diff --git a/README.md b/README.md
index 61b810c9..3b89dbbc 100644
--- a/README.md
+++ b/README.md
@@ -151,7 +151,11 @@ 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 96449 bytes.)
+<<<<<<< HEAD
+- Minified JavaScript code less than 100K. (The current size is 98573 bytes.)
+=======
+- Minified JavaScript code less than 100K. (The current size is 98573 bytes.)
+>>>>>>> libration
- 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 9e9395b4..8eb71e18 100644
--- a/demo/browser/astronomy.browser.js
+++ b/demo/browser/astronomy.browser.js
@@ -34,9 +34,9 @@
*/
'use strict';
Object.defineProperty(exports, "__esModule", { value: true });
-exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
-exports.ConstellationInfo = exports.Rotation_GAL_EQJ = exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = void 0;
+exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
+exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_GAL_EQJ = void 0;
/**
* @brief The speed of light in AU/day.
*/
@@ -1571,6 +1571,136 @@ function CalcMoon(time) {
distance_au: (ARC * EARTH_EQUATORIAL_RADIUS_AU) / (0.999953253 * SINPI)
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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, 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;
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+function Libration(date) {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * exports.KM_PER_AU;
+ // Inclination angle
+ const I = exports.DEG2RAD * 1.54242;
+ // Moon's argument of latitude in radians.
+ const f = exports.DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233 * t - 0.0036539 * t2 - t3 / 3526000 + t4 / 863310000);
+ // Moon's ascending node's mean longitude in radians.
+ const omega = exports.DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891 * t + 0.0020754 * t2 + t3 / 467441 - t4 / 60616000);
+ // Sun's mean anomaly.
+ const m = exports.DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909 * t - 0.0001536 * t2 + t3 / 24490000);
+ // Moon's mean anomaly.
+ const mdash = exports.DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055 * t + 0.0087414 * t2 + t3 / 69699 - t4 / 14712000);
+ // Moon's mean elongation.
+ const d = exports.DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034 * t - 0.0018819 * t2 + t3 / 545868 - t4 / 113065000);
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516 * t - 0.0000074 * t2;
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w) * Math.cos(mlat) * Math.cos(I) - Math.sin(mlat) * Math.sin(I), Math.cos(w) * Math.cos(mlat));
+ const ldash = LongitudeOffset(exports.RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w) * Math.cos(mlat) * Math.sin(I) - Math.sin(mlat) * Math.cos(I));
+ // Physical librations
+ const k1 = exports.DEG2RAD * (119.75 + 131.849 * t);
+ const k2 = exports.DEG2RAD * (72.56 + 20.186 * t);
+ const rho = (-0.02752 * Math.cos(mdash) +
+ -0.02245 * Math.sin(f) +
+ +0.00684 * Math.cos(mdash - 2 * f) +
+ -0.00293 * Math.cos(2 * f) +
+ -0.00085 * Math.cos(2 * f - 2 * d) +
+ -0.00054 * Math.cos(mdash - 2 * d) +
+ -0.00020 * Math.sin(mdash + f) +
+ -0.00020 * Math.cos(mdash + 2 * f) +
+ -0.00020 * Math.cos(mdash - f) +
+ +0.00014 * Math.cos(mdash + 2 * f - 2 * d));
+ const sigma = (-0.02816 * Math.sin(mdash) +
+ +0.02244 * Math.cos(f) +
+ -0.00682 * Math.sin(mdash - 2 * f) +
+ -0.00279 * Math.sin(2 * f) +
+ -0.00083 * Math.sin(2 * f - 2 * d) +
+ +0.00069 * Math.sin(mdash - 2 * d) +
+ +0.00040 * Math.cos(mdash + f) +
+ -0.00025 * Math.sin(2 * mdash) +
+ -0.00023 * Math.sin(mdash + 2 * f) +
+ +0.00020 * Math.cos(mdash - f) +
+ +0.00019 * Math.sin(mdash - f) +
+ +0.00013 * Math.sin(mdash + 2 * f - 2 * d) +
+ -0.00010 * Math.cos(mdash - 3 * f));
+ const tau = (+0.02520 * e * Math.sin(m) +
+ +0.00473 * Math.sin(2 * mdash - 2 * f) +
+ -0.00467 * Math.sin(mdash) +
+ +0.00396 * Math.sin(k1) +
+ +0.00276 * Math.sin(2 * mdash - 2 * d) +
+ +0.00196 * Math.sin(omega) +
+ -0.00183 * Math.cos(mdash - f) +
+ +0.00115 * Math.sin(mdash - 2 * d) +
+ -0.00096 * Math.sin(mdash - d) +
+ +0.00046 * Math.sin(2 * f - 2 * d) +
+ -0.00039 * Math.sin(mdash - f) +
+ -0.00032 * Math.sin(mdash - m - d) +
+ +0.00027 * Math.sin(2 * mdash - m - 2 * d) +
+ +0.00023 * Math.sin(k2) +
+ -0.00014 * Math.sin(2 * d) +
+ +0.00014 * Math.cos(2 * mdash - 2 * f) +
+ -0.00012 * Math.sin(mdash - 2 * f) +
+ -0.00012 * Math.sin(2 * mdash) +
+ +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);
+ 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) {
const r = precession_rot(time, dir);
return [
diff --git a/demo/nodejs/astronomy.js b/demo/nodejs/astronomy.js
index d610ef44..0b756685 100644
--- a/demo/nodejs/astronomy.js
+++ b/demo/nodejs/astronomy.js
@@ -33,9 +33,9 @@
*/
'use strict';
Object.defineProperty(exports, "__esModule", { value: true });
-exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
-exports.ConstellationInfo = exports.Rotation_GAL_EQJ = exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = void 0;
+exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
+exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_GAL_EQJ = void 0;
/**
* @brief The speed of light in AU/day.
*/
@@ -1570,6 +1570,136 @@ function CalcMoon(time) {
distance_au: (ARC * EARTH_EQUATORIAL_RADIUS_AU) / (0.999953253 * SINPI)
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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, 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;
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+function Libration(date) {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * exports.KM_PER_AU;
+ // Inclination angle
+ const I = exports.DEG2RAD * 1.54242;
+ // Moon's argument of latitude in radians.
+ const f = exports.DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233 * t - 0.0036539 * t2 - t3 / 3526000 + t4 / 863310000);
+ // Moon's ascending node's mean longitude in radians.
+ const omega = exports.DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891 * t + 0.0020754 * t2 + t3 / 467441 - t4 / 60616000);
+ // Sun's mean anomaly.
+ const m = exports.DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909 * t - 0.0001536 * t2 + t3 / 24490000);
+ // Moon's mean anomaly.
+ const mdash = exports.DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055 * t + 0.0087414 * t2 + t3 / 69699 - t4 / 14712000);
+ // Moon's mean elongation.
+ const d = exports.DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034 * t - 0.0018819 * t2 + t3 / 545868 - t4 / 113065000);
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516 * t - 0.0000074 * t2;
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w) * Math.cos(mlat) * Math.cos(I) - Math.sin(mlat) * Math.sin(I), Math.cos(w) * Math.cos(mlat));
+ const ldash = LongitudeOffset(exports.RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w) * Math.cos(mlat) * Math.sin(I) - Math.sin(mlat) * Math.cos(I));
+ // Physical librations
+ const k1 = exports.DEG2RAD * (119.75 + 131.849 * t);
+ const k2 = exports.DEG2RAD * (72.56 + 20.186 * t);
+ const rho = (-0.02752 * Math.cos(mdash) +
+ -0.02245 * Math.sin(f) +
+ +0.00684 * Math.cos(mdash - 2 * f) +
+ -0.00293 * Math.cos(2 * f) +
+ -0.00085 * Math.cos(2 * f - 2 * d) +
+ -0.00054 * Math.cos(mdash - 2 * d) +
+ -0.00020 * Math.sin(mdash + f) +
+ -0.00020 * Math.cos(mdash + 2 * f) +
+ -0.00020 * Math.cos(mdash - f) +
+ +0.00014 * Math.cos(mdash + 2 * f - 2 * d));
+ const sigma = (-0.02816 * Math.sin(mdash) +
+ +0.02244 * Math.cos(f) +
+ -0.00682 * Math.sin(mdash - 2 * f) +
+ -0.00279 * Math.sin(2 * f) +
+ -0.00083 * Math.sin(2 * f - 2 * d) +
+ +0.00069 * Math.sin(mdash - 2 * d) +
+ +0.00040 * Math.cos(mdash + f) +
+ -0.00025 * Math.sin(2 * mdash) +
+ -0.00023 * Math.sin(mdash + 2 * f) +
+ +0.00020 * Math.cos(mdash - f) +
+ +0.00019 * Math.sin(mdash - f) +
+ +0.00013 * Math.sin(mdash + 2 * f - 2 * d) +
+ -0.00010 * Math.cos(mdash - 3 * f));
+ const tau = (+0.02520 * e * Math.sin(m) +
+ +0.00473 * Math.sin(2 * mdash - 2 * f) +
+ -0.00467 * Math.sin(mdash) +
+ +0.00396 * Math.sin(k1) +
+ +0.00276 * Math.sin(2 * mdash - 2 * d) +
+ +0.00196 * Math.sin(omega) +
+ -0.00183 * Math.cos(mdash - f) +
+ +0.00115 * Math.sin(mdash - 2 * d) +
+ -0.00096 * Math.sin(mdash - d) +
+ +0.00046 * Math.sin(2 * f - 2 * d) +
+ -0.00039 * Math.sin(mdash - f) +
+ -0.00032 * Math.sin(mdash - m - d) +
+ +0.00027 * Math.sin(2 * mdash - m - 2 * d) +
+ +0.00023 * Math.sin(k2) +
+ -0.00014 * Math.sin(2 * d) +
+ +0.00014 * Math.cos(2 * mdash - 2 * f) +
+ -0.00012 * Math.sin(mdash - 2 * f) +
+ -0.00012 * Math.sin(2 * mdash) +
+ +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);
+ 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) {
const r = precession_rot(time, dir);
return [
diff --git a/demo/nodejs/calendar/astronomy.ts b/demo/nodejs/calendar/astronomy.ts
index 8705d9fe..6dc96327 100644
--- a/demo/nodejs/calendar/astronomy.ts
+++ b/demo/nodejs/calendar/astronomy.ts
@@ -1675,6 +1675,155 @@ function CalcMoon(time: AstroTime) {
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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(
+ public elat: number,
+ public elon: number,
+ public mlat: number,
+ public mlon: number,
+ public dist_km: number,
+ public diam_deg: number
+ ) {}
+}
+
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+export function Libration(date: FlexibleDateTime): LibrationInfo {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * KM_PER_AU;
+
+ // Inclination angle
+ const I = DEG2RAD * 1.54242;
+
+ // Moon's argument of latitude in radians.
+ const f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
+
+ // Moon's ascending node's mean longitude in radians.
+ const omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ // Sun's mean anomaly.
+ const m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ // Moon's mean anomaly.
+ const mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ // Moon's mean elongation.
+ const d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w)*Math.cos(mlat)*Math.cos(I) - Math.sin(mlat)*Math.sin(I), Math.cos(w)*Math.cos(mlat));
+ const ldash = LongitudeOffset(RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w)*Math.cos(mlat)*Math.sin(I) - Math.sin(mlat)*Math.cos(I));
+
+ // Physical librations
+ const k1 = DEG2RAD*(119.75 + 131.849*t);
+ const k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ const rho = (
+ -0.02752*Math.cos(mdash) +
+ -0.02245*Math.sin(f) +
+ +0.00684*Math.cos(mdash - 2*f) +
+ -0.00293*Math.cos(2*f) +
+ -0.00085*Math.cos(2*f - 2*d) +
+ -0.00054*Math.cos(mdash - 2*d) +
+ -0.00020*Math.sin(mdash + f) +
+ -0.00020*Math.cos(mdash + 2*f) +
+ -0.00020*Math.cos(mdash - f) +
+ +0.00014*Math.cos(mdash + 2*f - 2*d)
+ );
+
+ const sigma = (
+ -0.02816*Math.sin(mdash) +
+ +0.02244*Math.cos(f) +
+ -0.00682*Math.sin(mdash - 2*f) +
+ -0.00279*Math.sin(2*f) +
+ -0.00083*Math.sin(2*f - 2*d) +
+ +0.00069*Math.sin(mdash - 2*d) +
+ +0.00040*Math.cos(mdash + f) +
+ -0.00025*Math.sin(2*mdash) +
+ -0.00023*Math.sin(mdash + 2*f) +
+ +0.00020*Math.cos(mdash - f) +
+ +0.00019*Math.sin(mdash - f) +
+ +0.00013*Math.sin(mdash + 2*f - 2*d) +
+ -0.00010*Math.cos(mdash - 3*f)
+ );
+
+ const tau = (
+ +0.02520*e*Math.sin(m) +
+ +0.00473*Math.sin(2*mdash - 2*f) +
+ -0.00467*Math.sin(mdash) +
+ +0.00396*Math.sin(k1) +
+ +0.00276*Math.sin(2*mdash - 2*d) +
+ +0.00196*Math.sin(omega) +
+ -0.00183*Math.cos(mdash - f) +
+ +0.00115*Math.sin(mdash - 2*d) +
+ -0.00096*Math.sin(mdash - d) +
+ +0.00046*Math.sin(2*f - 2*d) +
+ -0.00039*Math.sin(mdash - f) +
+ -0.00032*Math.sin(mdash - m - d) +
+ +0.00027*Math.sin(2*mdash - m - 2*d) +
+ +0.00023*Math.sin(k2) +
+ -0.00014*Math.sin(2*d) +
+ +0.00014*Math.cos(2*mdash - 2*f) +
+ -0.00012*Math.sin(mdash - 2*f) +
+ -0.00012*Math.sin(2*mdash) +
+ +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);
+ 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 {
const r = precession_rot(time, dir);
return [
diff --git a/demo/python/astronomy.py b/demo/python/astronomy.py
index c707cb28..54157657 100644
--- a/demo/python/astronomy.py
+++ b/demo/python/astronomy.py
@@ -8537,3 +8537,157 @@ def NextTransit(body, prevTransitTime):
"""
startTime = prevTransitTime.AddDays(100.0)
return SearchTransit(body, startTime)
+
+
+class LibrationInfo:
+ """Lunar libration angles, returned by #Libration.
+
+ Contains lunar libration angles and lunar position information
+ for a given moment in time. See #Libration for more details.
+
+ Attributes
+ ----------
+ elat : float
+ Sub-Earth libration ecliptic latitude angle, in degrees.
+ elon : float
+ Sub-Earth libration ecliptic longitude angle, in degrees.
+ mlat : float
+ Moon's geocentric ecliptic latitude.
+ mlon : float
+ 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, 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):
+ """Calculates the Moon's libration angles at a given moment in time.
+
+ Libration is an observed back-and-forth wobble of the portion of the
+ Moon visible from the Earth. It is caused by the imperfect tidal locking
+ of the Moon's fixed rotation rate, compared to its variable angular speed
+ of orbit around the Earth.
+
+ 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`, 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
+ ----------
+ time : Time
+ The date and time for which to calculate the Moon's libration angles.
+
+ Returns
+ -------
+ LibrationInfo
+ """
+ t = time.tt / 36525.0
+ t2 = t * t
+ t3 = t2 * t
+ t4 = t2 * t2
+ moon = _CalcMoon(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)
+
+ # Moon's argument of latitude in radians.
+ f = math.radians(_NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000))
+
+ # Moon's ascending node's mean longitude in radians.
+ omega = math.radians(_NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000))
+
+ # Sun's mean anomaly.
+ m = math.radians(_NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000))
+
+ # Moon's mean anomaly.
+ mdash = math.radians(_NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000))
+
+ # Moon's mean elongation.
+ d = math.radians(_NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000))
+
+ # Eccentricity of the Earth's orbit.
+ e = 1.0 - 0.002516*t - 0.0000074*t2
+
+ # Optical librations
+ w = mlon - omega
+ a = math.atan2(math.sin(w)*math.cos(mlat)*math.cos(I) - math.sin(mlat)*math.sin(I), math.cos(w)*math.cos(mlat))
+ ldash = _LongitudeOffset(math.degrees(a - f))
+ bdash = math.asin(-math.sin(w)*math.cos(mlat)*math.sin(I) - math.sin(mlat)*math.cos(I))
+
+ # Physical librations
+ k1 = math.radians(119.75 + 131.849*t)
+ k2 = math.radians(72.56 + 20.186*t)
+
+ rho = (
+ -0.02752*math.cos(mdash) +
+ -0.02245*math.sin(f) +
+ +0.00684*math.cos(mdash - 2*f) +
+ -0.00293*math.cos(2*f) +
+ -0.00085*math.cos(2*f - 2*d) +
+ -0.00054*math.cos(mdash - 2*d) +
+ -0.00020*math.sin(mdash + f) +
+ -0.00020*math.cos(mdash + 2*f) +
+ -0.00020*math.cos(mdash - f) +
+ +0.00014*math.cos(mdash + 2*f - 2*d)
+ )
+
+ sigma = (
+ -0.02816*math.sin(mdash) +
+ +0.02244*math.cos(f) +
+ -0.00682*math.sin(mdash - 2*f) +
+ -0.00279*math.sin(2*f) +
+ -0.00083*math.sin(2*f - 2*d) +
+ +0.00069*math.sin(mdash - 2*d) +
+ +0.00040*math.cos(mdash + f) +
+ -0.00025*math.sin(2*mdash) +
+ -0.00023*math.sin(mdash + 2*f) +
+ +0.00020*math.cos(mdash - f) +
+ +0.00019*math.sin(mdash - f) +
+ +0.00013*math.sin(mdash + 2*f - 2*d) +
+ -0.00010*math.cos(mdash - 3*f)
+ )
+
+ tau = (
+ +0.02520*e*math.sin(m) +
+ +0.00473*math.sin(2*mdash - 2*f) +
+ -0.00467*math.sin(mdash) +
+ +0.00396*math.sin(k1) +
+ +0.00276*math.sin(2*mdash - 2*d) +
+ +0.00196*math.sin(omega) +
+ -0.00183*math.cos(mdash - f) +
+ +0.00115*math.sin(mdash - 2*d) +
+ -0.00096*math.sin(mdash - d) +
+ +0.00046*math.sin(2*f - 2*d) +
+ -0.00039*math.sin(mdash - f) +
+ -0.00032*math.sin(mdash - m - d) +
+ +0.00027*math.sin(2*mdash - m - 2*d) +
+ +0.00023*math.sin(k2) +
+ -0.00014*math.sin(2*d) +
+ +0.00014*math.cos(2*mdash - 2*f) +
+ -0.00012*math.sin(mdash - 2*f) +
+ -0.00012*math.sin(2*mdash) +
+ +0.00011*math.sin(2*mdash - 2*m - 2*d)
+ )
+
+ 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, diam_deg)
diff --git a/generate/ctest.c b/generate/ctest.c
index ea97a570..719da0c7 100644
--- a/generate/ctest.c
+++ b/generate/ctest.c
@@ -134,6 +134,7 @@ static int Issue103(void);
static int AberrationTest(void);
static int BaryStateTest(void);
static int Twilight(void);
+static int LibrationTest(void);
typedef int (* unit_test_func_t) (void);
@@ -156,6 +157,7 @@ static unit_test_t UnitTests[] =
{"global_solar_eclipse", GlobalSolarEclipseTest},
{"issue_103", Issue103},
{"jupiter_moons", JupiterMoonsTest},
+ {"libration", LibrationTest},
{"local_solar_eclipse", LocalSolarEclipseTest},
{"lunar_eclipse", LunarEclipseTest},
{"lunar_eclipse_78", LunarEclipseIssue78},
@@ -1707,6 +1709,46 @@ fail:
/*-----------------------------------------------------------------------------------------------------------*/
+static int ParseMonthName(const char *mtext, int *month)
+{
+ if (month == NULL)
+ return 1;
+
+ *month = -1;
+
+ if (mtext == NULL)
+ return 2;
+
+ if (!strcmp(mtext, "Jan"))
+ *month = 1;
+ else if (!strcmp(mtext, "Feb"))
+ *month = 2;
+ else if (!strcmp(mtext, "Mar"))
+ *month = 3;
+ else if (!strcmp(mtext, "Apr"))
+ *month = 4;
+ else if (!strcmp(mtext, "May"))
+ *month = 5;
+ else if (!strcmp(mtext, "Jun"))
+ *month = 6;
+ else if (!strcmp(mtext, "Jul"))
+ *month = 7;
+ else if (!strcmp(mtext, "Aug"))
+ *month = 8;
+ else if (!strcmp(mtext, "Sep"))
+ *month = 9;
+ else if (!strcmp(mtext, "Oct"))
+ *month = 10;
+ else if (!strcmp(mtext, "Nov"))
+ *month = 11;
+ else if (!strcmp(mtext, "Dec"))
+ *month = 12;
+ else
+ return 3;
+
+ return 0; /* success */
+}
+
static const char *ParseJplHorizonsDateTime(const char *text, astro_time_t *time)
{
int year, month, day, hour, minute;
@@ -4572,3 +4614,112 @@ fail:
}
/*-----------------------------------------------------------------------------------------------------------*/
+
+static int Libration(const char *filename, int *ndata, double *var_lon, double *var_lat)
+{
+ int error;
+ FILE *infile;
+ int lnum, count, nscanned;
+ char line[200];
+ int day, month, year, hour, minute;
+ char mtext[4];
+ 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, 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)
+ FAIL("C Libration: cannot open input file: %s\n", filename);
+
+ lnum = 0;
+ count = 0;
+ while (ReadLine(line, sizeof(line), infile, filename, lnum))
+ {
+ ++lnum;
+ if (lnum == 1)
+ {
+ if (strcmp(line, " Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA\n"))
+ FAIL("C Libration(%s line %d): unexpected header line\n", filename, lnum);
+ }
+ else
+ {
+ /* 01 Jan 2020 00:00 UT 29.95 5.783 1774.5 403898 23.2609 -10.0824 114.557 -0.045 0.773 6.360 336.353 */
+ nscanned = sscanf(line,
+ "%d %3s %d %d:%d UT %lf %lf %lf %lf %lf %lf %lf %lf %lf %lf %lf",
+ &day, mtext, &year, &hour, &minute,
+ &phase, &age, &diam, &dist, &ra, &dec, &slon, &slat, &elon, &elat, &axisa);
+
+ if (nscanned != 16)
+ FAIL("C Libration(%s line %d): expected 16 tokens, found %d\n", filename, lnum, nscanned);
+
+ /* Calculate the astronomy time value for this calendar date/time. */
+ if (ParseMonthName(mtext, &month))
+ FAIL("Libration(%s line %d): invalid month symbol '%s'\n", filename, lnum, mtext);
+
+ time = Astronomy_MakeTime(year, month, day, hour, minute, 0.0);
+ lib = Astronomy_Libration(time);
+
+ diff_elon = 60.0 * ABS(lib.elon - elon);
+ if (diff_elon > max_diff_elon)
+ max_diff_elon = diff_elon;
+
+ diff_elat = 60.0 * ABS(lib.elat - elat);
+ if (diff_elat > max_diff_elat)
+ max_diff_elat = diff_elat;
+
+ diff_distance = ABS(lib.dist_km - dist);
+ 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);
+
+ if (diff_elat > 1.666)
+ FAIL("C Libration(%s line %d): EXCESSIVE diff_elat = %0.4lf arcmin\n", filename, lnum, diff_elat);
+
+ if (diff_distance > 53.9)
+ FAIL("C Libration(%s line %d): EXCESSIVE diff_distance = %0.3lf km\n", filename, lnum, diff_distance);
+
+ /* Update sum-of-squared-errors. */
+ *var_lon += diff_elon * diff_elon;
+ *var_lat += diff_elat * diff_elat;
+
+ ++count;
+ }
+ }
+
+ 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;
+fail:
+ if (infile != NULL) fclose(infile);
+ return error;
+}
+
+static int LibrationTest(void)
+{
+ int error;
+ int ndata = 0;
+ double var_lat = 0.0;
+ double var_lon = 0.0;
+ double dev_lat, dev_lon;
+
+ CHECK(Libration("libration/mooninfo_2020.txt", &ndata, &var_lon, &var_lat));
+ CHECK(Libration("libration/mooninfo_2021.txt", &ndata, &var_lon, &var_lat));
+
+ dev_lon = sqrt(var_lon / ndata);
+ dev_lat = sqrt(var_lat / ndata);
+ printf("C LibrationTest: %d data points, dev_lon = %0.4lf arcmin, dev_lat = %0.4lf arcmin\n", ndata, dev_lon, dev_lat);
+fail:
+ return error;
+}
+
+/*-----------------------------------------------------------------------------------------------------------*/
diff --git a/generate/dotnet/csharp_test/csharp_test.cs b/generate/dotnet/csharp_test/csharp_test.cs
index 8fc8186e..f7857527 100644
--- a/generate/dotnet/csharp_test/csharp_test.cs
+++ b/generate/dotnet/csharp_test/csharp_test.cs
@@ -39,6 +39,7 @@ namespace csharp_test
new Test("elongation", ElongationTest),
new Test("global_solar_eclipse", GlobalSolarEclipseTest),
new Test("jupiter_moons", JupiterMoonsTest),
+ new Test("libration", LibrationTest),
new Test("local_solar_eclipse", LocalSolarEclipseTest),
new Test("lunar_apsis", LunarApsisTest),
new Test("lunar_eclipse", LunarEclipseTest),
@@ -1074,6 +1075,26 @@ namespace csharp_test
static readonly Regex JplRegex = new Regex(@"^\s*(\d{4})-(Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)-(\d{2})\s+(\d{2}):(\d{2})\s+(.*)");
+ static int MonthNumber(string mtext)
+ {
+ switch (mtext)
+ {
+ case "Jan": return 1;
+ case "Feb": return 2;
+ case "Mar": return 3;
+ case "Apr": return 4;
+ case "May": return 5;
+ case "Jun": return 6;
+ case "Jul": return 7;
+ case "Aug": return 8;
+ case "Sep": return 9;
+ case "Oct": return 10;
+ case "Nov": return 11;
+ case "Dec": return 12;
+ default:
+ throw new Exception(string.Format("Internal error: unexpected month name '{0}'", mtext));
+ }
+ }
static JplDateTime ParseJplHorizonsDateTime(string line)
{
@@ -1081,29 +1102,11 @@ namespace csharp_test
if (!m.Success)
return null;
int year = int.Parse(m.Groups[1].Value);
- string mtext = m.Groups[2].Value;
+ int month = MonthNumber(m.Groups[2].Value);
int day = int.Parse(m.Groups[3].Value);
int hour = int.Parse(m.Groups[4].Value);
int minute = int.Parse(m.Groups[5].Value);
string rest = m.Groups[6].Value;
- int month;
- switch (mtext)
- {
- case "Jan": month = 1; break;
- case "Feb": month = 2; break;
- case "Mar": month = 3; break;
- case "Apr": month = 4; break;
- case "May": month = 5; break;
- case "Jun": month = 6; break;
- case "Jul": month = 7; break;
- case "Aug": month = 8; break;
- case "Sep": month = 9; break;
- case "Oct": month = 10; break;
- case "Nov": month = 11; break;
- case "Dec": month = 12; break;
- default:
- throw new Exception(string.Format("Internal error: unexpected month name '{0}'", mtext));
- }
AstroTime time = new AstroTime(year, month, day, hour, minute, 0);
return new JplDateTime { Rest=rest, Time=time };
}
@@ -2997,5 +3000,107 @@ namespace csharp_test
Console.WriteLine($"C# TwilightTest: PASS ({lnum} test cases, max error = {max_diff} seconds)");
return 0;
}
+
+ static int Libration(string filename)
+ {
+ using StreamReader infile = File.OpenText(filename);
+ int lnum = 0;
+ int count = 0;
+ double max_diff_elon = 0.0;
+ double max_diff_elat = 0.0;
+ double max_diff_distance = 0.0;
+ double max_diff_diam = 0.0;
+ string line;
+ while (null != (line = infile.ReadLine()))
+ {
+ ++lnum;
+ if (lnum == 1)
+ {
+ // 0..2 3..4 5 6 7 8 9 10 11 12 13 14 15
+ if (line != " Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA")
+ {
+ Console.WriteLine($"C# Libration({filename} line {lnum}): unexpected header line.");
+ return 1;
+ }
+ }
+ else
+ {
+ // 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+ // 01 Jan 2020 00:00 UT 29.95 5.783 1774.5 403898 23.2609 -10.0824 114.557 -0.045 0.773 6.360 336.353
+ string[] token = Tokenize(line);
+ if (token.Length != 16)
+ {
+ Console.WriteLine($"C# Libration({filename} line {lnum}): expected 16 tokens, found {token.Length}.");
+ return 1;
+ }
+
+ int day = int.Parse(token[0]);
+ int month = MonthNumber(token[1]);
+ int year = int.Parse(token[2]);
+ string[] hmtoken = token[3].Split(':');
+ if (hmtoken.Length != 2)
+ {
+ Console.WriteLine($"C# Libration({filename} line {lnum}): expected hh:mm but found '{token[3]}'");
+ return 1;
+ }
+ int hour = int.Parse(hmtoken[0]);
+ 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]);
+
+ LibrationInfo lib = Astronomy.Libration(time);
+
+ double diff_elon = 60.0 * abs(lib.elon - elon);
+ if (diff_elon > max_diff_elon)
+ max_diff_elon = diff_elon;
+
+ double diff_elat = 60.0 * abs(lib.elat - elat);
+ if (diff_elat > max_diff_elat)
+ max_diff_elat = diff_elat;
+
+ double diff_distance = abs(lib.dist_km - dist);
+ 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($"C# Libration({filename} line {lnum}): EXCESSIVE diff_elon = {diff_elon} arcmin");
+ return 1;
+ }
+
+ if (diff_elat > 1.666)
+ {
+ Console.WriteLine($"C# Libration({filename} line {lnum}): EXCESSIVE diff_elat = {diff_elat} arcmin");
+ return 1;
+ }
+
+ if (diff_distance > 53.9)
+ {
+ Console.WriteLine($"C# Libration({filename} line {lnum}): EXCESSIVE diff_distance = {diff_distance} km");
+ return 1;
+ }
+ ++count;
+ }
+ }
+
+ Console.WriteLine($"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;
+ }
+
+
+ static int LibrationTest()
+ {
+ if (0 != Libration("../../libration/mooninfo_2020.txt")) return 1;
+ if (0 != Libration("../../libration/mooninfo_2021.txt")) return 1;
+ return 0;
+ }
}
}
diff --git a/generate/libration/README.md b/generate/libration/README.md
new file mode 100644
index 00000000..43ca4b35
--- /dev/null
+++ b/generate/libration/README.md
@@ -0,0 +1,5 @@
+# Acknowledgements
+
+This test data came from [mooninfo_2020.txt](https://svs.gsfc.nasa.gov/vis/a000000/a004700/a004768/mooninfo_2020.txt)
+on the NASA [Moon Phase and Libration 2020](https://svs.gsfc.nasa.gov/vis/a000000/a004700/a004768/) page.
