range": [
-                211248,
-                211257
+                211647,
+                211656
             ],
             "filename": "astronomy.js",
-            "lineno": 4715,
+            "lineno": 4720,
             "columnno": 10,
             "code": {
-                "id": "astnode100020371",
+                "id": "astnode100020405",
                 "name": "dt",
                 "type": "Literal",
                 "value": 0.01
@@ -40489,14 +40561,14 @@
         "comment": "",
         "meta": {
             "range": [
-                211263,
-                211725
+                211662,
+                212124
             ],
             "filename": "astronomy.js",
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+            "lineno": 4721,
             "columnno": 4,
             "code": {
-                "id": "astnode100020374",
+                "id": "astnode100020408",
                 "name": "neg_slope",
                 "type": "FunctionDeclaration",
                 "paramnames": [
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         "comment": "/**\n * @brief Calculates the inverse of a rotation matrix.\n *\n * Given a rotation matrix that performs some coordinate transform,\n * this function returns the matrix that reverses that trasnform.\n *\n * @param {RotationMatrix} rotation\n *      The rotation matrix to be inverted.\n *\n * @returns {RotationMatrix}\n *      The inverse rotation matrix.\n */",
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         "comment": "/**\n* @brief Re-orients a rotation matrix by pivoting it by an angle around one of its axes.\n*\n* Given a rotation matrix, a selected coordinate axis, and an angle in degrees,\n* this function pivots the rotation matrix by that angle around that coordinate axis.\n*\n* For example, if you have rotation matrix that converts ecliptic coordinates (ECL)\n* to horizontal coordinates (HOR), but you really want to convert ECL to the orientation\n* of a telescope camera pointed at a given body, you can use `Astronomy_Pivot` twice:\n* (1) pivot around the zenith axis by the body's azimuth, then (2) pivot around the\n* western axis by the body's altitude angle. The resulting rotation matrix will then\n* reorient ECL coordinates to the orientation of your telescope camera.\n*\n* @param {RotationMatrix} rotation\n*      The input rotation matrix.\n*\n* @param {number} axis\n*      An integer that selects which coordinate axis to rotate around:\n*      0 = x, 1 = y, 2 = z. Any other value will cause an exception.\n*\n* @param {number} angle\n*      An angle in degrees indicating the amount of rotation around the specified axis.\n*      Positive angles indicate rotation counterclockwise as seen from the positive\n*      direction along that axis, looking towards the origin point of the orientation system.\n*      Any finite number of degrees is allowed, but best precision will result from\n*      keeping `angle` in the range [-360, +360].\n*\n* @returns {RotationMatrix}\n*      A pivoted matrix object.\n*/",
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@@ -47102,14 +47174,14 @@
         "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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@@ -47270,14 +47342,14 @@
         "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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                 "name": "exports.VectorFromHorizon",
                 "type": "Identifier",
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@@ -47447,14 +47519,14 @@
         "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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+            }
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+        "name": "refr",
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+        "scope": "inner"
+    },
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@@ -47666,14 +47738,14 @@
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             "code": {
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                 "name": "exports.Refraction",
                 "type": "Identifier",
                 "value": "Refraction",
@@ -47690,14 +47762,14 @@
         "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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@@ -47757,14 +47829,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "altitude",
                 "type": "Identifier",
                 "funcscope": "InverseRefraction",
@@ -47833,14 +47905,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 0,
             "code": {
-                "id": "astnode100023416",
+                "id": "astnode100023450",
                 "name": "exports.InverseRefraction",
                 "type": "Identifier",
                 "value": "InverseRefraction",
@@ -47857,14 +47929,14 @@
         "comment": "/**\n * @brief Applies a rotation to a vector, yielding a rotated vector.\n *\n * This function transforms a vector in one orientation to a vector\n * in another orientation.\n *\n * @param {RotationMatrix} rotation\n *      A rotation matrix that specifies how the orientation of the vector is to be changed.\n *\n * @param {Vector} vector\n *      The vector whose orientation is to be changed.\n *\n * @returns {Vector}\n *      A vector in the orientation specified by `rotation`.\n */",
         "meta": {
             "range": [
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-                250764
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100023421",
+                "id": "astnode100023455",
                 "name": "RotateVector",
                 "type": "FunctionDeclaration",
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@@ -47920,14 +47992,14 @@
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             "columnno": 0,
             "code": {
-                "id": "astnode100023538",
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                 "name": "exports.RotateVector",
                 "type": "Identifier",
                 "value": "RotateVector",
