diff --git a/README.md b/README.md index ae160932..caa522d1 100644 --- a/README.md +++ b/README.md @@ -189,7 +189,7 @@ of complexity. So I decided to create Astronomy Engine with the following engine - Support JavaScript, C, C#, and Python with the same algorithms, and verify them to produce identical results. (Kotlin support was added in 2022.) - No external dependencies! The code must not require anything outside the standard library for each language. -- Minified JavaScript code less than 120K. (The current size is 115573 bytes.) +- Minified JavaScript code less than 120K. (The current size is 116026 bytes.) - Accuracy always within 1 arcminute of results from NOVAS. - It would be well documented, relatively easy to use, and support a wide variety of common use cases. diff --git a/demo/browser/astronomy.browser.js b/demo/browser/astronomy.browser.js index fab536d3..435a4dca 100644 --- a/demo/browser/astronomy.browser.js +++ b/demo/browser/astronomy.browser.js @@ -35,8 +35,8 @@ 'use strict'; Object.defineProperty(exports, "__esModule", { value: true }); exports.GeoEmbState = exports.GeoMoonState = exports.EclipticGeoMoon = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverState = 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.SiderealTime = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.e_tilt = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.PlanetOrbitalPeriod = exports.DefineStar = exports.Body = exports.AngleBetween = exports.MassProduct = 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.AU_PER_LY = exports.KM_PER_AU = exports.C_AUDAY = void 0; -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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = 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 = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; -exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = void 0; +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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.Atmosphere = exports.AtmosphereInfo = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; +exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = void 0; /** * @brief The speed of light in AU/day. */ @@ -4826,6 +4826,70 @@ function NextMoonQuarter(mq) { return SearchMoonQuarter(date); } exports.NextMoonQuarter = NextMoonQuarter; +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +class AtmosphereInfo { + constructor(pressure, temperature, density) { + this.pressure = pressure; + this.temperature = temperature; + this.density = density; + } +} +exports.AtmosphereInfo = AtmosphereInfo; +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +function Atmosphere(elevationMeters) { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + let temperature; + let pressure; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065 * elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } + else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } + else { + temperature = T1 + 0.001 * (elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} +exports.Atmosphere = Atmosphere; function BodyRadiusAu(body) { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/demo/nodejs/astronomy.js b/demo/nodejs/astronomy.js index 357c34f0..5226fd13 100644 --- a/demo/nodejs/astronomy.js +++ b/demo/nodejs/astronomy.js @@ -34,8 +34,8 @@ 'use strict'; Object.defineProperty(exports, "__esModule", { value: true }); exports.GeoEmbState = exports.GeoMoonState = exports.EclipticGeoMoon = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverState = 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.SiderealTime = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.e_tilt = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.PlanetOrbitalPeriod = exports.DefineStar = exports.Body = exports.AngleBetween = exports.MassProduct = 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.AU_PER_LY = exports.KM_PER_AU = exports.C_AUDAY = void 0; -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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = 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 = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; -exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = void 0; +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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.Atmosphere = exports.AtmosphereInfo = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; +exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = void 0; /** * @brief The speed of light in AU/day. */ @@ -4825,6 +4825,70 @@ function NextMoonQuarter(mq) { return SearchMoonQuarter(date); } exports.NextMoonQuarter = NextMoonQuarter; +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +class AtmosphereInfo { + constructor(pressure, temperature, density) { + this.pressure = pressure; + this.temperature = temperature; + this.density = density; + } +} +exports.AtmosphereInfo = AtmosphereInfo; +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +function Atmosphere(elevationMeters) { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + let temperature; + let pressure; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065 * elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } + else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } + else { + temperature = T1 + 0.001 * (elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} +exports.Atmosphere = Atmosphere; function BodyRadiusAu(body) { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/demo/nodejs/calendar/astronomy.ts b/demo/nodejs/calendar/astronomy.ts index 91b68d2d..8a46e747 100644 --- a/demo/nodejs/calendar/astronomy.ts +++ b/demo/nodejs/calendar/astronomy.ts @@ -5364,6 +5364,73 @@ export function NextMoonQuarter(mq: MoonQuarter): MoonQuarter { return SearchMoonQuarter(date); } + +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +export class AtmosphereInfo { + constructor( + public pressure: number, + public temperature: number, + public density: number + ) {} +} + + +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +export function Atmosphere(elevationMeters: number): AtmosphereInfo { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + + let temperature: number; + let pressure: number; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065*elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } else { + temperature = T1 + 0.001*(elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} + + function BodyRadiusAu(body: Body): number { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/generate/template/astronomy.ts b/generate/template/astronomy.ts index 34f65e18..57072056 100644 --- a/generate/template/astronomy.ts +++ b/generate/template/astronomy.ts @@ -4436,6 +4436,73 @@ export function NextMoonQuarter(mq: MoonQuarter): MoonQuarter { return SearchMoonQuarter(date); } + +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +export class AtmosphereInfo { + constructor( + public pressure: number, + public temperature: number, + public density: number + ) {} +} + + +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +export function Atmosphere(elevationMeters: number): AtmosphereInfo { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + + let temperature: number; + let pressure: number; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065*elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } else { + temperature = T1 + 0.001*(elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} + + function BodyRadiusAu(body: Body): number { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/generate/test.js b/generate/test.js index 91411ab4..f6eee0cb 100644 --- a/generate/test.js +++ b/generate/test.js @@ -3511,13 +3511,61 @@ function HourAngleTest() { } } - return Pass(`JS HourAngleTest (${context.cases} cases, maxdiff = ${context.maxdiff.toExponential(4)})`); + return Pass(`HourAngleTest (${context.cases} cases, maxdiff = ${context.maxdiff.toExponential(4)})`); +} + +//------------------------------------------------------------------------------------------------- + +function Atmosphere() { + const filename = 'riseset/atmosphere.csv'; + const lines = ReadLines(filename); + const tolerance = 8.8e-11; + let lnum = 0; + let ncases = 0; + let maxdiff = 0.0; + for (let line of lines) { + ++lnum; + if (lnum === 1) { + if (line != "elevation,temperature,pressure,density,relative_density") + Fail(`Atmosphere: Expected header line, but found: [${line}]`); + } else { + const tokens = line.split(','); + if (tokens.length !== 5) + Fail(`Atmosphere(${filename} line ${line}): expected 5 numeric tokens but found ${tokens.length}`); + + const elevation = float(tokens[0]); + const temperature = float(tokens[1]); + const pressure = float(tokens[2]); + // ignore tokens[3] = absolute_density + const relative_density = float(tokens[4]); + + const atmos = Astronomy.Atmosphere(elevation); + + let diff = abs(atmos.temperature - temperature); + if (diff > maxdiff) maxdiff = diff; + if (diff > tolerance) Fail(`Atmosphere(${filename} line ${lnum}): EXCESSIVE temperature difference = ${diff}`); + + diff = abs(atmos.pressure - pressure); + if (diff > maxdiff) maxdiff = diff; + if (diff > tolerance) Fail(`Atmosphere(${filename} line ${lnum}): EXCESSIVE pressure difference = ${diff}`); + + diff = abs(atmos.density - relative_density); + if (diff > maxdiff) maxdiff = diff; + if (diff > tolerance) Fail(`Atmosphere(${filename} line ${lnum}): EXCESSIVE density difference = ${diff}`); + + ++ncases; + } + } + if (ncases !== 34) + Fail(`Atmosphere: expected 34 test cases but found ${ncases}.`); + return Pass('Atmosphere'); } //------------------------------------------------------------------------------------------------- const UnitTests = { aberration: AberrationTest, + atmosphere: Atmosphere, axis: AxisTest, barystate: BaryStateTest, constellation: Constellation, diff --git a/source/js/README.md b/source/js/README.md index e2a8c3b9..fab2e951 100644 --- a/source/js/README.md +++ b/source/js/README.md @@ -501,6 +501,22 @@ and the velocities in AU/day. | time | [AstroTime](#AstroTime) | The date and time of the quarter lunar phase. | +* * * + + + +## AtmosphereInfo +**Kind**: global class +**Brief**: Information about idealized atmospheric variables at a given elevation. +**Properties** + +| Name | Type | Description | +| --- | --- | --- | +| pressure | number | Atmospheric pressure in pascals. | +| temperature | number | Atmospheric temperature in kelvins. | +| density | number | Atmospheric density relative to sea level. | + + * * * @@ -1189,6 +1205,28 @@ contains the centers of the Earth, the Sun, and `body`. | date | [FlexibleDateTime](#FlexibleDateTime) | The time at which the angle from the Sun is to be found. | +* * * + + + +## Atmosphere(elevationMeters) ⇒ [AtmosphereInfo](#AtmosphereInfo) +**Kind**: global function +**Brief**: Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + +This function calculates idealized values of pressure, temperature, and density +using the U.S. Standard Atmosphere (1976) model. +1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. +2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. +See: +https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml +https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf +https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + +| Param | Type | Description | +| --- | --- | --- | +| elevationMeters | number | The elevation above sea level at which to calculate atmospheric variables. Must be in the range -500 to +100000, or an exception will occur. | + + * * * diff --git a/source/js/astronomy.browser.js b/source/js/astronomy.browser.js index fab536d3..435a4dca 100644 --- a/source/js/astronomy.browser.js +++ b/source/js/astronomy.browser.js @@ -35,8 +35,8 @@ 'use strict'; Object.defineProperty(exports, "__esModule", { value: true }); exports.GeoEmbState = exports.GeoMoonState = exports.EclipticGeoMoon = exports.GeoMoon = exports.Ecliptic = exports.ObserverGravity = exports.VectorObserver = exports.ObserverState = 