+
diff --git a/generate/libration/mooninfo_2020.txt b/generate/libration/mooninfo_2020.txt
new file mode 100644
index 00000000..660e008a
--- /dev/null
+++ b/generate/libration/mooninfo_2020.txt
@@ -0,0 +1,8786 @@
+ Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA
+01 Jan 2020 00:00 UT 29.95 5.783 1774.5 403898 23.2609 -10.0824 114.557 -0.045 0.773 6.360 336.353
+01 Jan 2020 01:00 UT 30.32 5.824 1774.3 403952 23.2921 -9.9043 114.050 -0.046 0.721 6.382 336.326
+01 Jan 2020 02:00 UT 30.68 5.866 1774.0 404005 23.3233 -9.7256 113.543 -0.047 0.669 6.403 336.302
+01 Jan 2020 03:00 UT 31.05 5.908 1773.8 404055 23.3545 -9.5463 113.036 -0.047 0.617 6.424 336.279
+01 Jan 2020 04:00 UT 31.41 5.949 1773.6 404104 23.3856 -9.3664 112.529 -0.048 0.565 6.445 336.257
+01 Jan 2020 05:00 UT 31.78 5.991 1773.4 404150 23.4166 -9.1860 112.022 -0.049 0.512 6.465 336.238
+01 Jan 2020 06:00 UT 32.15 6.033 1773.2 404194 23.4477 -9.0051 111.515 -0.050 0.460 6.485 336.220
+01 Jan 2020 07:00 UT 32.52 6.074 1773.0 404236 23.4786 -8.8236 111.008 -0.051 0.408 6.504 336.204
+01 Jan 2020 08:00 UT 32.89 6.116 1772.9 404276 23.5096 -8.6416 110.501 -0.052 0.355 6.523 336.189
+01 Jan 2020 09:00 UT 33.26 6.158 1772.7 404314 23.5405 -8.4590 109.994 -0.052 0.302 6.541 336.177
+01 Jan 2020 10:00 UT 33.63 6.199 1772.5 404350 23.5714 -8.2760 109.487 -0.053 0.249 6.558 336.166
+01 Jan 2020 11:00 UT 34.00 6.241 1772.4 404383 23.6022 -8.0925 108.980 -0.054 0.197 6.576 336.156
+01 Jan 2020 12:00 UT 34.37 6.283 1772.3 404414 23.6330 -7.9085 108.473 -0.055 0.144 6.592 336.148
+01 Jan 2020 13:00 UT 34.75 6.324 1772.1 404443 23.6638 -7.7240 107.966 -0.056 0.091 6.609 336.142
+01 Jan 2020 14:00 UT 35.12 6.366 1772.0 404470 23.6945 -7.5391 107.459 -0.056 0.038 6.624 336.138
+01 Jan 2020 15:00 UT 35.50 6.408 1771.9 404495 23.7252 -7.3537 106.952 -0.057 -0.015 6.640 336.135
+01 Jan 2020 16:00 UT 35.88 6.449 1771.8 404517 23.7559 -7.1679 106.445 -0.058 -0.069 6.654 336.134
+01 Jan 2020 17:00 UT 36.26 6.491 1771.7 404538 23.7866 -6.9817 105.938 -0.059 -0.122 6.668 336.135
+01 Jan 2020 18:00 UT 36.63 6.533 1771.6 404556 23.8172 -6.7950 105.431 -0.060 -0.175 6.682 336.137
+01 Jan 2020 19:00 UT 37.01 6.574 1771.6 404572 23.8478 -6.6079 104.924 -0.061 -0.228 6.695 336.141
+01 Jan 2020 20:00 UT 37.39 6.616 1771.5 404585 23.8783 -6.4205 104.417 -0.061 -0.282 6.708 336.146
+01 Jan 2020 21:00 UT 37.77 6.658 1771.5 404597 23.9089 -6.2326 103.910 -0.062 -0.335 6.720 336.154
+01 Jan 2020 22:00 UT 38.16 6.699 1771.4 404606 23.9394 -6.0444 103.403 -0.063 -0.389 6.732 336.162
+01 Jan 2020 23:00 UT 38.54 6.741 1771.4 404613 23.9699 -5.8558 102.896 -0.064 -0.442 6.743 336.173
+02 Jan 2020 00:00 UT 38.92 6.783 1771.4 404617 0.0003 -5.6669 102.389 -0.065 -0.495 6.754 336.185
+02 Jan 2020 01:00 UT 39.30 6.824 1771.4 404619 0.0308 -5.4776 101.882 -0.066 -0.549 6.764 336.199
+02 Jan 2020 02:00 UT 39.69 6.866 1771.4 404620 0.0612 -5.2879 101.376 -0.066 -0.602 6.774 336.214
+02 Jan 2020 03:00 UT 40.07 6.908 1771.4 404617 0.0916 -5.0980 100.869 -0.067 -0.656 6.783 336.231
+02 Jan 2020 04:00 UT 40.46 6.949 1771.4 404613 0.1220 -4.9077 100.362 -0.068 -0.709 6.792 336.249
+02 Jan 2020 05:00 UT 40.85 6.991 1771.4 404606 0.1524 -4.7171 99.855 -0.069 -0.762 6.800 336.270
+02 Jan 2020 06:00 UT 41.23 7.033 1771.5 404597 0.1827 -4.5262 99.348 -0.070 -0.816 6.808 336.291
+02 Jan 2020 07:00 UT 41.62 7.074 1771.5 404586 0.2130 -4.3350 98.841 -0.071 -0.869 6.815 336.315
+02 Jan 2020 08:00 UT 42.01 7.116 1771.6 404572 0.2434 -4.1436 98.335 -0.071 -0.922 6.822 336.340
+02 Jan 2020 09:00 UT 42.39 7.158 1771.6 404556 0.2737 -3.9519 97.828 -0.072 -0.976 6.828 336.366
+02 Jan 2020 10:00 UT 42.78 7.199 1771.7 404538 0.3040 -3.7599 97.321 -0.073 -1.029 6.834 336.394
+02 Jan 2020 11:00 UT 43.17 7.241 1771.8 404518 0.3342 -3.5677 96.814 -0.074 -1.082 6.839 336.424
+02 Jan 2020 12:00 UT 43.56 7.283 1771.9 404495 0.3645 -3.3752 96.308 -0.075 -1.135 6.844 336.455
+02 Jan 2020 13:00 UT 43.95 7.324 1772.0 404470 0.3948 -3.1825 95.801 -0.076 -1.188 6.848 336.488
+02 Jan 2020 14:00 UT 44.34 7.366 1772.1 404442 0.4250 -2.9896 95.294 -0.077 -1.241 6.852 336.522
+02 Jan 2020 15:00 UT 44.73 7.408 1772.3 404413 0.4553 -2.7965 94.787 -0.077 -1.294 6.855 336.558
+02 Jan 2020 16:00 UT 45.12 7.449 1772.4 404381 0.4855 -2.6031 94.281 -0.078 -1.347 6.858 336.596
+02 Jan 2020 17:00 UT 45.51 7.491 1772.6 404346 0.5158 -2.4096 93.774 -0.079 -1.400 6.860 336.635
+02 Jan 2020 18:00 UT 45.91 7.533 1772.7 404310 0.5460 -2.2159 93.267 -0.080 -1.453 6.862 336.676
+02 Jan 2020 19:00 UT 46.30 7.574 1772.9 404271 0.5762 -2.0220 92.760 -0.081 -1.506 6.863 336.718
+02 Jan 2020 20:00 UT 46.69 7.616 1773.1 404230 0.6065 -1.8280 92.254 -0.082 -1.558 6.864 336.762
+02 Jan 2020 21:00 UT 47.08 7.658 1773.3 404186 0.6367 -1.6338 91.747 -0.083 -1.611 6.864 336.807
+02 Jan 2020 22:00 UT 47.48 7.699 1773.5 404140 0.6669 -1.4395 91.240 -0.083 -1.663 6.863 336.854
+02 Jan 2020 23:00 UT 47.87 7.741 1773.7 404092 0.6972 -1.2450 90.734 -0.084 -1.715 6.862 336.903
+03 Jan 2020 00:00 UT 48.26 7.783 1773.9 404042 0.7274 -1.0504 90.227 -0.085 -1.767 6.861 336.953
+03 Jan 2020 01:00 UT 48.66 7.824 1774.1 403989 0.7576 -0.8557 89.721 -0.086 -1.819 6.859 337.004
+03 Jan 2020 02:00 UT 49.05 7.866 1774.4 403934 0.7879 -0.6609 89.214 -0.087 -1.871 6.857 337.057
+03 Jan 2020 03:00 UT 49.44 7.908 1774.6 403877 0.8181 -0.4660 88.707 -0.088 -1.923 6.854 337.112
+03 Jan 2020 04:00 UT 49.84 7.949 1774.9 403818 0.8484 -0.2710 88.201 -0.089 -1.975 6.850 337.168
+03 Jan 2020 05:00 UT 50.23 7.991 1775.1 403756 0.8786 -0.0760 87.694 -0.089 -2.026 6.847 337.225
+03 Jan 2020 06:00 UT 50.63 8.033 1775.4 403692 0.9089 0.1192 87.188 -0.090 -2.077 6.842 337.285
+03 Jan 2020 07:00 UT 51.02 8.074 1775.7 403625 0.9392 0.3143 86.681 -0.091 -2.129 6.837 337.345
+03 Jan 2020 08:00 UT 51.42 8.116 1776.0 403557 0.9695 0.5096 86.174 -0.092 -2.180 6.832 337.408
+03 Jan 2020 09:00 UT 51.81 8.158 1776.3 403486 0.9998 0.7048 85.668 -0.093 -2.230 6.826 337.471
+03 Jan 2020 10:00 UT 52.21 8.199 1776.7 403413 1.0301 0.9001 85.161 -0.094 -2.281 6.819 337.537
+03 Jan 2020 11:00 UT 52.60 8.241 1777.0 403337 1.0605 1.0954 84.655 -0.095 -2.332 6.812 337.603
+03 Jan 2020 12:00 UT 52.99 8.283 1777.3 403260 1.0908 1.2907 84.148 -0.096 -2.382 6.805 337.672
+03 Jan 2020 13:00 UT 53.39 8.324 1777.7 403180 1.1212 1.4861 83.642 -0.097 -2.432 6.797 337.742
+03 Jan 2020 14:00 UT 53.78 8.366 1778.0 403098 1.1516 1.6814 83.135 -0.097 -2.482 6.788 337.813
+03 Jan 2020 15:00 UT 54.18 8.408 1778.4 403013 1.1820 1.8766 82.629 -0.098 -2.532 6.779 337.886
+03 Jan 2020 16:00 UT 54.57 8.449 1778.8 402927 1.2124 2.0719 82.122 -0.099 -2.581 6.769 337.960
+03 Jan 2020 17:00 UT 54.97 8.491 1779.2 402838 1.2428 2.2671 81.616 -0.100 -2.631 6.759 338.036
+03 Jan 2020 18:00 UT 55.36 8.533 1779.6 402747 1.2733 2.4622 81.110 -0.101 -2.680 6.749 338.113
+03 Jan 2020 19:00 UT 55.76 8.574 1780.0 402654 1.3038 2.6573 80.603 -0.102 -2.729 6.738 338.192
+03 Jan 2020 20:00 UT 56.15 8.616 1780.4 402559 1.3343 2.8523 80.097 -0.103 -2.778 6.726 338.272
+03 Jan 2020 21:00 UT 56.54 8.658 1780.9 402461 1.3649 3.0472 79.590 -0.104 -2.826 6.714 338.354
+03 Jan 2020 22:00 UT 56.94 8.699 1781.3 402362 1.3954 3.2421 79.084 -0.105 -2.874 6.701 338.438
+03 Jan 2020 23:00 UT 57.33 8.741 1781.7 402260 1.4260 3.4368 78.577 -0.106 -2.922 6.688 338.522
+04 Jan 2020 00:00 UT 57.72 8.783 1782.2 402156 1.4566 3.6314 78.071 -0.106 -2.970 6.674 338.609
+04 Jan 2020 01:00 UT 58.12 8.824 1782.7 402050 1.4873 3.8259 77.565 -0.107 -3.018 6.660 338.697
+04 Jan 2020 02:00 UT 58.51 8.866 1783.2 401941 1.5180 4.0202 77.058 -0.108 -3.065 6.645 338.786
+04 Jan 2020 03:00 UT 58.90 8.908 1783.6 401831 1.5487 4.2144 76.552 -0.109 -3.112 6.630 338.877
+04 Jan 2020 04:00 UT 59.29 8.949 1784.1 401719 1.5795 4.4085 76.046 -0.110 -3.159 6.614 338.969
+04 Jan 2020 05:00 UT 59.68 8.991 1784.7 401604 1.6102 4.6023 75.539 -0.111 -3.205 6.598 339.063
+04 Jan 2020 06:00 UT 60.07 9.033 1785.2 401487 1.6411 4.7960 75.033 -0.112 -3.251 6.581 339.158
+04 Jan 2020 07:00 UT 60.47 9.074 1785.7 401369 1.6719 4.9895 74.527 -0.113 -3.297 6.564 339.255
+04 Jan 2020 08:00 UT 60.86 9.116 1786.2 401248 1.7028 5.1828 74.020 -0.114 -3.343 6.546 339.353
+04 Jan 2020 09:00 UT 61.25 9.158 1786.8 401125 1.7338 5.3759 73.514 -0.115 -3.388 6.528 339.453
+04 Jan 2020 10:00 UT 61.64 9.199 1787.3 401000 1.7647 5.5688 73.008 -0.116 -3.433 6.509 339.554
+04 Jan 2020 11:00 UT 62.02 9.241 1787.9 400873 1.7958 5.7614 72.502 -0.117 -3.478 6.490 339.657
+04 Jan 2020 12:00 UT 62.41 9.283 1788.5 400744 1.8268 5.9538 71.995 -0.118 -3.523 6.470 339.761
+04 Jan 2020 13:00 UT 62.80 9.324 1789.1 400614 1.8579 6.1459 71.489 -0.119 -3.567 6.450 339.867
+04 Jan 2020 14:00 UT 63.19 9.366 1789.7 400481 1.8891 6.3378 70.983 -0.120 -3.611 6.429 339.974
+04 Jan 2020 15:00 UT 63.58 9.408 1790.3 400346 1.9203 6.5293 70.477 -0.120 -3.654 6.408 340.083
+04 Jan 2020 16:00 UT 63.96 9.449 1790.9 400209 1.9515 6.7206 69.970 -0.121 -3.697 6.386 340.193
+04 Jan 2020 17:00 UT 64.35 9.491 1791.5 400071 1.9828 6.9116 69.464 -0.122 -3.740 6.363 340.304
+04 Jan 2020 18:00 UT 64.73 9.533 1792.1 399930 2.0141 7.1022 68.958 -0.123 -3.783 6.341 340.417
+04 Jan 2020 19:00 UT 65.12 9.574 1792.8 399787 2.0455 7.2925 68.452 -0.124 -3.825 6.317 340.532
+04 Jan 2020 20:00 UT 65.50 9.616 1793.4 399643 2.0769 7.4825 67.946 -0.125 -3.867 6.293 340.648
+04 Jan 2020 21:00 UT 65.88 9.658 1794.1 399497 2.1084 7.6722 67.439 -0.126 -3.908 6.269 340.765
+04 Jan 2020 22:00 UT 66.27 9.699 1794.7 399349 2.1400 7.8614 66.933 -0.127 -3.949 6.244 340.884
+04 Jan 2020 23:00 UT 66.65 9.741 1795.4 399199 2.1716 8.0503 66.427 -0.128 -3.990 6.219 341.005
+05 Jan 2020 00:00 UT 67.03 9.783 1796.1 399047 2.2032 8.2388 65.921 -0.129 -4.030 6.193 341.127
+05 Jan 2020 01:00 UT 67.41 9.824 1796.8 398893 2.2349 8.4269 65.415 -0.130 -4.070 6.166 341.250
+05 Jan 2020 02:00 UT 67.79 9.866 1797.5 398738 2.2667 8.6145 64.909 -0.131 -4.110 6.139 341.375
+05 Jan 2020 03:00 UT 68.17 9.908 1798.2 398581 2.2985 8.8018 64.403 -0.132 -4.149 6.112 341.502
+05 Jan 2020 04:00 UT 68.54 9.949 1798.9 398422 2.3304 8.9886 63.897 -0.133 -4.188 6.084 341.629
+05 Jan 2020 05:00 UT 68.92 9.991 1799.6 398261 2.3623 9.1749 63.391 -0.134 -4.227 6.056 341.759
+05 Jan 2020 06:00 UT 69.30 10.033 1800.4 398099 2.3943 9.3608 62.884 -0.135 -4.265 6.027 341.889
+05 Jan 2020 07:00 UT 69.67 10.074 1801.1 397935 2.4264 9.5462 62.378 -0.136 -4.303 5.997 342.022
+05 Jan 2020 08:00 UT 70.05 10.116 1801.9 397770 2.4585 9.7311 61.872 -0.137 -4.340 5.967 342.155
+05 Jan 2020 09:00 UT 70.42 10.158 1802.6 397602 2.4907 9.9155 61.366 -0.138 -4.377 5.937 342.291
+05 Jan 2020 10:00 UT 70.79 10.199 1803.4 397433 2.5230 10.0993 60.860 -0.139 -4.413 5.906 342.427
+05 Jan 2020 11:00 UT 71.16 10.241 1804.2 397263 2.5553 10.2826 60.354 -0.140 -4.450 5.875 342.565
+05 Jan 2020 12:00 UT 71.53 10.283 1804.9 397091 2.5877 10.4654 59.848 -0.141 -4.485 5.843 342.705
+05 Jan 2020 13:00 UT 71.90 10.324 1805.7 396917 2.6202 10.6476 59.342 -0.142 -4.520 5.810 342.846
+05 Jan 2020 14:00 UT 72.27 10.366 1806.5 396742 2.6527 10.8292 58.836 -0.143 -4.555 5.777 342.989
+05 Jan 2020 15:00 UT 72.63 10.408 1807.3 396565 2.6853 11.0102 58.330 -0.144 -4.590 5.744 343.133
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+27 Dec 2020 02:00 UT 91.21 12.405 1782.6 402060 3.9446 18.6821 32.579 -0.426 -1.818 2.192 349.716
+27 Dec 2020 03:00 UT 91.44 12.447 1783.1 401963 3.9785 18.8263 32.073 -0.427 -1.867 2.135 349.898
+27 Dec 2020 04:00 UT 91.66 12.488 1783.5 401865 4.0124 18.9692 31.568 -0.429 -1.917 2.078 350.081
+27 Dec 2020 05:00 UT 91.88 12.530 1783.9 401766 4.0465 19.1108 31.062 -0.430 -1.966 2.021 350.266
+27 Dec 2020 06:00 UT 92.10 12.572 1784.4 401666 4.0806 19.2511 30.557 -0.431 -2.014 1.964 350.451
+27 Dec 2020 07:00 UT 92.31 12.613 1784.8 401564 4.1148 19.3900 30.051 -0.432 -2.063 1.907 350.637
+27 Dec 2020 08:00 UT 92.52 12.655 1785.3 401462 4.1491 19.5276 29.546 -0.433 -2.111 1.849 350.825
+27 Dec 2020 09:00 UT 92.73 12.697 1785.7 401358 4.1834 19.6637 29.040 -0.434 -2.159 1.791 351.013
+27 Dec 2020 10:00 UT 92.94 12.738 1786.2 401253 4.2179 19.7985 28.534 -0.435 -2.207 1.733 351.203
+27 Dec 2020 11:00 UT 93.15 12.780 1786.7 401147 4.2524 19.9319 28.029 -0.436 -2.254 1.675 351.394
+27 Dec 2020 12:00 UT 93.35 12.822 1787.2 401040 4.2870 20.0639 27.523 -0.438 -2.301 1.617 351.585
+27 Dec 2020 13:00 UT 93.55 12.863 1787.6 400932 4.3216 20.1944 27.018 -0.439 -2.348 1.558 351.778
+27 Dec 2020 14:00 UT 93.74 12.905 1788.1 400823 4.3564 20.3235 26.512 -0.440 -2.395 1.499 351.972
+27 Dec 2020 15:00 UT 93.94 12.947 1788.6 400713 4.3912 20.4511 26.007 -0.441 -2.441 1.441 352.166
+27 Dec 2020 16:00 UT 94.13 12.988 1789.1 400602 4.4261 20.5772 25.501 -0.442 -2.487 1.382 352.362
+27 Dec 2020 17:00 UT 94.32 13.030 1789.6 400490 4.4611 20.7018 24.996 -0.443 -2.533 1.323 352.559
+27 Dec 2020 18:00 UT 94.50 13.072 1790.1 400376 4.4962 20.8249 24.490 -0.444 -2.578 1.263 352.756
+27 Dec 2020 19:00 UT 94.69 13.113 1790.6 400262 4.5313 20.9465 23.985 -0.446 -2.623 1.204 352.955
+27 Dec 2020 20:00 UT 94.87 13.155 1791.2 400147 4.5665 21.0665 23.479 -0.447 -2.668 1.145 353.154
+27 Dec 2020 21:00 UT 95.04 13.197 1791.7 400031 4.6018 21.1849 22.974 -0.448 -2.713 1.085 353.355
+27 Dec 2020 22:00 UT 95.22 13.238 1792.2 399914 4.6372 21.3018 22.468 -0.449 -2.757 1.025 353.556
+27 Dec 2020 23:00 UT 95.39 13.280 1792.7 399797 4.6727 21.4171 21.963 -0.450 -2.801 0.966 353.759
+28 Dec 2020 00:00 UT 95.56 13.322 1793.3 399678 4.7082 21.5308 21.457 -0.451 -2.844 0.906 353.962
+28 Dec 2020 01:00 UT 95.72 13.363 1793.8 399558 4.7438 21.6428 20.952 -0.453 -2.888 0.846 354.166
+28 Dec 2020 02:00 UT 95.88 13.405 1794.3 399438 4.7795 21.7532 20.446 -0.454 -2.930 0.785 354.371
+28 Dec 2020 03:00 UT 96.04 13.447 1794.9 399317 4.8153 21.8620 19.941 -0.455 -2.973 0.725 354.577
+28 Dec 2020 04:00 UT 96.20 13.488 1795.4 399195 4.8512 21.9690 19.436 -0.456 -3.015 0.665 354.783
+28 Dec 2020 05:00 UT 96.36 13.530 1796.0 399072 4.8871 22.0744 18.930 -0.457 -3.057 0.604 354.991
+28 Dec 2020 06:00 UT 96.51 13.572 1796.5 398948 4.9231 22.1781 18.425 -0.458 -3.099 0.544 355.199
+28 Dec 2020 07:00 UT 96.65 13.613 1797.1 398824 4.9592 22.2801 17.919 -0.459 -3.140 0.483 355.408
+28 Dec 2020 08:00 UT 96.80 13.655 1797.7 398699 4.9954 22.3804 17.414 -0.461 -3.181 0.423 355.618
+28 Dec 2020 09:00 UT 96.94 13.697 1798.2 398573 5.0316 22.4789 16.908 -0.462 -3.222 0.362 355.829
+28 Dec 2020 10:00 UT 97.08 13.738 1798.8 398447 5.0679 22.5756 16.403 -0.463 -3.262 0.301 356.041
+28 Dec 2020 11:00 UT 97.22 13.780 1799.4 398320 5.1043 22.6706 15.898 -0.464 -3.302 0.240 356.253
+28 Dec 2020 12:00 UT 97.35 13.822 1799.9 398192 5.1408 22.7637 15.392 -0.465 -3.341 0.179 356.466
+28 Dec 2020 13:00 UT 97.48 13.863 1800.5 398063 5.1774 22.8551 14.887 -0.466 -3.381 0.118 356.679
+28 Dec 2020 14:00 UT 97.60 13.905 1801.1 397934 5.2140 22.9446 14.381 -0.468 -3.419 0.057 356.894
+28 Dec 2020 15:00 UT 97.73 13.947 1801.7 397804 5.2507 23.0324 13.876 -0.469 -3.458 -0.004 357.109
+28 Dec 2020 16:00 UT 97.85 13.988 1802.3 397674 5.2874 23.1182 13.370 -0.470 -3.496 -0.065 357.324
+28 Dec 2020 17:00 UT 97.97 14.030 1802.9 397543 5.3243 23.2022 12.865 -0.471 -3.534 -0.126 357.541
+28 Dec 2020 18:00 UT 98.08 14.072 1803.5 397411 5.3612 23.2843 12.360 -0.472 -3.571 -0.187 357.757
+28 Dec 2020 19:00 UT 98.19 14.113 1804.1 397279 5.3982 23.3646 11.854 -0.474 -3.608 -0.248 357.975
+28 Dec 2020 20:00 UT 98.30 14.155 1804.7 397146 5.4352 23.4429 11.349 -0.475 -3.645 -0.310 358.193
+28 Dec 2020 21:00 UT 98.40 14.197 1805.3 397013 5.4723 23.5193 10.843 -0.476 -3.681 -0.371 358.412
+28 Dec 2020 22:00 UT 98.50 14.238 1805.9 396879 5.5095 23.5938 10.338 -0.477 -3.717 -0.432 358.631
+28 Dec 2020 23:00 UT 98.60 14.280 1806.5 396745 5.5468 23.6663 9.833 -0.478 -3.752 -0.493 358.850
+29 Dec 2020 00:00 UT 98.70 14.322 1807.1 396610 5.5841 23.7369 9.327 -0.479 -3.788 -0.554 359.071
+29 Dec 2020 01:00 UT 98.79 14.363 1807.7 396475 5.6215 23.8055 8.822 -0.481 -3.822 -0.616 359.291
+29 Dec 2020 02:00 UT 98.88 14.405 1808.4 396339 5.6590 23.8721 8.317 -0.482 -3.857 -0.677 359.512
+29 Dec 2020 03:00 UT 98.96 14.447 1809.0 396203 5.6965 23.9367 7.811 -0.483 -3.891 -0.738 359.734
+29 Dec 2020 04:00 UT 99.04 14.488 1809.6 396066 5.7341 23.9993 7.306 -0.484 -3.924 -0.799 359.956
+29 Dec 2020 05:00 UT 99.12 14.530 1810.2 395929 5.7717 24.0599 6.800 -0.485 -3.958 -0.860 0.178
+29 Dec 2020 06:00 UT 99.20 14.572 1810.9 395792 5.8095 24.1184 6.295 -0.487 -3.990 -0.922 0.401
+29 Dec 2020 07:00 UT 99.27 14.613 1811.5 395654 5.8472 24.1749 5.790 -0.488 -4.023 -0.983 0.624
+29 Dec 2020 08:00 UT 99.34 14.655 1812.1 395516 5.8851 24.2294 5.284 -0.489 -4.055 -1.044 0.847
+29 Dec 2020 09:00 UT 99.40 14.697 1812.8 395378 5.9230 24.2817 4.779 -0.490 -4.087 -1.105 1.071
+29 Dec 2020 10:00 UT 99.46 14.738 1813.4 395239 5.9609 24.3320 4.274 -0.491 -4.118 -1.166 1.295
+29 Dec 2020 11:00 UT 99.52 14.780 1814.0 395100 5.9989 24.3802 3.768 -0.493 -4.149 -1.227 1.519
+29 Dec 2020 12:00 UT 99.57 14.822 1814.7 394960 6.0370 24.4263 3.263 -0.494 -4.179 -1.288 1.743
+29 Dec 2020 13:00 UT 99.63 14.863 1815.3 394820 6.0751 24.4703 2.758 -0.495 -4.209 -1.348 1.968
+29 Dec 2020 14:00 UT 99.67 14.905 1816.0 394680 6.1133 24.5121 2.252 -0.496 -4.239 -1.409 2.192
+29 Dec 2020 15:00 UT 99.72 14.947 1816.6 394540 6.1515 24.5518 1.747 -0.497 -4.268 -1.470 2.417
+29 Dec 2020 16:00 UT 99.76 14.988 1817.3 394399 6.1898 24.5894 1.242 -0.499 -4.297 -1.530 2.642
+29 Dec 2020 17:00 UT 99.80 15.030 1817.9 394258 6.2281 24.6248 0.736 -0.500 -4.325 -1.591 2.867
+29 Dec 2020 18:00 UT 99.83 15.072 1818.6 394117 6.2665 24.6580 0.231 -0.501 -4.353 -1.651 3.092
+29 Dec 2020 19:00 UT 99.86 15.113 1819.2 393976 6.3050 24.6891 -0.274 -0.502 -4.381 -1.711 3.317
+29 Dec 2020 20:00 UT 99.89 15.155 1819.9 393835 6.3434 24.7180 -0.780 -0.503 -4.408 -1.772 3.542
+29 Dec 2020 21:00 UT 99.91 15.197 1820.5 393693 6.3819 24.7447 -1.285 -0.505 -4.435 -1.832 3.768
+29 Dec 2020 22:00 UT 99.93 15.238 1821.2 393551 6.4205 24.7691 -1.790 -0.506 -4.461 -1.892 3.993
+29 Dec 2020 23:00 UT 99.95 15.280 1821.8 393409 6.4591 24.7914 -2.296 -0.507 -4.487 -1.951 4.218
+30 Dec 2020 00:00 UT 99.96 15.322 1822.5 393267 6.4978 24.8115 -2.801 -0.508 -4.513 -2.011 4.442
+30 Dec 2020 01:00 UT 99.97 15.363 1823.1 393125 6.5364 24.8293 -3.306 -0.510 -4.538 -2.071 4.667
+30 Dec 2020 02:00 UT 99.98 15.405 1823.8 392982 6.5752 24.8449 -3.812 -0.511 -4.562 -2.130 4.892
+30 Dec 2020 03:00 UT 99.98 15.447 1824.5 392839 6.6139 24.8583 -4.317 -0.512 -4.587 -2.189 5.116
+30 Dec 2020 04:00 UT 99.98 15.488 1825.1 392697 6.6527 24.8694 -4.822 -0.513 -4.611 -2.249 5.340
+30 Dec 2020 05:00 UT 99.97 15.530 1825.8 392554 6.6916 24.8782 -5.328 -0.514 -4.634 -2.308 5.564
+30 Dec 2020 06:00 UT 99.96 15.572 1826.5 392411 6.7304 24.8848 -5.833 -0.516 -4.657 -2.366 5.788
+30 Dec 2020 07:00 UT 99.95 15.613 1827.1 392268 6.7693 24.8892 -6.338 -0.517 -4.679 -2.425 6.011
+30 Dec 2020 08:00 UT 99.94 15.655 1827.8 392125 6.8083 24.8912 -6.844 -0.518 -4.702 -2.484 6.234
+30 Dec 2020 09:00 UT 99.92 15.697 1828.5 391982 6.8472 24.8910 -7.349 -0.519 -4.723 -2.542 6.457
+30 Dec 2020 10:00 UT 99.89 15.738 1829.1 391839 6.8862 24.8885 -7.854 -0.520 -4.745 -2.600 6.679
+30 Dec 2020 11:00 UT 99.87 15.780 1829.8 391696 6.9252 24.8838 -8.360 -0.522 -4.765 -2.658 6.901
+30 Dec 2020 12:00 UT 99.84 15.822 1830.5 391553 6.9642 24.8767 -8.865 -0.523 -4.786 -2.716 7.122
+30 Dec 2020 13:00 UT 99.80 15.863 1831.1 391410 7.0033 24.8673 -9.370 -0.524 -4.806 -2.774 7.343
+30 Dec 2020 14:00 UT 99.77 15.905 1831.8 391266 7.0424 24.8557 -9.876 -0.525 -4.825 -2.831 7.563
+30 Dec 2020 15:00 UT 99.72 15.947 1832.5 391123 7.0815 24.8417 -10.381 -0.527 -4.844 -2.888 7.783
+30 Dec 2020 16:00 UT 99.68 15.988 1833.1 390980 7.1206 24.8255 -10.886 -0.528 -4.863 -2.945 8.002
+30 Dec 2020 17:00 UT 99.63 16.030 1833.8 390837 7.1597 24.8069 -11.392 -0.529 -4.881 -3.002 8.221
+30 Dec 2020 18:00 UT 99.58 16.072 1834.5 390694 7.1989 24.7860 -11.897 -0.530 -4.899 -3.058 8.439
+30 Dec 2020 19:00 UT 99.52 16.113 1835.2 390551 7.2380 24.7628 -12.402 -0.531 -4.917 -3.115 8.656
+30 Dec 2020 20:00 UT 99.46 16.155 1835.8 390408 7.2772 24.7373 -12.908 -0.533 -4.934 -3.171 8.873
+30 Dec 2020 21:00 UT 99.40 16.197 1836.5 390265 7.3164 24.7095 -13.413 -0.534 -4.950 -3.227 9.089
+30 Dec 2020 22:00 UT 99.33 16.238 1837.2 390122 7.3556 24.6794 -13.918 -0.535 -4.966 -3.282 9.304
+30 Dec 2020 23:00 UT 99.26 16.280 1837.9 389979 7.3948 24.6470 -14.424 -0.536 -4.982 -3.338 9.518
+31 Dec 2020 00:00 UT 99.19 16.322 1838.5 389837 7.4340 24.6122 -14.929 -0.538 -4.997 -3.393 9.732
+31 Dec 2020 01:00 UT 99.11 16.363 1839.2 389694 7.4732 24.5752 -15.434 -0.539 -5.012 -3.448 9.945
+31 Dec 2020 02:00 UT 99.03 16.405 1839.9 389552 7.5124 24.5358 -15.940 -0.540 -5.026 -3.502 10.156
+31 Dec 2020 03:00 UT 98.95 16.447 1840.5 389409 7.5516 24.4941 -16.445 -0.541 -5.040 -3.557 10.367
+31 Dec 2020 04:00 UT 98.86 16.488 1841.2 389267 7.5909 24.4501 -16.950 -0.542 -5.054 -3.611 10.577
+31 Dec 2020 05:00 UT 98.76 16.530 1841.9 389125 7.6301 24.4038 -17.456 -0.544 -5.067 -3.664 10.786
+31 Dec 2020 06:00 UT 98.67 16.572 1842.6 388983 7.6693 24.3552 -17.961 -0.545 -5.079 -3.718 10.995
+31 Dec 2020 07:00 UT 98.57 16.613 1843.2 388841 7.7085 24.3042 -18.466 -0.546 -5.091 -3.771 11.202
+31 Dec 2020 08:00 UT 98.46 16.655 1843.9 388700 7.7477 24.2510 -18.972 -0.547 -5.103 -3.824 11.408
+31 Dec 2020 09:00 UT 98.36 16.697 1844.6 388558 7.7869 24.1955 -19.477 -0.549 -5.114 -3.876 11.613
+31 Dec 2020 10:00 UT 98.25 16.738 1845.2 388417 7.8261 24.1377 -19.982 -0.550 -5.125 -3.929 11.816
+31 Dec 2020 11:00 UT 98.13 16.780 1845.9 388276 7.8653 24.0775 -20.488 -0.551 -5.136 -3.980 12.019
+31 Dec 2020 12:00 UT 98.01 16.822 1846.6 388135 7.9045 24.0151 -20.993 -0.552 -5.146 -4.032 12.221
+31 Dec 2020 13:00 UT 97.89 16.863 1847.3 387994 7.9436 23.9504 -21.499 -0.553 -5.155 -4.083 12.421
+31 Dec 2020 14:00 UT 97.76 16.905 1847.9 387854 7.9828 23.8835 -22.004 -0.555 -5.164 -4.134 12.620
+31 Dec 2020 15:00 UT 97.63 16.947 1848.6 387713 8.0219 23.8142 -22.509 -0.556 -5.173 -4.185 12.818
+31 Dec 2020 16:00 UT 97.50 16.988 1849.3 387573 8.0610 23.7427 -23.015 -0.557 -5.181 -4.235 13.015
+31 Dec 2020 17:00 UT 97.36 17.030 1849.9 387433 8.1001 23.6689 -23.520 -0.558 -5.189 -4.285 13.210
+31 Dec 2020 18:00 UT 97.22 17.072 1850.6 387293 8.1392 23.5929 -24.025 -0.560 -5.196 -4.335 13.404
+31 Dec 2020 19:00 UT 97.08 17.113 1851.3 387154 8.1782 23.5146 -24.531 -0.561 -5.203 -4.384 13.597
+31 Dec 2020 20:00 UT 96.93 17.155 1851.9 387014 8.2173 23.4340 -25.036 -0.562 -5.210 -4.433 13.788
+31 Dec 2020 21:00 UT 96.78 17.197 1852.6 386875 8.2563 23.3512 -25.542 -0.563 -5.216 -4.481 13.978
+31 Dec 2020 22:00 UT 96.62 17.238 1853.3 386737 8.2953 23.2662 -26.047 -0.564 -5.222 -4.529 14.167
+31 Dec 2020 23:00 UT 96.47 17.280 1853.9 386598 8.3343 23.1790 -26.552 -0.566 -5.227 -4.577 14.354
+01 Jan 2021 00:00 UT 96.30 17.322 1854.6 386460 8.3732 23.0895 -27.058 -0.567 -5.232 -4.624 14.540
diff --git a/generate/libration/mooninfo_2021.txt b/generate/libration/mooninfo_2021.txt
new file mode 100644
index 00000000..1d48dc81
--- /dev/null
+++ b/generate/libration/mooninfo_2021.txt
@@ -0,0 +1,8761 @@
+ Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA
+01 Jan 2021 00:00 UT 96.30 17.322 1854.6 386460 8.3732 23.0895 -27.058 -0.567 -5.232 -4.624 14.540
+01 Jan 2021 01:00 UT 96.14 17.363 1855.3 386321 8.4121 22.9979 -27.563 -0.568 -5.236 -4.671 14.724
+01 Jan 2021 02:00 UT 95.97 17.405 1855.9 386184 8.4510 22.9040 -28.069 -0.569 -5.240 -4.718 14.906
+01 Jan 2021 03:00 UT 95.79 17.447 1856.6 386046 8.4899 22.8079 -28.574 -0.571 -5.243 -4.764 15.087
+01 Jan 2021 04:00 UT 95.61 17.488 1857.2 385909 8.5287 22.7097 -29.079 -0.572 -5.246 -4.810 15.267
+01 Jan 2021 05:00 UT 95.43 17.530 1857.9 385772 8.5675 22.6093 -29.585 -0.573 -5.249 -4.855 15.445
+01 Jan 2021 06:00 UT 95.25 17.572 1858.6 385635 8.6062 22.5067 -30.090 -0.574 -5.251 -4.900 15.621
+01 Jan 2021 07:00 UT 95.06 17.613 1859.2 385498 8.6450 22.4020 -30.596 -0.575 -5.253 -4.945 15.796
+01 Jan 2021 08:00 UT 94.87 17.655 1859.9 385362 8.6837 22.2951 -31.101 -0.577 -5.254 -4.989 15.969
+01 Jan 2021 09:00 UT 94.67 17.697 1860.5 385226 8.7223 22.1861 -31.607 -0.578 -5.255 -5.032 16.140
+01 Jan 2021 10:00 UT 94.47 17.738 1861.2 385090 8.7610 22.0749 -32.112 -0.579 -5.256 -5.075 16.310
+01 Jan 2021 11:00 UT 94.27 17.780 1861.8 384955 8.7995 21.9617 -32.617 -0.580 -5.256 -5.118 16.478
+01 Jan 2021 12:00 UT 94.07 17.822 1862.5 384820 8.8381 21.8464 -33.123 -0.581 -5.256 -5.161 16.645
+01 Jan 2021 13:00 UT 93.86 17.863 1863.1 384685 8.8766 21.7289 -33.628 -0.583 -5.255 -5.202 16.809
+01 Jan 2021 14:00 UT 93.64 17.905 1863.8 384551 8.9151 21.6094 -34.134 -0.584 -5.254 -5.244 16.972
+01 Jan 2021 15:00 UT 93.43 17.947 1864.4 384416 8.9535 21.4878 -34.639 -0.585 -5.252 -5.285 17.133
+01 Jan 2021 16:00 UT 93.21 17.988 1865.1 384282 8.9919 21.3642 -35.145 -0.586 -5.250 -5.325 17.292
+01 Jan 2021 17:00 UT 92.98 18.030 1865.7 384149 9.0303 21.2385 -35.650 -0.588 -5.248 -5.365 17.450
+01 Jan 2021 18:00 UT 92.75 18.072 1866.4 384015 9.0686 21.1108 -36.156 -0.589 -5.245 -5.405 17.605
+01 Jan 2021 19:00 UT 92.52 18.113 1867.0 383882 9.1068 20.9811 -36.661 -0.590 -5.242 -5.444 17.759
+01 Jan 2021 20:00 UT 92.29 18.155 1867.7 383750 9.1450 20.8494 -37.167 -0.591 -5.238 -5.482 17.911
+01 Jan 2021 21:00 UT 92.05 18.197 1868.3 383617 9.1832 20.7156 -37.672 -0.592 -5.234 -5.520 18.061
+01 Jan 2021 22:00 UT 91.81 18.238 1869.0 383485 9.2214 20.5800 -38.178 -0.594 -5.230 -5.558 18.209
+01 Jan 2021 23:00 UT 91.56 18.280 1869.6 383353 9.2594 20.4423 -38.683 -0.595 -5.225 -5.595 18.355
+02 Jan 2021 00:00 UT 91.32 18.322 1870.3 383222 9.2975 20.3027 -39.189 -0.596 -5.219 -5.632 18.499
+02 Jan 2021 01:00 UT 91.06 18.363 1870.9 383091 9.3355 20.1612 -39.694 -0.597 -5.214 -5.668 18.641
+02 Jan 2021 02:00 UT 90.81 18.405 1871.5 382960 9.3734 20.0177 -40.200 -0.598 -5.208 -5.703 18.782
+02 Jan 2021 03:00 UT 90.55 18.447 1872.2 382830 9.4113 19.8723 -40.705 -0.600 -5.201 -5.738 18.920
+02 Jan 2021 04:00 UT 90.29 18.488 1872.8 382699 9.4492 19.7251 -41.211 -0.601 -5.194 -5.773 19.056
+02 Jan 2021 05:00 UT 90.02 18.530 1873.4 382570 9.4870 19.5759 -41.716 -0.602 -5.187 -5.807 19.191
+02 Jan 2021 06:00 UT 89.75 18.572 1874.1 382440 9.5248 19.4250 -42.222 -0.603 -5.179 -5.840 19.323
+02 Jan 2021 07:00 UT 89.48 18.613 1874.7 382311 9.5625 19.2721 -42.727 -0.604 -5.171 -5.873 19.454
+02 Jan 2021 08:00 UT 89.21 18.655 1875.3 382182 9.6001 19.1174 -43.233 -0.606 -5.163 -5.906 19.582
+02 Jan 2021 09:00 UT 88.93 18.697 1876.0 382053 9.6378 18.9609 -43.739 -0.607 -5.154 -5.938 19.708
+02 Jan 2021 10:00 UT 88.65 18.738 1876.6 381925 9.6753 18.8027 -44.244 -0.608 -5.144 -5.969 19.832
+02 Jan 2021 11:00 UT 88.36 18.780 1877.2 381797 9.7128 18.6426 -44.750 -0.609 -5.135 -6.000 19.955
+02 Jan 2021 12:00 UT 88.07 18.822 1877.9 381670 9.7503 18.4807 -45.255 -0.610 -5.125 -6.030 20.075
+02 Jan 2021 13:00 UT 87.78 18.863 1878.5 381543 9.7877 18.3171 -45.761 -0.612 -5.114 -6.060 20.193
+02 Jan 2021 14:00 UT 87.48 18.905 1879.1 381416 9.8251 18.1518 -46.267 -0.613 -5.103 -6.089 20.309
+02 Jan 2021 15:00 UT 87.19 18.947 1879.7 381289 9.8624 17.9848 -46.772 -0.614 -5.092 -6.117 20.423
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+31 Dec 2021 07:00 UT 9.05 26.970 1987.9 360548 16.1688 -21.3743 -148.052 -0.978 -3.074 0.464 9.056
+31 Dec 2021 08:00 UT 8.77 27.012 1988.5 360427 16.2118 -21.5423 -148.560 -0.979 -3.004 0.537 8.825
+31 Dec 2021 09:00 UT 8.48 27.053 1989.2 360309 16.2550 -21.7080 -149.067 -0.980 -2.933 0.610 8.593
+31 Dec 2021 10:00 UT 8.20 27.095 1989.8 360193 16.2983 -21.8712 -149.575 -0.981 -2.862 0.683 8.359
+31 Dec 2021 11:00 UT 7.93 27.137 1990.5 360081 16.3417 -22.0320 -150.083 -0.982 -2.790 0.756 8.124
+31 Dec 2021 12:00 UT 7.66 27.178 1991.1 359971 16.3852 -22.1904 -150.590 -0.983 -2.718 0.829 7.887
+31 Dec 2021 13:00 UT 7.39 27.220 1991.7 359864 16.4288 -22.3462 -151.098 -0.984 -2.646 0.901 7.648
+31 Dec 2021 14:00 UT 7.12 27.262 1992.2 359759 16.4726 -22.4995 -151.606 -0.985 -2.573 0.974 7.408
+31 Dec 2021 15:00 UT 6.87 27.303 1992.8 359658 16.5165 -22.6502 -152.114 -0.985 -2.499 1.047 7.166
+31 Dec 2021 16:00 UT 6.61 27.345 1993.3 359559 16.5606 -22.7983 -152.621 -0.986 -2.425 1.119 6.923
+31 Dec 2021 17:00 UT 6.36 27.387 1993.9 359464 16.6047 -22.9438 -153.129 -0.987 -2.351 1.192 6.678
+31 Dec 2021 18:00 UT 6.12 27.428 1994.4 359371 16.6490 -23.0865 -153.637 -0.988 -2.276 1.264 6.432
+31 Dec 2021 19:00 UT 5.87 27.470 1994.9 359281 16.6934 -23.2266 -154.145 -0.989 -2.201 1.337 6.185
+31 Dec 2021 20:00 UT 5.64 27.512 1995.4 359194 16.7379 -23.3639 -154.652 -0.990 -2.126 1.409 5.936
+31 Dec 2021 21:00 UT 5.41 27.553 1995.8 359110 16.7825 -23.4985 -155.160 -0.991 -2.050 1.481 5.685
+31 Dec 2021 22:00 UT 5.18 27.595 1996.3 359029 16.8272 -23.6303 -155.668 -0.992 -1.974 1.553 5.434
+31 Dec 2021 23:00 UT 4.95 27.637 1996.7 358951 16.8721 -23.7592 -156.176 -0.993 -1.897 1.624 5.181
diff --git a/generate/template/astronomy.c b/generate/template/astronomy.c
index 4cc3b546..03236173 100644
--- a/generate/template/astronomy.c
+++ b/generate/template/astronomy.c
@@ -1868,6 +1868,134 @@ astro_vector_t Astronomy_GeoMoon(astro_time_t time)
return vector;
}
+
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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.