@@ -47944,14 +48016,14 @@
         "comment": "/**\n * @brief Applies a rotation to a state vector, yielding a rotated vector.\n *\n * This function transforms a state vector in one orientation to a vector\n * in another orientation.\n *\n * @param {RotationMatrix} rotation\n *      A rotation matrix that specifies how the orientation of the state vector is to be changed.\n *\n * @param {StateVector} state\n *      The state vector whose orientation is to be changed.\n *      Both the position and velocity components are transformed.\n *\n * @return {StateVector}\n *      A state vector in the orientation specified by `rotation`.\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100023543",
+                "id": "astnode100023577",
                 "name": "RotateState",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -48007,14 +48079,14 @@
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100023765",
+                "id": "astnode100023799",
                 "name": "exports.RotateState",
                 "type": "Identifier",
                 "value": "RotateState",
@@ -48031,14 +48103,14 @@
         "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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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100023770",
+                "id": "astnode100023804",
                 "name": "Rotation_EQJ_ECL",
                 "type": "FunctionDeclaration",
                 "paramnames": []
@@ -48076,14 +48148,14 @@
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@@ -48101,14 +48173,14 @@
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@@ -49380,14 +49452,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) 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: EQD = equatorial system, using equator of date.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @param {FlexibleDateTime} time\n *      The date and time of the source equator.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD to ECL.\n */",
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                 "type": "Identifier",
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@@ -49511,14 +49583,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) 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: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: EQD = equatorial system, using equator of date.\n *\n * @param {FlexibleDateTime} time\n *      The date and time of the desired equator.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts ECL to EQD.\n */",
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             "columnno": 0,
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                 "name": "Rotation_ECL_EQD",
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             ],
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                 "type": "Identifier",
                 "value": "Rotation_ECL_EQD",
@@ -49616,14 +49688,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) 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: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: HOR = horizontal system.\n *\n * Use {@link HorizonFromVector} to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param {FlexibleDateTime} time\n *      The date and time of the desired horizontal orientation.\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 ECL 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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                 "type": "Identifier",
                 "value": "Rotation_ECL_HOR",
@@ -49784,14 +49856,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) 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: HOR = horizontal system.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @param {FlexibleDateTime} time\n *      The date and time of the horizontal observation.\n *\n * @param {Observer} observer\n *      The location of the horizontal observer.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts HOR to ECL.\n */",
         "meta": {
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             ],
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             "columnno": 0,
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@@ -49850,14 +49922,14 @@
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                 "type": "Identifier",
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@@ -49899,14 +49971,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to galactic (GAL).\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 the equator at the J2000 epoch.\n * Target: GAL = galactic system (IAU 1958 definition).\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQJ to GAL.\n */",
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                 "name": "exports.Rotation_EQJ_GAL",
                 "type": "Identifier",
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@@ -49964,14 +50036,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from galactic (GAL) 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: GAL = galactic system (IAU 1958 definition).\n * Target: EQJ = equatorial system, using the equator at the J2000 epoch.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts GAL to EQJ.\n */",
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@@ -50005,14 +50077,14 @@
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                 "name": "exports.Rotation_GAL_EQJ",
                 "type": "Identifier",
                 "value": "Rotation_GAL_EQJ",
@@ -50029,14 +50101,14 @@
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                 "value": "[\"[\\\"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\\\"]\"]"
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@@ -50077,14 +50149,14 @@
         "comment": "",
         "meta": {
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             "filename": "astronomy.js",
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@@ -50099,14 +50171,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100026565",
+                "id": "astnode100026599",
                 "name": "Epoch2000"