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.SiderealTime = exports.Libration = exports.LibrationInfo = exports.CalcMoonCount = exports.e_tilt = exports.MakeTime = exports.AstroTime = exports.SetDeltaTFunction = exports.DeltaT_JplHorizons = exports.DeltaT_EspenakMeeus = exports.PlanetOrbitalPeriod = exports.DefineStar = exports.Body = exports.AngleBetween = exports.MassProduct = 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.AU_PER_LY = exports.KM_PER_AU = exports.C_AUDAY = void 0; -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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = 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 = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; -exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = void 0; +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.ApsisKind = exports.SearchPeakMagnitude = exports.SearchMaxElongation = exports.Elongation = exports.ElongationEvent = exports.Seasons = exports.SeasonInfo = exports.HourAngle = exports.SearchHourAngle = exports.HourAngleEvent = exports.SearchAltitude = exports.SearchRiseSet = exports.Atmosphere = exports.AtmosphereInfo = exports.NextMoonQuarter = exports.SearchMoonQuarter = exports.MoonQuarter = exports.SearchMoonPhase = exports.MoonPhase = exports.SearchRelativeLongitude = exports.Illumination = exports.IlluminationInfo = exports.EclipticLongitude = exports.AngleFromSun = exports.PairLongitude = exports.SearchSunLongitude = exports.Search = exports.HelioState = exports.BaryState = exports.GeoVector = exports.BackdatePosition = exports.CorrectLightTravel = exports.HelioDistance = exports.HelioVector = exports.JupiterMoons = exports.JupiterMoonsInfo = void 0; +exports.GravitySimulator = exports.LagrangePointFast = exports.LagrangePoint = exports.RotationAxis = exports.AxisInfo = exports.NextMoonNode = exports.SearchMoonNode = exports.NodeEventInfo = exports.NodeEventKind = 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.EclipseKind = exports.Constellation = exports.ConstellationInfo = exports.Rotation_EQD_ECT = exports.Rotation_ECT_EQD = 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_ECT_EQJ = exports.Rotation_EQJ_ECT = exports.Rotation_EQJ_EQD = exports.Rotation_ECL_EQJ = exports.Rotation_EQJ_ECL = exports.RotateState = exports.RotateVector = exports.InverseRefraction = exports.Refraction = void 0; /** * @brief The speed of light in AU/day. */ @@ -4826,6 +4826,70 @@ function NextMoonQuarter(mq) { return SearchMoonQuarter(date); } exports.NextMoonQuarter = NextMoonQuarter; +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +class AtmosphereInfo { + constructor(pressure, temperature, density) { + this.pressure = pressure; + this.temperature = temperature; + this.density = density; + } +} +exports.AtmosphereInfo = AtmosphereInfo; +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +function Atmosphere(elevationMeters) { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + let temperature; + let pressure; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065 * elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } + else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } + else { + temperature = T1 + 0.001 * (elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} +exports.Atmosphere = Atmosphere; function BodyRadiusAu(body) { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/source/js/astronomy.browser.min.js b/source/js/astronomy.browser.min.js index c344cde8..f5f56009 100644 --- a/source/js/astronomy.browser.min.js +++ b/source/js/astronomy.browser.min.js @@ -40,14 +40,14 @@ $jscomp.polyfill("Math.cbrt",function(r){return r?r:function(u){if(0===u)return (function(r){"object"===typeof exports&&"undefined"!==typeof module?module.exports=r():"function"===typeof define&&define.amd?define([],r):("undefined"!==typeof window?window:"undefined"!==typeof global?global:"undefined"!==typeof self?self:this).Astronomy=r()})(function(){return function(){function r(u,e,C){function A(N,T){if(!e[N]){if(!u[N]){var ka="function"==typeof require&&require;if(!T&&ka)return ka(N,!0);if(w)return w(N,!0);T=Error("Cannot find module '"+N+"'");throw T.code="MODULE_NOT_FOUND", T;}T=e[N]={exports:{}};u[N][0].call(T.exports,function(sa){return A(u[N][1][sa]||sa)},T,T.exports,r,u,e,C)}return e[N].exports}for(var w="function"==typeof require&&require,Q=0;QMath.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 T(a){a=jd.indexOf(a);return 0<=a?kd[a]:null}function ka(a){return(a=T(a))&&0b)return a=(b-1820)/100,-20+32*a*a; +Math.floor(a)}function N(a,b){var c=a.x*a.x+a.y*a.y+a.z*a.z;if(1E-8>Math.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 T(a){a=kd.indexOf(a);return 0<=a?ld[a]:null}function ka(a){return(a=T(a))&&0b)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 Vb(a){return a+Wb(a)/86400}function v(a){return a instanceof O?a:new O(a)}function Xb(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 da(a){if(!$a||1E-6=G;++G)0!==D[G]&&g(L.x,L.y,c(y,D[G],G),c(x,D[G],G),function(ta,ua){return L.x=ta,L.y=ua});return L}function k(D,G,P,fa,L,ta,ua,ub){L=l(L,ta,ua,ub);q+=D*L.y; -t+=G*L.y;ab+=P*L.x;va+=fa*L.x}++e.CalcMoonCount;a=a.tt/36525;var n,p,q,t,y=b(-6,6,1,4),x=b(-6,6,1,4);var z=a*a;var ab=t=q=0;var va=3422.7;var la=h(.19833+.05611*a);var ha=h(.27869+.04508*a);var V=h(.16827-.36903*a);var ba=h(.34734-5.37261*a);var La=h(.10498-5.37899*a);var bb=h(.42681-.41855*a),md=h(.14943-5.37511*a);var cb=.84*la+.31*ha+14.27*V+7.26*ba+.28*La+.24*bb;var wb=2.94*la+.31*ha+14.27*V+9.34*ba+1.12*La+.83*bb;var db=-6.4*la-1.89*bb;ha=.21*la+.31*ha+14.27*V-88.7*ba-15.3*La+.24*bb-1.86*md; +t+=G*L.y;ab+=P*L.x;va+=fa*L.x}++e.CalcMoonCount;a=a.tt/36525;var n,p,q,t,y=b(-6,6,1,4),x=b(-6,6,1,4);var z=a*a;var ab=t=q=0;var va=3422.7;var la=h(.19833+.05611*a);var ha=h(.27869+.04508*a);var V=h(.16827-.36903*a);var ba=h(.34734-5.37261*a);var La=h(.10498-5.37899*a);var bb=h(.42681-.41855*a),nd=h(.14943-5.37511*a);var cb=.84*la+.31*ha+14.27*V+7.26*ba+.28*La+.24*bb;var wb=2.94*la+.31*ha+14.27*V+9.34*ba+1.12*La+.83*bb;var