+ */
+astro_libration_t Astronomy_Libration(astro_time_t time)
+{
+ astro_libration_t lib;
+ double t, t2, t3, t4;
+ double f, omega, w, a, ldash, ldash2, bdash, bdash2;
+ double k1, k2, m, mdash, d, e, rho, sigma, tau;
+ double I = DEG2RAD * 1.54242;
+
+ t = time.tt / 36525.0;
+ t2 = t * t;
+ t3 = t2 * t;
+ t4 = t2 * t2;
+
+ 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);
+
+ /* Moon's ascending node's mean longitude in radians. */
+ omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ /* Sun's mean anomaly. */
+ m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ /* Moon's mean anomaly. */
+ mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ /* Moon's mean elongation. */
+ d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ /* Eccentricity of the Earth's orbit. */
+ e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ /* Optical librations */
+ w = lib.mlon - omega;
+ a = atan2(sin(w)*cos(lib.mlat)*cos(I) - sin(lib.mlat)*sin(I), cos(w)*cos(lib.mlat));
+ ldash = LongitudeOffset(RAD2DEG * (a - f));
+ bdash = asin(-sin(w)*cos(lib.mlat)*sin(I) - sin(lib.mlat)*cos(I));
+
+ /* Physical librations */
+ k1 = DEG2RAD*(119.75 + 131.849*t);
+ k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ rho = (
+ -0.02752*cos(mdash) +
+ -0.02245*sin(f) +
+ +0.00684*cos(mdash - 2*f) +
+ -0.00293*cos(2*f) +
+ -0.00085*cos(2*f - 2*d) +
+ -0.00054*cos(mdash - 2*d) +
+ -0.00020*sin(mdash + f) +
+ -0.00020*cos(mdash + 2*f) +
+ -0.00020*cos(mdash - f) +
+ +0.00014*cos(mdash + 2*f - 2*d)
+ );
+
+ sigma = (
+ -0.02816*sin(mdash) +
+ +0.02244*cos(f) +
+ -0.00682*sin(mdash - 2*f) +
+ -0.00279*sin(2*f) +
+ -0.00083*sin(2*f - 2*d) +
+ +0.00069*sin(mdash - 2*d) +
+ +0.00040*cos(mdash + f) +
+ -0.00025*sin(2*mdash) +
+ -0.00023*sin(mdash + 2*f) +
+ +0.00020*cos(mdash - f) +
+ +0.00019*sin(mdash - f) +
+ +0.00013*sin(mdash + 2*f - 2*d) +
+ -0.00010*cos(mdash - 3*f)
+ );
+
+ tau = (
+ +0.02520*e*sin(m) +
+ +0.00473*sin(2*mdash - 2*f) +
+ -0.00467*sin(mdash) +
+ +0.00396*sin(k1) +
+ +0.00276*sin(2*mdash - 2*d) +
+ +0.00196*sin(omega) +
+ -0.00183*cos(mdash - f) +
+ +0.00115*sin(mdash - 2*d) +
+ -0.00096*sin(mdash - d) +
+ +0.00046*sin(2*f - 2*d) +
+ -0.00039*sin(mdash - f) +
+ -0.00032*sin(mdash - m - d) +
+ +0.00027*sin(2*mdash - m - 2*d) +
+ +0.00023*sin(k2) +
+ -0.00014*sin(2*d) +
+ +0.00014*cos(2*mdash - 2*f) +
+ -0.00012*sin(mdash - 2*f) +
+ -0.00012*sin(2*mdash) +
+ +0.00011*sin(2*mdash - 2*m - 2*d)
+ );
+
+ ldash2 = -tau + (rho*cos(a) + sigma*sin(a))*tan(bdash);
+ bdash *= RAD2DEG;
+ bdash2 = sigma*cos(a) - rho*sin(a);
+
+ lib.elon = ldash + ldash2;
+ lib.elat = bdash + bdash2;
+
+ return lib;
+}
+
+
/*------------------ VSOP ------------------*/
/** @cond DOXYGEN_SKIP */
diff --git a/generate/template/astronomy.cs b/generate/template/astronomy.cs
index 546b0f08..d82fc27a 100644
--- a/generate/template/astronomy.cs
+++ b/generate/template/astronomy.cs
@@ -955,6 +955,30 @@ namespace CosineKitty
}
}
+ ///
+ /// Lunar libration angles, returned by #Astronomy.Libration.
+ ///
+ public struct LibrationInfo
+ {
+ /// Sub-Earth libration ecliptic latitude angle, in degrees.
+ public double elat;
+
+ /// Sub-Earth libration ecliptic longitude angle, in degrees.
+ public double elon;
+
+ /// Moon's geocentric ecliptic latitude.
+ public double mlat;
+
+ /// Moon's geocentric ecliptic longitude.
+ public double mlon;
+
+ /// Distance between the centers of the Earth and Moon in kilometers.
+ public double dist_km;
+
+ /// The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
+ public double diam_deg;
+ }
+
///
/// Information about a celestial body crossing a specific hour angle.
///
@@ -2800,7 +2824,6 @@ $ASTRO_JUPITER_MOONS();
return RotateState(Rotation_JUP_EQJ, state);
}
- ///
///
/// Calculates jovicentric positions and velocities of Jupiter's largest 4 moons.
///
@@ -3321,6 +3344,134 @@ $ASTRO_IAU_DATA()
return mpos2;
}
+ ///
+ /// Calculates the Moon's libration angles at a given moment in time.
+ ///
+ ///
+ /// Libration is an observed back-and-forth wobble of the portion of the
+ /// Moon visible from the Earth. It is caused by the imperfect tidal locking
+ /// of the Moon's fixed rotation rate, compared to its variable angular speed
+ /// of orbit around the Earth.
+ ///
+ /// 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`, 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`.
+ ///
+ /// The date and time for which to calculate lunar libration.
+ /// The Moon's ecliptic position and libration angles as seen from the Earth.
+ public static LibrationInfo Libration(AstroTime time)
+ {
+ double t = time.tt / 36525.0;
+ double t2 = t * t;
+ double t3 = t2 * t;
+ double t4 = t2 * t2;
+
+ var context = new MoonContext(t);
+ MoonResult moon = context.CalcMoon();
+
+ LibrationInfo lib;
+ 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;
+
+ // Moon's argument of latitude in radians.
+ double f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
+
+ // Moon's ascending node's mean longitude in radians.
+ double omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ // Sun's mean anomaly.
+ double m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ // Moon's mean anomaly.
+ double mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ // Moon's mean elongation.
+ double d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ // Eccentricity of the Earth's orbit.
+ double e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ // Optical librations
+ double w = lib.mlon - omega;
+ double a = Math.Atan2(Math.Sin(w)*Math.Cos(lib.mlat)*Math.Cos(I) - Math.Sin(lib.mlat)*Math.Sin(I), Math.Cos(w)*Math.Cos(lib.mlat));
+ double ldash = LongitudeOffset(RAD2DEG * (a - f));
+ double bdash = Math.Asin(-Math.Sin(w)*Math.Cos(lib.mlat)*Math.Sin(I) - Math.Sin(lib.mlat)*Math.Cos(I));
+
+ // Physical librations
+ double k1 = DEG2RAD*(119.75 + 131.849*t);
+ double k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ double rho = (
+ -0.02752*Math.Cos(mdash) +
+ -0.02245*Math.Sin(f) +
+ +0.00684*Math.Cos(mdash - 2*f) +
+ -0.00293*Math.Cos(2*f) +
+ -0.00085*Math.Cos(2*f - 2*d) +
+ -0.00054*Math.Cos(mdash - 2*d) +
+ -0.00020*Math.Sin(mdash + f) +
+ -0.00020*Math.Cos(mdash + 2*f) +
+ -0.00020*Math.Cos(mdash - f) +
+ +0.00014*Math.Cos(mdash + 2*f - 2*d)
+ );
+
+ double sigma = (
+ -0.02816*Math.Sin(mdash) +
+ +0.02244*Math.Cos(f) +
+ -0.00682*Math.Sin(mdash - 2*f) +
+ -0.00279*Math.Sin(2*f) +
+ -0.00083*Math.Sin(2*f - 2*d) +
+ +0.00069*Math.Sin(mdash - 2*d) +
+ +0.00040*Math.Cos(mdash + f) +
+ -0.00025*Math.Sin(2*mdash) +
+ -0.00023*Math.Sin(mdash + 2*f) +
+ +0.00020*Math.Cos(mdash - f) +
+ +0.00019*Math.Sin(mdash - f) +
+ +0.00013*Math.Sin(mdash + 2*f - 2*d) +
+ -0.00010*Math.Cos(mdash - 3*f)
+ );
+
+ double tau = (
+ +0.02520*e*Math.Sin(m) +
+ +0.00473*Math.Sin(2*mdash - 2*f) +
+ -0.00467*Math.Sin(mdash) +
+ +0.00396*Math.Sin(k1) +
+ +0.00276*Math.Sin(2*mdash - 2*d) +
+ +0.00196*Math.Sin(omega) +
+ -0.00183*Math.Cos(mdash - f) +
+ +0.00115*Math.Sin(mdash - 2*d) +
+ -0.00096*Math.Sin(mdash - d) +
+ +0.00046*Math.Sin(2*f - 2*d) +
+ -0.00039*Math.Sin(mdash - f) +
+ -0.00032*Math.Sin(mdash - m - d) +
+ +0.00027*Math.Sin(2*mdash - m - 2*d) +
+ +0.00023*Math.Sin(k2) +
+ -0.00014*Math.Sin(2*d) +
+ +0.00014*Math.Cos(2*mdash - 2*f) +
+ -0.00012*Math.Sin(mdash - 2*f) +
+ -0.00012*Math.Sin(2*mdash) +
+ +0.00011*Math.Sin(2*mdash - 2*m - 2*d)
+ );
+
+ double ldash2 = -tau + (rho*Math.Cos(a) + sigma*Math.Sin(a))*Math.Tan(bdash);
+ bdash *= RAD2DEG;
+ double bdash2 = sigma*Math.Cos(a) - rho*Math.Sin(a);
+
+ lib.elon = ldash + ldash2;
+ lib.elat = bdash + bdash2;
+
+ return lib;
+ }
+
private static AstroVector BarycenterContrib(AstroTime time, Body body, double planet_gm)
{
AstroVector p = CalcVsop(vsop[(int)body], time);
diff --git a/generate/template/astronomy.py b/generate/template/astronomy.py
index c5ef0ce7..4eca8fa1 100644
--- a/generate/template/astronomy.py
+++ b/generate/template/astronomy.py
@@ -6056,3 +6056,157 @@ def NextTransit(body, prevTransitTime):
"""
startTime = prevTransitTime.AddDays(100.0)
return SearchTransit(body, startTime)
+
+
+class LibrationInfo:
+ """Lunar libration angles, returned by #Libration.
+
+ Contains lunar libration angles and lunar position information
+ for a given moment in time. See #Libration for more details.
+
+ Attributes
+ ----------
+ elat : float
+ Sub-Earth libration ecliptic latitude angle, in degrees.
+ elon : float
+ Sub-Earth libration ecliptic longitude angle, in degrees.
+ mlat : float
+ Moon's geocentric ecliptic latitude.
+ mlon : float
+ 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, 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):
+ """Calculates the Moon's libration angles at a given moment in time.
+
+ Libration is an observed back-and-forth wobble of the portion of the
+ Moon visible from the Earth. It is caused by the imperfect tidal locking
+ of the Moon's fixed rotation rate, compared to its variable angular speed
+ of orbit around the Earth.
+
+ 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`, 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
+ ----------
+ time : Time
+ The date and time for which to calculate the Moon's libration angles.
+
+ Returns
+ -------
+ LibrationInfo
+ """
+ t = time.tt / 36525.0
+ t2 = t * t
+ t3 = t2 * t
+ t4 = t2 * t2
+ moon = _CalcMoon(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)
+
+ # Moon's argument of latitude in radians.
+ f = math.radians(_NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000))
+
+ # Moon's ascending node's mean longitude in radians.
+ omega = math.radians(_NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000))
+
+ # Sun's mean anomaly.
+ m = math.radians(_NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000))
+
+ # Moon's mean anomaly.
+ mdash = math.radians(_NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000))
+
+ # Moon's mean elongation.
+ d = math.radians(_NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000))
+
+ # Eccentricity of the Earth's orbit.
+ e = 1.0 - 0.002516*t - 0.0000074*t2
+
+ # Optical librations
+ w = mlon - omega
+ a = math.atan2(math.sin(w)*math.cos(mlat)*math.cos(I) - math.sin(mlat)*math.sin(I), math.cos(w)*math.cos(mlat))
+ ldash = _LongitudeOffset(math.degrees(a - f))
+ bdash = math.asin(-math.sin(w)*math.cos(mlat)*math.sin(I) - math.sin(mlat)*math.cos(I))
+
+ # Physical librations
+ k1 = math.radians(119.75 + 131.849*t)
+ k2 = math.radians(72.56 + 20.186*t)
+
+ rho = (
+ -0.02752*math.cos(mdash) +
+ -0.02245*math.sin(f) +
+ +0.00684*math.cos(mdash - 2*f) +
+ -0.00293*math.cos(2*f) +
+ -0.00085*math.cos(2*f - 2*d) +
+ -0.00054*math.cos(mdash - 2*d) +
+ -0.00020*math.sin(mdash + f) +
+ -0.00020*math.cos(mdash + 2*f) +
+ -0.00020*math.cos(mdash - f) +
+ +0.00014*math.cos(mdash + 2*f - 2*d)
+ )
+
+ sigma = (
+ -0.02816*math.sin(mdash) +
+ +0.02244*math.cos(f) +
+ -0.00682*math.sin(mdash - 2*f) +
+ -0.00279*math.sin(2*f) +
+ -0.00083*math.sin(2*f - 2*d) +
+ +0.00069*math.sin(mdash - 2*d) +
+ +0.00040*math.cos(mdash + f) +
+ -0.00025*math.sin(2*mdash) +
+ -0.00023*math.sin(mdash + 2*f) +
+ +0.00020*math.cos(mdash - f) +
+ +0.00019*math.sin(mdash - f) +
+ +0.00013*math.sin(mdash + 2*f - 2*d) +
+ -0.00010*math.cos(mdash - 3*f)
+ )
+
+ tau = (
+ +0.02520*e*math.sin(m) +
+ +0.00473*math.sin(2*mdash - 2*f) +
+ -0.00467*math.sin(mdash) +
+ +0.00396*math.sin(k1) +
+ +0.00276*math.sin(2*mdash - 2*d) +
+ +0.00196*math.sin(omega) +
+ -0.00183*math.cos(mdash - f) +
+ +0.00115*math.sin(mdash - 2*d) +
+ -0.00096*math.sin(mdash - d) +
+ +0.00046*math.sin(2*f - 2*d) +
+ -0.00039*math.sin(mdash - f) +
+ -0.00032*math.sin(mdash - m - d) +
+ +0.00027*math.sin(2*mdash - m - 2*d) +
+ +0.00023*math.sin(k2) +
+ -0.00014*math.sin(2*d) +
+ +0.00014*math.cos(2*mdash - 2*f) +
+ -0.00012*math.sin(mdash - 2*f) +
+ -0.00012*math.sin(2*mdash) +
+ +0.00011*math.sin(2*mdash - 2*m - 2*d)
+ )
+
+ 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, diam_deg)
diff --git a/generate/template/astronomy.ts b/generate/template/astronomy.ts
index c9ed0651..3e24339e 100644
--- a/generate/template/astronomy.ts
+++ b/generate/template/astronomy.ts
@@ -864,6 +864,155 @@ $ASTRO_ADDSOL()
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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(
+ public elat: number,
+ public elon: number,
+ public mlat: number,
+ public mlon: number,
+ public dist_km: number,
+ public diam_deg: number
+ ) {}
+}
+
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+export function Libration(date: FlexibleDateTime): LibrationInfo {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * KM_PER_AU;
+
+ // Inclination angle
+ const I = DEG2RAD * 1.54242;
+
+ // Moon's argument of latitude in radians.
+ const f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
+
+ // Moon's ascending node's mean longitude in radians.
+ const omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ // Sun's mean anomaly.
+ const m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ // Moon's mean anomaly.
+ const mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ // Moon's mean elongation.
+ const d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w)*Math.cos(mlat)*Math.cos(I) - Math.sin(mlat)*Math.sin(I), Math.cos(w)*Math.cos(mlat));
+ const ldash = LongitudeOffset(RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w)*Math.cos(mlat)*Math.sin(I) - Math.sin(mlat)*Math.cos(I));
+
+ // Physical librations
+ const k1 = DEG2RAD*(119.75 + 131.849*t);
+ const k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ const rho = (
+ -0.02752*Math.cos(mdash) +
+ -0.02245*Math.sin(f) +
+ +0.00684*Math.cos(mdash - 2*f) +
+ -0.00293*Math.cos(2*f) +
+ -0.00085*Math.cos(2*f - 2*d) +
+ -0.00054*Math.cos(mdash - 2*d) +
+ -0.00020*Math.sin(mdash + f) +
+ -0.00020*Math.cos(mdash + 2*f) +
+ -0.00020*Math.cos(mdash - f) +
+ +0.00014*Math.cos(mdash + 2*f - 2*d)
+ );
+
+ const sigma = (
+ -0.02816*Math.sin(mdash) +
+ +0.02244*Math.cos(f) +
+ -0.00682*Math.sin(mdash - 2*f) +
+ -0.00279*Math.sin(2*f) +
+ -0.00083*Math.sin(2*f - 2*d) +
+ +0.00069*Math.sin(mdash - 2*d) +
+ +0.00040*Math.cos(mdash + f) +
+ -0.00025*Math.sin(2*mdash) +
+ -0.00023*Math.sin(mdash + 2*f) +
+ +0.00020*Math.cos(mdash - f) +
+ +0.00019*Math.sin(mdash - f) +
+ +0.00013*Math.sin(mdash + 2*f - 2*d) +
+ -0.00010*Math.cos(mdash - 3*f)
+ );
+
+ const tau = (
+ +0.02520*e*Math.sin(m) +
+ +0.00473*Math.sin(2*mdash - 2*f) +
+ -0.00467*Math.sin(mdash) +
+ +0.00396*Math.sin(k1) +
+ +0.00276*Math.sin(2*mdash - 2*d) +
+ +0.00196*Math.sin(omega) +
+ -0.00183*Math.cos(mdash - f) +
+ +0.00115*Math.sin(mdash - 2*d) +
+ -0.00096*Math.sin(mdash - d) +
+ +0.00046*Math.sin(2*f - 2*d) +
+ -0.00039*Math.sin(mdash - f) +
+ -0.00032*Math.sin(mdash - m - d) +
+ +0.00027*Math.sin(2*mdash - m - 2*d) +
+ +0.00023*Math.sin(k2) +
+ -0.00014*Math.sin(2*d) +
+ +0.00014*Math.cos(2*mdash - 2*f) +
+ -0.00012*Math.sin(mdash - 2*f) +
+ -0.00012*Math.sin(2*mdash) +
+ +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);
+ 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 {
const r = precession_rot(time, dir);
return [
diff --git a/generate/test.js b/generate/test.js
index afe365f3..b4da4d74 100644
--- a/generate/test.js
+++ b/generate/test.js
@@ -1563,6 +1563,14 @@ function Refraction() {
}
+function MonthNumber(mtext) {
+ const index = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'].indexOf(mtext);
+ if (index < 0)
+ throw `Invalid month text "${mtext}"`;
+ return 1 + index;
+}
+
+
function Magnitude() {
function LoadMagnitudeData(filename) {
const text = fs.readFileSync(filename, 'utf8');
@@ -2331,6 +2339,95 @@ function TwilightTest() {
}
+function Libration(filename) {
+ const text = fs.readFileSync(filename, {encoding:'utf8'});
+ const lines = text.trimEnd().split(/\r?\n/);
+ 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) {
+ ++lnum;
+ if (lnum === 1) {
+ if (line !== " Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA") {
+ console.error(`JS Libration(${filename} line ${lnum}): unexpected header line.`);
+ return 1;
+ }
+ } else {
+ const token = line.split(/\s+/);
+ if (token.length !== 16) {
+ console.error(`JS Libration: FAIL(${filename} line ${lnum}): incorrect number of tokens = ${token.length}.`);
+ return 1;
+ }
+
+ const day = int(token[0]);
+ const month = MonthNumber(token[1]);
+ const year = int(token[2]);
+ const hmtoken = token[3].split(':');
+ if (hmtoken.length !== 2) {
+ Console.WriteLine(`JS Libration(${filename} line ${lnum}): expected hh:mm but found '${token[3]}'`);
+ return 1;
+ }
+ const hour = int(hmtoken[0]);
+ 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]);
+
+ const lib = Astronomy.Libration(time);
+
+ const diff_elon = 60.0 * abs(lib.elon - elon);
+ if (diff_elon > max_diff_elon)
+ max_diff_elon = diff_elon;
+
+ const diff_elat = 60.0 * abs(lib.elat - elat);
+ if (diff_elat > max_diff_elat)
+ max_diff_elat = diff_elat;
+
+ const diff_distance = abs(lib.dist_km - dist);
+ 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 = ${diff_elon} arcmin`);
+ return 1;
+ }
+
+ if (diff_elat > 1.666) {
+ console.error(`JS Libration(${filename} line ${lnum}): EXCESSIVE diff_elat = ${diff_elat} arcmin`);
+ return 1;
+ }
+
+ if (diff_distance > 53.9) {
+ console.error(`JS Libration(${filename} line ${lnum}): EXCESSIVE diff_distance = ${diff_distance} km`);
+ return 1;
+ }
+ ++count;
+ }
+ }
+ console.log(`JS Libration(${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, max_diff_diam = ${max_diff_diam} deg)`);
+ return 0;
+}
+
+
+function LibrationTest() {
+ return (
+ Libration("libration/mooninfo_2020.txt") ||
+ Libration("libration/mooninfo_2021.txt") ||
+ 0
+ );
+}
+
+
const UnitTests = {
aberration: AberrationTest,
barystate: BaryStateTest,
@@ -2340,6 +2437,7 @@ const UnitTests = {
global_solar_eclipse: GlobalSolarEclipse,
issue_103: Issue103,
jupiter_moons: JupiterMoons,
+ libration: LibrationTest,
local_solar_eclipse: LocalSolarEclipse,
lunar_apsis: LunarApsis,
lunar_eclipse: LunarEclipse,
diff --git a/generate/test.py b/generate/test.py
index 7bc15309..50c161f3 100755
--- a/generate/test.py
+++ b/generate/test.py
@@ -492,12 +492,15 @@ def Elongation():
#-----------------------------------------------------------------------------------------------------------
+def MonthNumber(mtext):
+ return 1 + ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'].index(mtext)
+
def ParseJplHorizonsDateTime(line):
m = re.match(r'^\s*(\d{4})-(Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)-(\d{2})\s(\d{2}):(\d{2})\s+(.*)$', line)
if not m:
return None, None
year = int(m.group(1))
- month = 1 + ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec'].index(m.group(2))
+ month = MonthNumber(m.group(2))
day = int(m.group(3))
hour = int(m.group(4))
minute = int(m.group(5))
@@ -2089,6 +2092,85 @@ def Twilight():
#-----------------------------------------------------------------------------------------------------------
+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
+ for line in infile:
+ lnum += 1
+ token = line.split()
+ if lnum == 1:
+ if line != " Date Time Phase Age Diam Dist RA Dec Slon Slat Elon Elat AxisA\n":
+ print('PY LibrationFile({} line {}): unexpected header line'.format(filename, lnum))
+ return 1
+ else:
+ if len(token) != 16:
+ print('PY LibrationFile({} line {}): expected 16 tokens, found {}'.format(filename, lnum, len(token)))
+ return 1
+ day = int(token[0])
+ month = MonthNumber(token[1])
+ year = int(token[2])
+ hmtoken = token[3].split(':')
+ if len(hmtoken) != 2:
+ print('PY LibrationFile({} line {}): expected hh:mm but found "{}"'.format(filename, lnum, hmtoken))
+ return 1
+ 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])
+ lib = astronomy.Libration(time)
+
+ diff_elon = 60.0 * vabs(lib.elon - elon)
+ if diff_elon > max_diff_elon:
+ max_diff_elon = diff_elon
+
+ diff_elat = 60.0 * vabs(lib.elat - elat)
+ if diff_elat > max_diff_elat:
+ max_diff_elat = diff_elat
+
+ diff_distance = vabs(lib.dist_km - dist)
+ 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
+
+ if diff_elat > 1.666:
+ print('PY LibrationFile({} line {}): EXCESSIVE diff_elat = {}'.format(filename, lnum, diff_elat))
+ return 1
+
+ if diff_distance > 53.9:
+ print('PY LibrationFile({} line {}): EXCESSIVE diff_distance = {}'.format(filename, lnum, diff_distance))
+ return 1
+
+ count += 1
+
+ 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
+
+def Libration():
+ if 0 != LibrationFile('libration/mooninfo_2020.txt'):
+ return 1
+ if 0 != LibrationFile('libration/mooninfo_2021.txt'):
+ return 1
+ return 0
+
+#-----------------------------------------------------------------------------------------------------------
+
UnitTests = {
'aberration': Aberration,
'barystate': BaryState,
@@ -2098,6 +2180,7 @@ UnitTests = {
'global_solar_eclipse': GlobalSolarEclipse,
'issue_103': Issue103,
'jupiter_moons': JupiterMoons,
+ 'libration': Libration,
'local_solar_eclipse': LocalSolarEclipse,
'lunar_apsis': LunarApsis,
'lunar_eclipse': LunarEclipse,
diff --git a/source/c/README.md b/source/c/README.md
index 0462939c..c2aba08e 100644
--- a/source/c/README.md
+++ b/source/c/README.md
@@ -905,6 +905,34 @@ To convert to heliocentric position vectors, call [`Astronomy_HelioVector`](#Ast
+---
+
+
+### Astronomy_Libration(time) ⇒ [`astro_libration_t`](#astro_libration_t)
+
+**Calculates the Moon's libration angles at a given moment in time.**
+
+
+
+Libration is an observed back-and-forth wobble of the portion of the Moon visible from the Earth. It is caused by the imperfect tidal locking of the Moon's fixed rotation rate, compared to its variable angular speed of orbit around the Earth.
+
+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`, 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`.
+
+
+
+**Returns:** The Moon's ecliptic position and libration angles as seen from the Earth.
+
+
+
+| Type | Parameter | Description |
+| --- | --- | --- |
+| [`astro_time_t`](#astro_time_t) | `time` | The date and time for which to calculate libration angles. |
+
+
+
+
---
@@ -3246,6 +3274,25 @@ The following integer constants may be useful for indexing into the `moon` array
| [`astro_state_vector_t`](#astro_state_vector_t) | `moon` | Jovicentric position and velocity of each moon, as described above. |
+---
+
+
+### `astro_libration_t`
+
+**Lunar libration angles, returned by [`Astronomy_Libration`](#Astronomy_Libration).**
+
+
+
+| Type | Member | Description |
+| ---- | ------ | ----------- |
+| `double` | `elat` | Sub-Earth libration ecliptic latitude angle, in degrees. |
+| `double` | `elon` | Sub-Earth libration ecliptic longitude angle, in degrees. |
+| `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 a8f7225d..0fba4197 100644
--- a/source/c/astronomy.c
+++ b/source/c/astronomy.c
@@ -2051,6 +2051,134 @@ astro_vector_t Astronomy_GeoMoon(astro_time_t time)
return vector;
}
+
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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.
+ */
+astro_libration_t Astronomy_Libration(astro_time_t time)
+{
+ astro_libration_t lib;
+ double t, t2, t3, t4;
+ double f, omega, w, a, ldash, ldash2, bdash, bdash2;
+ double k1, k2, m, mdash, d, e, rho, sigma, tau;
+ double I = DEG2RAD * 1.54242;
+
+ t = time.tt / 36525.0;
+ t2 = t * t;
+ t3 = t2 * t;
+ t4 = t2 * t2;
+
+ 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);
+
+ /* Moon's ascending node's mean longitude in radians. */
+ omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ /* Sun's mean anomaly. */
+ m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ /* Moon's mean anomaly. */
+ mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ /* Moon's mean elongation. */
+ d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ /* Eccentricity of the Earth's orbit. */
+ e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ /* Optical librations */
+ w = lib.mlon - omega;
+ a = atan2(sin(w)*cos(lib.mlat)*cos(I) - sin(lib.mlat)*sin(I), cos(w)*cos(lib.mlat));
+ ldash = LongitudeOffset(RAD2DEG * (a - f));
+ bdash = asin(-sin(w)*cos(lib.mlat)*sin(I) - sin(lib.mlat)*cos(I));
+
+ /* Physical librations */
+ k1 = DEG2RAD*(119.75 + 131.849*t);
+ k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ rho = (
+ -0.02752*cos(mdash) +
+ -0.02245*sin(f) +
+ +0.00684*cos(mdash - 2*f) +
+ -0.00293*cos(2*f) +
+ -0.00085*cos(2*f - 2*d) +
+ -0.00054*cos(mdash - 2*d) +
+ -0.00020*sin(mdash + f) +
+ -0.00020*cos(mdash + 2*f) +
+ -0.00020*cos(mdash - f) +
+ +0.00014*cos(mdash + 2*f - 2*d)
+ );
+
+ sigma = (
+ -0.02816*sin(mdash) +
+ +0.02244*cos(f) +
+ -0.00682*sin(mdash - 2*f) +
+ -0.00279*sin(2*f) +
+ -0.00083*sin(2*f - 2*d) +
+ +0.00069*sin(mdash - 2*d) +
+ +0.00040*cos(mdash + f) +
+ -0.00025*sin(2*mdash) +
+ -0.00023*sin(mdash + 2*f) +
+ +0.00020*cos(mdash - f) +
+ +0.00019*sin(mdash - f) +
+ +0.00013*sin(mdash + 2*f - 2*d) +
+ -0.00010*cos(mdash - 3*f)
+ );
+
+ tau = (
+ +0.02520*e*sin(m) +
+ +0.00473*sin(2*mdash - 2*f) +
+ -0.00467*sin(mdash) +
+ +0.00396*sin(k1) +
+ +0.00276*sin(2*mdash - 2*d) +
+ +0.00196*sin(omega) +
+ -0.00183*cos(mdash - f) +
+ +0.00115*sin(mdash - 2*d) +
+ -0.00096*sin(mdash - d) +
+ +0.00046*sin(2*f - 2*d) +
+ -0.00039*sin(mdash - f) +
+ -0.00032*sin(mdash - m - d) +
+ +0.00027*sin(2*mdash - m - 2*d) +
+ +0.00023*sin(k2) +
+ -0.00014*sin(2*d) +
+ +0.00014*cos(2*mdash - 2*f) +
+ -0.00012*sin(mdash - 2*f) +
+ -0.00012*sin(2*mdash) +
+ +0.00011*sin(2*mdash - 2*m - 2*d)
+ );
+
+ ldash2 = -tau + (rho*cos(a) + sigma*sin(a))*tan(bdash);
+ bdash *= RAD2DEG;
+ bdash2 = sigma*cos(a) - rho*sin(a);
+
+ lib.elon = ldash + ldash2;
+ lib.elat = bdash + bdash2;
+
+ return lib;
+}
+
+
/*------------------ VSOP ------------------*/
/** @cond DOXYGEN_SKIP */
diff --git a/source/c/astronomy.h b/source/c/astronomy.h
index 39f08003..06f3175b 100644
--- a/source/c/astronomy.h
+++ b/source/c/astronomy.h
@@ -892,6 +892,21 @@ typedef enum
}
astro_time_format_t;
+/**
+ * @brief Lunar libration angles, returned by #Astronomy_Libration.
+ */
+typedef struct
+{
+ double elat; /**< Sub-Earth libration ecliptic latitude angle, in degrees. */
+ double elon; /**< Sub-Earth libration ecliptic longitude angle, in degrees. */
+ 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;
+
+
/**
* \def TIME_TEXT_BYTES
* @brief The smallest number of characters that is always large enough for #Astronomy_FormatTime.
@@ -969,6 +984,7 @@ astro_func_result_t Astronomy_HelioDistance(astro_body_t body, astro_time_t time
astro_vector_t Astronomy_HelioVector(astro_body_t body, astro_time_t time);
astro_vector_t Astronomy_GeoVector(astro_body_t body, astro_time_t time, astro_aberration_t aberration);
astro_vector_t Astronomy_GeoMoon(astro_time_t time);
+astro_libration_t Astronomy_Libration(astro_time_t time);
astro_state_vector_t Astronomy_BaryState(astro_body_t body, astro_time_t time);
astro_jupiter_moons_t Astronomy_JupiterMoons(astro_time_t time);
diff --git a/source/csharp/README.md b/source/csharp/README.md
index 18d74c5c..00dd443e 100644
--- a/source/csharp/README.md
+++ b/source/csharp/README.md
@@ -696,6 +696,31 @@ to convert to geocentric positions.
**Returns:** Position and velocity vectors of Jupiter's largest 4 moons.
+
+### Astronomy.Libration(time) ⇒ [`LibrationInfo`](#LibrationInfo)
+
+**Calculates the Moon's libration angles at a given moment in time.**
+
+Libration is an observed back-and-forth wobble of the portion of the
+Moon visible from the Earth. It is caused by the imperfect tidal locking
+of the Moon's fixed rotation rate, compared to its variable angular speed
+of orbit around the Earth.
+
+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`, 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 |
+| --- | --- | --- |
+| [`AstroTime`](#AstroTime) | `time` | The date and time for which to calculate lunar libration. |
+
+**Returns:** The Moon's ecliptic position and libration angles as seen from the Earth.
+
### Astronomy.MoonPhase(time) ⇒ `double`
@@ -2188,6 +2213,22 @@ and the velocities in AU/day.