             }
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@@ -50121,14 +50193,14 @@
         "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 */",
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             "columnno": 0,
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-                "id": "astnode100026567",
+                "id": "astnode100026601",
                 "name": "ConstellationInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -50195,14 +50267,14 @@
         "comment": "",
         "meta": {
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             "columnno": 4,
             "code": {
-                "id": "astnode100026570",
+                "id": "astnode100026604",
                 "name": "ConstellationInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -50227,14 +50299,14 @@
         "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": "astnode100026567",
+                "id": "astnode100026601",
                 "name": "ConstellationInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -50300,14 +50372,14 @@
         "comment": "",
         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100026579",
+                "id": "astnode100026613",
                 "name": "this.symbol",
                 "type": "Identifier",
                 "value": "symbol",
@@ -50325,14 +50397,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100026585",
+                "id": "astnode100026619",
                 "name": "this.name",
                 "type": "Identifier",
                 "value": "name",
@@ -50350,14 +50422,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100026591",
+                "id": "astnode100026625",
                 "name": "this.ra1875",
                 "type": "Identifier",
                 "value": "ra1875",
@@ -50375,14 +50447,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100026597",
+                "id": "astnode100026631",
                 "name": "this.dec1875",
                 "type": "Identifier",
                 "value": "dec1875",
@@ -50400,14 +50472,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100026603",
+                "id": "astnode100026637",
                 "name": "exports.ConstellationInfo",
                 "type": "Identifier",
                 "value": "ConstellationInfo",
@@ -50424,14 +50496,14 @@
         "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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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100026608",
+                "id": "astnode100026642",
                 "name": "Constellation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -50503,14 +50575,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100026634",
+                "id": "astnode100026668",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -50529,14 +50601,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100026642",
+                "id": "astnode100026676",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -50555,14 +50627,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100026650",
+                "id": "astnode100026684",
                 "name": "ConstelRot",
                 "type": "CallExpression",
                 "funcscope": "Constellation",
@@ -50581,14 +50653,14 @@
         "comment": "",
         "meta": {
             "range": [
-                285382,
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             ],
             "filename": "astronomy.js",
-            "lineno": 6946,
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             "columnno": 8,
             "code": {
-                "id": "astnode100026659",
+                "id": "astnode100026693",
                 "name": "Epoch2000",
                 "type": "NewExpression",
                 "funcscope": "Constellation",
@@ -50607,14 +50679,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                285520
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100026665",
+                "id": "astnode100026699",
                 "name": "sph2000",
                 "type": "NewExpression",
                 "value": ""
@@ -50632,14 +50704,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                285977
             ],
             "filename": "astronomy.js",
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+            "lineno": 6955,
             "columnno": 10,
             "code": {
-                "id": "astnode100026675",
+                "id": "astnode100026709",
                 "name": "vec2000",
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@@ -50904,14 +50976,14 @@
         "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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@@ -51021,14 +51093,14 @@
         "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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@@ -51253,14 +51325,14 @@
         "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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@@ -51393,14 +51465,14 @@
         "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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             "code": {
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                 "name": "o.x",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55365,14 +55437,14 @@
         "comment": "",
         "meta": {
             "range": [
-                306312,
-                306334
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+                306733
             ],
             "filename": "astronomy.js",
-            "lineno": 7389,
+            "lineno": 7394,
             "columnno": 8,
             "code": {
-                "id": "astnode100028364",
+                "id": "astnode100028398",
                 "name": "o.y",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55391,14 +55463,14 @@
         "comment": "",
         "meta": {
             "range": [
-                306344,
-                306366
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+                306765