db=-6.4*la-1.89*bb;ha=.21*la+.31*ha+14.27*V-88.7*ba-15.3*La+.24*bb-1.86*nd; V=cb-db;la=-3.332E-6*h(.59734-5.37261*a)-5.39E-7*h(.35498-5.37899*a)-6.4E-8*h(.39943-5.37511*a);cb=U*Q(.60643382+1336.85522467*a-3.13E-6*z)+cb/ia;wb=U*Q(.37489701+1325.55240982*a+2.565E-5*z)+wb/ia;db=U*Q(.99312619+99.99735956*a-4.4E-7*z)+db/ia;ha=U*Q(.25909118+1342.2278298*a-8.92E-6*z)+ha/ia;La=U*Q(.82736186+1236.85308708*a-3.97E-6*z)+V/ia;for(n=1;4>=n;++n){switch(n){case 1:V=wb;z=4;ba=1.000002208;break;case 2:V=db;z=3;ba=.997504612-.002495388*a;break;case 3:V=ha;z=4;ba=1.000002708+139.978*la;break; case 4:V=La;z=6;ba=1;break;default:throw"Internal error: I = "+n;}d(0,n,1);d(1,n,Math.cos(V)*ba);f(0,n,0);f(1,n,Math.sin(V)*ba);for(p=2;p<=z;++p)g(c(y,p-1,n),c(x,p-1,n),c(y,1,n),c(x,1,n),function(D,G){return d(p,n,D),f(p,n,G)});for(p=1;p<=z;++p)d(-p,n,c(y,p,n)),f(-p,n,-c(x,p,n))}k(13.902,14.06,-.001,.2607,0,0,0,4);k(.403,-4.01,.394,.0023,0,0,0,3);k(2369.912,2373.36,.601,28.2333,0,0,0,2);k(-125.154,-112.79,-.725,-.9781,0,0,0,1);k(1.979,6.98,-.445,.0433,1,0,0,4);k(191.953,192.72,.029,3.0861,1,0,0,2); k(-8.466,-13.51,.455,-.1093,1,0,0,1);k(22639.5,22609.07,.079,186.5398,1,0,0,0);k(18.609,3.59,-.094,.0118,1,0,0,-1);k(-4586.465,-4578.13,-.077,34.3117,1,0,0,-2);k(3.215,5.44,.192,-.0386,1,0,0,-3);k(-38.428,-38.64,.001,.6008,1,0,0,-4);k(-.393,-1.43,-.092,.0086,1,0,0,-6);k(-.289,-1.59,.123,-.0053,0,1,0,4);k(-24.42,-25.1,.04,-.3,0,1,0,2);k(18.023,17.93,.007,.1494,0,1,0,1);k(-668.146,-126.98,-1.302,-.3997,0,1,0,0);k(.56,.32,-.001,-.0037,0,1,0,-1);k(-165.145,-165.06,.054,1.9178,0,1,0,-2);k(-1.877,-6.46, @@ -57,12 +57,12 @@ k(-8.466,-13.51,.455,-.1093,1,0,0,1);k(22639.5,22609.07,.079,186.5398,1,0,0,0);k .1268,2,-1,0,0);k(-.352,-.37,.001,-.0028,2,-1,0,-1);k(-2.494,-1.17,-.003,-.0017,2,-1,0,-2);k(.36,.2,-.012,-.0043,2,-1,0,-4);k(-1.167,-1.25,.008,-.0106,1,2,0,0);k(-7.412,-6.12,.117,.0484,1,2,0,-2);k(-.311,-.65,-.032,.0044,1,2,0,-4);k(.757,1.82,-.105,.0112,1,-2,0,2);k(2.58,2.32,.027,.0196,1,-2,0,0);k(2.533,2.4,-.014,-.0212,1,-2,0,-2);k(-.344,-.57,-.025,.0036,0,3,0,-2);k(-.992,-.02,0,0,1,0,2,2);k(-45.099,-.02,0,-.001,1,0,2,0);k(-.179,-9.52,0,-.0833,1,0,2,-2);k(-.301,-.33,0,.0014,1,0,2,-4);k(-6.382,-3.37, 0,-.0481,1,0,-2,2);k(39.528,85.13,0,-.7136,1,0,-2,0);k(9.366,.71,0,-.0112,1,0,-2,-2);k(.202,.02,0,0,1,0,-2,-4);k(.415,.1,0,.0013,0,1,2,0);k(-2.152,-2.26,0,-.0066,0,1,2,-2);k(-1.44,-1.3,0,.0014,0,1,-2,2);k(.384,-.04,0,0,0,1,-2,-2);k(1.938,3.6,-.145,.0401,4,0,0,0);k(-.952,-1.58,.052,-.013,4,0,0,-2);k(-.551,-.94,.032,-.0097,3,1,0,0);k(-.482,-.57,.005,-.0045,3,1,0,-2);k(.681,.96,-.026,.0115,3,-1,0,0);k(-.297,-.27,.002,-9E-4,2,2,0,-2);k(.254,.21,-.003,0,2,-2,0,-2);k(-.25,-.22,.004,.0014,1,3,0,-2);k(-3.996, 0,0,4E-4,2,0,2,0);k(.557,-.75,0,-.009,2,0,2,-2);k(-.459,-.38,0,-.0053,2,0,-2,2);k(-1.298,.74,0,4E-4,2,0,-2,0);k(.538,1.14,0,-.0141,2,0,-2,-2);k(.263,.02,0,0,1,1,2,0);k(.426,.07,0,-6E-4,1,1,-2,-2);k(-.304,.03,0,3E-4,1,-1,2,0);k(-.372,-.19,0,-.0027,1,-1,-2,2);k(.418,0,0,0,0,0,4,0);k(-.33,-.04,0,0,3,0,2,0);z=-526.069*l(0,0,1,-2).y;z+=-3.352*l(0,0,1,-4).y;z+=44.297*l(1,0,1,-2).y;z+=-6*l(1,0,1,-4).y;z+=20.599*l(-1,0,1,0).y;z+=-30.598*l(-1,0,1,-2).y;z+=-24.649*l(-2,0,1,0).y;z+=-2*l(-2,0,1,-2).y;z+=-22.571* -l(0,1,1,-2).y;z+=10.985*l(0,-1,1,-2).y;q+=.82*h(.7736-62.5512*a)+.31*h(.0466-125.1025*a)+.35*h(.5785-25.1042*a)+.66*h(.4591+1335.8075*a)+.64*h(.313-91.568*a)+1.14*h(.148+1331.2898*a)+.21*h(.5918+1056.5859*a)+.44*h(.5784+1322.8595*a)+.24*h(.2275-5.7374*a)+.28*h(.2965+2.6929*a)+.33*h(.3132+6.3368*a);a=ha+t/ia;a=(1.000002708+139.978*la)*(18518.511+1.189+ab)*Math.sin(a)-6.24*Math.sin(3*a)+z;return{geo_eclip_lon:U*Q((cb+q/ia)/U),geo_eclip_lat:Math.PI/648E3*a,distance_au:ia*nd/(.999953253*va)}}function ac(a, +l(0,1,1,-2).y;z+=10.985*l(0,-1,1,-2).y;q+=.82*h(.7736-62.5512*a)+.31*h(.0466-125.1025*a)+.35*h(.5785-25.1042*a)+.66*h(.4591+1335.8075*a)+.64*h(.313-91.568*a)+1.14*h(.148+1331.2898*a)+.21*h(.5918+1056.5859*a)+.44*h(.5784+1322.8595*a)+.24*h(.2275-5.7374*a)+.28*h(.2965+2.6929*a)+.33*h(.3132+6.3368*a);a=ha+t/ia;a=(1.000002708+139.978*la)*(18518.511+1.189+ab)*Math.sin(a)-6.24*Math.sin(3*a)+z;return{geo_eclip_lon:U*Q((cb+q/ia)/U),geo_eclip_lat:Math.PI/648E3*a,distance_au:ia*od/(.999953253*va)}}function ac(a, b){return[a.rot[0][0]*b[0]+a.rot[1][0]*b[1]+a.rot[2][0]*b[2],a.rot[0][1]*b[0]+a.rot[1][1]*b[1]+a.rot[2][1]*b[2],a.rot[0][2]*b[0]+a.rot[1][2]*b[1]+a.rot[2][2]*b[2]]}function wa(a,b,c){b=Ma(b,c);return ac(b,a)}function Ma(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 g=((((-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 h=Math.sin(-f);f=Math.cos(-f);var l=Math.sin(-d);d=Math.cos(-d);var k=Math.sin(g),n=Math.cos(g);g=n*f-h*k*d;var p=n*h*c+k*d*f*c-a*k*l,q=n*h*a+k*d*f*a+c*k*l,t=-k*f-h*n*d,y=-k*h*c+n*d*f*c-a*n*l;k=-k*h*a+n*d*f*a+c*n*l;h*=l;n=-l*f*c-a*d;a=-l*f*a+d*c;if(b===F.Into2000)return new J([[g,p,q],[t,y,k],[h,n,a]]);if(b===F.From2000)return new J([[g,t,h],[p,y,n],[q,k,a]]);throw"Invalid precess direction";}function ca(a){if(!eb||eb.tt!== a.tt){var b=a.tt/36525,c=15*da(a).ee,d=(.779057273264+.00273781191135448*a.ut+a.ut%1)%1*360;0>d&&(d+=360);b=((c+.014506+((((-3.68E-8*b-2.9956E-5)*b-4.4E-7)*b+1.3915817)*b+4612.156534)*b)/3600+d)%360/15;0>b&&(b+=24);eb={tt:a.tt,st:b}}return eb.st}function bc(a){a=v(a);return ca(a)}function xb(a,b){var c=a.latitude*e.DEG2RAD,d=Math.sin(c);c=Math.cos(c);var f=1/Math.hypot(c,.996647180302104*d),g=a.height/1E3,h=6378.1366*f+g;b=(15*b+a.longitude)*e.DEG2RAD;a=Math.sin(b);b=Math.cos(b);return{pos:[h*c*b/ e.KM_PER_AU,h*c*a/e.KM_PER_AU,(6335.438815127603*f+g)*d/e.KM_PER_AU],vel:[-7.292115E-5*h*c*a*86400/e.KM_PER_AU,7.292115E-5*h*c*b*86400/e.KM_PER_AU,0]}}function xa(a,b,c){b=Na(b,c);return ac(b,a)}function Na(a,b){a=da(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 g=Math.cos(d),h=Math.sin(d);d=Math.cos(f);var l=Math.sin(f);f=-l*a;var k=-l*c,n=l*g,p=d*a*g+c*h,q=d*c*g-a*h;l*=h;var t=d*a*h-c*g;a=d*c*h+a*g;if(b===F.From2000)return new J([[d,n, -l],[f,p,t],[k,q,a]]);if(b===F.Into2000)return new J([[d,f,k],[n,p,q],[l,t,a]]);throw"Invalid precess direction";}function fb(a,b,c){return c===F.Into2000?wa(xa(a,b,c),b,c):xa(wa(a,b,c),b,c)}function cc(a,b){var c=ca(a);b=xb(b,c).pos;return fb(b,a,F.Into2000)}function od(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 yb(a,b){return new E(a[0],a[1], +l],[f,p,t],[k,q,a]]);if(b===F.Into2000)return new J([[d,f,k],[n,p,q],[l,t,a]]);throw"Invalid precess direction";}function fb(a,b,c){return c===F.Into2000?wa(xa(a,b,c),b,c):xa(wa(a,b,c),b,c)}function cc(a,b){var c=ca(a);b=xb(b,c).pos;return fb(b,a,F.Into2000)}function pd(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 yb(a,b){return new E(a[0],a[1], a[2],b)}function dc(a,b){b=yb(a,b);var c=b.x*b.x+b.y*b.y,d=Math.sqrt(c+b.z*b.z);if(0===c){if(0===b.z)throw"Indeterminate sky coordinates";return new gb(0,0>b.z?