---
+
+## `struct LibrationInfo`
+
+**Lunar libration angles, returned by [`Astronomy.Libration`](#Astronomy.Libration).**
+
+| Type | Name | Description |
+| --- | --- | --- |
+| `double` | `elat` | Sub-Earth libration ecliptic latitude angle, in degrees. |
+| `double` | `elon` | Sub-Earth libration ecliptic longitude angle, in degrees. |
+| `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. |
+
+---
+
## `struct LocalSolarEclipseInfo`
diff --git a/source/csharp/astronomy.cs b/source/csharp/astronomy.cs
index f8c70079..d79bf2ae 100644
--- a/source/csharp/astronomy.cs
+++ b/source/csharp/astronomy.cs
@@ -955,6 +955,30 @@ namespace CosineKitty
}
}
+ ///
+ /// Lunar libration angles, returned by #Astronomy.Libration.
+ ///
+ public struct LibrationInfo
+ {
+ /// Sub-Earth libration ecliptic latitude angle, in degrees.
+ public double elat;
+
+ /// Sub-Earth libration ecliptic longitude angle, in degrees.
+ public double elon;
+
+ /// Moon's geocentric ecliptic latitude.
+ public double mlat;
+
+ /// Moon's geocentric ecliptic longitude.
+ public double mlon;
+
+ /// Distance between the centers of the Earth and Moon in kilometers.
+ public double dist_km;
+
+ /// The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth.
+ public double diam_deg;
+ }
+
///
/// Information about a celestial body crossing a specific hour angle.
///
@@ -3922,7 +3946,6 @@ namespace CosineKitty
return RotateState(Rotation_JUP_EQJ, state);
}
- ///
///
/// Calculates jovicentric positions and velocities of Jupiter's largest 4 moons.
///
@@ -4521,6 +4544,134 @@ namespace CosineKitty
return mpos2;
}
+ ///
+ /// Calculates the Moon's libration angles at a given moment in time.
+ ///
+ ///
+ /// Libration is an observed back-and-forth wobble of the portion of the
+ /// Moon visible from the Earth. It is caused by the imperfect tidal locking
+ /// of the Moon's fixed rotation rate, compared to its variable angular speed
+ /// of orbit around the Earth.
+ ///
+ /// 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`, 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`.
+ ///
+ /// The date and time for which to calculate lunar libration.
+ /// The Moon's ecliptic position and libration angles as seen from the Earth.
+ public static LibrationInfo Libration(AstroTime time)
+ {
+ double t = time.tt / 36525.0;
+ double t2 = t * t;
+ double t3 = t2 * t;
+ double t4 = t2 * t2;
+
+ var context = new MoonContext(t);
+ MoonResult moon = context.CalcMoon();
+
+ LibrationInfo lib;
+ 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;
+
+ // Moon's argument of latitude in radians.
+ double f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
+
+ // Moon's ascending node's mean longitude in radians.
+ double omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ // Sun's mean anomaly.
+ double m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ // Moon's mean anomaly.
+ double mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ // Moon's mean elongation.
+ double d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ // Eccentricity of the Earth's orbit.
+ double e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ // Optical librations
+ double w = lib.mlon - omega;
+ double a = Math.Atan2(Math.Sin(w)*Math.Cos(lib.mlat)*Math.Cos(I) - Math.Sin(lib.mlat)*Math.Sin(I), Math.Cos(w)*Math.Cos(lib.mlat));
+ double ldash = LongitudeOffset(RAD2DEG * (a - f));
+ double bdash = Math.Asin(-Math.Sin(w)*Math.Cos(lib.mlat)*Math.Sin(I) - Math.Sin(lib.mlat)*Math.Cos(I));
+
+ // Physical librations
+ double k1 = DEG2RAD*(119.75 + 131.849*t);
+ double k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ double rho = (
+ -0.02752*Math.Cos(mdash) +
+ -0.02245*Math.Sin(f) +
+ +0.00684*Math.Cos(mdash - 2*f) +
+ -0.00293*Math.Cos(2*f) +
+ -0.00085*Math.Cos(2*f - 2*d) +
+ -0.00054*Math.Cos(mdash - 2*d) +
+ -0.00020*Math.Sin(mdash + f) +
+ -0.00020*Math.Cos(mdash + 2*f) +
+ -0.00020*Math.Cos(mdash - f) +
+ +0.00014*Math.Cos(mdash + 2*f - 2*d)
+ );
+
+ double sigma = (
+ -0.02816*Math.Sin(mdash) +
+ +0.02244*Math.Cos(f) +
+ -0.00682*Math.Sin(mdash - 2*f) +
+ -0.00279*Math.Sin(2*f) +
+ -0.00083*Math.Sin(2*f - 2*d) +
+ +0.00069*Math.Sin(mdash - 2*d) +
+ +0.00040*Math.Cos(mdash + f) +
+ -0.00025*Math.Sin(2*mdash) +
+ -0.00023*Math.Sin(mdash + 2*f) +
+ +0.00020*Math.Cos(mdash - f) +
+ +0.00019*Math.Sin(mdash - f) +
+ +0.00013*Math.Sin(mdash + 2*f - 2*d) +
+ -0.00010*Math.Cos(mdash - 3*f)
+ );
+
+ double tau = (
+ +0.02520*e*Math.Sin(m) +
+ +0.00473*Math.Sin(2*mdash - 2*f) +
+ -0.00467*Math.Sin(mdash) +
+ +0.00396*Math.Sin(k1) +
+ +0.00276*Math.Sin(2*mdash - 2*d) +
+ +0.00196*Math.Sin(omega) +
+ -0.00183*Math.Cos(mdash - f) +
+ +0.00115*Math.Sin(mdash - 2*d) +
+ -0.00096*Math.Sin(mdash - d) +
+ +0.00046*Math.Sin(2*f - 2*d) +
+ -0.00039*Math.Sin(mdash - f) +
+ -0.00032*Math.Sin(mdash - m - d) +
+ +0.00027*Math.Sin(2*mdash - m - 2*d) +
+ +0.00023*Math.Sin(k2) +
+ -0.00014*Math.Sin(2*d) +
+ +0.00014*Math.Cos(2*mdash - 2*f) +
+ -0.00012*Math.Sin(mdash - 2*f) +
+ -0.00012*Math.Sin(2*mdash) +
+ +0.00011*Math.Sin(2*mdash - 2*m - 2*d)
+ );
+
+ double ldash2 = -tau + (rho*Math.Cos(a) + sigma*Math.Sin(a))*Math.Tan(bdash);
+ bdash *= RAD2DEG;
+ double bdash2 = sigma*Math.Cos(a) - rho*Math.Sin(a);
+
+ lib.elon = ldash + ldash2;
+ lib.elat = bdash + bdash2;
+
+ return lib;
+ }
+
private static AstroVector BarycenterContrib(AstroTime time, Body body, double planet_gm)
{
AstroVector p = CalcVsop(vsop[(int)body], time);
diff --git a/source/js/README.md b/source/js/README.md
index d0973c8d..0fc50f9c 100644
--- a/source/js/README.md
+++ b/source/js/README.md
@@ -227,6 +227,25 @@ an `AstroTime` value that can be passed to Astronomy Engine functions.
| tt | number | The number of days since the J2000 epoch as expressed in Terrestrial Time. |
+* * *
+
+
+
+## LibrationInfo
+**Kind**: global class
+**Brief**: Lunar libration angles, returned by [Libration](#Libration).
+**Properties**
+
+| Name | Type | Description |
+| --- | --- | --- |
+| elat | number | Sub-Earth libration ecliptic latitude angle, in degrees. |
+| elon | number | Sub-Earth libration ecliptic longitude angle, in degrees. |
+| mlat | number | Moon's geocentric ecliptic latitude. |
+| mlon | number | Moon's geocentric ecliptic longitude. |
+| dist_km | number | Distance between the centers of the Earth and Moon in kilometers. |
+| diam_deg | number | The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth. |
+
+
* * *
@@ -891,6 +910,33 @@ function calls may be more efficient than passing in native JavaScript Date obje
| date | [FlexibleDateTime](#FlexibleDateTime) | A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000), or an AstroTime object. See remarks above. |
+* * *
+
+
+
+## Libration(date) ⇒ [LibrationInfo](#LibrationInfo)
+**Kind**: global function
+**Brief**: Calculates the Moon's libration angles at a given moment in time.
+
+Libration is an observed back-and-forth wobble of the portion of the
+Moon visible from the Earth. It is caused by the imperfect tidal locking
+of the Moon's fixed rotation rate, compared to its variable angular speed
+of orbit around the Earth.
+
+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`, 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 |
+| --- | --- | --- |
+| date | [FlexibleDateTime](#FlexibleDateTime) | A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000), or an AstroTime object. |
+
+
* * *
diff --git a/source/js/astronomy.browser.js b/source/js/astronomy.browser.js
index 9e9395b4..8eb71e18 100644
--- a/source/js/astronomy.browser.js
+++ b/source/js/astronomy.browser.js
@@ -34,9 +34,9 @@
*/
'use strict';
Object.defineProperty(exports, "__esModule", { value: true });
-exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
-exports.ConstellationInfo = exports.Rotation_GAL_EQJ = exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = void 0;
-exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = void 0;
+exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.BaryState = exports.GeoVector = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverVector = exports.Equator = exports.SunPosition = exports.Observer = exports.Horizon = exports.EclipticCoordinates = exports.HorizontalCoordinates = exports.MakeRotation = exports.RotationMatrix = exports.EquatorialCoordinates = exports.Spherical = exports.StateVector = exports.Vector = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.Body = exports.AngleBetween = exports.CALLISTO_RADIUS_KM = exports.GANYMEDE_RADIUS_KM = exports.EUROPA_RADIUS_KM = exports.IO_RADIUS_KM = exports.JUPITER_MEAN_RADIUS_KM = exports.JUPITER_POLAR_RADIUS_KM = exports.JUPITER_EQUATORIAL_RADIUS_KM = exports.RAD2HOUR = exports.RAD2DEG = exports.HOUR2RAD = exports.DEG2RAD = exports.KM_PER_AU = exports.C_AUDAY = void 0;
+exports.Rotation_EQJ_GAL = exports.Rotation_HOR_ECL = exports.Rotation_ECL_HOR = exports.Rotation_ECL_EQD = exports.Rotation_EQD_ECL = exports.Rotation_EQJ_HOR = exports.Rotation_HOR_EQJ = exports.Rotation_HOR_EQD = exports.Rotation_EQD_HOR = exports.Rotation_EQD_EQJ = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = exports.VectorFromHorizon = exports.HorizonFromVector = exports.SphereFromVector = exports.EquatorFromVector = exports.VectorFromSphere = exports.Pivot = exports.IdentityMatrix = exports.CombineRotation = exports.InverseRotation = exports.NextPlanetApsis = exports.SearchPlanetApsis = exports.NextLunarApsis = exports.SearchLunarApsis = exports.Apsis = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = void 0;
+exports.NextTransit = exports.SearchTransit = exports.TransitInfo = exports.NextLocalSolarEclipse = exports.SearchLocalSolarEclipse = exports.LocalSolarEclipseInfo = exports.EclipseEvent = exports.NextGlobalSolarEclipse = exports.SearchGlobalSolarEclipse = exports.NextLunarEclipse = exports.GlobalSolarEclipseInfo = exports.SearchLunarEclipse = exports.LunarEclipseInfo = exports.Constellation = exports.ConstellationInfo = exports.Rotation_GAL_EQJ = void 0;
/**
* @brief The speed of light in AU/day.
*/
@@ -1571,6 +1571,136 @@ function CalcMoon(time) {
distance_au: (ARC * EARTH_EQUATORIAL_RADIUS_AU) / (0.999953253 * SINPI)
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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, 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;
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+function Libration(date) {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * exports.KM_PER_AU;
+ // Inclination angle
+ const I = exports.DEG2RAD * 1.54242;
+ // Moon's argument of latitude in radians.
+ const f = exports.DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233 * t - 0.0036539 * t2 - t3 / 3526000 + t4 / 863310000);
+ // Moon's ascending node's mean longitude in radians.
+ const omega = exports.DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891 * t + 0.0020754 * t2 + t3 / 467441 - t4 / 60616000);
+ // Sun's mean anomaly.
+ const m = exports.DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909 * t - 0.0001536 * t2 + t3 / 24490000);
+ // Moon's mean anomaly.
+ const mdash = exports.DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055 * t + 0.0087414 * t2 + t3 / 69699 - t4 / 14712000);
+ // Moon's mean elongation.
+ const d = exports.DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034 * t - 0.0018819 * t2 + t3 / 545868 - t4 / 113065000);
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516 * t - 0.0000074 * t2;
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w) * Math.cos(mlat) * Math.cos(I) - Math.sin(mlat) * Math.sin(I), Math.cos(w) * Math.cos(mlat));
+ const ldash = LongitudeOffset(exports.RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w) * Math.cos(mlat) * Math.sin(I) - Math.sin(mlat) * Math.cos(I));
+ // Physical librations
+ const k1 = exports.DEG2RAD * (119.75 + 131.849 * t);
+ const k2 = exports.DEG2RAD * (72.56 + 20.186 * t);
+ const rho = (-0.02752 * Math.cos(mdash) +
+ -0.02245 * Math.sin(f) +
+ +0.00684 * Math.cos(mdash - 2 * f) +
+ -0.00293 * Math.cos(2 * f) +
+ -0.00085 * Math.cos(2 * f - 2 * d) +
+ -0.00054 * Math.cos(mdash - 2 * d) +
+ -0.00020 * Math.sin(mdash + f) +
+ -0.00020 * Math.cos(mdash + 2 * f) +
+ -0.00020 * Math.cos(mdash - f) +
+ +0.00014 * Math.cos(mdash + 2 * f - 2 * d));
+ const sigma = (-0.02816 * Math.sin(mdash) +
+ +0.02244 * Math.cos(f) +
+ -0.00682 * Math.sin(mdash - 2 * f) +
+ -0.00279 * Math.sin(2 * f) +
+ -0.00083 * Math.sin(2 * f - 2 * d) +
+ +0.00069 * Math.sin(mdash - 2 * d) +
+ +0.00040 * Math.cos(mdash + f) +
+ -0.00025 * Math.sin(2 * mdash) +
+ -0.00023 * Math.sin(mdash + 2 * f) +
+ +0.00020 * Math.cos(mdash - f) +
+ +0.00019 * Math.sin(mdash - f) +
+ +0.00013 * Math.sin(mdash + 2 * f - 2 * d) +
+ -0.00010 * Math.cos(mdash - 3 * f));
+ const tau = (+0.02520 * e * Math.sin(m) +
+ +0.00473 * Math.sin(2 * mdash - 2 * f) +
+ -0.00467 * Math.sin(mdash) +
+ +0.00396 * Math.sin(k1) +
+ +0.00276 * Math.sin(2 * mdash - 2 * d) +
+ +0.00196 * Math.sin(omega) +
+ -0.00183 * Math.cos(mdash - f) +
+ +0.00115 * Math.sin(mdash - 2 * d) +
+ -0.00096 * Math.sin(mdash - d) +
+ +0.00046 * Math.sin(2 * f - 2 * d) +
+ -0.00039 * Math.sin(mdash - f) +
+ -0.00032 * Math.sin(mdash - m - d) +
+ +0.00027 * Math.sin(2 * mdash - m - 2 * d) +
+ +0.00023 * Math.sin(k2) +
+ -0.00014 * Math.sin(2 * d) +
+ +0.00014 * Math.cos(2 * mdash - 2 * f) +
+ -0.00012 * Math.sin(mdash - 2 * f) +
+ -0.00012 * Math.sin(2 * mdash) +
+ +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);
+ 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) {
const r = precession_rot(time, dir);
return [
diff --git a/source/js/astronomy.browser.min.js b/source/js/astronomy.browser.min.js
index ac4b27ed..7faff1af 100644
--- a/source/js/astronomy.browser.min.js
+++ b/source/js/astronomy.browser.min.js
@@ -31,21 +31,21 @@ var $jscomp=$jscomp||{};$jscomp.scope={};$jscomp.createTemplateTagFirstArg=funct
$jscomp.ASSUME_ES5=!1;$jscomp.ASSUME_NO_NATIVE_MAP=!1;$jscomp.ASSUME_NO_NATIVE_SET=!1;$jscomp.SIMPLE_FROUND_POLYFILL=!1;$jscomp.ISOLATE_POLYFILLS=!1;$jscomp.FORCE_POLYFILL_PROMISE=!1;$jscomp.FORCE_POLYFILL_PROMISE_WHEN_NO_UNHANDLED_REJECTION=!1;$jscomp.defineProperty=$jscomp.ASSUME_ES5||"function"==typeof Object.defineProperties?Object.defineProperty:function(q,t,e){if(q==Array.prototype||q==Object.prototype)return q;q[t]=e.value;return q};
$jscomp.getGlobal=function(q){q=["object"==typeof globalThis&&globalThis,q,"object"==typeof window&&window,"object"==typeof self&&self,"object"==typeof global&&global];for(var t=0;tMath.abs(c))throw"AngleBetween: first vector is too short.";var d=b.x*b.x+b.y*b.y+b.z*b.z;if(1E-8>Math.abs(d))throw"AngleBetween: second vector is too short.";a=(a.x*b.x+a.y*b.y+a.z*b.z)/Math.sqrt(c*d);return-1>=a?180:1<=a?0:e.RAD2DEG*Math.acos(a)}function M(a){var b=2E3+(a-14)/365.24217;if(-500>b)return a=(b-1820)/100,-20+32*a*a;if(500>b){a=b/100;b=a*a;var c=a*b;return 10583.6-1014.41*a+33.78311*b-5.952053*c-.1798452*b*b+.022174192*b*c+.0090316521*c*c}if(1600>b)return a=(b-
1E3)/100,b=a*a,c=a*b,1574.2-556.01*a+71.23472*b+.319781*c-.8503463*b*b-.005050998*b*c+.0083572073*c*c;if(1700>b)return a=b-1600,b=a*a,120-.9808*a-.01532*b+a*b/7129;if(1800>b)return a=b-1700,b=a*a,8.83+.1603*a-.0059285*b+1.3336E-4*a*b-b*b/1174E3;if(1860>b){a=b-1800;b=a*a;c=a*b;var d=b*b;return 13.72-.332447*a+.0068612*b+.0041116*c-3.7436E-4*d+1.21272E-5*b*c-1.699E-7*c*c+8.75E-10*c*d}if(1900>b)return a=b-1860,b=a*a,c=a*b,7.62+.5737*a-.251754*b+.01680668*c-4.473624E-4*b*b+b*c/233174;if(1920>b)return a=
b-1900,b=a*a,-2.79+1.494119*a-.0598939*b+.0061966*a*b-1.97E-4*b*b;if(1941>b)return a=b-1920,b=a*a,21.2+.84493*a-.0761*b+.0020936*a*b;if(1961>b)return a=b-1950,b=a*a,29.07+.407*a-b/233+a*b/2547;if(1986>b)return a=b-1975,b=a*a,45.45+1.067*a-b/260-a*b/718;if(2005>b)return a=b-2E3,b=a*a,c=a*b,63.86+.3345*a-.060374*b+.0017275*c+6.51814E-4*b*b+2.373599E-5*b*c;if(2050>b)return a=b-2E3,62.92+.32217*a+.005589*a*a;if(2150>b)return a=(b-1820)/100,-20+32*a*a-.5628*(2150-b);a=(b-1820)/100;return-20+32*a*a}function P(a){return a+
-Ab(a)/86400}function w(a){return a instanceof N?a:new N(a)}function sa(a){a=a.tt/36525;return(((((-4.34E-8*a-5.76E-7)*a+.0020034)*a-1.831E-4)*a-46.836769)*a+84381.406)/3600}function Ka(a){var b;if(!La||1E-6=B;++B)0!==x[B]&&h(G.x,G.y,c(y,x[B],B),c(D,x[B],B),function(ja,ka){return G.x=ja,G.y=ka});return G}function g(x,
-B,K,U,G,ja,ka,bb){G=k(G,ja,ka,bb);p+=x*G.y;v+=B*G.y;ta+=K*G.x;aa+=U*G.x}++e.CalcMoonCount;a=a.tt/36525;var m,n,p,v,y=b(-6,6,1,4),D=b(-6,6,1,4);var z=a*a;var ta=v=p=0;var aa=3422.7;var ba=l(.19833+.05611*a);var V=l(.27869+.04508*a);var Q=l(.16827-.36903*a);var T=l(.34734-5.37261*a);var ua=l(.10498-5.37899*a);var Ma=l(.42681-.41855*a),Gc=l(.14943-5.37511*a);var Na=.84*ba+.31*V+14.27*Q+7.26*T+.28*ua+.24*Ma;var db=2.94*ba+.31*V+14.27*Q+9.34*T+1.12*ua+.83*Ma;var Oa=-6.4*ba-1.89*Ma;V=.21*ba+.31*V+14.27*
-Q-88.7*T-15.3*ua+.24*Ma-1.86*Gc;Q=Na-Oa;ba=-3.332E-6*l(.59734-5.37261*a)-5.39E-7*l(.35498-5.37899*a)-6.4E-8*l(.39943-5.37511*a);Na=O*L(.60643382+1336.85522467*a-3.13E-6*z)+Na/W;db=O*L(.37489701+1325.55240982*a+2.565E-5*z)+db/W;Oa=O*L(.99312619+99.99735956*a-4.4E-7*z)+Oa/W;V=O*L(.25909118+1342.2278298*a-8.92E-6*z)+V/W;ua=O*L(.82736186+1236.85308708*a-3.97E-6*z)+Q/W;for(m=1;4>=m;++m){switch(m){case 1:Q=db;z=4;T=1.000002208;break;case 2:Q=Oa;z=3;T=.997504612-.002495388*a;break;case 3:Q=V;z=4;T=1.000002708+
-139.978*ba;break;case 4:Q=ua;z=6;T=1;break;default:throw"Internal error: I = "+m;}d(0,m,1);d(1,m,Math.cos(Q)*T);f(0,m,0);f(1,m,Math.sin(Q)*T);for(n=2;n<=z;++n)h(c(y,n-1,m),c(D,n-1,m),c(y,1,m),c(D,1,m),function(x,B){return d(n,m,x),f(n,m,B)});for(n=1;n<=z;++n)d(-n,m,c(y,n,m)),f(-n,m,-c(D,n,m))}g(13.902,14.06,-.001,.2607,0,0,0,4);g(.403,-4.01,.394,.0023,0,0,0,3);g(2369.912,2373.36,.601,28.2333,0,0,0,2);g(-125.154,-112.79,-.725,-.9781,0,0,0,1);g(1.979,6.98,-.445,.0433,1,0,0,4);g(191.953,192.72,.029,
+Bb(a)/86400}function x(a){return a instanceof N?a:new N(a)}function ua(a){a=a.tt/36525;return(((((-4.34E-8*a-5.76E-7)*a+.0020034)*a-1.831E-4)*a-46.836769)*a+84381.406)/3600}function La(a){var b;if(!Ma||1E-6=C;++C)0!==y[C]&&h(G.x,G.y,c(w,y[C],C),c(B,y[C],C),function(ja,ka){return G.x=ja,G.y=ka});return G}function g(y,
+C,K,U,G,ja,ka,cb){G=k(G,ja,ka,cb);p+=y*G.y;u+=C*G.y;va+=K*G.x;ba+=U*G.x}++e.CalcMoonCount;a=a.tt/36525;var m,n,p,u,w=b(-6,6,1,4),B=b(-6,6,1,4);var z=a*a;var va=u=p=0;var ba=3422.7;var ca=l(.19833+.05611*a);var V=l(.27869+.04508*a);var Q=l(.16827-.36903*a);var T=l(.34734-5.37261*a);var wa=l(.10498-5.37899*a);var Na=l(.42681-.41855*a),Ic=l(.14943-5.37511*a);var Oa=.84*ca+.31*V+14.27*Q+7.26*T+.28*wa+.24*Na;var eb=2.94*ca+.31*V+14.27*Q+9.34*T+1.12*wa+.83*Na;var Pa=-6.4*ca-1.89*Na;V=.21*ca+.31*V+14.27*
+Q-88.7*T-15.3*wa+.24*Na-1.86*Ic;Q=Oa-Pa;ca=-3.332E-6*l(.59734-5.37261*a)-5.39E-7*l(.35498-5.37899*a)-6.4E-8*l(.39943-5.37511*a);Oa=O*L(.60643382+1336.85522467*a-3.13E-6*z)+Oa/W;eb=O*L(.37489701+1325.55240982*a+2.565E-5*z)+eb/W;Pa=O*L(.99312619+99.99735956*a-4.4E-7*z)+Pa/W;V=O*L(.25909118+1342.2278298*a-8.92E-6*z)+V/W;wa=O*L(.82736186+1236.85308708*a-3.97E-6*z)+Q/W;for(m=1;4>=m;++m){switch(m){case 1:Q=eb;z=4;T=1.000002208;break;case 2:Q=Pa;z=3;T=.997504612-.002495388*a;break;case 3:Q=V;z=4;T=1.000002708+
+139.978*ca;break;case 4:Q=wa;z=6;T=1;break;default:throw"Internal error: I = "+m;}d(0,m,1);d(1,m,Math.cos(Q)*T);f(0,m,0);f(1,m,Math.sin(Q)*T);for(n=2;n<=z;++n)h(c(w,n-1,m),c(B,n-1,m),c(w,1,m),c(B,1,m),function(y,C){return d(n,m,y),f(n,m,C)});for(n=1;n<=z;++n)d(-n,m,c(w,n,m)),f(-n,m,-c(B,n,m))}g(13.902,14.06,-.001,.2607,0,0,0,4);g(.403,-4.01,.394,.0023,0,0,0,3);g(2369.912,2373.36,.601,28.2333,0,0,0,2);g(-125.154,-112.79,-.725,-.9781,0,0,0,1);g(1.979,6.98,-.445,.0433,1,0,0,4);g(191.953,192.72,.029,
3.0861,1,0,0,2);g(-8.466,-13.51,.455,-.1093,1,0,0,1);g(22639.5,22609.07,.079,186.5398,1,0,0,0);g(18.609,3.59,-.094,.0118,1,0,0,-1);g(-4586.465,-4578.13,-.077,34.3117,1,0,0,-2);g(3.215,5.44,.192,-.0386,1,0,0,-3);g(-38.428,-38.64,.001,.6008,1,0,0,-4);g(-.393,-1.43,-.092,.0086,1,0,0,-6);g(-.289,-1.59,.123,-.0053,0,1,0,4);g(-24.42,-25.1,.04,-.3,0,1,0,2);g(18.023,17.93,.007,.1494,0,1,0,1);g(-668.146,-126.98,-1.302,-.3997,0,1,0,0);g(.56,.32,-.001,-.0037,0,1,0,-1);g(-165.145,-165.06,.054,1.9178,0,1,0,-2);
g(-1.877,-6.46,-.416,.0339,0,1,0,-4);g(.213,1.02,-.074,.0054,2,0,0,4);g(14.387,14.78,-.017,.2833,2,0,0,2);g(-.586,-1.2,.054,-.01,2,0,0,1);g(769.016,767.96,.107,10.1657,2,0,0,0);g(1.75,2.01,-.018,.0155,2,0,0,-1);g(-211.656,-152.53,5.679,-.3039,2,0,0,-2);g(1.225,.91,-.03,-.0088,2,0,0,-3);g(-30.773,-34.07,-.308,.3722,2,0,0,-4);g(-.57,-1.4,-.074,.0109,2,0,0,-6);g(-2.921,-11.75,.787,-.0484,1,1,0,2);g(1.267,1.52,-.022,.0164,1,1,0,1);g(-109.673,-115.18,.461,-.949,1,1,0,0);g(-205.962,-182.36,2.056,1.4437,
1,1,0,-2);g(.233,.36,.012,-.0025,1,1,0,-3);g(-4.391,-9.66,-.471,.0673,1,1,0,-4);g(.283,1.53,-.111,.006,1,-1,0,4);g(14.577,31.7,-1.54,.2302,1,-1,0,2);g(147.687,138.76,.679,1.1528,1,-1,0,0);g(-1.089,.55,.021,0,1,-1,0,-1);g(28.475,23.59,-.443,-.2257,1,-1,0,-2);g(-.276,-.38,-.006,-.0036,1,-1,0,-3);g(.636,2.27,.146,-.0102,1,-1,0,-4);g(-.189,-1.68,.131,-.0028,0,2,0,2);g(-7.486,-.66,-.037,-.0086,0,2,0,0);g(-8.096,-16.35,-.74,.0918,0,2,0,-2);g(-5.741,-.04,0,-9E-4,0,0,2,2);g(.255,0,0,0,0,0,2,1);g(-411.608,
@@ -53,62 +53,62 @@ g(-1.877,-6.46,-.416,.0339,0,1,0,-4);g(.213,1.02,-.074,.0054,2,0,0,4);g(14.387,1
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-z+=-2*k(-2,0,1,-2).y;z+=-22.571*k(0,1,1,-2).y;z+=10.985*k(0,-1,1,-2).y;p+=.82*l(.7736-62.5512*a)+.31*l(.0466-125.1025*a)+.35*l(.5785-25.1042*a)+.66*l(.4591+1335.8075*a)+.64*l(.313-91.568*a)+1.14*l(.148+1331.2898*a)+.21*l(.5918+1056.5859*a)+.44*l(.5784+1322.8595*a)+.24*l(.2275-5.7374*a)+.28*l(.2965+2.6929*a)+.33*l(.3132+6.3368*a);a=V+v/W;a=(1.000002708+139.978*ba)*(18518.511+1.189+ta)*Math.sin(a)-6.24*Math.sin(3*a)+z;return{geo_eclip_lon:O*L((Na+p/W)/O),geo_eclip_lat:Math.PI/648E3*a,distance_au:W*
-Hc/(.999953253*aa)}}function Pa(a,b,c){b=eb(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 eb(a,b){a=a.tt/36525;var c=84381.406,d=((((3.337E-7*a-4.67E-7)*a-.00772503)*a+.0512623)*a-.025754)*a+c;c*=4.84813681109536E-6;var f=((((-9.51E-8*a+1.32851E-4)*a-.00114045)*a-1.0790069)*a+5038.481507)*a*4.84813681109536E-6;d*=4.84813681109536E-6;var h=((((-5.6E-8*a+1.70663E-4)*a-.00121197)*
-a-2.3814292)*a+10.556403)*a*4.84813681109536E-6;a=Math.sin(c);c=Math.cos(c);var l=Math.sin(-f);f=Math.cos(-f);var k=Math.sin(-d);d=Math.cos(-d);var g=Math.sin(h),m=Math.cos(h);h=m*f-l*g*d;var n=m*l*c+g*d*f*c-a*g*k,p=m*l*a+g*d*f*a+c*g*k,v=-g*f-l*m*d,y=-g*l*c+m*d*f*c-a*m*k;g=-g*l*a+m*d*f*a+c*m*k;l*=k;m=-k*f*c-a*d;a=-k*f*a+d*c;if(b===F.Into2000)return new J([[h,n,p],[v,y,g],[l,m,a]]);if(b===F.From2000)return new J([[h,v,l],[n,y,m],[p,g,a]]);throw"Invalid precess direction";}function ca(a){var b=a.tt/
-36525,c=15*Ka(a).ee;a=(.779057273264+.00273781191135448*a.ut+a.ut%1)%1*360;0>a&&(a+=360);b=((c+.014506+((((-3.68E-8*b-2.9956E-5)*b-4.4E-7)*b+1.3915817)*b+4612.156534)*b)/3600+a)%360/15;0>b&&(b+=24);return b}function Eb(a,b){var c=a.latitude*e.DEG2RAD,d=Math.sin(c);c=Math.cos(c);var f=1/Math.sqrt(c*c+.9933056020041345*d*d),h=a.height/1E3,l=6378.1366*f+h;b=(15*b+a.longitude)*e.DEG2RAD;a=Math.sin(b);b=Math.cos(b);return{pos:[l*c*b/e.KM_PER_AU,l*c*a/e.KM_PER_AU,(6335.438815127603*f+h)*d/e.KM_PER_AU],
-vel:[-7.292115E-5*l*c*a*86400,7.292115E-5*l*c*b*86400,0]}}function fb(a,b,c){b=gb(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 gb(a,b){a=Ka(a);var c=a.mobl*e.DEG2RAD,d=a.tobl*e.DEG2RAD,f=4.84813681109536E-6*a.dpsi;a=Math.cos(c);c=Math.sin(c);var h=Math.cos(d),l=Math.sin(d);d=Math.cos(f);var k=Math.sin(f);f=-k*a;var g=-k*c,m=k*h,n=d*a*h+c*l,p=d*c*h-a*l;k*=l;var v=d*a*l-
-c*h;a=d*c*l+a*h;if(b===F.From2000)return new J([[d,m,k],[f,n,v],[g,p,a]]);if(b===F.Into2000)return new J([[d,f,g],[m,n,p],[k,v,a]]);throw"Invalid precess direction";}function Qa(a,b,c){return c===F.Into2000?Pa(fb(a,b,c),b,c):fb(Pa(a,b,c),b,c)}function Fb(a,b){var c=ca(a);b=Eb(b,c).pos;return Qa(b,a,F.Into2000)}function Ic(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}
-function Gb(a,b){b=new C(a[0],a[1],a[2],b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return new Ra(0,0>b.z?-90:90,d,b)}var f=e.RAD2HOUR*Math.atan2(b.y,b.x);0>f&&(f+=24);return new Ra(f,e.RAD2DEG*Math.atan2(a[2],Math.sqrt(c)),d,b)}function la(a,b){var c=a*e.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}function va(a,b,c,d,f){a=w(a);ma(b);u(c);u(d);var h=Math.sin(b.latitude*e.DEG2RAD),l=Math.cos(b.latitude*e.DEG2RAD),
-k=Math.sin(b.longitude*e.DEG2RAD),g=Math.cos(b.longitude*e.DEG2RAD);b=Math.sin(d*e.DEG2RAD);var m=Math.cos(d*e.DEG2RAD),n=Math.sin(c*e.HOUR2RAD),p=Math.cos(c*e.HOUR2RAD),v=[l*g,l*k,h];h=[-h*g,-h*k,l];k=[k,-g,0];l=-15*ca(a);a=la(l,v);v=la(l,h);k=la(l,k);b=[m*p,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];m=b[0]*v[0]+b[1]*v[1]+b[2]*v[2];v=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];p=Math.sqrt(m*m+v*v);0m&&(m+=360)):m=0;n=e.RAD2DEG*Math.atan2(p,n);p=d;if(f&&(d=n,f=wa(f,90-n),n-=f,0k;++k)f.push((b[k]-d*a[k])/v*c+a[k]*p);p=Math.sqrt(f[0]*f[0]+f[1]*f[1]);0c&&(c+=24)):c=0;p=e.RAD2DEG*Math.atan2(f[2],p)}return new Hb(m,90-n,c,p)}function ma(a){if(!(a instanceof hb))throw"Not an instance of the Observer class: "+a;u(a.latitude);u(a.longitude);u(a.height);if(-90>a.latitude||90b&&(b+=360));h=e.RAD2DEG*Math.atan2(c,h);a=new C(d,f,c,a.t);return new Kb(a,h,b)}function ya(a){void 0===Sa&&(Sa=e.DEG2RAD*Ka(w(ib)).mobl,Lb=Math.cos(Sa),Mb=Math.sin(Sa));return Jb(a,Lb,Mb)}function Y(a){a=w(a);var b=ia(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)];var d=sa(a)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);b=Pa([b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],