             ],
             "filename": "astronomy.js",
-            "lineno": 7390,
+            "lineno": 7395,
             "columnno": 8,
             "code": {
-                "id": "astnode100028374",
+                "id": "astnode100028408",
                 "name": "o.z",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -55417,14 +55489,14 @@
         "comment": "",
         "meta": {
             "range": [
-                306475,
-                306545
+                306874,
+                306944
             ],
             "filename": "astronomy.js",
-            "lineno": 7392,
+            "lineno": 7397,
             "columnno": 14,
             "code": {
-                "id": "astnode100028384",
+                "id": "astnode100028418",
                 "name": "surface",
                 "type": "CallExpression",
                 "value": ""
@@ -55442,14 +55514,14 @@
         "comment": "",
         "meta": {
             "range": [
-                306870,
-                306908
+                307269,
+                307307
             ],
             "filename": "astronomy.js",
-            "lineno": 7397,
+            "lineno": 7402,
             "columnno": 8,
             "code": {
-                "id": "astnode100028416",
+                "id": "astnode100028450",
                 "name": "kind",
                 "type": "CallExpression",
                 "funcscope": "GeoidIntersect",
@@ -55468,14 +55540,14 @@
         "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 `peak` 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": [
-                307579,
-                307718
+                307978,
+                308117
             ],
             "filename": "astronomy.js",
-            "lineno": 7415,
+            "lineno": 7420,
             "columnno": 0,
             "code": {
-                "id": "astnode100028431",
+                "id": "astnode100028465",
                 "name": "NextLunarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -55523,14 +55595,14 @@
         "comment": "",
         "meta": {
             "range": [
-                307634,
-                307673
+                308033,
+                308072
             ],
             "filename": "astronomy.js",
-            "lineno": 7416,
+            "lineno": 7421,
             "columnno": 10,
             "code": {
-                "id": "astnode100028436",
+                "id": "astnode100028470",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -55548,14 +55620,14 @@
         "comment": "",
         "meta": {
             "range": [
-                307719,
-                307762
+                308118,
+                308161
             ],
             "filename": "astronomy.js",
-            "lineno": 7419,
+            "lineno": 7424,
             "columnno": 0,
             "code": {
-                "id": "astnode100028448",
+                "id": "astnode100028482",
                 "name": "exports.NextLunarEclipse",
                 "type": "Identifier",
                 "value": "NextLunarEclipse",
@@ -55572,14 +55644,14 @@
         "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": [
-                308399,
-                310016
+                308798,
+                310415
             ],
             "filename": "astronomy.js",
-            "lineno": 7435,
+            "lineno": 7440,
             "columnno": 0,
             "code": {
-                "id": "astnode100028453",
+                "id": "astnode100028487",
                 "name": "SearchGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -55632,14 +55704,14 @@
         "comment": "",
         "meta": {
             "range": [
-                308456,
-                308475
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100028458",
+                "id": "astnode100028492",
                 "name": "PruneLatitude",
                 "type": "Literal",
                 "value": 1.8
@@ -55657,14 +55729,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                308669
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+                309068
             ],
             "filename": "astronomy.js",
-            "lineno": 7438,
+            "lineno": 7443,
             "columnno": 8,
             "code": {
-                "id": "astnode100028462",
+                "id": "astnode100028496",
                 "name": "nmtime",
                 "type": "Identifier",
                 "value": "startTime"
@@ -55682,14 +55754,14 @@
         "comment": "",
         "meta": {
             "range": [
-                308679,
-                308686
+                309078,
+                309085
             ],
             "filename": "astronomy.js",
-            "lineno": 7439,
+            "lineno": 7444,
             "columnno": 8,
             "code": {
-                "id": "astnode100028466",
+                "id": "astnode100028500",
                 "name": "nmcount"
             }
         },
@@ -55705,14 +55777,14 @@
         "comment": "",
         "meta": {
             "range": [
-                308697,
-                308708
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+                309107
             ],
             "filename": "astronomy.js",
-            "lineno": 7440,
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             "columnno": 9,
             "code": {
-                "id": "astnode100028469",
+                "id": "astnode100028503",
                 "name": "nmcount",
                 "type": "Literal",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -55731,14 +55803,14 @@
         "comment": "",
         "meta": {
             "range": [
-                308821,
-                308865
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+                309264
             ],
             "filename": "astronomy.js",
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             "columnno": 14,
             "code": {
-                "id": "astnode100028479",
+                "id": "astnode100028513",