-90:90,d,b)}var f=e.RAD2HOUR*Math.atan2(b.y,b.x);0>f&&(f+=24);return new gb(f,e.RAD2DEG*Math.atan2(a[2],Math.sqrt(c)),d,b)}function ya(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 hb(a,b,c,d,f){a=v(a);za(b);w(c);w(d);var g=Math.sin(b.latitude*e.DEG2RAD),h=Math.cos(b.latitude*e.DEG2RAD), l=Math.sin(b.longitude*e.DEG2RAD),k=Math.cos(b.longitude*e.DEG2RAD);b=Math.sin(d*e.DEG2RAD);var n=Math.cos(d*e.DEG2RAD),p=Math.sin(c*e.HOUR2RAD),q=Math.cos(c*e.HOUR2RAD),t=[h*k,h*l,g];g=[-g*k,-g*l,h];l=[l,-k,0];h=-15*ca(a);a=ya(h,t);t=ya(h,g);l=ya(h,l);b=[n*q,n*p,b];p=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];n=b[0]*t[0]+b[1]*t[1]+b[2]*t[2];t=b[0]*l[0]+b[1]*l[1]+b[2]*l[2];q=Math.hypot(n,t);0n&&(n+=360)):n=0;p=e.RAD2DEG*Math.atan2(q,p);q=d;if(f&&(d=p,f=Oa(f,90-p),p-=f,0l;++l)f.push((b[l]-d*a[l])/t*c+a[l]*q);q=Math.hypot(f[0],f[1]);0c&&(c+=24)):c=0;q=e.RAD2DEG*Math.atan2(f[2],q)}return new ec(n,90-p,c,q)}function za(a){if(!(a instanceof zb))throw"Not an instance of the Observer class: "+a;w(a.latitude);w(a.longitude);w(a.height);if(-90>a.latitude||90d[1]&&(d[1]+=U);f=$jscomp.makeIterator(b.z);for(g=f.next();!g.done;g=f.next())h=$jscomp.makeIterator(g.value),g=h.next().value,l=h.next().value,h=h.next().value,l+=c*h,d[2]+=g*Math.cos(l),d[3]+=g*Math.sin(l);f=$jscomp.makeIterator(b.zeta);for(g=f.next();!g.done;g=f.next())h=$jscomp.makeIterator(g.value),g=h.next().value,l=h.next().value,h=h.next().value,l+=c*h,d[4]+=g*Math.cos(l),d[5]+=g*Math.sin(l);f=d[0];h=d[1]; -g=d[2];l=d[3];c=d[4];d=d[5];var k=Math.sqrt(b.mu/(f*f*f));b=h+g*Math.sin(h)-l*Math.cos(h);do{var n=Math.cos(b);var p=Math.sin(b);n=(h-b+g*p-l*n)/(1-g*n-l*p);b+=n}while(1E-12<=Math.abs(n));n=Math.cos(b);p=Math.sin(b);h=l*n-g*p;var q=-g*n-l*p,t=1/(1+q),y=1/(1+Math.sqrt(1-g*g-l*l));b=f*(n-g-y*l*h);h=f*(p-l+y*g*h);l=k*t*f*(-p-y*l*q);f=k*t*f*(+n+y*g*q);g=2*Math.sqrt(1-c*c-d*d);k=1-2*d*d;n=1-2*c*c;p=2*d*c;a=new I(b*k+h*p,b*p+h*n,(c*h-b*d)*g,l*k+f*p,l*p+f*n,(c*f-l*d)*g,a);return Ea(pd,a)}function Z(a,b){b= +g=d[2];l=d[3];c=d[4];d=d[5];var k=Math.sqrt(b.mu/(f*f*f));b=h+g*Math.sin(h)-l*Math.cos(h);do{var n=Math.cos(b);var p=Math.sin(b);n=(h-b+g*p-l*n)/(1-g*n-l*p);b+=n}while(1E-12<=Math.abs(n));n=Math.cos(b);p=Math.sin(b);h=l*n-g*p;var q=-g*n-l*p,t=1/(1+q),y=1/(1+Math.sqrt(1-g*g-l*l));b=f*(n-g-y*l*h);h=f*(p-l+y*g*h);l=k*t*f*(-p-y*l*q);f=k*t*f*(+n+y*g*q);g=2*Math.sqrt(1-c*c-d*d);k=1-2*d*d;n=1-2*c*c;p=2*d*c;a=new I(b*k+h*p,b*p+h*n,(c*h-b*d)*g,l*k+f*p,l*p+f*n,(c*f-l*d)*g,a);return Ea(qd,a)}function Z(a,b){b= v(b);if(a in M)return Aa(M[a],b);if(a===m.Pluto)return a=Hb(b,!0),new E(a.x,a.y,a.z,b);if(a===m.Sun)return new E(0,0,0,b);if(a===m.Moon){a=Aa(M.Earth,b);var c=Y(b);return new E(a.x+c.x,a.y+c.y,a.z+c.z,b)}if(a===m.EMB)return a=Aa(M.Earth,b),c=Y(b),new E(a.x+c.x/82.30056,a.y+c.y/82.30056,a.z+c.z/82.30056,b);if(a===m.SSB)return a=new E(0,0,0,b),jb(a,b,m.Jupiter,2.825345909524226E-7),jb(a,b,m.Saturn,8.459715185680659E-8),jb(a,b,m.Uranus,1.292024916781969E-8),jb(a,b,m.Neptune,1.524358900784276E-8),a;if(c= ka(a))return a=new Ba(c.dec,15*c.ra,c.dist),lb(a,b);throw'HelioVector: Unknown body "'+a+'"';}function oa(a,b){var c=ka(a);if(c)return c.dist;b=v(b);return a in M?ma(M[a][2],b.tt/365250,!1):Z(a,b).Length()}function lc(a,b){for(var c=b,d=0,f=0;10>f;++f){var g=a(c);d=g.Length()/e.C_AUDAY;if(1d)return g;c=h}throw"Light-travel time solver did not converge: dt = "+d;}function mc(a,b,c,d){A(d);a=v(a); if(ka(c)){c=Z(c,a);if(d)return b=mb(b,a),d=new E(c.x-b.x,c.y-b.y,c.z-b.z,a),c=e.C_AUDAY/d.Length(),new E(d.x+b.vx/c,d.y+b.vy/c,d.z+b.vz/c,a);b=Z(b,a);return new E(c.x-b.x,c.y-b.y,c.z-b.z,a)}var f=d?new E(0,0,0,a):Z(b,a);var g=new nc(b,c,d,f);return lc(function(h){return g.Position(h)},a)}function W(a,b,c){A(c);b=v(b);switch(a){case m.Earth:return new E(0,0,0,b);case m.Moon:return Y(b);default:return a=mc(b,m.Earth,a,c),a.t=b,a}}function pa(a,b){return new I(a.r.x,a.r.y,a.r.z,a.v.x,a.v.y,a.v.z,b)} function mb(a,b){b=v(b);switch(a){case m.Sun:return new I(0,0,0,0,0,0,b);case m.SSB:return a=new Da(b.tt),new I(-a.Sun.r.x,-a.Sun.r.y,-a.Sun.r.z,-a.Sun.v.x,-a.Sun.v.y,-a.Sun.v.z,b);case m.Mercury:case m.Venus:case m.Earth:case m.Mars:case m.Jupiter:case m.Saturn:case m.Uranus:case m.Neptune:return a=Sa(M[a],b.tt),pa(a,b);case m.Pluto:return Hb(b,!0);case m.Moon:case m.EMB:var c=Sa(M.Earth,b.tt);a=a==m.Moon?Ra(b):Bb(b);return new I(a.x+c.r.x,a.y+c.r.y,a.z+c.r.z,a.vx+c.v.x,a.vy+c.v.y,a.vz+c.v.z,b); -default:if(ka(a))return a=Z(a,b),new I(a.x,a.y,a.z,0,0,0,b);throw'HelioState: Unsupported body "'+a+'"';}}function qd(a,b,c,d,f){var g=(f+c)/2-d;c=(f-c)/2;if(0==g){if(0==c)return null;d=-d/c;if(-1>d||1=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*g);f=(-c-f)/(2*g);if(-1<=d&&1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{t:a+d*b,df_dt:(2*g*d+c)/b}}function K(a,b,c,d){var f=w(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var g=d&& -d.init_f1||a(b),h=d&&d.init_f2||a(c),l=NaN,k=0;d=d&&d.iter_limit||20;for(var n=!0;;){if(++k>d)throw"Excessive iteration in Search()";var p=new O(b.ut+.5*(c.ut-b.ut)),q=p.ut-b.ut;if(Math.abs(q)(q.ut-b.ut)*(q.ut-c.ut)&&0>(y.ut-b.ut)*(y.ut-c.ut))){t=a(q);var z=a(y);if(0>t&&0<=z){g=t;h=z;b=q;c=y;l=x; +default:if(ka(a))return