-a,F.Into2000);return new C(b[0],b[1],b[2],a)}function da(a,b,c){var d=1,f=0;a=$jscomp.makeIterator(a);for(var h=a.next();!h.done;h=a.next()){var l=0;h=$jscomp.makeIterator(h.value);for(var k=h.next();!k.done;k=h.next()){var g=$jscomp.makeIterator(k.value);k=g.next().value;var m=g.next().value;g=g.next().value;l+=k*Math.cos(m+b*g)}l*=d;c&&(l%=O);f+=l;d*=b}return f}function jb(a,b){var c=1,d=0,f=0,h=0;a=$jscomp.makeIterator(a);for(var l=a.next();!l.done;l=a.next()){var k=0,g=0;l=$jscomp.makeIterator(l.value);
-for(var m=l.next();!m.done;m=l.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var p=n.next().value;n=n.next().value;p+=b*n;k+=m*n*Math.sin(p);0
-a?0:a>=b?b-1:a}function mb(a){var b=$jscomp.makeIterator(a);a=b.next().value;var c=$jscomp.makeIterator(b.next().value);var d=c.next().value;var f=c.next().value;c=c.next().value;var h=$jscomp.makeIterator(b.next().value);b=h.next().value;var l=h.next().value;h=h.next().value;d=new Ta(a,new E(d,f,c),new E(b,l,h));a=new Aa(d.tt);f=d.r.add(a.Sun.r);c=d.v.add(a.Sun.v);b=a.Acceleration(f);d=new Pb(d.tt,f,c,b);return new Qb(a,d)}function Sb(a,b,c){a=mb(a);for(var d=Math.ceil((b-a.grav.tt)/c),f=0;fea[40][0])a=null;else{a=Rb((a-c)/36500,40);if(!nb[a]){c=nb[a]=[];c[0]=mb(ea[a]).grav;c[146]=mb(ea[a+1]).grav;var d,f=c[0].tt;for(d=1;146>d;++d)c[d]=lb(f+=250,c[d-1]).grav;f=c[146].tt;var h=[];h[146]=c[146];for(d=145;0
-k;++k){f=Ba(a,l);c?d=R(H.Earth,l):d||(d=R(H.Earth,b));f=new C(f.x-d.x,f.y-d.y,f.z-d.z,b);var g=b.AddDays(-f.Length()/e.C_AUDAY);h=Math.abs(g.tt-l.tt);if(1E-9>h)return f;l=g}throw"Light-travel time solver did not converge: dt="+h;}function Ca(a,b){return new na(a.r.x,a.r.y,a.r.z,a.v.x,a.v.y,a.v.z,b)}function Jc(a,b,c,d,f){var h=(f+c)/2-d;c=(f-c)/2;if(0==h){if(0==c)return null;d=-d/c;if(-1>d||1=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*h);f=(-c-f)/(2*h);if(-1<=d&&
-1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{x:d,t:a+d*b,df_dt:(2*h*d+c)/b}}function I(a,b,c,d){var f=u(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var h=d&&d.init_f1||a(b),l=d&&d.init_f2||a(c),k=NaN,g=0;d=d&&d.iter_limit||20;for(var m=!0;;){if(++g>d)throw"Excessive iteration in Search()";var n=new N(b.ut+.5*(c.ut-b.ut)),p=n.ut-b.ut;if(Math.abs(p)(p.ut-b.ut)*(p.ut-c.ut)&&0>(y.ut-b.ut)*(y.ut-c.ut))){v=a(p);var z=a(y);if(0>v&&0<=z){h=v;l=z;b=p;c=y;k=D;m=!1;continue}}}}if(0>h&&0<=k)c=n,l=k;else if(0>k&&0<=l)b=n,h=k;else return null}}function Da(a){for(;-180>=a;)a+=360;for(;180b;)b+=360;for(;360<=b;)b-=360;return b}function oa(a,b){if(a==r.Earth)throw"The Earth does not have an angle as seen from itself.";var c=w(b);b=X(r.Sun,c,!0);a=X(a,c,!0);return S(b,a)}function ha(a,b){if(a===r.Sun)throw"Cannot calculate heliocentric longitude of the Sun.";a=Ba(a,b);return ya(a).elon}function Xa(a,b){if(a===r.Earth)throw"The illumination of the Earth is not defined.";var c=w(b),d=R(H.Earth,c);if(a===r.Sun){var f=
-new C(-d.x,-d.y,-d.z,c);b=new C(0,0,0,c);d=0}else a===r.Moon?(f=Y(c),b=new C(d.x+f.x,d.y+f.y,d.z+f.z,c)):(b=Ba(a,b),f=new C(b.x-d.x,b.y-d.y,b.z-d.z,c)),d=S(f,b);var h=f.Length(),l=b.Length();if(a===r.Sun)var k=Kc+5*Math.log10(h);else if(a===r.Moon)a=d*e.DEG2RAD,k=a*a,a=-12.717+1.49*Math.abs(a)+.0431*k*k,k=a+=5*Math.log10(h/(385000.6/e.KM_PER_AU)*l);else if(a===r.Saturn){var g=d;a=ya(f);k=28.06*e.DEG2RAD;var m=e.DEG2RAD*a.elat;a=Math.asin(Math.sin(m)*Math.cos(k)-Math.cos(m)*Math.sin(k)*Math.sin(e.DEG2RAD*
-a.elon-e.DEG2RAD*(169.51+3.82E-5*c.tt)));k=Math.sin(Math.abs(a));g=-9+.044*g+k*(-2.6+1.2*k)+5*Math.log10(l*h);a*=e.RAD2DEG;k=g;g=a}else{var n=m=k=0;switch(a){case r.Mercury:a=-.6;k=4.98;m=-4.88;n=3.02;break;case r.Venus:163.6>d?(a=-4.47,k=1.03,m=.57,n=.13):(a=.98,k=-1.02);break;case r.Mars:a=-1.52;k=1.6;break;case r.Jupiter:a=-9.4;k=.5;break;case r.Uranus:a=-7.19;k=.25;break;case r.Neptune:a=-6.87;break;case r.Pluto:a=-1;k=4;break;default:throw"VisualMagnitude: unsupported body "+a;}var p=d/100;k=
-a+p*(k+p*(m+p*n))+5*Math.log10(l*h)}return new Ub(c,k,d,l,h,f,b,g)}function Ea(a){if(a===r.Earth)throw"The Earth does not have a synodic period as seen from itself.";if(a===r.Moon)return 29.530588;var b=Z[a];if(!b)throw"Not a valid planet name: "+a;a=Z.Earth.OrbitalPeriod;return Math.abs(a/(a/b.OrbitalPeriod-1))}function pa(a,b,c){function d(m){var n=ha(a,m);m=ha(r.Earth,m);return Da(h*(m-n)-b)}u(b);var f=Z[a];if(!f)throw"Cannot search relative longitude because body is not a planet: "+a;if(a===r.Earth)throw"Cannot search relative longitude for the Earth (it is always 0)";
-var h=f.OrbitalPeriod>Z.Earth.OrbitalPeriod?1:-1;f=Ea(a);c=w(c);var l=d(c);0k;++k){var g=-l/360*f;c=c.AddDays(g);if(1>86400*Math.abs(g))return c;g=l;l=d(c);30>Math.abs(g)&&g!==l&&(g/=g-l,.5g&&(f*=g))}throw"Relative longitude search failed to converge for "+a+" near "+c.toString()+" (error_angle = "+l+").";}function pb(a){return ob(r.Moon,r.Sun,a)}function Fa(a,b,c){function d(l){l=pb(l);return Da(l-a)}u(a);u(c);b=w(b);var f=d(b);0c)return null;c=Math.min(c,h+1.5);f=b.AddDays(f);b=b.AddDays(c);return I(d,f,b)}function Vb(a){var b=pb(a);b=(Math.floor(b/90)+1)%4;a=Fa(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new Wb(b,a)}function Xb(a,b,c,d,f,h){ma(b);u(f);if(0>=f)throw"Invalid value for limitDays: "+f;if(a===r.Earth)throw"Cannot find altitude event for the Earth.";if(1===c){c=12;var l=0}else if(-1===c)c=0,l=12;else throw"Invalid direction parameter "+c+" -- must be +1 or -1";d=w(d);var k=h(d);var g;
-if(0=k&&0=d.ut+f)return null;m=k.time;k=h(k.time);g=h(n.time)}}function Ga(a,b,c,d){ma(b);d=w(d);var f=0;if(a===r.Earth)throw"Cannot search for hour angle of the Earth.";u(c);if(0>c||24<=c)throw"Invalid hour angle "+c;for(;;){++f;var h=ca(d),l=xa(a,d,b,!0,!0);h=(c+l.ra-b.longitude/15-h)%24;1===f?0>h&&(h+=24):
--12>h?h+=24:123600*Math.abs(h))return a=va(d,b,l.ra,l.dec,"normal"),new Yb(d,a);d=d.AddDays(h/24*.9972695717592592)}}function Zb(a,b){b=w(b);var c=ob(a,r.Sun,b);if(1805*f;++f){var h=a.AddDays(5),l=b(h);if(0>=d*l){if(0>d||
-0l){a=I(c,a,h,{init_f1:-d,init_f2:-l});if(!a)throw"SearchLunarApsis INTERNAL ERROR: apogee search failed!";d=ia(a).distance_au;return new Ha(a,1,d)}throw"SearchLunarApsis INTERNAL ERROR: cannot classify apsis event!";}a=h;d=l}throw"SearchLunarApsis INTERNAL ERROR: could not find apsis within 2 synodic months of start date.";}function bc(a,b,c,
-d){for(var f=1===b?1:-1;;){d/=9;if(d<1/1440)return c=c.AddDays(d/2),a=fa(a,c),new Ha(c,b,a);for(var h=-1,l=0,k=0;10>k;++k){var g=c.AddDays(k*d);g=f*fa(a,g);if(0==k||g>l)h=k,l=g}c=c.AddDays((h-1)*d);d*=2}}function Lc(a,b){var c=b.AddDays(-30/360*Z[a].OrbitalPeriod),d=b.AddDays(.75*Z[a].OrbitalPeriod),f=c,h=c,l=-1,k=-1;d=(d.ut-c.ut)/99;for(var g=0;100>g;++g){var m=c.AddDays(g*d),n=fa(a,m);0===g?k=l=n:(n>k&&(k=n,h=m),n=
-b.tt)return a.time.tt>=b.tt&&a.time.tt=b.tt)return a;throw"Internal error: failed to find Neptune apsis.";}function cc(a,b){function c(n){var p=n.AddDays(-5E-4);n=n.AddDays(5E-4);p=fa(a,p);return(fa(a,n)-p)/.001}function d(n){return-c(n)}if(a===r.Neptune||a===r.Pluto)return Lc(a,b);for(var f=Z[a].OrbitalPeriod,h=f/6,l=c(b),k=0;k*h<2*f;++k){var g=b.AddDays(h),m=c(g);if(0>=l*m){f=h=void 0;if(0>l||0m)h=d,f=1;else throw"Internal error with slopes in SearchPlanetApsis";
-b=I(h,b,g);if(!b)throw"Failed to find slope transition in planetary apsis search.";l=fa(a,b);return new Ha(b,f,l)}b=g;l=m}throw"Internal error: should have found planetary apsis within 2 orbital periods.";}function qa(a){return new J([[a.rot[0][0],a.rot[1][0],a.rot[2][0]],[a.rot[0][1],a.rot[1][1],a.rot[2][1]],[a.rot[0][2],a.rot[1][2],a.rot[2][2]]])}function ra(a,b){return new J([[b.rot[0][0]*a.rot[0][0]+b.rot[1][0]*a.rot[0][1]+b.rot[2][0]*a.rot[0][2],b.rot[0][1]*a.rot[0][0]+b.rot[1][1]*a.rot[0][1]+
+z+=-2*k(-2,0,1,-2).y;z+=-22.571*k(0,1,1,-2).y;z+=10.985*k(0,-1,1,-2).y;p+=.82*l(.7736-62.5512*a)+.31*l(.0466-125.1025*a)+.35*l(.5785-25.1042*a)+.66*l(.4591+1335.8075*a)+.64*l(.313-91.568*a)+1.14*l(.148+1331.2898*a)+.21*l(.5918+1056.5859*a)+.44*l(.5784+1322.8595*a)+.24*l(.2275-5.7374*a)+.28*l(.2965+2.6929*a)+.33*l(.3132+6.3368*a);a=V+u/W;a=(1.000002708+139.978*ca)*(18518.511+1.189+va)*Math.sin(a)-6.24*Math.sin(3*a)+z;return{geo_eclip_lon:O*L((Oa+p/W)/O),geo_eclip_lat:Math.PI/648E3*a,distance_au:W*
+Jc/(.999953253*ba)}}function Qa(a,b,c){b=fb(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 fb(a,b){a=a.tt/36525;var c=84381.406,d=((((3.337E-7*a-4.67E-7)*a-.00772503)*a+.0512623)*a-.025754)*a+c;c*=4.84813681109536E-6;var f=((((-9.51E-8*a+1.32851E-4)*a-.00114045)*a-1.0790069)*a+5038.481507)*a*4.84813681109536E-6;d*=4.84813681109536E-6;var h=((((-5.6E-8*a+1.70663E-4)*a-.00121197)*
+a-2.3814292)*a+10.556403)*a*4.84813681109536E-6;a=Math.sin(c);c=Math.cos(c);var l=Math.sin(-f);f=Math.cos(-f);var k=Math.sin(-d);d=Math.cos(-d);var g=Math.sin(h),m=Math.cos(h);h=m*f-l*g*d;var n=m*l*c+g*d*f*c-a*g*k,p=m*l*a+g*d*f*a+c*g*k,u=-g*f-l*m*d,w=-g*l*c+m*d*f*c-a*m*k;g=-g*l*a+m*d*f*a+c*m*k;l*=k;m=-k*f*c-a*d;a=-k*f*a+d*c;if(b===F.Into2000)return new J([[h,n,p],[u,w,g],[l,m,a]]);if(b===F.From2000)return new J([[h,u,l],[n,w,m],[p,g,a]]);throw"Invalid precess direction";}function da(a){var b=a.tt/
+36525,c=15*La(a).ee;a=(.779057273264+.00273781191135448*a.ut+a.ut%1)%1*360;0>a&&(a+=360);b=((c+.014506+((((-3.68E-8*b-2.9956E-5)*b-4.4E-7)*b+1.3915817)*b+4612.156534)*b)/3600+a)%360/15;0>b&&(b+=24);return b}function Fb(a,b){var c=a.latitude*e.DEG2RAD,d=Math.sin(c);c=Math.cos(c);var f=1/Math.sqrt(c*c+.9933056020041345*d*d),h=a.height/1E3,l=6378.1366*f+h;b=(15*b+a.longitude)*e.DEG2RAD;a=Math.sin(b);b=Math.cos(b);return{pos:[l*c*b/e.KM_PER_AU,l*c*a/e.KM_PER_AU,(6335.438815127603*f+h)*d/e.KM_PER_AU],
+vel:[-7.292115E-5*l*c*a*86400,7.292115E-5*l*c*b*86400,0]}}function gb(a,b,c){b=hb(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 hb(a,b){a=La(a);var c=a.mobl*e.DEG2RAD,d=a.tobl*e.DEG2RAD,f=4.84813681109536E-6*a.dpsi;a=Math.cos(c);c=Math.sin(c);var h=Math.cos(d),l=Math.sin(d);d=Math.cos(f);var k=Math.sin(f);f=-k*a;var g=-k*c,m=k*h,n=d*a*h+c*l,p=d*c*h-a*l;k*=l;var u=d*a*l-
+c*h;a=d*c*l+a*h;if(b===F.From2000)return new J([[d,m,k],[f,n,u],[g,p,a]]);if(b===F.Into2000)return new J([[d,f,g],[m,n,p],[k,u,a]]);throw"Invalid precess direction";}function Ra(a,b,c){return c===F.Into2000?Qa(gb(a,b,c),b,c):gb(Qa(a,b,c),b,c)}function Gb(a,b){var c=da(a);b=Fb(b,c).pos;return Ra(b,a,F.Into2000)}function Kc(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}
+function Hb(a,b){b=new D(a[0],a[1],a[2],b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return new Sa(0,0>b.z?-90:90,d,b)}var f=e.RAD2HOUR*Math.atan2(b.y,b.x);0>f&&(f+=24);return new Sa(f,e.RAD2DEG*Math.atan2(a[2],Math.sqrt(c)),d,b)}function la(a,b){var c=a*e.DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1],a*b[1]-c*b[0],b[2]]}function xa(a,b,c,d,f){a=x(a);ma(b);v(c);v(d);var h=Math.sin(b.latitude*e.DEG2RAD),l=Math.cos(b.latitude*e.DEG2RAD),
+k=Math.sin(b.longitude*e.DEG2RAD),g=Math.cos(b.longitude*e.DEG2RAD);b=Math.sin(d*e.DEG2RAD);var m=Math.cos(d*e.DEG2RAD),n=Math.sin(c*e.HOUR2RAD),p=Math.cos(c*e.HOUR2RAD),u=[l*g,l*k,h];h=[-h*g,-h*k,l];k=[k,-g,0];l=-15*da(a);a=la(l,u);u=la(l,h);k=la(l,k);b=[m*p,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];m=b[0]*u[0]+b[1]*u[1]+b[2]*u[2];u=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];p=Math.sqrt(m*m+u*u);0m&&(m+=360)):m=0;n=e.RAD2DEG*Math.atan2(p,n);p=d;if(f&&(d=n,f=ya(f,90-n),n-=f,0k;++k)f.push((b[k]-d*a[k])/u*c+a[k]*p);p=Math.sqrt(f[0]*f[0]+f[1]*f[1]);0c&&(c+=24)):c=0;p=e.RAD2DEG*Math.atan2(f[2],p)}return new Ib(m,90-n,c,p)}function ma(a){if(!(a instanceof ib))throw"Not an instance of the Observer class: "+a;v(a.latitude);v(a.longitude);v(a.height);if(-90>a.latitude||90b&&(b+=360));h=e.RAD2DEG*Math.atan2(c,h);a=new D(d,f,c,a.t);return new Lb(a,h,b)}function Aa(a){void 0===Ta&&(Ta=e.DEG2RAD*La(x(jb)).mobl,Mb=Math.cos(Ta),Nb=Math.sin(Ta));return Kb(a,Mb,Nb)}function Y(a){a=x(a);var b=aa(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)];var d=ua(a)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);b=Qa([b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],
+a,F.Into2000);return new D(b[0],b[1],b[2],a)}function ea(a,b,c){var d=1,f=0;a=$jscomp.makeIterator(a);for(var h=a.next();!h.done;h=a.next()){var l=0;h=$jscomp.makeIterator(h.value);for(var k=h.next();!k.done;k=h.next()){var g=$jscomp.makeIterator(k.value);k=g.next().value;var m=g.next().value;g=g.next().value;l+=k*Math.cos(m+b*g)}l*=d;c&&(l%=O);f+=l;d*=b}return f}function kb(a,b){var c=1,d=0,f=0,h=0;a=$jscomp.makeIterator(a);for(var l=a.next();!l.done;l=a.next()){var k=0,g=0;l=$jscomp.makeIterator(l.value);
+for(var m=l.next();!m.done;m=l.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var p=n.next().value;n=n.next().value;p+=b*n;k+=m*n*Math.sin(p);0
+a?0:a>=b?b-1:a}function nb(a){var b=$jscomp.makeIterator(a);a=b.next().value;var c=$jscomp.makeIterator(b.next().value);var d=c.next().value;var f=c.next().value;c=c.next().value;var h=$jscomp.makeIterator(b.next().value);b=h.next().value;var l=h.next().value;h=h.next().value;d=new Ua(a,new E(d,f,c),new E(b,l,h));a=new Ca(d.tt);f=d.r.add(a.Sun.r);c=d.v.add(a.Sun.v);b=a.Acceleration(f);d=new Qb(d.tt,f,c,b);return new Rb(a,d)}function Tb(a,b,c){a=nb(a);for(var d=Math.ceil((b-a.grav.tt)/c),f=0;ffa[40][0])a=null;else{a=Sb((a-c)/36500,40);if(!ob[a]){c=ob[a]=[];c[0]=nb(fa[a]).grav;c[146]=nb(fa[a+1]).grav;var d,f=c[0].tt;for(d=1;146>d;++d)c[d]=mb(f+=250,c[d-1]).grav;f=c[146].tt;var h=[];h[146]=c[146];for(d=145;0
+k;++k){f=Da(a,l);c?d=R(H.Earth,l):d||(d=R(H.Earth,b));f=new D(f.x-d.x,f.y-d.y,f.z-d.z,b);var g=b.AddDays(-f.Length()/e.C_AUDAY);h=Math.abs(g.tt-l.tt);if(1E-9>h)return f;l=g}throw"Light-travel time solver did not converge: dt="+h;}function Ea(a,b){return new na(a.r.x,a.r.y,a.r.z,a.v.x,a.v.y,a.v.z,b)}function Lc(a,b,c,d,f){var h=(f+c)/2-d;c=(f-c)/2;if(0==h){if(0==c)return null;d=-d/c;if(-1>d||1=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*h);f=(-c-f)/(2*h);if(-1<=d&&
+1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{x:d,t:a+d*b,df_dt:(2*h*d+c)/b}}function I(a,b,c,d){var f=v(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var h=d&&d.init_f1||a(b),l=d&&d.init_f2||a(c),k=NaN,g=0;d=d&&d.iter_limit||20;for(var m=!0;;){if(++g>d)throw"Excessive iteration in Search()";var n=new N(b.ut+.5*(c.ut-b.ut)),p=n.ut-b.ut;if(Math.abs(p)(p.ut-b.ut)*(p.ut-c.ut)&&0>(w.ut-b.ut)*(w.ut-c.ut))){u=a(p);var z=a(w);if(0>u&&0<=z){h=u;l=z;b=p;c=w;k=B;m=!1;continue}}}}if(0>h&&0<=k)c=n,l=k;else if(0>k&&0<=l)b=n,h=k;else return null}}function oa(a){for(;-180>=a;)a+=360;for(;180a;)a+=360;for(;360<=a;)a-=360;return a}function Ub(a,b,c){v(a);v(c);b=x(b);c=b.AddDays(c);return I(function(d){d=Jb(d);return oa(d.elon-
+a)},b,c)}function pb(a,b,c){if(a===r.Earth||b===r.Earth)throw"The Earth does not have a longitude as seen from itself.";c=x(c);a=X(a,c,!1);a=Aa(a);b=X(b,c,!1);b=Aa(b);return pa(a.elon-b.elon)}function qa(a,b){if(a==r.Earth)throw"The Earth does not have an angle as seen from itself.";var c=x(b);b=X(r.Sun,c,!0);a=X(a,c,!0);return S(b,a)}function ia(a,b){if(a===r.Sun)throw"Cannot calculate heliocentric longitude of the Sun.";a=Da(a,b);return Aa(a).elon}function Ya(a,b){if(a===r.Earth)throw"The illumination of the Earth is not defined.";
+var c=x(b),d=R(H.Earth,c);if(a===r.Sun){var f=new D(-d.x,-d.y,-d.z,c);b=new D(0,0,0,c);d=0}else a===r.Moon?(f=Y(c),b=new D(d.x+f.x,d.y+f.y,d.z+f.z,c)):(b=Da(a,b),f=new D(b.x-d.x,b.y-d.y,b.z-d.z,c)),d=S(f,b);var h=f.Length(),l=b.Length();if(a===r.Sun)var k=Mc+5*Math.log10(h);else if(a===r.Moon)a=d*e.DEG2RAD,k=a*a,a=-12.717+1.49*Math.abs(a)+.0431*k*k,k=a+=5*Math.log10(h/(385000.6/e.KM_PER_AU)*l);else if(a===r.Saturn){var g=d;a=Aa(f);k=28.06*e.DEG2RAD;var m=e.DEG2RAD*a.elat;a=Math.asin(Math.sin(m)*Math.cos(k)-
+Math.cos(m)*Math.sin(k)*Math.sin(e.DEG2RAD*a.elon-e.DEG2RAD*(169.51+3.82E-5*c.tt)));k=Math.sin(Math.abs(a));g=-9+.044*g+k*(-2.6+1.2*k)+5*Math.log10(l*h);a*=e.RAD2DEG;k=g;g=a}else{var n=m=k=0;switch(a){case r.Mercury:a=-.6;k=4.98;m=-4.88;n=3.02;break;case r.Venus:163.6>d?(a=-4.47,k=1.03,m=.57,n=.13):(a=.98,k=-1.02);break;case r.Mars:a=-1.52;k=1.6;break;case r.Jupiter:a=-9.4;k=.5;break;case r.Uranus:a=-7.19;k=.25;break;case r.Neptune:a=-6.87;break;case r.Pluto:a=-1;k=4;break;default:throw"VisualMagnitude: unsupported body "+
+a;}var p=d/100;k=a+p*(k+p*(m+p*n))+5*Math.log10(l*h)}return new Vb(c,k,d,l,h,f,b,g)}function Fa(a){if(a===r.Earth)throw"The Earth does not have a synodic period as seen from itself.";if(a===r.Moon)return 29.530588;var b=Z[a];if(!b)throw"Not a valid planet name: "+a;a=Z.Earth.OrbitalPeriod;return Math.abs(a/(a/b.OrbitalPeriod-1))}function ra(a,b,c){function d(m){var n=ia(a,m);m=ia(r.Earth,m);return oa(h*(m-n)-b)}v(b);var f=Z[a];if(!f)throw"Cannot search relative longitude because body is not a planet: "+
+a;if(a===r.Earth)throw"Cannot search relative longitude for the Earth (it is always 0)";var h=f.OrbitalPeriod>Z.Earth.OrbitalPeriod?1:-1;f=Fa(a);c=x(c);var l=d(c);0k;++k){var g=-l/360*f;c=c.AddDays(g);if(1>86400*Math.abs(g))return c;g=l;l=d(c);30>Math.abs(g)&&g!==l&&(g/=g-l,.5g&&(f*=g))}throw"Relative longitude search failed to converge for "+a+" near "+c.toString()+" (error_angle = "+l+").";}function qb(a){return pb(r.Moon,r.Sun,a)}function Ga(a,b,c){function d(l){l=
+qb(l);return oa(l-a)}v(a);v(c);b=x(b);var f=d(b);0c)return null;c=Math.min(c,h+1.5);f=b.AddDays(f);b=b.AddDays(c);return I(d,f,b)}function Wb(a){var b=qb(a);b=(Math.floor(b/90)+1)%4;a=Ga(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new Xb(b,a)}function Yb(a,b,c,d,f,h){ma(b);v(f);if(0>=f)throw"Invalid value for limitDays: "+f;if(a===r.Earth)throw"Cannot find altitude event for the Earth.";if(1===c){c=12;var l=0}else if(-1===c)c=0,l=12;else throw"Invalid direction parameter "+
+c+" -- must be +1 or -1";d=x(d);var k=h(d);var g;if(0=k&&0=d.ut+f)return null;m=k.time;k=h(k.time);g=h(n.time)}}function Ha(a,b,c,d){ma(b);d=x(d);var f=0;if(a===r.Earth)throw"Cannot search for hour angle of the Earth.";v(c);if(0>c||24<=c)throw"Invalid hour angle "+c;for(;;){++f;var h=da(d),l=za(a,d,b,!0,!0);
+h=(c+l.ra-b.longitude/15-h)%24;1===f?0>h&&(h+=24):-12>h?h+=24:123600*Math.abs(h))return a=xa(d,b,l.ra,l.dec,"normal"),new Zb(d,a);d=d.AddDays(h/24*.9972695717592592)}}function $b(a,b){b=x(b);var c=pb(a,r.Sun,b);if(1805*f;++f){var h=
+a.AddDays(5),l=b(h);if(0>=d*l){if(0>d||0l){a=I(c,a,h,{init_f1:-d,init_f2:-l});if(!a)throw"SearchLunarApsis INTERNAL ERROR: apogee search failed!";d=aa(a).distance_au;return new Ia(a,1,d)}throw"SearchLunarApsis INTERNAL ERROR: cannot classify apsis event!";}a=h;d=l}throw"SearchLunarApsis INTERNAL ERROR: could not find apsis within 2 synodic months of start date.";
+}function cc(a,b,c,d){for(var f=1===b?1:-1;;){d/=9;if(d<1/1440)return c=c.AddDays(d/2),a=ha(a,c),new Ia(c,b,a);for(var h=-1,l=0,k=0;10>k;++k){var g=c.AddDays(k*d);g=f*ha(a,g);if(0==k||g>l)h=k,l=g}c=c.AddDays((h-1)*d);d*=2}}function Nc(a,b){var c=b.AddDays(-30/360*Z[a].OrbitalPeriod),d=b.AddDays(.75*Z[a].OrbitalPeriod),f=c,h=c,l=-1,k=-1;d=(d.ut-c.ut)/99;for(var g=0;100>g;++g){var m=c.AddDays(g*d),n=ha(a,m);0===g?k=l=n:(n>k&&(k=n,h=m),n=b.tt)return a.time.tt>=b.tt&&a.time.tt=b.tt)return a;throw"Internal error: failed to find Neptune apsis.";}function dc(a,b){function c(n){var p=n.AddDays(-5E-4);n=n.AddDays(5E-4);p=ha(a,p);return(ha(a,n)-p)/.001}function d(n){return-c(n)}if(a===r.Neptune||a===r.Pluto)return Nc(a,b);for(var f=Z[a].OrbitalPeriod,h=f/6,l=c(b),k=0;k*h<2*f;++k){var g=b.AddDays(h),m=c(g);if(0>=l*m){f=h=void 0;if(0>l||0m)h=d,f=1;else throw"Internal error with slopes in SearchPlanetApsis";
+b=I(h,b,g);if(!b)throw"Failed to find slope transition in planetary apsis search.";l=ha(a,b);return new Ia(b,f,l)}b=g;l=m}throw"Internal error: should have found planetary apsis within 2 orbital periods.";}function sa(a){return new J([[a.rot[0][0],a.rot[1][0],a.rot[2][0]],[a.rot[0][1],a.rot[1][1],a.rot[2][1]],[a.rot[0][2],a.rot[1][2],a.rot[2][2]]])}function ta(a,b){return new J([[b.rot[0][0]*a.rot[0][0]+b.rot[1][0]*a.rot[0][1]+b.rot[2][0]*a.rot[0][2],b.rot[0][1]*a.rot[0][0]+b.rot[1][1]*a.rot[0][1]+
b.rot[2][1]*a.rot[0][2],b.rot[0][2]*a.rot[0][0]+b.rot[1][2]*a.rot[0][1]+b.rot[2][2]*a.rot[0][2]],[b.rot[0][0]*a.rot[1][0]+b.rot[1][0]*a.rot[1][1]+b.rot[2][0]*a.rot[1][2],b.rot[0][1]*a.rot[1][0]+b.rot[1][1]*a.rot[1][1]+b.rot[2][1]*a.rot[1][2],b.rot[0][2]*a.rot[1][0]+b.rot[1][2]*a.rot[1][1]+b.rot[2][2]*a.rot[1][2]],[b.rot[0][0]*a.rot[2][0]+b.rot[1][0]*a.rot[2][1]+b.rot[2][0]*a.rot[2][2],b.rot[0][1]*a.rot[2][0]+b.rot[1][1]*a.rot[2][1]+b.rot[2][1]*a.rot[2][2],b.rot[0][2]*a.rot[2][0]+b.rot[1][2]*a.rot[2][1]+
-b.rot[2][2]*a.rot[2][2]]])}function qb(a,b){var c=a.lat*e.DEG2RAD,d=a.lon*e.DEG2RAD,f=a.dist*Math.cos(c);return new C(f*Math.cos(d),f*Math.sin(d),a.dist*Math.sin(c),b)}function dc(a){var b=rb(a);return new Ra(b.lon/15,b.lat,b.dist,a)}function rb(a){var b=a.x*a.x+a.y*a.y,c=Math.sqrt(b+a.z*a.z);if(0===b){if(0===a.z)throw"Zero-length vector not allowed.";var d=0;a=0>a.z?-90:90}else d=e.RAD2DEG*Math.atan2(a.y,a.x),0>d&&(d+=360),a=e.RAD2DEG*Math.atan2(a.z,Math.sqrt(b));return new Ya(a,d,c)}function ec(a){a=
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-aa*p*z);g=v*ta*g*(+y+aa*m*z);m=2*Math.sqrt(1-l*l-k*k);v=1-2*k*k;y=1-2*l*l;D=2*k*l;d=new na(d*v+n*D,d*D+n*y,(l*n-d*k)*m,p*v+g*D,p*D+g*y,(l*g-p*k)*m,a);d=gc(Uc,d);h.call(f,d)}return new Bc(b)};e.HelioVector=Ba;e.HelioDistance=fa;e.GeoVector=X;e.BaryState=function(a,b){b=w(b);if(a==r.SSB)return new na(0,0,0,0,0,0,b);var c=new Aa(b.tt);switch(a){case r.Sun:return Ca(c.Sun,b);case r.Jupiter:return Ca(c.Jupiter,b);case r.Saturn:return Ca(c.Saturn,b);case r.Uranus:return Ca(c.Uranus,b);case r.Neptune:return Ca(c.Neptune,
-b)}if(a in H)return a=Ob(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=Tb;e.PairLongitude=ob;e.AngleFromSun=oa;e.EclipticLongitude=ha;var Ub=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=Ub;e.Illumination=
-Xa;e.SearchRelativeLongitude=pa;e.MoonPhase=pb;e.SearchMoonPhase=Fa;var Wb=function(a,b){this.quarter=a;this.time=b};e.MoonQuarter=Wb;e.SearchMoonQuarter=Vb;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Vb(a)};e.SearchRiseSet=function(a,b,c,d,f){a:switch(a){case r.Sun:var h=Rc;break a;case r.Moon:h=Sc;break a;default:h=0}return Xb(a,b,c,d,f,function(l){var k=xa(a,l,b,!0,!0);l=va(l,b,k.ra,k.dec).altitude+h/k.dist*e.RAD2DEG+Tc;return c*l})};e.SearchAltitude=function(a,
-b,c,d,f,h){if(!Number.isFinite(h)||-90>h||90=++f;){var h=ha(a,b),l=ha(r.Earth,b),k=Da(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=-Ea(a)/4,l=+d.s1,h=+d.s2):(g=-Ea(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(g);l=pa(a,l,k);h=pa(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 Zb(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=Xa(a,m).mag;return(Xa(a,g).mag-m)/.01}if(a!==r.Venus)throw"SearchPeakMagnitude currently works for Venus only.";
-b=w(b);for(var d=0;2>=++d;){var f=ha(a,b),h=ha(r.Earth,b),l=Da(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=-Ea(a)/4,h=10,f=30):(k=-Ea(a)/4,h=-30,f=-10);l=b.AddDays(k);h=pa(a,h,l);f=pa(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 Xa(a,l);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Ha=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Ha;e.SearchLunarApsis=ac;e.NextLunarApsis=function(a){var b=ac(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=cc;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=cc(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=qa;e.CombineRotation=ra;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=
-u(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=qb;e.EquatorFromVector=dc;e.SphereFromVector=rb;e.HorizonFromVector=function(a,b){a=rb(a);a.lon=
-ec(a.lon);a.lat+=wa(b,a.lat);return a};e.VectorFromHorizon=function(a,b,c){var d=ec(a.lon);c=a.lat+fc(c,a.lat);a=new Ya(c,d,a.dist);return qb(a,b)};e.Refraction=wa;e.InverseRefraction=fc;e.RotateVector=Ia;e.RotateState=gc;e.Rotation_EQJ_ECL=hc;e.Rotation_ECL_EQJ=function(){return new J([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=sb;e.Rotation_EQD_EQJ=tb;e.Rotation_EQD_HOR=ub;e.Rotation_HOR_EQD=ic;e.Rotation_HOR_EQJ=jc;e.Rotation_EQJ_HOR=
-function(a,b){a=jc(a,b);return qa(a)};e.Rotation_EQD_ECL=kc;e.Rotation_ECL_EQD=lc;e.Rotation_ECL_HOR=mc;e.Rotation_HOR_ECL=function(a,b){a=mc(a,b);return qa(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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+function(a){return new E(a*this.x,a*this.y,a*this.z)};E.prototype.div=function(a){return new E(this.x/a,this.y/a,this.z/a)};E.prototype.mean=function(a){return new E((this.x+a.x)/2,(this.y+a.y)/2,(this.z+a.z)/2)};var Ua=function(a,b,c){this.tt=a;this.r=b;this.v=c},Ca=function(a){var b=new Ua(a,new E(0,0,0),new E(0,0,0));this.Jupiter=Wa(b,a,r.Jupiter,2.825345909524226E-7);this.Saturn=Wa(b,a,r.Saturn,8.459715185680659E-8);this.Uranus=Wa(b,a,r.Uranus,1.292024916781969E-8);this.Neptune=Wa(b,a,r.Neptune,
+1.524358900784276E-8);this.Jupiter.r.decr(b.r);this.Jupiter.v.decr(b.v);this.Saturn.r.decr(b.r);this.Saturn.v.decr(b.v);this.Uranus.r.decr(b.r);this.Uranus.v.decr(b.v);this.Neptune.r.decr(b.r);this.Neptune.v.decr(b.v);this.Sun=new Ua(a,b.r.mul(-1),b.v.mul(-1))};Ca.prototype.Acceleration=function(a){var b=Ba(a,2.959122082855911E-4,this.Sun.r);b.incr(Ba(a,2.825345909524226E-7,this.Jupiter.r));b.incr(Ba(a,8.459715185680659E-8,this.Saturn.r));b.incr(Ba(a,1.292024916781969E-8,this.Uranus.r));b.incr(Ba(a,