                 "name": "newmoon",
                 "type": "CallExpression",
                 "value": ""
@@ -55756,14 +55828,14 @@
         "comment": "",
         "meta": {
             "range": [
-                309048,
-                309096
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+                309495
             ],
             "filename": "astronomy.js",
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             "columnno": 14,
             "code": {
-                "id": "astnode100028492",
+                "id": "astnode100028526",
                 "name": "eclip_lat",
                 "type": "CallExpression",
                 "value": ""
@@ -55781,14 +55853,14 @@
         "comment": "",
         "meta": {
             "range": [
-                309336,
-                309368
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+                309767
             ],
             "filename": "astronomy.js",
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             "columnno": 18,
             "code": {
-                "id": "astnode100028507",
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                 "name": "shadow",
                 "type": "CallExpression",
                 "value": ""
@@ -55806,14 +55878,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                309813
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+                310212
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100028528",
+                "id": "astnode100028562",
                 "name": "nmtime",
                 "type": "CallExpression",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -55832,14 +55904,14 @@
         "comment": "",
         "meta": {
             "range": [
-                310017,
-                310076
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+                310475
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100028538",
+                "id": "astnode100028572",
                 "name": "exports.SearchGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "SearchGlobalSolarEclipse",
@@ -55856,14 +55928,14 @@
         "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": [
-                310692,
-                310845
+                311091,
+                311244
             ],
             "filename": "astronomy.js",
-            "lineno": 7479,
+            "lineno": 7484,
             "columnno": 0,
             "code": {
-                "id": "astnode100028543",
+                "id": "astnode100028577",
                 "name": "NextGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -55911,14 +55983,14 @@
         "comment": "",
         "meta": {
             "range": [
-                310753,
-                310794
+                311152,
+                311193
             ],
             "filename": "astronomy.js",
-            "lineno": 7480,
+            "lineno": 7485,
             "columnno": 10,
             "code": {
-                "id": "astnode100028548",
+                "id": "astnode100028582",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -55936,14 +56008,14 @@
         "comment": "",
         "meta": {
             "range": [
-                310846,
-                310901
+                311245,
+                311300
             ],
             "filename": "astronomy.js",
-            "lineno": 7483,
+            "lineno": 7488,
             "columnno": 0,
             "code": {
-                "id": "astnode100028560",
+                "id": "astnode100028594",
                 "name": "exports.NextGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "NextGlobalSolarEclipse",
@@ -55960,14 +56032,14 @@
         "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": [
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-                312022
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+                312421
             ],
             "filename": "astronomy.js",
-            "lineno": 7505,
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             "columnno": 0,
             "code": {
-                "id": "astnode100028565",
+                "id": "astnode100028599",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56014,14 +56086,14 @@
         "comment": "",
         "meta": {
             "range": [
-                311925,
-                312020
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+                312419
             ],
             "filename": "astronomy.js",
-            "lineno": 7506,
+            "lineno": 7511,
             "columnno": 4,
             "code": {
-                "id": "astnode100028568",
+                "id": "astnode100028602",
                 "name": "EclipseEvent",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -56044,14 +56116,14 @@
         "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": [
-                311900,
-                312022
+                312299,
+                312421
             ],
             "filename": "astronomy.js",
-            "lineno": 7505,
+            "lineno": 7510,
             "columnno": 0,
             "code": {
-                "id": "astnode100028565",
+                "id": "astnode100028599",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56097,14 +56169,14 @@
         "comment": "",
         "meta": {
             "range": [
-                311963,
-                311979
+                312362,
+                312378
             ],
             "filename": "astronomy.js",
-            "lineno": 7507,
+            "lineno": 7512,
             "columnno": 8,
             "code": {
-                "id": "astnode100028575",
+                "id": "astnode100028609",
                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -56122,14 +56194,14 @@
         "comment": "",
         "meta": {
             "range": [
-                311989,
-                312013
+                312388,
+                312412
             ],
             "filename": "astronomy.js",
-            "lineno": 7508,