a=Z(a,b),new I(a.x,a.y,a.z,0,0,0,b);throw'HelioState: Unsupported body "'+a+'"';}}function rd(a,b,c,d,f){var g=(f+c)/2-d;c=(f-c)/2;if(0==g){if(0==c)return null;d=-d/c;if(-1>d||1=d)return null;f=Math.sqrt(d);d=(-c+f)/(2*g);f=(-c-f)/(2*g);if(-1<=d&&1>=d){if(-1<=f&&1>=f)return null}else if(-1<=f&&1>=f)d=f;else return null}return{t:a+d*b,df_dt:(2*g*d+c)/b}}function K(a,b,c,d){var f=w(d&&d.dt_tolerance_seconds||1);f=Math.abs(f/86400);var g=d&& +d.init_f1||a(b),h=d&&d.init_f2||a(c),l=NaN,k=0;d=d&&d.iter_limit||20;for(var n=!0;;){if(++k>d)throw"Excessive iteration in Search()";var p=new O(b.ut+.5*(c.ut-b.ut)),q=p.ut-b.ut;if(Math.abs(q)(q.ut-b.ut)*(q.ut-c.ut)&&0>(y.ut-b.ut)*(y.ut-c.ut))){t=a(q);var z=a(y);if(0>t&&0<=z){g=t;h=z;b=q;c=y;l=x; n=!1;continue}}}}if(0>g&&0<=l)c=p,h=l;else if(0>l&&0<=h)b=p,g=l;else return null}}function Fa(a){for(;-180>=a;)a+=360;for(;180a;)a+=360;for(;360<=a;)a-=360;return a}function oc(a,b,c){w(a);w(c);b=v(b);c=b.AddDays(c);return K(function(d){d=fc(d);return Fa(d.elon-a)},b,c,{dt_tolerance_seconds:.01})}function Jb(a,b,c){if(a===m.Earth||b===m.Earth)throw"The Earth does not have a longitude as seen from itself.";c=v(c);a=W(a,c,!1);a=Qa(a);b=W(b,c,!1);b=Qa(b);return Ga(a.elon- b.elon)}function Ha(a,b){if(a==m.Earth)throw"The Earth does not have an angle as seen from itself.";var c=v(b);b=W(m.Sun,c,!0);a=W(a,c,!0);return N(b,a)}function qa(a,b){if(a===m.Sun)throw"Cannot calculate heliocentric longitude of the Sun.";a=Z(a,b);return Qa(a).elon}function nb(a,b){if(a===m.Earth)throw"The illumination of the Earth is not defined.";var c=v(b),d=Aa(M.Earth,c);if(a===m.Sun){var f=new E(-d.x,-d.y,-d.z,c);b=new E(0,0,0,c);d=0}else a===m.Moon?(f=Y(c),b=new E(d.x+f.x,d.y+f.y,d.z+f.z, -c)):(b=Z(a,b),f=new E(b.x-d.x,b.y-d.y,b.z-d.z,c)),d=N(f,b);var g=f.Length(),h=b.Length();if(a===m.Sun)var l=rd+5*Math.log10(g);else if(a===m.Moon)a=d*e.DEG2RAD,l=a*a,a=-12.717+1.49*Math.abs(a)+.0431*l*l,l=a+=5*Math.log10(g/(385000.6/e.KM_PER_AU)*h);else if(a===m.Saturn){var k=d;a=Qa(f);l=28.06*e.DEG2RAD;var n=e.DEG2RAD*a.elat;a=Math.asin(Math.sin(n)*Math.cos(l)-Math.cos(n)*Math.sin(l)*Math.sin(e.DEG2RAD*a.elon-e.DEG2RAD*(169.51+3.82E-5*c.tt)));l=Math.sin(Math.abs(a));k=-9+.044*k+l*(-2.6+1.2*l)+5* +c)):(b=Z(a,b),f=new E(b.x-d.x,b.y-d.y,b.z-d.z,c)),d=N(f,b);var g=f.Length(),h=b.Length();if(a===m.Sun)var l=sd+5*Math.log10(g);else if(a===m.Moon)a=d*e.DEG2RAD,l=a*a,a=-12.717+1.49*Math.abs(a)+.0431*l*l,l=a+=5*Math.log10(g/(385000.6/e.KM_PER_AU)*h);else if(a===m.Saturn){var k=d;a=Qa(f);l=28.06*e.DEG2RAD;var n=e.DEG2RAD*a.elat;a=Math.asin(Math.sin(n)*Math.cos(l)-Math.cos(n)*Math.sin(l)*Math.sin(e.DEG2RAD*a.elon-e.DEG2RAD*(169.51+3.82E-5*c.tt)));l=Math.sin(Math.abs(a));k=-9+.044*k+l*(-2.6+1.2*l)+5* Math.log10(h*g);a*=e.RAD2DEG;l=k;k=a}else{var p=n=l=0;switch(a){case m.Mercury:a=-.6;l=4.98;n=-4.88;p=3.02;break;case m.Venus:163.6>d?(a=-4.47,l=1.03,n=.57,p=.13):(a=.98,l=-1.02);break;case m.Mars:a=-1.52;l=1.6;break;case m.Jupiter:a=-9.4;l=.5;break;case m.Uranus:a=-7.19;l=.25;break;case m.Neptune:a=-6.87;break;case m.Pluto:a=-1;l=4;break;default:throw"VisualMagnitude: unsupported body "+a;}var q=d/100;l=a+q*(l+q*(n+q*p))+5*Math.log10(h*g)}return new pc(c,l,d,h,g,f,b,k)}function Va(a){if(a===m.Earth)throw"The Earth does not have a synodic period as seen from itself."; if(a===m.Moon)return 29.530588;var b=aa[a];if(!b)throw"Not a valid planet name: "+a;a=aa.Earth.OrbitalPeriod;return Math.abs(a/(a/b.OrbitalPeriod-1))}function Ia(a,b,c){function d(n){var p=qa(a,n);n=qa(m.Earth,n);return Fa(g*(n-p)-b)}w(b);var f=aa[a];if(!f)throw"Cannot search relative longitude because body is not a planet: "+a;if(a===m.Earth)throw"Cannot search relative longitude for the Earth (it is always 0)";var g=f.OrbitalPeriod>aa.Earth.OrbitalPeriod?1:-1;f=Va(a);c=v(c);var h=d(c);0l;++l){var k=-h/360*f;c=c.AddDays(k);if(1>86400*Math.abs(k))return c;k=h;h=d(c);30>Math.abs(k)&&k!==h&&(k/=k-h,.5k&&(f*=k))}throw"Relative longitude search failed to converge for "+a+" near "+c.toString()+" (error_angle = "+h+").";}function Kb(a){return Jb(m.Moon,m.Sun,a)}function Wa(a,b,c){function d(l){l=Kb(l);return Fa(l-a)}w(a);w(c);b=v(b);var f=d(b);if(0>c){0>f&&(f+=360);var g=-(29.530588*f)/360;f=g+1.5;if(fc)return null;f=Math.min(c,g+1.5)}c=b.AddDays(h);b=b.AddDays(f);return K(d,c,b,{dt_tolerance_seconds:.1})}function qc(a){var b=Kb(a);b=(Math.floor(b/90)+1)%4;a=Wa(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new rc(b,a)}function Lb(a,b,c,d,f,g,h){if(0>g&&0<=h)return new sd(d,f,g,h);if(0<=g&&0>h)return null;if(1786400*l||Math.min(Math.abs(g),Math.abs(h))>l/2*c)return null;l=new O((d.ut+ -f.ut)/2);var k=b(l);return Lb(1+a,b,c,d,l,g,k)||Lb(1+a,b,c,l,f,k,h)}function td(a,b){if(-90>b||90h||90f?(n=p.AddDays(-.42),q=l(n)):(p=n.AddDays(.42),t=l(p));var y=Lb(0,l,k,n, +g=-(29.530588*f)/360;h=g-1.5;if(h>c)return null;f=Math.min(c,g+1.5)}c=b.AddDays(h);b=b.AddDays(f);return K(d,c,b,{dt_tolerance_seconds:.1})}function qc(a){var b=Kb(a);b=(Math.floor(b/90)+1)%4;a=Wa(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new rc(b,a)}function Lb(a,b,c,d,f,g,h){if(0>g&&0<=h)return new td(d,f,g,h);if(0<=g&&0>h)return null;if(1786400*l||Math.min(Math.abs(g),Math.abs(h))>l/2*c)return null;l=new O((d.ut+ +f.ut)/2);var k=b(l);return Lb(1+a,b,c,d,l,g,k)||Lb(1+a,b,c,l,f,k,h)}function ud(a,b){if(-90>b||90h||90f?