+1.524358900784276E-8,this.Neptune.r));return b};var Qb=function(a,b,c,d){this.tt=a;this.r=b;this.v=c;this.a=d},Rb=function(a,b){this.bary=a;this.grav=b},ob=[],Wc=new J([[.9994327653386544,-.03367710746976414,0],[.030395942890628476,.902057912352809,.43054338854229507],[-.014499455966335291,-.43029916940910073,.902569881273754]]),Xc=[{mu:2.82489428433814E-7,al:[1.446213296021224,3.5515522861824],a:[[.0028210960212903,0,0]],l:[[-1.925258348666E-4,4.9369589722645,.01358483658305],[-9.70803596076E-5,
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+[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=++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","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"]],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],[82,4320,4350,1080],[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||90a&&(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=t;++t)0!==
-q[t]&&f(v.x,v.y,c(u,q[t],t),c(y,q[t],t),function(D,E){return v.x=D,v.y=E});return v}function h(q,t,w,A,v,D,E,J){v=k(v,D,E,J);n+=q*v.y;p+=t*v.y;O+=w*v.x;P+=A*v.x}++exports.CalcMoonCount;a=a.tt/36525;var l,m,n,p,u=b(-6,6,1,4),y=b(-6,6,1,4);var r=a*a;var O=p=n=0;var P=3422.7;var C=g(.19833+.05611*a);var B=g(.27869+.04508*a);var x=g(.16827-.36903*a);var z=g(.34734-5.37261*a);var F=g(.10498-5.37899*a);var G=g(.42681-.41855*a),R=g(.14943-5.37511*a);var H=.84*C+.31*B+14.27*x+7.26*z+.28*F+.24*G;var L=2.94*
-C+.31*B+14.27*x+9.34*z+1.12*F+.83*G;var I=-6.4*C-1.89*G;B=.21*C+.31*B+14.27*x-88.7*z-15.3*F+.24*G-1.86*R;x=H-I;C=-3.332E-6*g(.59734-5.37261*a)-5.39E-7*g(.35498-5.37899*a)-6.4E-8*g(.39943-5.37511*a);H=PI2*Frac(.60643382+1336.85522467*a-3.13E-6*r)+H/ARC;L=PI2*Frac(.37489701+1325.55240982*a+2.565E-5*r)+L/ARC;I=PI2*Frac(.99312619+99.99735956*a-4.4E-7*r)+I/ARC;B=PI2*Frac(.25909118+1342.2278298*a-8.92E-6*r)+B/ARC;F=PI2*Frac(.82736186+1236.85308708*a-3.97E-6*r)+x/ARC;for(l=1;4>=l;++l){switch(l){case 1:x=
-L;r=4;z=1.000002208;break;case 2:x=I;r=3;z=.997504612-.002495388*a;break;case 3:x=B;r=4;z=1.000002708+139.978*C;break;case 4:x=F;r=6;z=1;break;default:throw"Internal error: I = "+l;}d(0,l,1);d(1,l,Math.cos(x)*z);e(0,l,0);e(1,l,Math.sin(x)*z);for(m=2;m<=r;++m)f(c(u,m-1,l),c(y,m-1,l),c(u,1,l),c(y,1,l),function(q,t){return d(m,l,q),e(m,l,t)});for(m=1;m<=r;++m)d(-m,l,c(u,m,l)),e(-m,l,-c(y,m,l))}h(13.902,14.06,-.001,.2607,0,0,0,4);h(.403,-4.01,.394,.0023,0,0,0,3);h(2369.912,2373.36,.601,28.2333,0,0,0,
+function CalcMoon(a){function b(q,u,w,A){for(var v=[],D=0;D<=u-q;++D){var E=v,J=E.push,K,M=w,Q=A,N=[];for(K=0;K<=Q-M;++K)N.push(0);J.call(E,{min:M,array:N})}return{min:q,array:v}}function c(q,u,w){q=q.array[u-q.min];return q.array[w-q.min]}function d(q,u,w){q=r.array[q-r.min];q.array[u-q.min]=w}function e(q,u,w){q=x.array[q-x.min];q.array[u-q.min]=w}function f(q,u,w,A,v){v(q*w-u*A,u*w+q*A)}function g(q){return Math.sin(PI2*q)}function k(q,u,w,A){var v={x:1,y:0};q=[0,q,u,w,A];for(u=1;4>=u;++u)0!==
+q[u]&&f(v.x,v.y,c(r,q[u],u),c(x,q[u],u),function(D,E){return v.x=D,v.y=E});return v}function h(q,u,w,A,v,D,E,J){v=k(v,D,E,J);n+=q*v.y;p+=u*v.y;O+=w*v.x;P+=A*v.x}++exports.CalcMoonCount;a=a.tt/36525;var l,m,n,p,r=b(-6,6,1,4),x=b(-6,6,1,4);var t=a*a;var O=p=n=0;var P=3422.7;var C=g(.19833+.05611*a);var B=g(.27869+.04508*a);var y=g(.16827-.36903*a);var z=g(.34734-5.37261*a);var F=g(.10498-5.37899*a);var G=g(.42681-.41855*a),R=g(.14943-5.37511*a);var H=.84*C+.31*B+14.27*y+7.26*z+.28*F+.24*G;var L=2.94*
+C+.31*B+14.27*y+9.34*z+1.12*F+.83*G;var I=-6.4*C-1.89*G;B=.21*C+.31*B+14.27*y-88.7*z-15.3*F+.24*G-1.86*R;y=H-I;C=-3.332E-6*g(.59734-5.37261*a)-5.39E-7*g(.35498-5.37899*a)-6.4E-8*g(.39943-5.37511*a);H=PI2*Frac(.60643382+1336.85522467*a-3.13E-6*t)+H/ARC;L=PI2*Frac(.37489701+1325.55240982*a+2.565E-5*t)+L/ARC;I=PI2*Frac(.99312619+99.99735956*a-4.4E-7*t)+I/ARC;B=PI2*Frac(.25909118+1342.2278298*a-8.92E-6*t)+B/ARC;F=PI2*Frac(.82736186+1236.85308708*a-3.97E-6*t)+y/ARC;for(l=1;4>=l;++l){switch(l){case 1:y=
+L;t=4;z=1.000002208;break;case 2:y=I;t=3;z=.997504612-.002495388*a;break;case 3:y=B;t=4;z=1.000002708+139.978*C;break;case 4:y=F;t=6;z=1;break;default:throw"Internal error: I = "+l;}d(0,l,1);d(1,l,Math.cos(y)*z);e(0,l,0);e(1,l,Math.sin(y)*z);for(m=2;m<=t;++m)f(c(r,m-1,l),c(x,m-1,l),c(r,1,l),c(x,1,l),function(q,u){return d(m,l,q),e(m,l,u)});for(m=1;m<=t;++m)d(-m,l,c(r,m,l)),e(-m,l,-c(x,m,l))}h(13.902,14.06,-.001,.2607,0,0,0,4);h(.403,-4.01,.394,.0023,0,0,0,3);h(2369.912,2373.36,.601,28.2333,0,0,0,
2);h(-125.154,-112.79,-.725,-.9781,0,0,0,1);h(1.979,6.98,-.445,.0433,1,0,0,4);h(191.953,192.72,.029,3.0861,1,0,0,2);h(-8.466,-13.51,.455,-.1093,1,0,0,1);h(22639.5,22609.07,.079,186.5398,1,0,0,0);h(18.609,3.59,-.094,.0118,1,0,0,-1);h(-4586.465,-4578.13,-.077,34.3117,1,0,0,-2);h(3.215,5.44,.192,-.0386,1,0,0,-3);h(-38.428,-38.64,.001,.6008,1,0,0,-4);h(-.393,-1.43,-.092,.0086,1,0,0,-6);h(-.289,-1.59,.123,-.0053,0,1,0,4);h(-24.42,-25.1,.04,-.3,0,1,0,2);h(18.023,17.93,.007,.1494,0,1,0,1);h(-668.146,-126.98,
-1.302,-.3997,0,1,0,0);h(.56,.32,-.001,-.0037,0,1,0,-1);h(-165.145,-165.06,.054,1.9178,0,1,0,-2);h(-1.877,-6.46,-.416,.0339,0,1,0,-4);h(.213,1.02,-.074,.0054,2,0,0,4);h(14.387,14.78,-.017,.2833,2,0,0,2);h(-.586,-1.2,.054,-.01,2,0,0,1);h(769.016,767.96,.107,10.1657,2,0,0,0);h(1.75,2.01,-.018,.0155,2,0,0,-1);h(-211.656,-152.53,5.679,-.3039,2,0,0,-2);h(1.225,.91,-.03,-.0088,2,0,0,-3);h(-30.773,-34.07,-.308,.3722,2,0,0,-4);h(-.57,-1.4,-.074,.0109,2,0,0,-6);h(-2.921,-11.75,.787,-.0484,1,1,0,2);h(1.267,
1.52,-.022,.0164,1,1,0,1);h(-109.673,-115.18,.461,-.949,1,1,0,0);h(-205.962,-182.36,2.056,1.4437,1,1,0,-2);h(.233,.36,.012,-.0025,1,1,0,-3);h(-4.391,-9.66,-.471,.0673,1,1,0,-4);h(.283,1.53,-.111,.006,1,-1,0,4);h(14.577,31.7,-1.54,.2302,1,-1,0,2);h(147.687,138.76,.679,1.1528,1,-1,0,0);h(-1.089,.55,.021,0,1,-1,0,-1);h(28.475,23.59,-.443,-.2257,1,-1,0,-2);h(-.276,-.38,-.006,-.0036,1,-1,0,-3);h(.636,2.27,.146,-.0102,1,-1,0,-4);h(-.189,-1.68,.131,-.0028,0,2,0,2);h(-7.486,-.66,-.037,-.0086,0,2,0,0);h(-8.096,
-16.35,-.74,.0918,0,2,0,-2);h(-5.741,-.04,0,-9E-4,0,0,2,2);h(.255,0,0,0,0,0,2,1);h(-411.608,-.2,0,-.0124,0,0,2,0);h(.584,.84,0,.0071,0,0,2,-1);h(-55.173,-52.14,0,-.1052,0,0,2,-2);h(.254,.25,0,-.0017,0,0,2,-3);h(.025,-1.67,0,.0031,0,0,2,-4);h(1.06,2.96,-.166,.0243,3,0,0,2);h(36.124,50.64,-1.3,.6215,3,0,0,0);h(-13.193,-16.4,.258,-.1187,3,0,0,-2);h(-1.187,-.74,.042,.0074,3,0,0,-4);h(-.293,-.31,-.002,.0046,3,0,0,-6);h(-.29,-1.45,.116,-.0051,2,1,0,2);h(-7.649,-10.56,.259,-.1038,2,1,0,0);h(-8.627,-7.59,
.078,-.0192,2,1,0,-2);h(-2.74,-2.54,.022,.0324,2,1,0,-4);h(1.181,3.32,-.212,.0213,2,-1,0,2);h(9.703,11.67,-.151,.1268,2,-1,0,0);h(-.352,-.37,.001,-.0028,2,-1,0,-1);h(-2.494,-1.17,-.003,-.0017,2,-1,0,-2);h(.36,.2,-.012,-.0043,2,-1,0,-4);h(-1.167,-1.25,.008,-.0106,1,2,0,0);h(-7.412,-6.12,.117,.0484,1,2,0,-2);h(-.311,-.65,-.032,.0044,1,2,0,-4);h(.757,1.82,-.105,.0112,1,-2,0,2);h(2.58,2.32,.027,.0196,1,-2,0,0);h(2.533,2.4,-.014,-.0212,1,-2,0,-2);h(-.344,-.57,-.025,.0036,0,3,0,-2);h(-.992,-.02,0,0,1,0,
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);r=-526.069*k(0,0,1,-2).y;r+=-3.352*k(0,0,1,-4).y;r+=44.297*k(1,0,1,-2).y;r+=-6*k(1,
-0,1,-4).y;r+=20.599*k(-1,0,1,0).y;r+=-30.598*k(-1,0,1,-2).y;r+=-24.649*k(-2,0,1,0).y;r+=-2*k(-2,0,1,-2).y;r+=-22.571*k(0,1,1,-2).y;r+=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)+
-r;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)}}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]]}
+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,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,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,u=-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,u,h],[g,l,a]]);if(b===PrecessDirection.From2000)return new RotationMatrix([[f,p,g],[m,u,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}
+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}
function inverse_terra(a,b){var c=a[0]*exports.KM_PER_AU,d=a[1]*exports.KM_PER_AU;a=a[2]*exports.KM_PER_AU;var e=Math.sqrt(c*c+d*d);if(1E-6>e){b=0;var f=0=b;)b+=360;for(;180Math.abs(p))break;
f-=p/(h*((l-m)/k-m*l*(c-1)/(h*n))+a*g+e*d)}f*=exports.RAD2DEG;k=EARTH_EQUATORIAL_RADIUS_KM/k;a=Math.abs(g)>Math.abs(d)?a/g-c*k:e/d-k}return new Observer(f,b,1E3*a)}
@@ -172,7 +177,7 @@ var Rotation_JUP_EQJ=new RotationMatrix([[.9994327653386544,-.03367710746976414,
[-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]]}],JupiterMoonsInfo=function(a){this.moon=a};exports.JupiterMoonsInfo=JupiterMoonsInfo;
-function JupiterMoon_elem2pv(a,b,c){var d=c[0],e=c[1],f=c[2],g=c[3],k=c[4];c=c[5];var h=Math.sqrt(b/(d*d*d));b=e+f*Math.sin(e)-g*Math.cos(e);do{var l=Math.cos(b);var m=Math.sin(b);l=(e-b+f*m-g*l)/(1-f*l-g*m);b+=l}while(1E-12<=Math.abs(l));l=Math.cos(b);m=Math.sin(b);b=g*l-f*m;var n=-f*l-g*m,p=1/(1+n),u=1/(1+Math.sqrt(1-f*f-g*g));e=d*(l-f-u*g*b);b=d*(m-g+u*f*b);g=h*p*d*(-m-u*g*n);d=h*p*d*(+l+u*f*n);f=2*Math.sqrt(1-k*k-c*c);h=1-2*c*c;l=1-2*k*k;m=2*c*k;return new StateVector(e*h+b*m,e*m+b*l,(k*b-e*c)*
+function JupiterMoon_elem2pv(a,b,c){var d=c[0],e=c[1],f=c[2],g=c[3],k=c[4];c=c[5];var h=Math.sqrt(b/(d*d*d));b=e+f*Math.sin(e)-g*Math.cos(e);do{var l=Math.cos(b);var m=Math.sin(b);l=(e-b+f*m-g*l)/(1-f*l-g*m);b+=l}while(1E-12<=Math.abs(l));l=Math.cos(b);m=Math.sin(b);b=g*l-f*m;var n=-f*l-g*m,p=1/(1+n),r=1/(1+Math.sqrt(1-f*f-g*g));e=d*(l-f-r*g*b);b=d*(m-g+r*f*b);g=h*p*d*(-m-r*g*n);d=h*p*d*(+l+r*f*n);f=2*Math.sqrt(1-k*k-c*c);h=1-2*c*c;l=1-2*k*k;m=2*c*k;return new StateVector(e*h+b*m,e*m+b*l,(k*b-e*c)*
f,g*h+d*m,g*m+d*l,(k*d-g*c)*f,a)}
function CalcJupiterMoon(a,b){for(var c=a.tt+18262.5,d=[0,b.al[0]+c*b.al[1],0,0,0,0],e=$jscomp.makeIterator(b.a),f=e.next();!f.done;f=e.next()){var g=$jscomp.makeIterator(f.value);f=g.next().value;var k=g.next().value;g=g.next().value;d[0]+=f*Math.cos(k+c*g)}e=$jscomp.makeIterator(b.l);for(f=e.next();!f.done;f=e.next())g=$jscomp.makeIterator(f.value),f=g.next().value,k=g.next().value,g=g.next().value,d[1]+=f*Math.sin(k+c*g);d[1]%=PI2;0>d[1]&&(d[1]+=PI2);e=$jscomp.makeIterator(b.z);for(f=e.next();!f.done;f=
e.next())g=$jscomp.makeIterator(f.value),f=g.next().value,k=g.next().value,g=g.next().value,k+=c*g,d[2]+=f*Math.cos(k),d[3]+=f*Math.sin(k);e=$jscomp.makeIterator(b.zeta);for(f=e.next();!f.done;f=e.next())g=$jscomp.makeIterator(f.value),f=g.next().value,k=g.next().value,g=g.next().value,k+=c*g,d[4]+=f*Math.cos(k),d[5]+=f*Math.sin(k);a=JupiterMoon_elem2pv(a,b.mu,d);return RotateState(Rotation_JUP_EQJ,a)}
@@ -183,8 +188,8 @@ function GeoVector(a,b,c){VerifyBoolean(c);b=MakeTime(b);if(a===Body.Moon)return
function ExportState(a,b){return new StateVector(a.r.x,a.r.y,a.r.z,a.v.x,a.v.y,a.v.z,b)}
function BaryState(a,b){b=MakeTime(b);if(a==Body.SSB)return new StateVector(0,0,0,0,0,0,b);var c=new major_bodies_t(b.tt);switch(a){case Body.Sun:return ExportState(c.Sun,b);case Body.Jupiter:return ExportState(c.Jupiter,b);case Body.Saturn:return ExportState(c.Saturn,b);case Body.Uranus:return ExportState(c.Uranus,b);case Body.Neptune:return ExportState(c.Neptune,b)}if(a in vsop)return a=CalcVsopPosVel(vsop[a],b.tt),new StateVector(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+'"';}exports.BaryState=BaryState;function QuadInterp(a,b,c,d,e){var f=(e+c)/2-d;c=(e-c)/2;if(0==f){if(0==c)return null;d=-d/c;if(-1>d||1=d)return null;e=Math.sqrt(d);d=(-c+e)/(2*f);e=(-c-e)/(2*f);if(-1<=d&&1>=d){if(-1<=e&&1>=e)return null}else if(-1<=e&&1>=e)d=e;else return null}return{x:d,t:a+d*b,df_dt:(2*f*d+c)/b}}
-function Search(a,b,c,d){var e=VerifyNumber(d&&d.dt_tolerance_seconds||1);e=Math.abs(e/SECONDS_PER_DAY);var f=d&&d.init_f1||a(b),g=d&&d.init_f2||a(c),k=NaN,h=0;d=d&&d.iter_limit||20;for(var l=!0;;){if(++h>d)throw"Excessive iteration in Search()";var m=InterpolateTime(b,c,.5),n=m.ut-b.ut;if(Math.abs(n)(n.ut-b.ut)*(n.ut-c.ut)&&0>(u.ut-b.ut)*(u.ut-c.ut))){p=a(n);var r=a(u);if(0>p&&0<=r){f=p;g=r;b=n;c=u;k=y;l=!1;continue}}}}if(0>f&&0<=k)c=m,g=k;else if(0>k&&0<=g)b=m,f=k;else return null}}exports.Search=Search;function LongitudeOffset(a){for(;-180>=a;)a+=360;for(;180a;)a+=360;for(;360<=a;)a-=360;return a}
+function Search(a,b,c,d){var e=VerifyNumber(d&&d.dt_tolerance_seconds||1);e=Math.abs(e/SECONDS_PER_DAY);var f=d&&d.init_f1||a(b),g=d&&d.init_f2||a(c),k=NaN,h=0;d=d&&d.iter_limit||20;for(var l=!0;;){if(++h>d)throw"Excessive iteration in Search()";var m=InterpolateTime(b,c,.5),n=m.ut-b.ut;if(Math.abs(n)(n.ut-b.ut)*(n.ut-c.ut)&&0>(r.ut-b.ut)*(r.ut-c.ut))){p=a(n);var t=a(r);if(0>p&&0<=t){f=p;g=t;b=n;c=r;k=x;l=!1;continue}}}}if(0>f&&0<=k)c=m,g=k;else if(0>k&&0<=g)b=m,f=k;else return null}}exports.Search=Search;function LongitudeOffset(a){for(;-180>=a;)a+=360;for(;180a;)a+=360;for(;360<=a;)a-=360;return a}
function SearchSunLongitude(a,b,c){VerifyNumber(a);VerifyNumber(c);b=MakeTime(b);c=b.AddDays(c);return Search(function(d){d=SunPosition(d);return LongitudeOffset(d.elon-a)},b,c)}exports.SearchSunLongitude=SearchSunLongitude;function PairLongitude(a,b,c){if(a===Body.Earth||b===Body.Earth)throw"The Earth does not have a longitude as seen from itself.";c=MakeTime(c);a=GeoVector(a,c,!1);a=Ecliptic(a);b=GeoVector(b,c,!1);b=Ecliptic(b);return NormalizeLongitude(a.elon-b.elon)}exports.PairLongitude=PairLongitude;
function AngleFromSun(a,b){if(a==Body.Earth)throw"The Earth does not have an angle as seen from itself.";var c=MakeTime(b);b=GeoVector(Body.Sun,c,!0);a=GeoVector(a,c,!0);return AngleBetween(b,a)}exports.AngleFromSun=AngleFromSun;function EclipticLongitude(a,b){if(a===Body.Sun)throw"Cannot calculate heliocentric longitude of the Sun.";a=HelioVector(a,b);return Ecliptic(a).elon}exports.EclipticLongitude=EclipticLongitude;
function VisualMagnitude(a,b,c,d){var e=0,f=0,g=0;switch(a){case Body.Mercury:a=-.6;e=4.98;f=-4.88;g=3.02;break;case Body.Venus:163.6>b?(a=-4.47,e=1.03,f=.57,g=.13):(a=.98,e=-1.02);break;case Body.Mars:a=-1.52;e=1.6;break;case Body.Jupiter:a=-9.4;e=.5;break;case Body.Uranus:a=-7.19;e=.25;break;case Body.Neptune:a=-6.87;break;case Body.Pluto:a=-1;e=4;break;default:throw"VisualMagnitude: unsupported body "+a;}b/=100;return a+b*(e+b*(f+b*g))+5*Math.log10(c*d)}
diff --git a/source/js/astronomy.ts b/source/js/astronomy.ts
index 8705d9fe..6dc96327 100644
--- a/source/js/astronomy.ts
+++ b/source/js/astronomy.ts
@@ -1675,6 +1675,155 @@ function CalcMoon(time: AstroTime) {
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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(
+ public elat: number,
+ public elon: number,
+ public mlat: number,
+ public mlon: number,
+ public dist_km: number,
+ public diam_deg: number
+ ) {}
+}
+
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+export function Libration(date: FlexibleDateTime): LibrationInfo {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * KM_PER_AU;
+
+ // Inclination angle
+ const I = DEG2RAD * 1.54242;
+
+ // Moon's argument of latitude in radians.
+ const f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000);
+
+ // Moon's ascending node's mean longitude in radians.
+ const omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000);
+
+ // Sun's mean anomaly.
+ const m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000);
+
+ // Moon's mean anomaly.
+ const mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000);
+
+ // Moon's mean elongation.
+ const d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000);
+
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516*t - 0.0000074*t2;
+
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w)*Math.cos(mlat)*Math.cos(I) - Math.sin(mlat)*Math.sin(I), Math.cos(w)*Math.cos(mlat));
+ const ldash = LongitudeOffset(RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w)*Math.cos(mlat)*Math.sin(I) - Math.sin(mlat)*Math.cos(I));
+
+ // Physical librations
+ const k1 = DEG2RAD*(119.75 + 131.849*t);
+ const k2 = DEG2RAD*(72.56 + 20.186*t);
+
+ const rho = (
+ -0.02752*Math.cos(mdash) +
+ -0.02245*Math.sin(f) +
+ +0.00684*Math.cos(mdash - 2*f) +
+ -0.00293*Math.cos(2*f) +
+ -0.00085*Math.cos(2*f - 2*d) +
+ -0.00054*Math.cos(mdash - 2*d) +
+ -0.00020*Math.sin(mdash + f) +
+ -0.00020*Math.cos(mdash + 2*f) +
+ -0.00020*Math.cos(mdash - f) +
+ +0.00014*Math.cos(mdash + 2*f - 2*d)
+ );
+
+ const sigma = (
+ -0.02816*Math.sin(mdash) +
+ +0.02244*Math.cos(f) +
+ -0.00682*Math.sin(mdash - 2*f) +
+ -0.00279*Math.sin(2*f) +
+ -0.00083*Math.sin(2*f - 2*d) +
+ +0.00069*Math.sin(mdash - 2*d) +
+ +0.00040*Math.cos(mdash + f) +
+ -0.00025*Math.sin(2*mdash) +
+ -0.00023*Math.sin(mdash + 2*f) +
+ +0.00020*Math.cos(mdash - f) +
+ +0.00019*Math.sin(mdash - f) +
+ +0.00013*Math.sin(mdash + 2*f - 2*d) +
+ -0.00010*Math.cos(mdash - 3*f)
+ );
+
+ const tau = (
+ +0.02520*e*Math.sin(m) +
+ +0.00473*Math.sin(2*mdash - 2*f) +
+ -0.00467*Math.sin(mdash) +
+ +0.00396*Math.sin(k1) +
+ +0.00276*Math.sin(2*mdash - 2*d) +
+ +0.00196*Math.sin(omega) +
+ -0.00183*Math.cos(mdash - f) +
+ +0.00115*Math.sin(mdash - 2*d) +
+ -0.00096*Math.sin(mdash - d) +
+ +0.00046*Math.sin(2*f - 2*d) +
+ -0.00039*Math.sin(mdash - f) +
+ -0.00032*Math.sin(mdash - m - d) +
+ +0.00027*Math.sin(2*mdash - m - 2*d) +
+ +0.00023*Math.sin(k2) +
+ -0.00014*Math.sin(2*d) +
+ +0.00014*Math.cos(2*mdash - 2*f) +
+ -0.00012*Math.sin(mdash - 2*f) +
+ -0.00012*Math.sin(2*mdash) +
+ +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);
+ 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 {
const r = precession_rot(time, dir);
return [
diff --git a/source/js/esm/astronomy.js b/source/js/esm/astronomy.js
index e241e072..a4d8fc99 100644
--- a/source/js/esm/astronomy.js
+++ b/source/js/esm/astronomy.js
@@ -1560,6 +1560,134 @@ function CalcMoon(time) {
distance_au: (ARC * EARTH_EQUATORIAL_RADIUS_AU) / (0.999953253 * SINPI)
};
}
+/**
+ * @brief Lunar libration angles, returned by {@link Libration}.
+ *
+ * @property {number} elat
+ * Sub-Earth libration ecliptic latitude angle, in degrees.
+ * @property {number} elon
+ * Sub-Earth libration ecliptic longitude angle, in degrees.
+ * @property {number} mlat
+ * Moon's geocentric ecliptic latitude.
+ * @property {number} mlon
+ * 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, diam_deg) {
+ this.elat = elat;
+ this.elon = elon;
+ this.mlat = mlat;
+ this.mlon = mlon;
+ this.dist_km = dist_km;
+ this.diam_deg = diam_deg;
+ }
+}
+/**
+ * @brief Calculates the Moon's libration angles at a given moment in time.
+ *
+ * Libration is an observed back-and-forth wobble of the portion of the
+ * Moon visible from the Earth. It is caused by the imperfect tidal locking
+ * of the Moon's fixed rotation rate, compared to its variable angular speed
+ * of orbit around the Earth.
+ *
+ * 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`, 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),
+ * or an AstroTime object.
+ *
+ * @returns {LibrationInfo}
+ */
+export function Libration(date) {
+ const time = MakeTime(date);
+ const t = time.tt / 36525.0;
+ const t2 = t * t;
+ const t3 = t2 * t;
+ const t4 = t2 * t2;
+ const moon = CalcMoon(time);
+ const mlon = moon.geo_eclip_lon;
+ const mlat = moon.geo_eclip_lat;
+ const dist_km = moon.distance_au * KM_PER_AU;
+ // Inclination angle
+ const I = DEG2RAD * 1.54242;
+ // Moon's argument of latitude in radians.
+ const f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233 * t - 0.0036539 * t2 - t3 / 3526000 + t4 / 863310000);
+ // Moon's ascending node's mean longitude in radians.
+ const omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891 * t + 0.0020754 * t2 + t3 / 467441 - t4 / 60616000);
+ // Sun's mean anomaly.
+ const m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909 * t - 0.0001536 * t2 + t3 / 24490000);
+ // Moon's mean anomaly.
+ const mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055 * t + 0.0087414 * t2 + t3 / 69699 - t4 / 14712000);
+ // Moon's mean elongation.
+ const d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034 * t - 0.0018819 * t2 + t3 / 545868 - t4 / 113065000);
+ // Eccentricity of the Earth's orbit.
+ const e = 1.0 - 0.002516 * t - 0.0000074 * t2;
+ // Optical librations
+ const w = mlon - omega;
+ const a = Math.atan2(Math.sin(w) * Math.cos(mlat) * Math.cos(I) - Math.sin(mlat) * Math.sin(I), Math.cos(w) * Math.cos(mlat));
+ const ldash = LongitudeOffset(RAD2DEG * (a - f));
+ const bdash = Math.asin(-Math.sin(w) * Math.cos(mlat) * Math.sin(I) - Math.sin(mlat) * Math.cos(I));
+ // Physical librations
+ const k1 = DEG2RAD * (119.75 + 131.849 * t);
+ const k2 = DEG2RAD * (72.56 + 20.186 * t);
+ const rho = (-0.02752 * Math.cos(mdash) +
+ -0.02245 * Math.sin(f) +
+ +0.00684 * Math.cos(mdash - 2 * f) +
+ -0.00293 * Math.cos(2 * f) +
+ -0.00085 * Math.cos(2 * f - 2 * d) +
+ -0.00054 * Math.cos(mdash - 2 * d) +
+ -0.00020 * Math.sin(mdash + f) +
+ -0.00020 * Math.cos(mdash + 2 * f) +
+ -0.00020 * Math.cos(mdash - f) +
+ +0.00014 * Math.cos(mdash + 2 * f - 2 * d));
+ const sigma = (-0.02816 * Math.sin(mdash) +
+ +0.02244 * Math.cos(f) +
+ -0.00682 * Math.sin(mdash - 2 * f) +
+ -0.00279 * Math.sin(2 * f) +
+ -0.00083 * Math.sin(2 * f - 2 * d) +
+ +0.00069 * Math.sin(mdash - 2 * d) +
+ +0.00040 * Math.cos(mdash + f) +
+ -0.00025 * Math.sin(2 * mdash) +
+ -0.00023 * Math.sin(mdash + 2 * f) +
+ +0.00020 * Math.cos(mdash - f) +
+ +0.00019 * Math.sin(mdash - f) +
+ +0.00013 * Math.sin(mdash + 2 * f - 2 * d) +
+ -0.00010 * Math.cos(mdash - 3 * f));
+ const tau = (+0.02520 * e * Math.sin(m) +
+ +0.00473 * Math.sin(2 * mdash - 2 * f) +
+ -0.00467 * Math.sin(mdash) +
+ +0.00396 * Math.sin(k1) +
+ +0.00276 * Math.sin(2 * mdash - 2 * d) +
+ +0.00196 * Math.sin(omega) +
+ -0.00183 * Math.cos(mdash - f) +
+ +0.00115 * Math.sin(mdash - 2 * d) +
+ -0.00096 * Math.sin(mdash - d) +
+ +0.00046 * Math.sin(2 * f - 2 * d) +
+ -0.00039 * Math.sin(mdash - f) +
+ -0.00032 * Math.sin(mdash - m - d) +
+ +0.00027 * Math.sin(2 * mdash - m - 2 * d) +
+ +0.00023 * Math.sin(k2) +
+ -0.00014 * Math.sin(2 * d) +
+ +0.00014 * Math.cos(2 * mdash - 2 * f) +
+ -0.00012 * Math.sin(mdash - 2 * f) +
+ -0.00012 * Math.sin(2 * mdash) +
+ +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);
+ 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);
return [
diff --git a/source/python/README.md b/source/python/README.md
index 41045af0..8ed6cef8 100644
--- a/source/python/README.md
+++ b/source/python/README.md
@@ -461,6 +461,25 @@ and the velocities in AU/day.
---
+
+### class LibrationInfo
+
+**Lunar libration angles, returned by [`Libration`](#Libration).**
+
+Contains lunar libration angles and lunar position information
+for a given moment in time. See [`Libration`](#Libration) for more details.
+
+| Type | Attribute | Description |
+| --- | --- | --- |
+| `float` | `elat` | Sub-Earth libration ecliptic latitude angle, in degrees. |
+| `float` | `elon` | Sub-Earth libration ecliptic longitude angle, in degrees. |
+| `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. |
+
+---
+
### class LocalSolarEclipseInfo
@@ -1485,6 +1504,31 @@ The positions and velocities of Jupiter's 4 largest moons.
---
+
+### Libration(time)
+
+**Calculates the Moon's libration angles at a given moment in time.**
+
+Libration is an observed back-and-forth wobble of the portion of the
+Moon visible from the Earth. It is caused by the imperfect tidal locking
+of the Moon's fixed rotation rate, compared to its variable angular speed
+of orbit around the Earth.
+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`, 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 |
+| --- | --- | --- |
+| [`Time`](#Time) | `time` | The date and time for which to calculate the Moon's libration angles. |
+
+### Returns: [`LibrationInfo`](#LibrationInfo)
+
+---
+
### MoonPhase(time)
diff --git a/source/python/astronomy.py b/source/python/astronomy.py
index c707cb28..54157657 100644
--- a/source/python/astronomy.py
+++ b/source/python/astronomy.py
@@ -8537,3 +8537,157 @@ def NextTransit(body, prevTransitTime):
"""
startTime = prevTransitTime.AddDays(100.0)
return SearchTransit(body, startTime)
+
+
+class LibrationInfo:
+ """Lunar libration angles, returned by #Libration.
+
+ Contains lunar libration angles and lunar position information
+ for a given moment in time. See #Libration for more details.
+
+ Attributes
+ ----------
+ elat : float
+ Sub-Earth libration ecliptic latitude angle, in degrees.
+ elon : float
+ Sub-Earth libration ecliptic longitude angle, in degrees.
+ mlat : float
+ Moon's geocentric ecliptic latitude.
+ mlon : float
+ 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, 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):
+ """Calculates the Moon's libration angles at a given moment in time.
+
+ Libration is an observed back-and-forth wobble of the portion of the
+ Moon visible from the Earth. It is caused by the imperfect tidal locking
+ of the Moon's fixed rotation rate, compared to its variable angular speed
+ of orbit around the Earth.
+
+ 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`, 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
+ ----------
+ time : Time
+ The date and time for which to calculate the Moon's libration angles.
+
+ Returns
+ -------
+ LibrationInfo
+ """
+ t = time.tt / 36525.0
+ t2 = t * t
+ t3 = t2 * t
+ t4 = t2 * t2
+ moon = _CalcMoon(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)
+
+ # Moon's argument of latitude in radians.
+ f = math.radians(_NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000))
+
+ # Moon's ascending node's mean longitude in radians.
+ omega = math.radians(_NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000))
+
+ # Sun's mean anomaly.
+ m = math.radians(_NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000))
+
+ # Moon's mean anomaly.
+ mdash = math.radians(_NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000))
+
+ # Moon's mean elongation.
+ d = math.radians(_NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000))
+
+ # Eccentricity of the Earth's orbit.