+            "lineno": 7513,
             "columnno": 8,
             "code": {
-                "id": "astnode100028581",
+                "id": "astnode100028615",
                 "name": "this.altitude",
                 "type": "Identifier",
                 "value": "altitude",
@@ -56147,14 +56219,14 @@
         "comment": "",
         "meta": {
             "range": [
-                312023,
-                312058
+                312422,
+                312457
             ],
             "filename": "astronomy.js",
-            "lineno": 7511,
+            "lineno": 7516,
             "columnno": 0,
             "code": {
-                "id": "astnode100028587",
+                "id": "astnode100028621",
                 "name": "exports.EclipseEvent",
                 "type": "Identifier",
                 "value": "EclipseEvent",
@@ -56171,14 +56243,14 @@
         "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": [
-                314444,
-                314775
+                314843,
+                315174
             ],
             "filename": "astronomy.js",
-            "lineno": 7555,
+            "lineno": 7560,
             "columnno": 0,
             "code": {
-                "id": "astnode100028592",
+                "id": "astnode100028626",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56267,14 +56339,14 @@
         "comment": "",
         "meta": {
             "range": [
-                314478,
-                314773
+                314877,
+                315172
             ],
             "filename": "astronomy.js",
-            "lineno": 7556,
+            "lineno": 7561,
             "columnno": 4,
             "code": {
-                "id": "astnode100028595",
+                "id": "astnode100028629",
                 "name": "LocalSolarEclipseInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -56301,14 +56373,14 @@
         "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": [
-                314444,
-                314775
+                314843,
+                315174
             ],
             "filename": "astronomy.js",
-            "lineno": 7555,
+            "lineno": 7560,
             "columnno": 0,
             "code": {
-                "id": "astnode100028592",
+                "id": "astnode100028626",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -56396,14 +56468,14 @@
         "comment": "",
         "meta": {
             "range": [
-                314564,
-                314580
+                314963,
+                314979
             ],
             "filename": "astronomy.js",
-            "lineno": 7557,
+            "lineno": 7562,
             "columnno": 8,
             "code": {
-                "id": "astnode100028606",
+                "id": "astnode100028640",
                 "name": "this.kind",
                 "type": "Identifier",
                 "value": "kind",
@@ -56421,14 +56493,14 @@
         "comment": "",
         "meta": {
             "range": [
-                314590,
-                314624
+                314989,
+                315023
             ],
             "filename": "astronomy.js",
-            "lineno": 7558,
+            "lineno": 7563,
             "columnno": 8,
             "code": {
-                "id": "astnode100028612",
+                "id": "astnode100028646",
                 "name": "this.partial_begin",
                 "type": "Identifier",
                 "value": "partial_begin",
@@ -56446,14 +56518,14 @@
         "comment": "",
         "meta": {
             "range": [
-                314634,
-                314664
+                315033,
+                315063
             ],
             "filename": "astronomy.js",
-            "lineno": 7559,
+            "lineno": 7564,
             "columnno": 8,
             "code": {
-                "id": "astnode100028618",
+                "id": "astnode100028652",
                 "name": "this.total_begin",
                 "type": "Identifier",
                 "value": "total_begin",
@@ -56471,14 +56543,14 @@
         "comment": "",
         "meta": {
             "range": [
-                314674,
-                314690
+                315073,
+                315089
             ],
             "filename": "astronomy.js",
-            "lineno": 7560,
+            "lineno": 7565,
             "columnno": 8,
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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,
             "code": {
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                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -57769,14 +57841,14 @@
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         "meta": {
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             "columnno": 4,
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                 "name": "TransitInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -57801,14 +57873,14 @@
         "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,
             "code": {
-                "id": "astnode100029058",
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                 "name": "TransitInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -57874,14 +57946,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "this.start",
                 "type": "Identifier",
                 "value": "start",
@@ -57899,14 +57971,14 @@
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         "meta": {
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             "columnno": 8,
             "code": {
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                 "name": "this.peak",
                 "type": "Identifier",
                 "value": "peak",
@@ -57924,14 +57996,14 @@
         "comment": "",
         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100029082",
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                 "name": "this.finish",
                 "type": "Identifier",
                 "value": "finish",
@@ -57949,14 +58021,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100029088",