(n=p.AddDays(-.42),q=l(n)):(p=n.AddDays(.42),t=l(p));var y=Lb(0,l,k,n, p,q,t);if(y){if(k=K(l,y.tx,y.ty,{dt_tolerance_seconds:.1,init_f1:y.ax,init_f2:y.ay})){if(0>f){if(k.utd.ut+f)return null;return k}throw"Rise/set search failed after finding ascent: t1="+n+", t2="+p+", a1="+q+", a2="+t;}if(0>f){if(n.utd.ut+f)return null;n=p;q=t}}}function tc(a,b){b=v(b);var c=Jb(a,m.Sun,b);if(1805*f;++f){var g=a.AddDays(5),h=b(g);if(0>=d*h){if(0>d||0h){a=K(c,a,g,{init_f1:-d,init_f2:-h});if(!a)throw"SearchLunarApsis INTERNAL ERROR: apogee search failed!";d=ea(a).distance_au;return new Xa(a,1,d)}throw"SearchLunarApsis INTERNAL ERROR: cannot classify apsis event!"; -}a=g;d=h}throw"SearchLunarApsis INTERNAL ERROR: could not find apsis within 2 synodic months of start date.";}function wc(a,b,c,d){for(var f=b===Ja.Apocenter?1:-1;;){d/=9;if(d<1/1440)return c=c.AddDays(d/2),a=oa(a,c),new Xa(c,b,a);for(var g=-1,h=0,l=0;10>l;++l){var k=c.AddDays(l*d);k=f*oa(a,k);if(0==l||k>h)g=l,h=k}c=c.AddDays((g-1)*d);d*=2}}function ud(a,b){var c=b.AddDays(-30/360*aa[a].OrbitalPeriod),d=b.AddDays(.75*aa[a].OrbitalPeriod),f=c,g=c,h=-1,l=-1;d=(d.ut-c.ut)/99;for(var k=0;100>k;++k){var n= -c.AddDays(k*d),p=oa(a,n);0===k?l=h=p:(p>l&&(l=p,g=n),p=b.tt)return a.time.tt>=b.tt&&a.time.tt=b.tt)return a;throw"Internal error: failed to find Neptune apsis.";}function xc(a,b){function c(p){var q=p.AddDays(-5E-4);p=p.AddDays(5E-4);q=oa(a,q);return(oa(a,p)-q)/.001}function d(p){return-c(p)}b=v(b);if(a===m.Neptune||a===m.Pluto)return ud(a,b);for(var f=aa[a].OrbitalPeriod,g=f/6,h=c(b), +}a=g;d=h}throw"SearchLunarApsis INTERNAL ERROR: could not find apsis within 2 synodic months of start date.";}function wc(a,b,c,d){for(var f=b===Ja.Apocenter?1:-1;;){d/=9;if(d<1/1440)return c=c.AddDays(d/2),a=oa(a,c),new Xa(c,b,a);for(var g=-1,h=0,l=0;10>l;++l){var k=c.AddDays(l*d);k=f*oa(a,k);if(0==l||k>h)g=l,h=k}c=c.AddDays((g-1)*d);d*=2}}function vd(a,b){var c=b.AddDays(-30/360*aa[a].OrbitalPeriod),d=b.AddDays(.75*aa[a].OrbitalPeriod),f=c,g=c,h=-1,l=-1;d=(d.ut-c.ut)/99;for(var k=0;100>k;++k){var n= +c.AddDays(k*d),p=oa(a,n);0===k?l=h=p:(p>l&&(l=p,g=n),p=b.tt)return a.time.tt>=b.tt&&a.time.tt=b.tt)return a;throw"Internal error: failed to find Neptune apsis.";}function xc(a,b){function c(p){var q=p.AddDays(-5E-4);p=p.AddDays(5E-4);q=oa(a,q);return(oa(a,p)-q)/.001}function d(p){return-c(p)}b=v(b);if(a===m.Neptune||a===m.Pluto)return vd(a,b);for(var f=aa[a].OrbitalPeriod,g=f/6,h=c(b), l=0;l*g<2*f;++l){var k=b.AddDays(g),n=c(k);if(0>=h*n){f=g=void 0;if(0>h||0n)g=d,f=Ja.Apocenter;else throw"Internal error with slopes in SearchPlanetApsis";b=K(g,b,k);if(!b)throw"Failed to find slope transition in planetary apsis search.";h=oa(a,b);return new Xa(b,f,h)}b=k;h=n}throw"Internal error: should have found planetary apsis within 2 orbital periods.";}function Ka(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 ja(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 lb(a,b){b=v(b);var c=a.lat*e.DEG2RAD,d=a.lon*e.DEG2RAD,f=a.dist*Math.cos(c);return new E(f*Math.cos(d),f*Math.sin(d),a.dist*Math.sin(c),b)}function Mb(a){var b=Nb(a);return new gb(b.lon/15,b.lat,b.dist,a)}function Nb(a){var b=a.x*a.x+a.y*a.y,c=Math.sqrt(b+a.z*a.z);if(0=== @@ -105,74 +105,74 @@ b){if(0===a.z)throw"Zero-length vector not allowed.";var d=0;a=0>a.z?-90:90}else b){if(-90>b||90Math.abs(d))return c-b;c-=d}}function Ya(a,b){return new E(a.rot[0][0]*b.x+a.rot[1][0]*b.y+a.rot[2][0]*b.z,a.rot[0][1]*b.x+a.rot[1][1]*b.y+a.rot[2][1]*b.z,a.rot[0][2]*b.x+a.rot[1][2]*b.y+a.rot[2][2]*b.z,b.t)}function Ea(a,b){return new I(a.rot[0][0]*b.x+a.rot[1][0]*b.y+a.rot[2][0]*b.z,a.rot[0][1]*b.x+a.rot[1][1]*b.y+a.rot[2][1]*b.z,a.rot[0][2]*b.x+a.rot[1][2]*b.y+a.rot[2][2]*b.z,a.rot[0][0]*b.vx+a.rot[1][0]*b.vy+a.rot[2][0]* b.vz,a.rot[0][1]*b.vx+a.rot[1][1]*b.vy+a.rot[2][1]*b.vz,a.rot[0][2]*b.vx+a.rot[1][2]*b.vy+a.rot[2][2]*b.vz,b.t)}function Ac(){return new J([[1,0,0],[0,.9174821430670688,-.3977769691083922],[0,.3977769691083922,.9174821430670688]])}function ob(a){a=v(a);var b=Ma(a,F.From2000);a=Na(a,F.From2000);return ja(b,a)}function pb(a){a=v(a);var b=Na(a,F.Into2000);a=Ma(a,F.Into2000);return ja(b,a)}function Ob(a,b){a=v(a);var c=Math.sin(b.latitude*e.DEG2RAD),d=Math.cos(b.latitude*e.DEG2RAD),f=Math.sin(b.longitude* e.DEG2RAD),g=Math.cos(b.longitude*e.DEG2RAD);b=[d*g,d*f,c];c=[-c*g,-c*f,d];f=[f,-g,0];a=-15*ca(a);b=ya(a,b);c=ya(a,c);a=ya(a,f);return new J([[c[0],a[0],b[0]],[c[1],a[1],b[1]],[c[2],a[2],b[2]]])}function Bc(a,b){a=Ob(a,b);return Ka(a)}function Cc(a,b){a=v(a);b=Bc(a,b);a=pb(a);return ja(b,a)}function Dc(a){a=pb(a);var b=Ac();return ja(a,b)}function Ec(a){a=Dc(a);return Ka(a)}function Fc(a,b){a=v(a);var c=Ec(a);a=Ob(a,b);return ja(c,a)}function Gc(a){var b=da(v(a)).tobl*e.DEG2RAD;a=Math.cos(b);b=Math.sin(b); -return new J([[1,0,0],[0,+a,+b],[0,-b,+a]])}function Hc(a){var b=da(v(a)).tobl*e.DEG2RAD;a=Math.cos(b);b=Math.sin(b);return new J([[1,0,0],[0,+a,-b],[0,+b,+a]])}function Za(a,b,c,d){var f=(d.x*c.x+d.y*c.y+d.z*c.z)/(d.x*d.x+d.y*d.y+d.z*d.z);return new vd(b,f,e.KM_PER_AU*Math.hypot(f*d.x-c.x,f*d.y-c.y,f*d.z-c.z),695700-(1+f)*(695700-a),-695700+(1+f)*(695700+a),c,d)}function qb(a){var b=W(m.Sun,a,!0);b=new E(-b.x,-b.y,-b.z,b.t);var c=Y(a);return Za(6459,a,c,b)}function Ic(a){var b=W(m.Sun,a,!0),c=Y(a), -d=new E(-c.x,-c.y,-c.z,c.t);c.x-=b.x;c.y-=b.y;c.z-=b.z;return Za(1737.4,a,d,c)}function Pb(a,b){var c=cc(a,b);b=W(m.Sun,a,!0);var d=Y(a);c=new E(c[0]-d.x,c[1]-d.y,c[2]-d.z,a);d.x-=b.x;d.y-=b.y;d.z-=b.z;return Za(1737.4,a,c,d)}function rb(a,b,c){a=W(a,c,!0);var d=W(m.Sun,c,!0),f=new E(a.x-d.x,a.y-d.y,a.z-d.z,c);d.x=-a.x;d.y=-a.y;d.z=-a.z;return Za(b,c,d,f)}function Qb(a,b){var c=1/86400,d=b.AddDays(-c);b=b.AddDays(+c);d=a(d);return(a(b).r-d.r)/c}function wd(a){var b=a.AddDays(-.03);a=a.AddDays(.03); -b=K(function(c){return Qb(qb,c)},b,a);if(!b)throw"Failed to find peak Earth shadow time.";return qb(b)}function xd(a){var b=a.AddDays(-.03);a=a.AddDays(.03);b=K(function(c){return Qb(Ic,c)},b,a);if(!b)throw"Failed to find peak Moon shadow time.";return Ic(b)}function yd(a,b,c){var d=c.AddDays(-1);c=c.AddDays(1);d=K(function(f){var g=1/86400,h=rb(a,b,f.AddDays(-g));return(rb(a,b,f.AddDays(+g)).r-h.r)/g},d,c);if(!d)throw"Failed to find peak planet shadow time.";return rb(a,b,d)}function zd(a,b){function c(g){return Pb(g, +return new J([[1,0,0],[0,+a,+b],[0,-b,+a]])}function Hc(a){var b=da(v(a)).tobl*e.DEG2RAD;a=Math.cos(b);b=Math.sin(b);return new J([[1,0,0],[0,+a,-b],[0,+b,+a]])}function Za(a,b,c,d){var f=(d.x*c.x+d.y*c.y+d.z*c.z)/(d.x*d.x+d.y*d.y+d.z*d.z);return new wd(b,f,e.KM_PER_AU*Math.hypot(f*d.x-c.x,f*d.y-c.y,f*d.z-c.z),695700-(1+f)*(695700-a),-695700+(1+f)*(695700+a),c,d)}function qb(a){var