+ e = 1.0 - 0.002516*t - 0.0000074*t2
+
+ # Optical librations
+ w = mlon - omega
+ a = math.atan2(math.sin(w)*math.cos(mlat)*math.cos(I) - math.sin(mlat)*math.sin(I), math.cos(w)*math.cos(mlat))
+ ldash = _LongitudeOffset(math.degrees(a - f))
+ bdash = math.asin(-math.sin(w)*math.cos(mlat)*math.sin(I) - math.sin(mlat)*math.cos(I))
+
+ # Physical librations
+ k1 = math.radians(119.75 + 131.849*t)
+ k2 = math.radians(72.56 + 20.186*t)
+
+ rho = (
+ -0.02752*math.cos(mdash) +
+ -0.02245*math.sin(f) +
+ +0.00684*math.cos(mdash - 2*f) +
+ -0.00293*math.cos(2*f) +
+ -0.00085*math.cos(2*f - 2*d) +
+ -0.00054*math.cos(mdash - 2*d) +
+ -0.00020*math.sin(mdash + f) +
+ -0.00020*math.cos(mdash + 2*f) +
+ -0.00020*math.cos(mdash - f) +
+ +0.00014*math.cos(mdash + 2*f - 2*d)
+ )
+
+ sigma = (
+ -0.02816*math.sin(mdash) +
+ +0.02244*math.cos(f) +
+ -0.00682*math.sin(mdash - 2*f) +
+ -0.00279*math.sin(2*f) +
+ -0.00083*math.sin(2*f - 2*d) +
+ +0.00069*math.sin(mdash - 2*d) +
+ +0.00040*math.cos(mdash + f) +
+ -0.00025*math.sin(2*mdash) +
+ -0.00023*math.sin(mdash + 2*f) +
+ +0.00020*math.cos(mdash - f) +
+ +0.00019*math.sin(mdash - f) +
+ +0.00013*math.sin(mdash + 2*f - 2*d) +
+ -0.00010*math.cos(mdash - 3*f)
+ )
+
+ tau = (
+ +0.02520*e*math.sin(m) +
+ +0.00473*math.sin(2*mdash - 2*f) +
+ -0.00467*math.sin(mdash) +
+ +0.00396*math.sin(k1) +
+ +0.00276*math.sin(2*mdash - 2*d) +
+ +0.00196*math.sin(omega) +
+ -0.00183*math.cos(mdash - f) +
+ +0.00115*math.sin(mdash - 2*d) +
+ -0.00096*math.sin(mdash - d) +
+ +0.00046*math.sin(2*f - 2*d) +
+ -0.00039*math.sin(mdash - f) +
+ -0.00032*math.sin(mdash - m - d) +
+ +0.00027*math.sin(2*mdash - m - 2*d) +
+ +0.00023*math.sin(k2) +
+ -0.00014*math.sin(2*d) +
+ +0.00014*math.cos(2*mdash - 2*f) +
+ -0.00012*math.sin(mdash - 2*f) +
+ -0.00012*math.sin(2*mdash) +
+ +0.00011*math.sin(2*mdash - 2*m - 2*d)
+ )
+
+ 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, diam_deg)
diff --git a/website/src/assets/documentation.json b/website/src/assets/documentation.json
index 03aac415..0eda8eee 100644
--- a/website/src/assets/documentation.json
+++ b/website/src/assets/documentation.json
@@ -46,61 +46,13 @@
"meta": {
"range": [
1519,
- 2714
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
"columnno": 0,
"code": {
"id": "astnode100000015",
- "name": "exports.IlluminationInfo",
- "type": "AssignmentExpression",
- "value": "exports.EclipticLongitude",
- "paramnames": []
- }
- },
- "undocumented": true,
- "name": "IlluminationInfo",
- "longname": "IlluminationInfo",
- "kind": "member",
- "scope": "global"
- },
- {
- "comment": "",
- "meta": {
- "range": [
- 1546,
- 2714
- ],
- "filename": "astronomy.js",
- "lineno": 36,
- "columnno": 27,
- "code": {
- "id": "astnode100000019",
- "name": "exports.EclipticLongitude",
- "type": "AssignmentExpression",
- "value": "exports.AngleFromSun",
- "paramnames": []
- }
- },
- "undocumented": true,
- "name": "EclipticLongitude",
- "longname": "EclipticLongitude",
- "kind": "member",
- "scope": "global"
- },
- {
- "comment": "",
- "meta": {
- "range": [
- 1574,
- 2714
- ],
- "filename": "astronomy.js",
- "lineno": 36,
- "columnno": 55,
- "code": {
- "id": "astnode100000023",
"name": "exports.AngleFromSun",
"type": "AssignmentExpression",
"value": "exports.PairLongitude",
@@ -109,23 +61,22 @@
},
"undocumented": true,
"name": "AngleFromSun",
- "longname": "IlluminationInfo#AngleFromSun",
+ "longname": "AngleFromSun",
"kind": "member",
- "memberof": "IlluminationInfo",
- "scope": "instance"
+ "scope": "global"
},
{
"comment": "",
"meta": {
"range": [
- 1597,
- 2714
+ 1542,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 78,
+ "columnno": 23,
"code": {
- "id": "astnode100000027",
+ "id": "astnode100000019",
"name": "exports.PairLongitude",
"type": "AssignmentExpression",
"value": "exports.SearchSunLongitude",
@@ -134,23 +85,22 @@
},
"undocumented": true,
"name": "PairLongitude",
- "longname": "EclipticLongitude#PairLongitude",
+ "longname": "PairLongitude",
"kind": "member",
- "memberof": "EclipticLongitude",
- "scope": "instance"
+ "scope": "global"
},
{
"comment": "",
"meta": {
"range": [
- 1621,
- 2714
+ 1566,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 102,
+ "columnno": 47,
"code": {
- "id": "astnode100000031",
+ "id": "astnode100000023",
"name": "exports.SearchSunLongitude",
"type": "AssignmentExpression",
"value": "exports.Search",
@@ -159,23 +109,23 @@
},
"undocumented": true,
"name": "SearchSunLongitude",
- "longname": "IlluminationInfo#AngleFromSun#SearchSunLongitude",
+ "longname": "AngleFromSun#SearchSunLongitude",
"kind": "member",
- "memberof": "IlluminationInfo#AngleFromSun",
+ "memberof": "AngleFromSun",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1650,
- 2714
+ 1595,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 131,
+ "columnno": 76,
"code": {
- "id": "astnode100000035",
+ "id": "astnode100000027",
"name": "exports.Search",
"type": "AssignmentExpression",
"value": "exports.BaryState",
@@ -184,23 +134,23 @@
},
"undocumented": true,
"name": "Search",
- "longname": "EclipticLongitude#PairLongitude#Search",
+ "longname": "PairLongitude#Search",
"kind": "member",
- "memberof": "EclipticLongitude#PairLongitude",
+ "memberof": "PairLongitude",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1667,
- 2714
+ 1612,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 148,
+ "columnno": 93,
"code": {
- "id": "astnode100000039",
+ "id": "astnode100000031",
"name": "exports.BaryState",
"type": "AssignmentExpression",
"value": "exports.GeoVector",
@@ -209,23 +159,23 @@
},
"undocumented": true,
"name": "BaryState",
- "longname": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState",
+ "longname": "AngleFromSun#SearchSunLongitude#BaryState",
"kind": "member",
- "memberof": "IlluminationInfo#AngleFromSun#SearchSunLongitude",
+ "memberof": "AngleFromSun#SearchSunLongitude",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1687,
- 2714
+ 1632,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 168,
+ "columnno": 113,
"code": {
- "id": "astnode100000043",
+ "id": "astnode100000035",
"name": "exports.GeoVector",
"type": "AssignmentExpression",
"value": "exports.HelioDistance",
@@ -234,23 +184,23 @@
},
"undocumented": true,
"name": "GeoVector",
- "longname": "EclipticLongitude#PairLongitude#Search#GeoVector",
+ "longname": "PairLongitude#Search#GeoVector",
"kind": "member",
- "memberof": "EclipticLongitude#PairLongitude#Search",
+ "memberof": "PairLongitude#Search",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1707,
- 2714
+ 1652,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 188,
+ "columnno": 133,
"code": {
- "id": "astnode100000047",
+ "id": "astnode100000039",
"name": "exports.HelioDistance",
"type": "AssignmentExpression",
"value": "exports.HelioVector",
@@ -259,23 +209,23 @@
},
"undocumented": true,
"name": "HelioDistance",
- "longname": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState#HelioDistance",
+ "longname": "AngleFromSun#SearchSunLongitude#BaryState#HelioDistance",
"kind": "member",
- "memberof": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState",
+ "memberof": "AngleFromSun#SearchSunLongitude#BaryState",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1731,
- 2714
+ 1676,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 212,
+ "columnno": 157,
"code": {
- "id": "astnode100000051",
+ "id": "astnode100000043",
"name": "exports.HelioVector",
"type": "AssignmentExpression",
"value": "exports.JupiterMoons",
@@ -284,23 +234,23 @@
},
"undocumented": true,
"name": "HelioVector",
- "longname": "EclipticLongitude#PairLongitude#Search#GeoVector#HelioVector",
+ "longname": "PairLongitude#Search#GeoVector#HelioVector",
"kind": "member",
- "memberof": "EclipticLongitude#PairLongitude#Search#GeoVector",
+ "memberof": "PairLongitude#Search#GeoVector",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1753,
- 2714
+ 1698,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 234,
+ "columnno": 179,
"code": {
- "id": "astnode100000055",
+ "id": "astnode100000047",
"name": "exports.JupiterMoons",
"type": "AssignmentExpression",
"value": "exports.JupiterMoonsInfo",
@@ -309,23 +259,23 @@
},
"undocumented": true,
"name": "JupiterMoons",
- "longname": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons",
+ "longname": "AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons",
"kind": "member",
- "memberof": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState#HelioDistance",
+ "memberof": "AngleFromSun#SearchSunLongitude#BaryState#HelioDistance",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1776,
- 2714
+ 1721,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 257,
+ "columnno": 202,
"code": {
- "id": "astnode100000059",
+ "id": "astnode100000051",
"name": "exports.JupiterMoonsInfo",
"type": "AssignmentExpression",
"value": "exports.GeoMoon",
@@ -334,23 +284,23 @@
},
"undocumented": true,
"name": "JupiterMoonsInfo",
- "longname": "EclipticLongitude#PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo",
+ "longname": "PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo",
"kind": "member",
- "memberof": "EclipticLongitude#PairLongitude#Search#GeoVector#HelioVector",
+ "memberof": "PairLongitude#Search#GeoVector#HelioVector",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1803,
- 2714
+ 1748,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 284,
+ "columnno": 229,
"code": {
- "id": "astnode100000063",
+ "id": "astnode100000055",
"name": "exports.GeoMoon",
"type": "AssignmentExpression",
"value": "exports.Ecliptic",
@@ -359,23 +309,23 @@
},
"undocumented": true,
"name": "GeoMoon",
- "longname": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons#GeoMoon",
+ "longname": "AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons#GeoMoon",
"kind": "member",
- "memberof": "IlluminationInfo#AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons",
+ "memberof": "AngleFromSun#SearchSunLongitude#BaryState#HelioDistance#JupiterMoons",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1821,
- 2714
+ 1766,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 302,
+ "columnno": 247,
"code": {
- "id": "astnode100000067",
+ "id": "astnode100000059",
"name": "exports.Ecliptic",
"type": "AssignmentExpression",
"value": "exports.ObserverGravity",
@@ -384,23 +334,23 @@
},
"undocumented": true,
"name": "Ecliptic",
- "longname": "EclipticLongitude#PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo#Ecliptic",
+ "longname": "PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo#Ecliptic",
"kind": "member",
- "memberof": "EclipticLongitude#PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo",
+ "memberof": "PairLongitude#Search#GeoVector#HelioVector#JupiterMoonsInfo",
"scope": "instance"
},
{
"comment": "",
"meta": {
"range": [
- 1840,
- 2714
+ 1785,
+ 2703
],
"filename": "astronomy.js",
"lineno": 36,
- "columnno": 321,
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@@ -1432,23 +1382,23 @@
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"comment": "/**\n * @brief The factor to convert degrees to radians = pi/180.\n */",
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"comment": "/**\n * @brief The factor to convert sidereal hours to radians = pi/12.\n */",
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"comment": "/**\n * @brief The factor to convert radians to degrees = 180/pi.\n */",
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"comment": "/**\n * @brief The factor to convert radians to sidereal hours = 12/pi.\n */",
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@@ -3075,14 +3125,14 @@
"comment": "/**\n * @brief The equatorial radius of Jupiter, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The polar radius of Jupiter, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The volumetric mean radius of Jupiter, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The mean radius of Jupiter's moon Io, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The mean radius of Jupiter's moon Europa, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The mean radius of Jupiter's moon Ganymede, expressed in kilometers.\n */",
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"comment": "/**\n * @brief The mean radius of Jupiter's moon Callisto, expressed in kilometers.\n */",
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+ "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 */",
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+ "name": "Libration",
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+ },
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+ "time": "Libration~time",
+ "t": "Libration~t",
+ "t2": "Libration~t2",
+ "t3": "Libration~t3",
+ "t4": "Libration~t4",
+ "moon": "Libration~moon",
+ "mlon": "Libration~mlon",
+ "mlat": "Libration~mlat",
+ "dist_km": "Libration~dist_km",
+ "I": "Libration~I",
+ "f": "Libration~f",
+ "omega": "Libration~omega",
+ "m": "Libration~m",
+ "mdash": "Libration~mdash",
+ "d": "Libration~d",
+ "e": "Libration~e",
+ "w": "Libration~w",
+ "a": "Libration~a",
+ "ldash": "Libration~ldash",
+ "bdash": "Libration~bdash",
+ "k1": "Libration~k1",
+ "k2": "Libration~k2",
+ "rho": "Libration~rho",
+ "sigma": "Libration~sigma",
+ "tau": "Libration~tau",
+ "ldash2": "Libration~ldash2",
+ "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`, 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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+ },
+ "description": "A Date object, a number of UTC days since the J2000 epoch (noon on January 1, 2000),\n or an AstroTime object.",
+ "name": "date"
+ }
+ ],
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+ {
+ "type": {
+ "names": [
+ "LibrationInfo"
+ ]
+ }
+ }
+ ],
+ "name": "Libration",
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+ "id": "astnode100010852",
"name": "spsi",
"type": "CallExpression",
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@@ -15507,14 +16758,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100009845",
+ "id": "astnode100010860",
"name": "xx",
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"value": "cpsi"
@@ -15532,14 +16783,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -15557,14 +16808,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"name": "zx",
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@@ -15582,14 +16833,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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- "id": "astnode100009863",
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"name": "xy",
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"value": ""
@@ -15607,14 +16858,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
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- "id": "astnode100009869",
+ "id": "astnode100010884",
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@@ -15632,14 +16883,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -15657,14 +16908,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
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"name": "xz",
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"value": ""
@@ -15682,14 +16933,14 @@
"comment": "",
"meta": {
"range": [
- 81056,
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],
"filename": "astronomy.js",
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"columnno": 10,
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"name": "yz",
"type": "BinaryExpression",
"value": ""
@@ -15707,14 +16958,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100009911",
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"name": "zz",
"type": "BinaryExpression",
"value": ""
@@ -15732,14 +16983,14 @@
"comment": "",
"meta": {
"range": [
- 81609,
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100009970",
+ "id": "astnode100010985",
"name": "gyration",
"type": "FunctionDeclaration",
"paramnames": [
@@ -15760,14 +17011,14 @@
"comment": "",
"meta": {
"range": [
- 82015,
- 82191
+ 88155,
+ 88331
],
"filename": "astronomy.js",
- "lineno": 1795,
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"columnno": 0,
"code": {
- "id": "astnode100010001",
+ "id": "astnode100011016",
"name": "geo_pos",
"type": "FunctionDeclaration",
"paramnames": [
@@ -15791,14 +17042,14 @@
"comment": "",
"meta": {
"range": [
- 82060,
- 82086
+ 88200,
+ 88226
],
"filename": "astronomy.js",
- "lineno": 1796,
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"columnno": 10,
"code": {
- "id": "astnode100010007",
+ "id": "astnode100011022",
"name": "gast",
"type": "CallExpression",
"value": ""
@@ -15816,14 +17067,14 @@
"comment": "",
"meta": {
"range": [
- 82098,
- 82129
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+ 88269
],
"filename": "astronomy.js",
- "lineno": 1797,
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"columnno": 10,
"code": {
- "id": "astnode100010013",
+ "id": "astnode100011028",
"name": "pos",
"type": "MemberExpression",
"value": ".pos"
@@ -15841,14 +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": [
- 82707,
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+ 89188
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010029",
+ "id": "astnode100011044",
"name": "Vector",
"type": "ClassDeclaration",
"paramnames": [
@@ -15915,14 +17166,14 @@
"comment": "",
"meta": {
"range": [
- 82726,
- 82837
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+ 88977
],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100010032",
+ "id": "astnode100011047",
"name": "Vector",
"type": "MethodDefinition",
"paramnames": [
@@ -15947,14 +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": [
- 82707,
- 83048
+ 88847,
+ 89188
],
"filename": "astronomy.js",
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+ "lineno": 1941,
"columnno": 0,
"code": {
- "id": "astnode100010029",
+ "id": "astnode100011044",
"name": "Vector",
"type": "ClassDeclaration",
"paramnames": [
@@ -16020,14 +17271,14 @@
"comment": "",
"meta": {
"range": [
- 82760,
- 82770
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+ 88910
],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010041",
+ "id": "astnode100011056",
"name": "this.x",
"type": "Identifier",
"value": "x",
@@ -16045,14 +17296,14 @@
"comment": "",
"meta": {
"range": [
- 82780,
- 82790
+ 88920,
+ 88930
],
"filename": "astronomy.js",
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+ "lineno": 1944,
"columnno": 8,
"code": {
- "id": "astnode100010047",
+ "id": "astnode100011062",
"name": "this.y",
"type": "Identifier",
"value": "y",
@@ -16070,14 +17321,14 @@
"comment": "",
"meta": {
"range": [
- 82800,
- 82810
+ 88940,
+ 88950
],
"filename": "astronomy.js",
- "lineno": 1815,
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"columnno": 8,
"code": {
- "id": "astnode100010053",
+ "id": "astnode100011068",
"name": "this.z",
"type": "Identifier",
"value": "z",
@@ -16095,14 +17346,14 @@
"comment": "",
"meta": {
"range": [
- 82820,
- 82830
+ 88960,
+ 88970
],
"filename": "astronomy.js",
- "lineno": 1816,
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"columnno": 8,
"code": {
- "id": "astnode100010059",
+ "id": "astnode100011074",
"name": "this.t",
"type": "Identifier",
"value": "t",
@@ -16120,14 +17371,14 @@
"comment": "/**\n * Returns the length of the vector in astronomical units (AU).\n * @returns {number}\n */",
"meta": {
"range": [
- 82951,
- 83046
+ 89091,
+ 89186
],
"filename": "astronomy.js",
- "lineno": 1822,
+ "lineno": 1952,
"columnno": 4,
"code": {
- "id": "astnode100010064",
+ "id": "astnode100011079",
"name": "Vector#Length",
"type": "MethodDefinition",
"paramnames": []
@@ -16157,14 +17408,14 @@
"comment": "",
"meta": {
"range": [
- 83049,
- 83072
+ 89189,
+ 89212
],
"filename": "astronomy.js",
- "lineno": 1826,
+ "lineno": 1956,
"columnno": 0,
"code": {
- "id": "astnode100010097",
+ "id": "astnode100011112",
"name": "exports.Vector",
"type": "Identifier",
"value": "Vector",
@@ -16181,14 +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": [
- 83873,
- 84088
+ 90013,
+ 90228
],
"filename": "astronomy.js",
- "lineno": 1841,
+ "lineno": 1971,
"columnno": 0,
"code": {
- "id": "astnode100010102",
+ "id": "astnode100011117",
"name": "StateVector",
"type": "ClassDeclaration",
"paramnames": [
@@ -16285,14 +17536,14 @@
"comment": "",
"meta": {
"range": [
- 83897,
- 84086
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+ 90226
],
"filename": "astronomy.js",
- "lineno": 1842,
+ "lineno": 1972,
"columnno": 4,
"code": {
- "id": "astnode100010105",
+ "id": "astnode100011120",
"name": "StateVector",
"type": "MethodDefinition",
"paramnames": [
@@ -16320,14 +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": [
- 83873,
- 84088
+ 90013,
+ 90228
],
"filename": "astronomy.js",
- "lineno": 1841,
+ "lineno": 1971,
"columnno": 0,
"code": {
- "id": "astnode100010102",
+ "id": "astnode100011117",
"name": "StateVector",
"type": "ClassDeclaration",
"paramnames": [
@@ -16423,14 +17674,14 @@
"comment": "",
"meta": {
"range": [
- 83943,
- 83953
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+ 90093
],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010117",
+ "id": "astnode100011132",
"name": "this.x",
"type": "Identifier",
"value": "x",
@@ -16448,14 +17699,14 @@
"comment": "",
"meta": {
"range": [
- 83963,
- 83973
+ 90103,
+ 90113
],
"filename": "astronomy.js",
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+ "lineno": 1974,
"columnno": 8,
"code": {
- "id": "astnode100010123",
+ "id": "astnode100011138",
"name": "this.y",
"type": "Identifier",
"value": "y",
@@ -16473,14 +17724,14 @@
"comment": "",
"meta": {
"range": [
- 83983,
- 83993
+ 90123,
+ 90133
],
"filename": "astronomy.js",
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+ "lineno": 1975,
"columnno": 8,
"code": {
- "id": "astnode100010129",
+ "id": "astnode100011144",
"name": "this.z",
"type": "Identifier",
"value": "z",
@@ -16498,14 +17749,14 @@
"comment": "",
"meta": {
"range": [
- 84003,
- 84015
+ 90143,
+ 90155
],
"filename": "astronomy.js",
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+ "lineno": 1976,
"columnno": 8,
"code": {
- "id": "astnode100010135",
+ "id": "astnode100011150",
"name": "this.vx",
"type": "Identifier",
"value": "vx",
@@ -16523,14 +17774,14 @@
"comment": "",
"meta": {
"range": [
- 84025,
- 84037
+ 90165,
+ 90177
],
"filename": "astronomy.js",
- "lineno": 1847,
+ "lineno": 1977,
"columnno": 8,
"code": {
- "id": "astnode100010141",
+ "id": "astnode100011156",
"name": "this.vy",
"type": "Identifier",
"value": "vy",
@@ -16548,14 +17799,14 @@
"comment": "",
"meta": {
"range": [
- 84047,
- 84059
+ 90187,
+ 90199
],
"filename": "astronomy.js",
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+ "lineno": 1978,
"columnno": 8,
"code": {
- "id": "astnode100010147",
+ "id": "astnode100011162",
"name": "this.vz",
"type": "Identifier",
"value": "vz",
@@ -16573,14 +17824,14 @@
"comment": "",
"meta": {
"range": [
- 84069,
- 84079
+ 90209,
+ 90219
],
"filename": "astronomy.js",
- "lineno": 1849,
+ "lineno": 1979,
"columnno": 8,
"code": {
- "id": "astnode100010153",
+ "id": "astnode100011168",
"name": "this.t",
"type": "Identifier",
"value": "t",
@@ -16598,14 +17849,14 @@
"comment": "",
"meta": {
"range": [
- 84089,
- 84122
+ 90229,
+ 90262
],
"filename": "astronomy.js",
- "lineno": 1852,
+ "lineno": 1982,
"columnno": 0,
"code": {
- "id": "astnode100010159",
+ "id": "astnode100011174",
"name": "exports.StateVector",
"type": "Identifier",
"value": "StateVector",
@@ -16622,14 +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": [
- 84490,
- 84665
+ 90630,
+ 90805
],
"filename": "astronomy.js",
- "lineno": 1863,
+ "lineno": 1993,
"columnno": 0,
"code": {
- "id": "astnode100010164",
+ "id": "astnode100011179",
"name": "Spherical",
"type": "ClassDeclaration",
"paramnames": [
@@ -16686,14 +17937,14 @@
"comment": "",
"meta": {
"range": [
- 84512,
- 84663
+ 90652,
+ 90803
],
"filename": "astronomy.js",
- "lineno": 1864,
+ "lineno": 1994,
"columnno": 4,
"code": {
- "id": "astnode100010167",
+ "id": "astnode100011182",
"name": "Spherical",
"type": "MethodDefinition",
"paramnames": [
@@ -16717,14 +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": [
- 84490,
- 84665
+ 90630,
+ 90805
],
"filename": "astronomy.js",
- "lineno": 1863,
+ "lineno": 1993,
"columnno": 0,
"code": {
- "id": "astnode100010164",
+ "id": "astnode100011179",
"name": "Spherical",
"type": "ClassDeclaration",
"paramnames": [
@@ -16780,14 +18031,14 @@
"comment": "",
"meta": {
"range": [
- 84550,
- 84578
+ 90690,
+ 90718
],
"filename": "astronomy.js",
- "lineno": 1865,
+ "lineno": 1995,
"columnno": 8,
"code": {
- "id": "astnode100010175",
+ "id": "astnode100011190",
"name": "this.lat",
"type": "CallExpression",
"value": "",
@@ -16805,14 +18056,14 @@
"comment": "",
"meta": {
"range": [
- 84588,
- 84616
+ 90728,
+ 90756
],
"filename": "astronomy.js",
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+ "lineno": 1996,
"columnno": 8,
"code": {
- "id": "astnode100010183",
+ "id": "astnode100011198",
"name": "this.lon",
"type": "CallExpression",
"value": "",
@@ -16830,14 +18081,14 @@
"comment": "",
"meta": {
"range": [
- 84626,
- 84656
+ 90766,
+ 90796
],
"filename": "astronomy.js",
- "lineno": 1867,
+ "lineno": 1997,
"columnno": 8,
"code": {
- "id": "astnode100010191",
+ "id": "astnode100011206",
"name": "this.dist",
"type": "CallExpression",
"value": "",
@@ -16855,14 +18106,14 @@
"comment": "",
"meta": {
"range": [
- 84666,
- 84695
+ 90806,
+ 90835
],
"filename": "astronomy.js",
- "lineno": 1870,
+ "lineno": 2000,
"columnno": 0,
"code": {
- "id": "astnode100010199",
+ "id": "astnode100011214",
"name": "exports.Spherical",
"type": "Identifier",
"value": "Spherical",
@@ -16879,14 +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 * astronomical units (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": [
- 85334,
- 85547
+ 91474,
+ 91687
],
"filename": "astronomy.js",
- "lineno": 1890,
+ "lineno": 2020,
"columnno": 0,
"code": {
- "id": "astnode100010204",
+ "id": "astnode100011219",
"name": "EquatorialCoordinates",
"type": "ClassDeclaration",
"paramnames": [
@@ -16953,14 +18204,14 @@
"comment": "",
"meta": {
"range": [
- 85368,
- 85545
+ 91508,
+ 91685
],
"filename": "astronomy.js",
- "lineno": 1891,
+ "lineno": 2021,
"columnno": 4,
"code": {
- "id": "astnode100010207",
+ "id": "astnode100011222",
"name": "EquatorialCoordinates",
"type": "MethodDefinition",
"paramnames": [
@@ -16985,14 +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 * astronomical units (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": [
- 85334,
- 85547
+ 91474,
+ 91687
],
"filename": "astronomy.js",
- "lineno": 1890,
+ "lineno": 2020,
"columnno": 0,
"code": {
- "id": "astnode100010204",
+ "id": "astnode100011219",
"name": "EquatorialCoordinates",
"type": "ClassDeclaration",
"paramnames": [
@@ -17058,14 +18309,14 @@
"comment": "",
"meta": {
"range": [
- 85410,
- 85436
+ 91550,
+ 91576
],
"filename": "astronomy.js",
- "lineno": 1892,
+ "lineno": 2022,
"columnno": 8,
"code": {
- "id": "astnode100010216",
+ "id": "astnode100011231",
"name": "this.ra",
"type": "CallExpression",
"value": "",
@@ -17083,14 +18334,14 @@
"comment": "",
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"meta": {
"range": [
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"filename": "astronomy.js",
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"range": [
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],
"filename": "astronomy.js",
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- "id": "astnode100010240",
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"value": "vec",
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"comment": "",
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"range": [
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"filename": "astronomy.js",
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- "id": "astnode100010246",
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"type": "Identifier",
"value": "EquatorialCoordinates",
@@ -17182,14 +18433,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100010251",
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"type": "FunctionDeclaration",
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"comment": "",
"meta": {
"range": [
- 85730,
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],
"filename": "astronomy.js",
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"columnno": 13,
"code": {
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@@ -17237,14 +18488,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 17,
"code": {
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@@ -17262,14 +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": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010321",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100010324",
+ "id": "astnode100011339",
"name": "RotationMatrix",
"type": "MethodDefinition",
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@@ -17335,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010321",
+ "id": "astnode100011336",
"name": "RotationMatrix",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010330",
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"name": "this.rot",
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"value": "rot",
@@ -17403,14 +18654,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010336",
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"name": "exports.RotationMatrix",
"type": "Identifier",
"value": "RotationMatrix",
@@ -17427,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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"name": "MakeRotation",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010357",
+ "id": "astnode100011372",
"name": "exports.MakeRotation",
"type": "Identifier",
"value": "MakeRotation",
@@ -17503,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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"comment": "",
"meta": {
"range": [
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],
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"columnno": 4,
"code": {
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"name": "HorizontalCoordinates",
"type": "MethodDefinition",
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@@ -17609,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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"name": "HorizontalCoordinates",
"type": "ClassDeclaration",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010374",
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"name": "this.azimuth",
"type": "CallExpression",
"value": "",
@@ -17707,14 +18958,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010382",
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"name": "this.altitude",
"type": "CallExpression",
"value": "",
@@ -17732,14 +18983,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010390",
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"name": "this.ra",
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"value": "",
@@ -17757,14 +19008,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010398",
+ "id": "astnode100011413",
"name": "this.dec",
"type": "CallExpression",
"value": "",
@@ -17782,14 +19033,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010406",
+ "id": "astnode100011421",
"name": "exports.HorizontalCoordinates",
"type": "Identifier",
"value": "HorizontalCoordinates",
@@ -17806,14 +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 * astronomical units (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 * equinox.\n * The y-axis is within the ecliptic plane and is oriented 90 degrees\n * counterclockwise from the equinox, as seen from above the Sun's north pole.\n * The z-axis is oriented perpendicular to the ecliptic plane,\n * along the direction of the Sun's north pole.\n *\n * @property {number} elat\n * The ecliptic latitude of the body in degrees.\n * This is the angle north or south of the ecliptic plane.\n * The value is in the range [-90, +90].\n * Positive values are north and negative values are south.\n *\n * @property {number} elon\n * The ecliptic longitude of the body in degrees.\n * This is the angle measured counterclockwise around the ecliptic plane,\n * as seen from above the Sun's north pole.\n * This is the same direction that the Earth orbits around the Sun.\n * The angle is measured starting at 0 from the equinox and increases\n * up to 360 degrees.\n */",
"meta": {
"range": [
- 90708,
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+ 97022
],
"filename": "astronomy.js",
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+ "lineno": 2148,
"columnno": 0,
"code": {
- "id": "astnode100010411",
+ "id": "astnode100011426",
"name": "EclipticCoordinates",
"type": "ClassDeclaration",
"paramnames": [
@@ -17870,14 +19121,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100010414",
+ "id": "astnode100011429",
"name": "EclipticCoordinates",
"type": "MethodDefinition",
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@@ -17901,14 +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 * astronomical units (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 * equinox.\n * The y-axis is within the ecliptic plane and is oriented 90 degrees\n * counterclockwise from the equinox, as seen from above the Sun's north pole.\n * The z-axis is oriented perpendicular to the ecliptic plane,\n * along the direction of the Sun's north pole.\n *\n * @property {number} elat\n * The ecliptic latitude of the body in degrees.\n * This is the angle north or south of the ecliptic plane.\n * The value is in the range [-90, +90].\n * Positive values are north and negative values are south.\n *\n * @property {number} elon\n * The ecliptic longitude of the body in degrees.\n * This is the angle measured counterclockwise around the ecliptic plane,\n * as seen from above the Sun's north pole.\n * This is the same direction that the Earth orbits around the Sun.\n * The angle is measured starting at 0 from the equinox and increases\n * up to 360 degrees.\n */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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+ "lineno": 2148,
"columnno": 0,
"code": {
- "id": "astnode100010411",
+ "id": "astnode100011426",
"name": "EclipticCoordinates",
"type": "ClassDeclaration",
"paramnames": [
@@ -17964,14 +19215,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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+ "lineno": 2150,
"columnno": 8,
"code": {
- "id": "astnode100010422",
+ "id": "astnode100011437",
"name": "this.vec",
"type": "Identifier",
"value": "vec",
@@ -17989,14 +19240,14 @@
"comment": "",
"meta": {
"range": [
- 90803,
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],
"filename": "astronomy.js",
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+ "lineno": 2151,
"columnno": 8,
"code": {
- "id": "astnode100010428",
+ "id": "astnode100011443",
"name": "this.elat",
"type": "CallExpression",
"value": "",
@@ -18014,14 +19265,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
- "lineno": 2022,
+ "lineno": 2152,
"columnno": 8,
"code": {
- "id": "astnode100010436",
+ "id": "astnode100011451",
"name": "this.elon",
"type": "CallExpression",
"value": "",
@@ -18039,14 +19290,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010444",
+ "id": "astnode100011459",
"name": "exports.EclipticCoordinates",
"type": "Identifier",
"value": "EclipticCoordinates",
@@ -18063,14 +19314,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010449",
+ "id": "astnode100011464",
"name": "VectorFromArray",
"type": "FunctionDeclaration",
"paramnames": [
@@ -18090,14 +19341,14 @@
"comment": "",
"meta": {
"range": [
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+ 97755
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010467",
+ "id": "astnode100011482",
"name": "vector2radec",
"type": "FunctionDeclaration",
"paramnames": [
@@ -18124,14 +19375,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100010473",
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"name": "vec",
"type": "CallExpression",
"value": ""
@@ -18149,14 +19400,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100010480",
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"value": ""
@@ -18174,14 +19425,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100010498",
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"value": ""
@@ -18199,14 +19450,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010543",
+ "id": "astnode100011558",
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"type": "BinaryExpression",
"value": ""
@@ -18224,14 +19475,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100010564",
+ "id": "astnode100011579",
"name": "ra",
"type": "Literal",
"funcscope": "vector2radec",
@@ -18250,14 +19501,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100010568",
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"name": "dec",
"type": "BinaryExpression",
"value": ""
@@ -18275,14 +19526,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100010593",
+ "id": "astnode100011608",
"name": "spin",
"type": "FunctionDeclaration",
"paramnames": [
@@ -18307,14 +19558,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100010599",
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"name": "angr",
"type": "BinaryExpression",
"value": ""
@@ -18332,14 +19583,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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+ "lineno": 2176,
"columnno": 10,
"code": {
- "id": "astnode100010607",
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"name": "c",
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@@ -19711,14 +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 */",
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@@ -19873,14 +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 * Geocentric means coordinates as the Sun would appear to a hypothetical observer\n * at the center of the Earth.\n * Ecliptic coordinates of date are measured along the plane of the Earth's mean\n * orbit around the Sun, using the\n * equinox\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 */",
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@@ -20011,14 +21262,14 @@
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"comment": "",
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"filename": "astronomy.js",
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@@ -20136,14 +21387,14 @@
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"name": "exports.SunPosition",
"type": "Identifier",
"value": "SunPosition",
@@ -20160,14 +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 * Topocentric refers to a position as seen by an observer on the surface of the Earth.\n * This function corrects for\n * parallax\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 * aberration,\n * or `false` to leave uncorrected.\n *\n * @returns {EquatorialCoordinates}\n * The topocentric coordinates of the body as adjusted for the given observer.\n */",
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@@ -20260,14 +21511,14 @@
"comment": "",
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],
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@@ -20310,14 +21561,14 @@
"comment": "",
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],
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@@ -20335,14 +21586,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"type": "ArrayExpression",
"value": "[\"\",\"\",\"\"]"
@@ -20360,14 +21611,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -20385,14 +21636,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"name": "exports.Equator",
"type": "Identifier",
"value": "Equator",
@@ -20409,14 +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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],
"filename": "astronomy.js",
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"columnno": 0,
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+ "id": "astnode100012516",
"name": "ObserverVector",
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"paramnames": [
@@ -20487,14 +21738,14 @@
"comment": "",
"meta": {
"range": [
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],
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@@ -20512,14 +21763,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -20537,14 +21788,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -20562,14 +21813,14 @@
"comment": "",
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"range": [
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],
"filename": "astronomy.js",
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@@ -20588,14 +21839,14 @@
"comment": "",
"meta": {
"range": [
- 106278,
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+ 112457
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100011547",
+ "id": "astnode100012562",
"name": "exports.ObserverVector",
"type": "Identifier",
"value": "ObserverVector",
@@ -20612,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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@@ -20679,14 +21930,14 @@
"comment": "",
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],
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@@ -20704,14 +21955,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"value": "[\"vector.x\",\"vector.y\",\"vector.z\"]"
@@ -20729,14 +21980,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -20755,14 +22006,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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@@ -20781,14 +22032,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"name": "exports.VectorObserver",
"type": "Identifier",
"value": "VectorObserver",
@@ -20805,14 +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 */",
"meta": {
"range": [
- 109088,
- 109409
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100011617",
+ "id": "astnode100012632",
"name": "ObserverGravity",
"type": "FunctionDeclaration",
"paramnames": [
@@ -20873,14 +22124,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"value": ""
@@ -20898,14 +22149,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"value": ""
@@ -20923,14 +22174,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"type": "BinaryExpression",
"value": ""
@@ -20948,14 +22199,14 @@
"comment": "",
"meta": {
"range": [
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"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100011679",
+ "id": "astnode100012694",
"name": "exports.ObserverGravity",
"type": "Identifier",
"value": "ObserverGravity",
@@ -20972,14 +22223,14 @@
"comment": "",
"meta": {
"range": [
- 109453,
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"comment": "/**\n * @brief Calculates the distance between a body and the Sun at a given time.\n *\n * Given a date and time, this function calculates the distance between\n * the center of `body` and the center of the Sun.\n * For the planets Mercury through Neptune, this function is significantly\n * more efficient than calling {@link HelioVector} followed by taking the length\n * of the resulting vector.\n *\n * @param {Body} body\n * A body for which to calculate a heliocentric distance:\n * the Sun, Moon, or any of the planets.\n *\n * @param {FlexibleDateTime} date\n * The date and time for which to calculate the heliocentric distance.\n *\n * @returns {number}\n * The heliocentric distance in AU.\n */",
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"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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],
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"type": "FunctionDeclaration",
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@@ -33234,14 +34485,14 @@
"comment": "",
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"comment": "",
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"comment": "",
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"comment": "",
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"comment": "",
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"comment": "",
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"comment": "",
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"funcscope": "MoonMagnitude",
@@ -33410,14 +34661,14 @@
"comment": "/**\n * @brief Information about the apparent brightness and sunlit phase of a celestial object.\n *\n * @property {AstroTime} time\n * The date and time pertaining to the other calculated values in this object.\n *\n * @property {number} mag\n * The apparent visual magnitude 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 * astronomical units (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 JPL Horizons 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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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+ "id": "astnode100018643",
"name": "IlluminationInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -33534,14 +34785,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
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+ "id": "astnode100018646",
"name": "IlluminationInfo",
"type": "MethodDefinition",
"paramnames": [
@@ -33570,14 +34821,14 @@
"comment": "/**\n * @brief Information about the apparent brightness and sunlit phase of a celestial object.\n *\n * @property {AstroTime} time\n * The date and time pertaining to the other calculated values in this object.\n *\n * @property {number} mag\n * The apparent visual magnitude 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 * astronomical units (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 JPL Horizons 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 */",
"meta": {
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],
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@@ -33693,14 +34944,14 @@
"comment": "",
"meta": {
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],
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"comment": "",
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],
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"name": "this.mag",
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],
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],
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"value": "helio_dist",
@@ -33793,14 +35044,14 @@
"comment": "",
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],
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@@ -33818,14 +35069,14 @@
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],
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],
"filename": "astronomy.js",
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"name": "this.hc",
"type": "Identifier",
"value": "hc",
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"comment": "",
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],
"filename": "astronomy.js",
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"comment": "",
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],
"filename": "astronomy.js",
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"name": "this.phase_fraction",
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"comment": "",
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],
"filename": "astronomy.js",
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"name": "exports.IlluminationInfo",
"type": "Identifier",
"value": "IlluminationInfo",
@@ -33942,14 +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": {
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],
"filename": "astronomy.js",
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"name": "Illumination",
"type": "FunctionDeclaration",
"paramnames": [
@@ -34016,14 +35267,14 @@
"comment": "",
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],
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"comment": "",
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],
"filename": "astronomy.js",
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"name": "earth",
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@@ -34066,14 +35317,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"name": "phase"
}
},
@@ -34089,14 +35340,14 @@
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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+ "id": "astnode100018763",
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}
},
@@ -34112,14 +35363,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -34135,14 +35386,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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}
},
@@ -34158,14 +35409,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -34184,14 +35435,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -34210,14 +35461,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -34236,14 +35487,14 @@
"comment": "",
"meta": {
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],
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@@ -34262,14 +35513,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -34314,14 +35565,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -34340,14 +35591,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"funcscope": "Illumination",
@@ -34366,14 +35617,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"value": ""
@@ -34391,14 +35642,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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"value": ""
@@ -34416,14 +35667,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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"name": "ring_tilt"
}
},
@@ -34439,14 +35690,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -34465,14 +35716,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"comment": "",
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+ "id": "astnode100019269",
"name": "exports.SearchRelativeLongitude",
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@@ -35295,14 +36546,14 @@
"comment": "/**\n * @brief Determines the moon's phase expressed as an ecliptic longitude.\n *\n * @param {FlexibleDateTime} date\n * The date and time for which to calculate the moon's phase.\n *\n * @returns {number}\n * A value in the range [0, 360) indicating the difference\n * in ecliptic longitude between the center of the Sun and the\n * center of the Moon, as seen from the center of the Earth.\n * Certain longitude values have conventional meanings:\n *\n * * 0 = new moon\n * * 90 = first quarter\n * * 180 = full moon\n * * 270 = third quarter\n */",
"meta": {
"range": [
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],
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+ "id": "astnode100019274",
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"comment": "",
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- "id": "astnode100018274",
+ "id": "astnode100019289",
"name": "exports.MoonPhase",
"type": "Identifier",
"value": "MoonPhase",
@@ -35372,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100018279",
+ "id": "astnode100019294",
"name": "SearchMoonPhase",
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@@ -35457,14 +36708,14 @@
"comment": "",
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- "id": "astnode100018285",
+ "id": "astnode100019300",
"name": "moon_offset",
"type": "FunctionDeclaration",
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@@ -35487,14 +36738,14 @@
"comment": "",
"meta": {
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],
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@@ -35512,14 +36763,14 @@
"comment": "",
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],
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@@ -35537,14 +36788,14 @@
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],
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"comment": "",
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],
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"comment": "",
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@@ -35613,14 +36864,14 @@
"comment": "",
"meta": {
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],
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@@ -35638,14 +36889,14 @@
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@@ -35663,14 +36914,14 @@
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@@ -35688,14 +36939,14 @@
"comment": "",