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                 "name": "this.separation",
                 "type": "Identifier",
                 "value": "separation",
@@ -57974,14 +58046,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100029094",
+                "id": "astnode100029128",
                 "name": "exports.TransitInfo",
                 "type": "Identifier",
                 "value": "TransitInfo",
@@ -57998,14 +58070,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
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                 "name": "PlanetShadowBoundary",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58030,14 +58102,14 @@
         "comment": "",
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             "columnno": 10,
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                 "name": "shadow",
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@@ -58055,14 +58127,14 @@
         "comment": "",
         "meta": {
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             "columnno": 0,
             "code": {
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                 "name": "PlanetTransitBoundary",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58089,14 +58161,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
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                 "name": "tx",
                 "type": "CallExpression",
                 "value": ""
@@ -58114,14 +58186,14 @@
         "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 */",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100029154",
+                "id": "astnode100029188",
                 "name": "SearchTransit",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58190,14 +58262,14 @@
         "comment": "",
         "meta": {
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             "columnno": 10,
             "code": {
-                "id": "astnode100029160",
+                "id": "astnode100029194",
                 "name": "threshold_angle",
                 "type": "Literal",
                 "value": 0.4
@@ -58215,14 +58287,14 @@
         "comment": "",
         "meta": {
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             "columnno": 10,
             "code": {
-                "id": "astnode100029164",
+                "id": "astnode100029198",
                 "name": "dt_days",
                 "type": "Literal",
                 "value": 1
@@ -58240,14 +58312,14 @@
         "comment": "",
         "meta": {
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100029168",
+                "id": "astnode100029202",
                 "name": "planet_radius_km"
             }
         },
@@ -58263,14 +58335,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100029177",
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                 "name": "planet_radius_km",
                 "type": "Literal",
                 "funcscope": "SearchTransit",
@@ -58289,14 +58361,14 @@
         "comment": "",
         "meta": {
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             "columnno": 12,
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+                "id": "astnode100029220",
                 "name": "planet_radius_km",
                 "type": "Literal",
                 "funcscope": "SearchTransit",
@@ -58315,14 +58387,14 @@
         "comment": "",
         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100029197",
+                "id": "astnode100029231",
                 "name": "search_time",
                 "type": "Identifier",
                 "value": "startTime"
@@ -58340,14 +58412,14 @@
         "comment": "",
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@@ -58365,14 +58437,14 @@
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             "columnno": 14,
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@@ -58390,14 +58462,14 @@
         "comment": "",
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@@ -58415,14 +58487,14 @@
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@@ -58440,14 +58512,14 @@
         "comment": "",
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@@ -58465,14 +58537,14 @@
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             "columnno": 22,
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@@ -58490,14 +58562,14 @@
         "comment": "",
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@@ -58515,14 +58587,14 @@
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@@ -58540,14 +58612,14 @@
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             ],
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             "columnno": 8,
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@@ -58566,14 +58638,14 @@
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             "columnno": 0,
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+                "id": "astnode100029350",
                 "name": "exports.SearchTransit",
                 "type": "Identifier",
                 "value": "SearchTransit",
@@ -58590,14 +58662,14 @@
         "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 */",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100029321",
+                "id": "astnode100029355",
                 "name": "NextTransit",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -58655,14 +58727,14 @@
         "comment": "",
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             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
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                 "name": "startTime",
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@@ -58680,14 +58752,14 @@
         "comment": "",
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             "columnno": 0,
             "code": {
-                "id": "astnode100029340",
+                "id": "astnode100029374",
                 "name": "exports.NextTransit",
                 "type": "Identifier",
                 "value": "NextTransit",