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],
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@@ -35713,14 +36964,14 @@
"comment": "",
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@@ -35738,14 +36989,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100018388",
+ "id": "astnode100019403",
"name": "exports.SearchMoonPhase",
"type": "Identifier",
"value": "SearchMoonPhase",
@@ -35762,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100018393",
+ "id": "astnode100019408",
"name": "MoonQuarter",
"type": "ClassDeclaration",
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@@ -35816,14 +37067,14 @@
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"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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],
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"comment": "",
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"range": [
- 183566,
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
"range": [
- 183592,
- 183625
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],
"filename": "astronomy.js",
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"name": "exports.MoonQuarter",
"type": "Identifier",
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@@ -35973,14 +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 */",
"meta": {
"range": [
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"filename": "astronomy.js",
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"value": ""
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"comment": "",
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"filename": "astronomy.js",
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@@ -36106,14 +37357,14 @@
"comment": "",
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],
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"name": "exports.SearchMoonQuarter",
"type": "Identifier",
"value": "SearchMoonQuarter",
@@ -36155,14 +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": [
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -36226,14 +37477,14 @@
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],
"filename": "astronomy.js",
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"name": "exports.NextMoonQuarter",
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"value": "NextMoonQuarter",
@@ -36250,14 +37501,14 @@
"comment": "",
"meta": {
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],
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@@ -36276,14 +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": [
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"comment": "",
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],
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],
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"comment": "",
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"filename": "astronomy.js",
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"comment": "",
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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"name": "exports.SearchRiseSet",
"type": "Identifier",
"value": "SearchRiseSet",
@@ -36530,14 +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": [
- 190312,
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
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],
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@@ -36668,14 +37919,14 @@
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],
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@@ -36693,14 +37944,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -36718,14 +37969,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100018680",
+ "id": "astnode100019695",
"name": "exports.SearchAltitude",
"type": "Identifier",
"value": "SearchAltitude",
@@ -36742,14 +37993,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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+ "id": "astnode100019700",
"name": "InternalSearchAltitude",
"type": "FunctionDeclaration",
"paramnames": [
@@ -36784,14 +38035,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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"name": "ha_before"
}
},
@@ -36807,14 +38058,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -36830,14 +38081,14 @@
"comment": "",
"meta": {
"range": [
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],
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"funcscope": "InternalSearchAltitude",
@@ -36856,14 +38107,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"funcscope": "InternalSearchAltitude",
@@ -36882,14 +38133,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
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"name": "ha_before",
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"funcscope": "InternalSearchAltitude",
@@ -36908,14 +38159,14 @@
"comment": "",
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"range": [
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],
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"funcscope": "InternalSearchAltitude",
@@ -36934,14 +38185,14 @@
"comment": "",
"meta": {
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],
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"code": {
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"value": ""
@@ -36959,14 +38210,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100018765",
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"name": "time_before"
}
},
@@ -36982,14 +38233,14 @@
"comment": "",
"meta": {
"range": [
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],
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"columnno": 8,
"code": {
- "id": "astnode100018768",
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"name": "evt_before"
}
},
@@ -37005,14 +38256,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100018771",
+ "id": "astnode100019786",
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}
},
@@ -37028,14 +38279,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100018774",
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@@ -37053,14 +38304,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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- "id": "astnode100018780",
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},
@@ -37076,14 +38327,14 @@
"comment": "",
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],
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"funcscope": "InternalSearchAltitude",
@@ -37102,14 +38353,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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"funcscope": "InternalSearchAltitude",
@@ -37128,14 +38379,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"columnno": 8,
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@@ -37154,14 +38405,14 @@
"comment": "",
"meta": {
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],
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"name": "time_before",
"type": "Identifier",
"funcscope": "InternalSearchAltitude",
@@ -37180,14 +38431,14 @@
"comment": "",
"meta": {
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"comment": "/**\n * @brief Finds when a body will reach a given hour angle.\n *\n * Finds the next time the given body is seen to reach the specified\n * hour angle\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 * sidereal\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 * meridian.\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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"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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"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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"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": {
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"comment": "/**\n * @brief The viewing conditions of a body relative to the Sun.\n *\n * Represents the angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n *\n * @property {AstroTime} time\n * The date and time of the observation.\n *\n * @property {string} visibility\n * Either `\"morning\"` or `\"evening\"`,\n * indicating when the body is most easily seen.\n *\n * @property {number} elongation\n * The angle in degrees, as seen from the center of the Earth,\n * of the apparent separation between the body and the Sun.\n * This angle is measured in 3D space and is not projected onto the ecliptic plane.\n * When `elongation` is less than a few degrees, the body is very\n * difficult to see from the Earth because it is lost in the Sun's glare.\n * The elongation is always in the range [0, 180].\n *\n * @property {number} ecliptic_separation\n * The absolute value of the difference between the body's ecliptic longitude\n * and the Sun's ecliptic longitude, both as seen from the center of the Earth.\n * This angle measures around the plane of the Earth's orbit (the ecliptic),\n * and ignores how far above or below that plane the body is.\n * The ecliptic separation is measured in degrees and is always in the range [0, 180].\n *\n * @see {@link Elongation}\n */",
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"comment": "/**\n * @brief Calculates the viewing conditions of a body relative to the Sun.\n *\n * Calculates angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n * See the return type {@link ElongationEvent} for details.\n *\n * This function is helpful for determining how easy\n * it is to view a planet away from the Sun's glare on a given date.\n * It also determines whether the object is visible in the morning or evening;\n * this is more important the smaller the elongation is.\n * It is also used to determine how far a planet is from opposition, conjunction, or quadrature.\n *\n * @param {Body} body\n * The name of the observed body. Not allowed to be `\"Earth\"`.\n *\n * @returns {ElongationEvent}\n */",
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"comment": "",
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@@ -39203,14 +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 */",
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"comment": "",
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@@ -39688,14 +40939,14 @@
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"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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"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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@@ -46268,14 +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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@@ -46511,14 +47762,14 @@
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"meta": {
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@@ -46578,14 +47829,14 @@
"comment": "",
"meta": {
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"filename": "astronomy.js",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"funcscope": "InverseRefraction",
@@ -46654,14 +47905,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"name": "exports.InverseRefraction",
"type": "Identifier",
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@@ -46678,14 +47929,14 @@
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"meta": {
"range": [
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"filename": "astronomy.js",
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@@ -46741,14 +47992,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100022566",
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"name": "exports.RotateVector",
"type": "Identifier",
"value": "RotateVector",
@@ -46765,14 +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": {
"range": [
- 245727,
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],
"filename": "astronomy.js",
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"code": {
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"name": "RotateState",
"type": "FunctionDeclaration",
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@@ -46828,14 +48079,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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- "id": "astnode100022793",
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"name": "exports.RotateState",
"type": "Identifier",
"value": "RotateState",
@@ -46852,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"type": "FunctionDeclaration",
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@@ -46897,14 +48148,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -46922,14 +48173,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -46947,14 +48198,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
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"name": "exports.Rotation_EQJ_ECL",
"type": "Identifier",
"value": "Rotation_EQJ_ECL",
@@ -46971,14 +48222,14 @@
"comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @returns {RotationMatrix}\n * A rotation matrix that converts ECL to EQJ.\n */",
"meta": {
"range": [
- 247640,
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100022835",
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"name": "Rotation_ECL_EQJ",
"type": "FunctionDeclaration",
"paramnames": []
@@ -47016,14 +48267,14 @@
"comment": "",
"meta": {
"range": [
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],
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@@ -47041,14 +48292,14 @@
"comment": "",
"meta": {
"range": [
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],
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@@ -47066,14 +48317,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100022867",
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"name": "exports.Rotation_ECL_EQJ",
"type": "Identifier",
"value": "Rotation_ECL_EQJ",
@@ -47090,14 +48341,14 @@
"comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using equator at J2000 epoch.\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {FlexibleDateTime} time\n * The date and time at which the Earth's equator defines the target orientation.\n *\n * @returns {RotationMatrix}\n * A rotation matrix that converts EQJ to EQD at `time`.\n */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100022872",
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"name": "Rotation_EQJ_EQD",
"type": "FunctionDeclaration",
"paramnames": [
@@ -47148,14 +48399,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -47174,14 +48425,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -47199,14 +48450,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -47224,14 +48475,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100022906",
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"name": "exports.Rotation_EQJ_EQD",
"type": "Identifier",
"value": "Rotation_EQJ_EQD",
@@ -47248,14 +48499,14 @@
"comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @param {FlexibleDateTime} time\n * The date and time at which the Earth's equator defines the source orientation.\n *\n * @returns {RotationMatrix}\n * A rotation matrix that converts EQD at `time` to EQJ.\n */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100022911",
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"name": "Rotation_EQD_EQJ",
"type": "FunctionDeclaration",
"paramnames": [
@@ -47306,14 +48557,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -47332,14 +48583,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -47357,14 +48608,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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- "id": "astnode100022931",
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@@ -47382,14 +48633,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100022945",
+ "id": "astnode100023960",
"name": "exports.Rotation_EQD_EQJ",
"type": "Identifier",
"value": "Rotation_EQD_EQJ",
@@ -47406,14 +48657,14 @@
"comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: HOR = horizontal system.\n *\n * Use `HorizonFromVector` to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param {FlexibleDateTime} time\n * The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n * A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n * A rotation matrix that converts EQD to HOR at `time` and for `observer`.\n * The components of the horizontal vector are:\n * x = north, y = west, z = zenith (straight up from the observer).\n * These components are chosen so that the \"right-hand rule\" works for the vector\n * and so that north represents the direction where azimuth = 0.\n */",
"meta": {
"range": [
- 250792,
- 251587
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100022950",
+ "id": "astnode100023965",
"name": "Rotation_EQD_HOR",
"type": "FunctionDeclaration",
"paramnames": [
@@ -47483,14 +48734,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
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"funcscope": "Rotation_EQD_HOR",
@@ -47509,14 +48760,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100022962",
+ "id": "astnode100023977",
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"value": ""
@@ -47534,14 +48785,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100022976",
+ "id": "astnode100023991",
"name": "coslat",
"type": "CallExpression",
"value": ""
@@ -47559,14 +48810,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100022990",
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"name": "sinlon",
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"value": ""
@@ -47584,14 +48835,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100023004",
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"name": "coslon",
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"value": ""
@@ -47609,14 +48860,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100023018",
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"value": "[\"\",\"\",\"sinlat\"]"
@@ -47634,14 +48885,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100023029",
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"type": "ArrayExpression",
"value": "[\"\",\"\",\"coslat\"]"
@@ -47659,14 +48910,14 @@
"comment": "",
"meta": {
"range": [
- 251261,
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100023042",
+ "id": "astnode100024057",
"name": "uwe",
"type": "ArrayExpression",
"value": "[\"sinlon\",\"-coslon\",0]"
@@ -47684,14 +48935,14 @@
"comment": "",
"meta": {
"range": [
- 251299,
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+ 257477
],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100023050",
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@@ -47709,14 +48960,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100023059",
+ "id": "astnode100024074",
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"value": ""
@@ -47734,14 +48985,14 @@
"comment": "",
"meta": {
"range": [
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+ 257553
],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100023066",
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@@ -47759,14 +49010,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
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@@ -47784,14 +49035,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100023114",
+ "id": "astnode100024129",
"name": "exports.Rotation_EQD_HOR",
"type": "Identifier",
"value": "Rotation_EQD_HOR",
@@ -47808,14 +49059,14 @@
"comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: HOR = horizontal system (x=North, y=West, z=Zenith).\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {FlexibleDateTime} time\n * The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n * A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n * A rotation matrix that converts HOR to EQD at `time` and for `observer`.\n */",
"meta": {
"range": [
- 252335,
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"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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"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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"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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"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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"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 */",
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"filename": "astronomy.js",
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"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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"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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"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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"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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@@ -52242,14 +53493,14 @@
"comment": "",
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@@ -52267,14 +53518,14 @@
"comment": "",
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"filename": "astronomy.js",
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@@ -52292,14 +53543,14 @@
"comment": "",
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"filename": "astronomy.js",
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@@ -52317,14 +53568,14 @@
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@@ -52342,14 +53593,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -52367,14 +53618,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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"name": "MoonEclipticLatitudeDegrees",
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@@ -52396,14 +53647,14 @@
"comment": "",
"meta": {
"range": [
- 291069,
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@@ -52421,14 +53672,14 @@
"comment": "/**\n * @brief Searches for a lunar eclipse.\n *\n * This function finds the first lunar eclipse that occurs after `startTime`.\n * A lunar eclipse may be penumbral, partial, or total.\n * See {@link LunarEclipseInfo} for more information.\n * To find a series of lunar eclipses, call this function once,\n * then keep calling {@link NextLunarEclipse} as many times as desired,\n * passing in the `peak` value returned from the previous call.\n *\n * @param {FlexibleDateTime} date\n * The date and time for starting the search for a lunar eclipse.\n *\n * @returns {LunarEclipseInfo}\n */",
"meta": {
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"comment": "",
"meta": {
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@@ -52510,14 +53761,14 @@
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"filename": "astronomy.js",
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@@ -52535,14 +53786,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -52560,14 +53811,14 @@
"comment": "",
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"range": [
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],
"filename": "astronomy.js",
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@@ -52585,14 +53836,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -52610,14 +53861,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"code": {
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"value": "penumbral"
@@ -52660,14 +53911,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -52685,14 +53936,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -52735,14 +53986,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -52761,14 +54012,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -52787,14 +54038,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -52813,14 +54064,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"code": {
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"type": "CallExpression",
"funcscope": "SearchLunarEclipse",
@@ -52839,14 +54090,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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"name": "fmtime",
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"funcscope": "SearchLunarEclipse",
@@ -52865,14 +54116,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100026928",
+ "id": "astnode100027943",
"name": "exports.SearchLunarEclipse",
"type": "Identifier",
"value": "SearchLunarEclipse",
@@ -52889,14 +54140,14 @@
"comment": "/**\n * @brief Reports the time and geographic location of the peak of a solar eclipse.\n *\n * Returned by {@link SearchGlobalSolarEclipse} or {@link NextGlobalSolarEclipse}\n * to report information about a solar eclipse event.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, defined as\n * the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.\n *\n * The eclipse is classified as partial, annular, or total, depending on the\n * maximum amount of the Sun's disc obscured, as seen at the peak location\n * on the surface of the Earth.\n *\n * The `kind` field thus holds one of the strings `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.\n * An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface\n * to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.\n * A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth\n * observes either a total or annular eclipse.\n *\n * If `kind` is `\"total\"` or `\"annular\"`, the `latitude` and `longitude`\n * fields give the geographic coordinates of the center of the Moon's shadow projected\n * onto the daytime side of the Earth at the instant of the eclipse's peak.\n * If `kind` has any other value, `latitude` and `longitude` are undefined and should\n * not be used.\n *\n * @property {string} kind\n * One of the following string values: `\"partial\"`, `\"annular\"`, `\"total\"`.\n *\n * @property {AstroTime} peak\n * The date and time of the peak of the eclipse, defined as the instant\n * when the axis of the Moon's shadow cone passes closest to the Earth's center.\n *\n * @property {number} distance\n * The distance in kilometers between the axis of the Moon's shadow cone\n * and the center of the Earth at the time indicated by `peak`.\n *\n * @property {number | undefined} latitude\n * If `kind` holds `\"total\"`, the geographic latitude in degrees\n * where the center of the Moon's shadow falls on the Earth at the\n * time indicated by `peak`; otherwise, `latitude` holds `undefined`.\n *\n * @property {number | undefined} longitude\n * If `kind` holds `\"total\"`, the geographic longitude in degrees\n * where the center of the Moon's shadow falls on the Earth at the\n * time indicated by `peak`; otherwise, `longitude` holds `undefined`.\n */",
"meta": {
"range": [
- 296579,
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100026933",
+ "id": "astnode100027948",
"name": "GlobalSolarEclipseInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -52975,14 +54226,14 @@
"comment": "",
"meta": {
"range": [
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+ 302972
],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100026936",
+ "id": "astnode100027951",
"name": "GlobalSolarEclipseInfo",
"type": "MethodDefinition",
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@@ -53008,14 +54259,14 @@
"comment": "/**\n * @brief Reports the time and geographic location of the peak of a solar eclipse.\n *\n * Returned by {@link SearchGlobalSolarEclipse} or {@link NextGlobalSolarEclipse}\n * to report information about a solar eclipse event.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, defined as\n * the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.\n *\n * The eclipse is classified as partial, annular, or total, depending on the\n * maximum amount of the Sun's disc obscured, as seen at the peak location\n * on the surface of the Earth.\n *\n * The `kind` field thus holds one of the strings `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.\n * An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface\n * to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.\n * A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth\n * observes either a total or annular eclipse.\n *\n * If `kind` is `\"total\"` or `\"annular\"`, the `latitude` and `longitude`\n * fields give the geographic coordinates of the center of the Moon's shadow projected\n * onto the daytime side of the Earth at the instant of the eclipse's peak.\n * If `kind` has any other value, `latitude` and `longitude` are undefined and should\n * not be used.\n *\n * @property {string} kind\n * One of the following string values: `\"partial\"`, `\"annular\"`, `\"total\"`.\n *\n * @property {AstroTime} peak\n * The date and time of the peak of the eclipse, defined as the instant\n * when the axis of the Moon's shadow cone passes closest to the Earth's center.\n *\n * @property {number} distance\n * The distance in kilometers between the axis of the Moon's shadow cone\n * and the center of the Earth at the time indicated by `peak`.\n *\n * @property {number | undefined} latitude\n * If `kind` holds `\"total\"`, the geographic latitude in degrees\n * where the center of the Moon's shadow falls on the Earth at the\n * time indicated by `peak`; otherwise, `latitude` holds `undefined`.\n *\n * @property {number | undefined} longitude\n * If `kind` holds `\"total\"`, the geographic longitude in degrees\n * where the center of the Moon's shadow falls on the Earth at the\n * time indicated by `peak`; otherwise, `longitude` holds `undefined`.\n */",
"meta": {
"range": [
- 296579,
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+ 302974
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100026933",
+ "id": "astnode100027948",
"name": "GlobalSolarEclipseInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -53093,14 +54344,14 @@
"comment": "",
"meta": {
"range": [
- 296679,
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100026946",
+ "id": "astnode100027961",
"name": "this.kind",
"type": "Identifier",
"value": "kind",
@@ -53118,14 +54369,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100026952",
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"name": "this.peak",
"type": "Identifier",
"value": "peak",
@@ -53143,14 +54394,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100026958",
+ "id": "astnode100027973",
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"type": "Identifier",
"value": "distance",
@@ -53168,14 +54419,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100026964",
+ "id": "astnode100027979",
"name": "this.latitude",
"type": "Identifier",
"value": "latitude",
@@ -53193,14 +54444,14 @@
"comment": "",
"meta": {
"range": [
- 296799,
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100026970",
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"name": "this.longitude",
"type": "Identifier",
"value": "longitude",
@@ -53218,14 +54469,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100026976",
+ "id": "astnode100027991",
"name": "exports.GlobalSolarEclipseInfo",
"type": "Identifier",
"value": "GlobalSolarEclipseInfo",
@@ -53242,14 +54493,14 @@
"comment": "",
"meta": {
"range": [
- 296892,
- 297210
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+ 303350
],
"filename": "astronomy.js",
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+ "lineno": 7329,
"columnno": 0,
"code": {
- "id": "astnode100026981",
+ "id": "astnode100027996",
"name": "EclipseKindFromUmbra",
"type": "FunctionDeclaration",
"paramnames": [
@@ -53268,14 +54519,14 @@
"comment": "",
"meta": {
"range": [
- 297211,
- 301343
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+ 307483
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100026992",
+ "id": "astnode100028007",
"name": "GeoidIntersect",
"type": "FunctionDeclaration",
"paramnames": [
@@ -53327,14 +54578,14 @@
"comment": "",
"meta": {
"range": [
- 297253,
- 297269
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],
"filename": "astronomy.js",
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+ "lineno": 7336,
"columnno": 8,
"code": {
- "id": "astnode100026997",
+ "id": "astnode100028012",
"name": "kind",
"type": "Literal",
"value": "partial"
@@ -53352,14 +54603,14 @@
"comment": "",
"meta": {
"range": [
- 297279,
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],
"filename": "astronomy.js",
- "lineno": 7207,
+ "lineno": 7337,
"columnno": 8,
"code": {
- "id": "astnode100027001",
+ "id": "astnode100028016",
"name": "peak",
"type": "MemberExpression",
"value": "shadow.time"
@@ -53377,14 +54628,14 @@
"comment": "",
"meta": {
"range": [
- 297307,
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],
"filename": "astronomy.js",
- "lineno": 7208,
+ "lineno": 7338,
"columnno": 8,
"code": {
- "id": "astnode100027007",
+ "id": "astnode100028022",
"name": "distance",
"type": "MemberExpression",
"value": "shadow.r"
@@ -53402,14 +54653,14 @@
"comment": "",
"meta": {
"range": [
- 297336,
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100027013",
+ "id": "astnode100028028",
"name": "latitude"
}
},
@@ -53425,14 +54676,14 @@
"comment": "",
"meta": {
"range": [
- 297393,
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100027016",
+ "id": "astnode100028031",
"name": "longitude"
}
},
@@ -53448,14 +54699,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100027019",
+ "id": "astnode100028034",
"name": "rot",
"type": "CallExpression",
"value": ""
@@ -53473,14 +54724,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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+ "lineno": 7346,
"columnno": 10,
"code": {
- "id": "astnode100027027",
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"name": "v",
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"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": {
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],
"filename": "astronomy.js",
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"code": {
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@@ -54835,14 +56086,14 @@
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@@ -54865,14 +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": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027593",
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"name": "EclipseEvent",
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"comment": "",
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100027603",
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"name": "this.time",
"type": "Identifier",
"value": "time",
@@ -54943,14 +56194,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100027609",
+ "id": "astnode100028624",
"name": "this.altitude",
"type": "Identifier",
"value": "altitude",
@@ -54968,14 +56219,14 @@
"comment": "",
"meta": {
"range": [
- 306367,
- 306402
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+ 312542
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027615",
+ "id": "astnode100028630",
"name": "exports.EclipseEvent",
"type": "Identifier",
"value": "EclipseEvent",
@@ -54992,14 +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": [
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+ 314928,
+ 315259
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027620",
+ "id": "astnode100028635",
"name": "LocalSolarEclipseInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -55088,14 +56339,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100027623",
+ "id": "astnode100028638",
"name": "LocalSolarEclipseInfo",
"type": "MethodDefinition",
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@@ -55122,14 +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": [
- 308788,
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+ 314928,
+ 315259
],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027620",
+ "id": "astnode100028635",
"name": "LocalSolarEclipseInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -55217,14 +56468,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100027634",
+ "id": "astnode100028649",
"name": "this.kind",
"type": "Identifier",
"value": "kind",
@@ -55242,14 +56493,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100027640",
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"name": "this.partial_begin",
"type": "Identifier",
"value": "partial_begin",
@@ -55267,14 +56518,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"name": "this.total_begin",
"type": "Identifier",
"value": "total_begin",
@@ -55292,14 +56543,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100027652",
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"name": "this.peak",
"type": "Identifier",
"value": "peak",
@@ -55317,14 +56568,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"value": "total_end",
@@ -55342,14 +56593,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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"code": {
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"name": "this.partial_end",
"type": "Identifier",
"value": "partial_end",
@@ -55367,14 +56618,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027670",
+ "id": "astnode100028685",
"name": "exports.LocalSolarEclipseInfo",
"type": "Identifier",
"value": "LocalSolarEclipseInfo",
@@ -55391,14 +56642,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027675",
+ "id": "astnode100028690",
"name": "local_partial_distance",
"type": "FunctionDeclaration",
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@@ -55417,14 +56668,14 @@
"comment": "",
"meta": {
"range": [
- 309251,
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100027687",
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"name": "local_total_distance",
"type": "FunctionDeclaration",
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@@ -55443,14 +56694,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100027703",
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"name": "LocalEclipse",
"type": "FunctionDeclaration",
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@@ -55482,14 +56733,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100027709",
+ "id": "astnode100028724",
"name": "PARTIAL_WINDOW",
"type": "Literal",
"value": 0.2
@@ -55507,14 +56758,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"name": "TOTAL_WINDOW",
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"value": 0.01
@@ -55532,14 +56783,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"name": "peak",
"type": "CallExpression",
"value": ""
@@ -55557,14 +56808,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -55582,14 +56833,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -55607,14 +56858,14 @@
"comment": "",
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],
"filename": "astronomy.js",
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@@ -55632,14 +56883,14 @@
"comment": "",
"meta": {
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],
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@@ -55657,14 +56908,14 @@
"comment": "",
"meta": {
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],
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}
},
@@ -55680,14 +56931,14 @@
"comment": "",
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}
},
@@ -55703,14 +56954,14 @@
"comment": "",
"meta": {
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}
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@@ -55726,14 +56977,14 @@
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],
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"funcscope": "LocalEclipse",
@@ -55752,14 +57003,14 @@
"comment": "",
"meta": {
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],
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@@ -55778,14 +57029,14 @@
"comment": "",
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@@ -55804,14 +57055,14 @@
"comment": "",
"meta": {
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],
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@@ -55830,14 +57081,14 @@
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],
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@@ -55856,14 +57107,14 @@
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@@ -56051,14 +57302,14 @@
"comment": "",
"meta": {
"range": [
- 311075,
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],
"filename": "astronomy.js",
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- "id": "astnode100027925",
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"name": "SunAltitude",
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"paramnames": [
@@ -56082,14 +57333,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -56107,14 +57358,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -56132,14 +57383,14 @@
"comment": "/**\n * @brief Searches for a solar eclipse visible at a specific location 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 LocalSolarEclipseInfo} for more information.\n *\n * To find a series of solar eclipses, call this function once,\n * then keep calling {@link NextLocalSolarEclipse} as many times as desired,\n * passing in the `peak` value returned from the previous call.\n *\n * IMPORTANT: An eclipse reported by this function might be partly or\n * completely invisible to the observer due to the time of day.\n * See {@link LocalSolarEclipseInfo} for more information about this topic.\n *\n * @param {AstroTime} startTime\n * The date and time for starting the search for a solar eclipse.\n *\n * @param {Observer} observer\n * The geographic location of the observer.\n *\n * @returns {LocalSolarEclipseInfo}\n */",
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"range": [
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"filename": "astronomy.js",
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"comment": "",
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],
"filename": "astronomy.js",
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"value": 1.8
@@ -56227,14 +57478,14 @@
"comment": "",
"meta": {
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],
"filename": "astronomy.js",
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@@ -56252,14 +57503,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -56277,14 +57528,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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@@ -56302,14 +57553,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"comment": "",
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],
"filename": "astronomy.js",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"funcscope": "SearchLocalSolarEclipse",
@@ -56378,14 +57629,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100028057",
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"name": "exports.SearchLocalSolarEclipse",
"type": "Identifier",
"value": "SearchLocalSolarEclipse",
@@ -56402,14 +57653,14 @@
"comment": "/**\n * @brief Searches for the next local solar eclipse in a series.\n *\n * After using {@link SearchLocalSolarEclipse} 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 LocalSolarEclipseInfo} returned by the\n * previous call to `SearchLocalSolarEclipse` or `NextLocalSolarEclipse`\n * to find the next solar eclipse.\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 LocalSolarEclipseInfo} for more information.\n *\n * @param {AstroTime} prevEclipseTime\n * The date and time for starting the search for a solar eclipse.\n *\n * @param {Observer} observer\n * The geographic location of the observer.\n *\n * @returns {LocalSolarEclipseInfo}\n */",
"meta": {
"range": [
- 314841,
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],
"filename": "astronomy.js",
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"code": {
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"name": "NextLocalSolarEclipse",
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"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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@@ -56492,14 +57743,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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"name": "exports.NextLocalSolarEclipse",
"type": "Identifier",
"value": "NextLocalSolarEclipse",
@@ -56516,14 +57767,14 @@
"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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
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+ "id": "astnode100029101",
"name": "TransitInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -56590,14 +57841,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 4,
"code": {
- "id": "astnode100028089",
+ "id": "astnode100029104",
"name": "TransitInfo",
"type": "MethodDefinition",
"paramnames": [
@@ -56622,14 +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 */",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100028086",
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"name": "TransitInfo",
"type": "ClassDeclaration",
"paramnames": [
@@ -56695,14 +57946,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
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"name": "this.start",
"type": "Identifier",
"value": "start",
@@ -56720,14 +57971,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028104",
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"name": "this.peak",
"type": "Identifier",
"value": "peak",
@@ -56745,14 +57996,14 @@
"comment": "",
"meta": {
"range": [
- 316310,
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028110",
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"name": "this.finish",
"type": "Identifier",
"value": "finish",
@@ -56770,14 +58021,14 @@
"comment": "",
"meta": {
"range": [
- 316340,
- 316368
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028116",
+ "id": "astnode100029131",
"name": "this.separation",
"type": "Identifier",
"value": "separation",
@@ -56795,14 +58046,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100028122",
+ "id": "astnode100029137",
"name": "exports.TransitInfo",
"type": "Identifier",
"value": "TransitInfo",
@@ -56819,14 +58070,14 @@
"comment": "",
"meta": {
"range": [
- 316413,
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100028127",
+ "id": "astnode100029142",
"name": "PlanetShadowBoundary",
"type": "FunctionDeclaration",
"paramnames": [
@@ -56851,14 +58102,14 @@
"comment": "",
"meta": {
"range": [
- 316496,
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+ 322687
],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100028135",
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"name": "shadow",
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"value": ""
@@ -56876,14 +58127,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100028152",
+ "id": "astnode100029167",
"name": "PlanetTransitBoundary",
"type": "FunctionDeclaration",
"paramnames": [
@@ -56910,14 +58161,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100028161",
+ "id": "astnode100029176",
"name": "tx",
"type": "CallExpression",
"value": ""
@@ -56935,14 +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": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 0,
"code": {
- "id": "astnode100028182",
+ "id": "astnode100029197",
"name": "SearchTransit",
"type": "FunctionDeclaration",
"paramnames": [
@@ -57011,14 +58262,14 @@
"comment": "",
"meta": {
"range": [
- 317686,
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],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100028188",
+ "id": "astnode100029203",
"name": "threshold_angle",
"type": "Literal",
"value": 0.4
@@ -57036,14 +58287,14 @@
"comment": "",
"meta": {
"range": [
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+ 323933
],
"filename": "astronomy.js",
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"columnno": 10,
"code": {
- "id": "astnode100028192",
+ "id": "astnode100029207",
"name": "dt_days",
"type": "Literal",
"value": 1
@@ -57061,14 +58312,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028196",
+ "id": "astnode100029211",
"name": "planet_radius_km"
}
},
@@ -57084,14 +58335,14 @@
"comment": "",
"meta": {
"range": [
- 317933,
- 317958
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+ 324098
],
"filename": "astronomy.js",
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"columnno": 12,
"code": {
- "id": "astnode100028205",
+ "id": "astnode100029220",
"name": "planet_radius_km",
"type": "Literal",
"funcscope": "SearchTransit",
@@ -57110,14 +58361,14 @@
"comment": "",
"meta": {
"range": [
- 318016,
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],
"filename": "astronomy.js",
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"columnno": 12,
"code": {
- "id": "astnode100028214",
+ "id": "astnode100029229",
"name": "planet_radius_km",
"type": "Literal",
"funcscope": "SearchTransit",
@@ -57136,14 +58387,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028225",
+ "id": "astnode100029240",
"name": "search_time",
"type": "Identifier",
"value": "startTime"
@@ -57161,14 +58412,14 @@
"comment": "",
"meta": {
"range": [
- 318393,
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+ 324587
],
"filename": "astronomy.js",
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"columnno": 14,
"code": {
- "id": "astnode100028231",
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"name": "conj",
"type": "CallExpression",
"value": ""
@@ -57186,14 +58437,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100028239",
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"name": "conj_separation",
"type": "CallExpression",
"value": ""
@@ -57211,14 +58462,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 18,
"code": {
- "id": "astnode100028251",
+ "id": "astnode100029266",
"name": "shadow",
"type": "CallExpression",
"value": ""
@@ -57236,14 +58487,14 @@
"comment": "",
"meta": {
"range": [
- 319170,
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],
"filename": "astronomy.js",
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"columnno": 22,
"code": {
- "id": "astnode100028268",
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"name": "time_before",
"type": "CallExpression",
"value": ""
@@ -57261,14 +58512,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 22,
"code": {
- "id": "astnode100028279",
+ "id": "astnode100029294",
"name": "start",
"type": "CallExpression",
"value": ""
@@ -57286,14 +58537,14 @@
"comment": "",
"meta": {
"range": [
- 319346,
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],
"filename": "astronomy.js",
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"columnno": 22,
"code": {
- "id": "astnode100028292",
+ "id": "astnode100029307",
"name": "time_after",
"type": "CallExpression",
"value": ""
@@ -57311,14 +58562,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 22,
"code": {
- "id": "astnode100028303",
+ "id": "astnode100029318",
"name": "finish",
"type": "CallExpression",
"value": ""
@@ -57336,14 +58587,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 22,
"code": {
- "id": "astnode100028316",
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"name": "min_separation",
"type": "BinaryExpression",
"value": ""
@@ -57361,14 +58612,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"columnno": 8,
"code": {
- "id": "astnode100028336",
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"name": "search_time",
"type": "CallExpression",
"funcscope": "SearchTransit",
@@ -57387,14 +58638,14 @@
"comment": "",
"meta": {
"range": [
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],
"filename": "astronomy.js",
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"code": {
- "id": "astnode100028344",
+ "id": "astnode100029359",
"name": "exports.SearchTransit",
"type": "Identifier",
"value": "SearchTransit",
@@ -57411,14 +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": {
"range": [
- 320396,
- 320540
+ 326536,
+ 326680
],
"filename": "astronomy.js",
- "lineno": 7694,
+ "lineno": 7824,
"columnno": 0,
"code": {
- "id": "astnode100028349",
+ "id": "astnode100029364",
"name": "NextTransit",
"type": "FunctionDeclaration",
"paramnames": [
@@ -57476,14 +58727,14 @@
"comment": "",
"meta": {
"range": [
- 320452,
- 320494
+ 326592,
+ 326634
],
"filename": "astronomy.js",
- "lineno": 7695,
+ "lineno": 7825,
"columnno": 10,
"code": {
- "id": "astnode100028355",
+ "id": "astnode100029370",
"name": "startTime",
"type": "CallExpression",
"value": ""
@@ -57501,14 +58752,14 @@
"comment": "",
"meta": {
"range": [
- 320541,
- 320574
+ 326681,
+ 326714
],
"filename": "astronomy.js",
- "lineno": 7698,
+ "lineno": 7828,
"columnno": 0,
"code": {
- "id": "astnode100028368",
+ "id": "astnode100029383",
"name": "exports.NextTransit",
"type": "Identifier",
"value": "NextTransit",