b=W(m.Sun,a,!0);b=new E(-b.x,-b.y,-b.z,b.t);var c=Y(a);return Za(6459,a,c,b)}function Ic(a){var b=W(m.Sun,a,!0),c=Y(a), +d=new E(-c.x,-c.y,-c.z,c.t);c.x-=b.x;c.y-=b.y;c.z-=b.z;return Za(1737.4,a,d,c)}function Pb(a,b){var c=cc(a,b);b=W(m.Sun,a,!0);var d=Y(a);c=new E(c[0]-d.x,c[1]-d.y,c[2]-d.z,a);d.x-=b.x;d.y-=b.y;d.z-=b.z;return Za(1737.4,a,c,d)}function rb(a,b,c){a=W(a,c,!0);var d=W(m.Sun,c,!0),f=new E(a.x-d.x,a.y-d.y,a.z-d.z,c);d.x=-a.x;d.y=-a.y;d.z=-a.z;return Za(b,c,d,f)}function Qb(a,b){var c=1/86400,d=b.AddDays(-c);b=b.AddDays(+c);d=a(d);return(a(b).r-d.r)/c}function xd(a){var b=a.AddDays(-.03);a=a.AddDays(.03); +b=K(function(c){return Qb(qb,c)},b,a);if(!b)throw"Failed to find peak Earth shadow time.";return qb(b)}function yd(a){var b=a.AddDays(-.03);a=a.AddDays(.03);b=K(function(c){return Qb(Ic,c)},b,a);if(!b)throw"Failed to find peak Moon shadow time.";return Ic(b)}function zd(a,b,c){var d=c.AddDays(-1);c=c.AddDays(1);d=K(function(f){var g=1/86400,h=rb(a,b,f.AddDays(-g));return(rb(a,b,f.AddDays(+g)).r-h.r)/g},d,c);if(!d)throw"Failed to find peak planet shadow time.";return rb(a,b,d)}function Ad(a,b){function c(g){return Pb(g, b)}var d=a.AddDays(-.2),f=a.AddDays(.2);d=K(function(g){return Qb(c,g)},d,f);if(!d)throw"PeakLocalMoonShadow: search failure for search_center_time = "+a;return Pb(d,b)}function Rb(a,b,c){var d=c/1440;c=a.AddDays(-d);d=a.AddDays(+d);c=K(function(f){return-(qb(f).r-b)},c,a);a=K(function(f){return+(qb(f).r-b)},a,d);if(!c||!a)throw"Failed to find shadow semiduration";return 720*(a.ut-c.ut)}function Sb(a){a=ea(a);return e.RAD2DEG*a.geo_eclip_lat}function Jc(a,b,c){if(0>=a)throw"Radius of first disc must be positive."; -if(0>=b)throw"Radius of second disc must be positive.";if(0>c)throw"Distance between discs is not allowed to be negative.";if(c>=a+b)return 0;if(0==c)return a<=b?1:b*b/(a*a);var d=(a*a-b*b+c*c)/(2*c),f=a*a-d*d;if(0>=f)return a<=b?1:b*b/(a*a);f=Math.sqrt(f);return(a*a*Math.acos(d/a)-d*f+(b*b*Math.acos((c-d)/b)-(c-d)*f))/(Math.PI*a*a)}function Kc(a,b){var c=new E(a.x+b.x,a.y+b.y,a.z+b.z,a.t);a=Math.asin(Lc/c.Length());var d=Math.asin(Ad/b.Length());b=N(b,c);b=Jc(a,d,b*e.DEG2RAD);return Math.min(.9999, -b)}function Mc(a){a=v(a);for(var b=0;12>b;++b){var c=Wa(180,a,40);if(!c)throw"Cannot find full moon.";a=Sb(c);if(1.8>Math.abs(a)&&(a=wd(c),a.rb;++b){var c= -Wa(0,a,40);if(!c)throw"Cannot find new moon";a=Sb(c);if(1.8>Math.abs(a)&&(a=xd(c),a.r=b)throw"Radius of second disc must be positive.";if(0>c)throw"Distance between discs is not allowed to be negative.";if(c>=a+b)return 0;if(0==c)return a<=b?1:b*b/(a*a);var d=(a*a-b*b+c*c)/(2*c),f=a*a-d*d;if(0>=f)return a<=b?1:b*b/(a*a);f=Math.sqrt(f);return(a*a*Math.acos(d/a)-d*f+(b*b*Math.acos((c-d)/b)-(c-d)*f))/(Math.PI*a*a)}function Kc(a,b){var c=new E(a.x+b.x,a.y+b.y,a.z+b.z,a.t);a=Math.asin(Lc/c.Length());var d=Math.asin(Bd/b.Length());b=N(b,c);b=Jc(a,d,b*e.DEG2RAD);return Math.min(.9999, +b)}function Mc(a){a=v(a);for(var b=0;12>b;++b){var c=Wa(180,a,40);if(!c)throw"Cannot find full moon.";a=Sb(c);if(1.8>Math.abs(a)&&(a=xd(c),a.rb;++b){var c= +Wa(0,a,40);if(!c)throw"Cannot find new moon";a=Sb(c);if(1.8>Math.abs(a)&&(a=yd(c),a.r=d?d+=360:180h.r)throw"Unexpected shadow distance from geoid intersection = "+h.r;g=.014 -Math.abs(c)){var d=zd(a,b);if(d.rHa(a,d)&&(b=yd(a,c,d),b.rHa(a,d)&&(b=zd(a,c,d),b.r=c.lat*f.lat){a.$jscomp$loop$prop$kind$33=f.lat>c.lat?ra.Ascending:ra.Descending;b=K(function(g){return function(h){return g.$jscomp$loop$prop$kind$33*ib(h).lat}}(a),b,d);if(!b)throw"Could not find moon node.";return new $c(a.$jscomp$loop$prop$kind$33,b)}b=d;c=f}}function ad(a,b,c,d,f){if(1>a||5=c)throw"Major mass must be a positive number.";if(!Number.isFinite(f)||0>=f)throw"Minor mass must be a negative number."; var g=d.x-b.x,h=d.y-b.y,l=d.z-b.z,k=g*g+h*h+l*l,n=Math.sqrt(k),p=d.vx-b.vx,q=d.vy-b.vy;d=d.vz-b.vz;if(4===a||5===a){k=h*d-l*q;c=l*p-g*d;var t=g*q-h*p,y=c*l-t*h;t=t*g-k*l;k=k*h-c*g;c=Math.sqrt(y*y+t*t+k*k);y/=c;t/=c;k/=c;g/=n;h/=n;l/=n;a=4==a?.8660254037844386:-.8660254037844386;c=.5*g+a*y;f=.5*h+a*t;var x=.5*l+a*k,z=p*g+q*h+d*l;p=p*y+q*t+d*k;b=new I(n*c,n*f,n*x,z*c+p*(.5*y-a*g),z*f+p*(.5*t-a*h),z*x+p*(.5*k-a*l),b.t)}else{y=f/(c+f)*-n;t=c/(c+f)*+n;k=(c+f)/(k*n);if(1===a||2===a)x=c/(c+f)*Math.cbrt(f/ (3*c)),c=-c,1==a?(x=1-x,a=+f):(x=1+x,a=-f);else if(3===a)x=(7/12*f-c)/(f+c),c=+c,a=+f;else throw"Invalid Langrage point "+a+". Must be an integer 1..5.";f=n*x-y;do x=f-y,z=f-t,x=(k*f+c/(x*x)+a/(z*z))/(k-2*c/(x*x*x)-2*a/(z*z*z)),f-=x;while(1E-14b||24<=b)throw"Invalid right ascension for star: "+b;if(-90>c||90d)throw"Invalid star distance: "+d;f.ra=b;f.dec=c;f.dist=d*e.AU_PER_LY};var F;(function(a){a[a.From2000=0]="From2000";a[a.Into2000=1]="Into2000"})(F||(F={}));var aa={Mercury:{OrbitalPeriod:87.969},Venus:{OrbitalPeriod:224.701},Earth:{OrbitalPeriod:365.256}, -Mars:{OrbitalPeriod:686.98},Jupiter:{OrbitalPeriod:4332.589},Saturn:{OrbitalPeriod:10759.22},Uranus:{OrbitalPeriod:30685.4},Neptune:{OrbitalPeriod:60189},Pluto:{OrbitalPeriod:90560}};e.PlanetOrbitalPeriod=function(a){if(a in aa)return aa[a].OrbitalPeriod;throw"Unknown orbital period for: "+a;};var M={Mercury:[[[[4.40250710144,0,0],[.40989414977,1.48302034195,26087.9031415742],[.050462942,4.47785489551,52175.8062831484],[.00855346844,1.16520322459,78263.70942472259],[.00165590362,4.11969163423,104351.61256629678], 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throw"Argument must be a Date object, an AstroTime object, or a numeric UTC Julian date."; };O.FromTerrestrialTime=function(a){for(var b=new O(a);;){var c=a-b.tt;if(1E-12>Math.abs(c))return b;b=b.AddDays(c)}};O.prototype.toString=function(){return this.date.toISOString()};O.prototype.AddDays=function(a){return new O(this.ut+a)};e.AstroTime=O;e.MakeTime=v;var $a;e.e_tilt=da;e.CalcMoonCount=0;var cd=function(a,b,c,d,f,g){this.elat=a;this.elon=b;this.mlat=c;this.mlon=d;this.dist_km=f;this.diam_deg=g};e.LibrationInfo=cd;e.Libration=function(a){var b=v(a);a=b.tt/36525;var c=a*a,d=c*a,f=c*c, g=ea(b);b=g.geo_eclip_lon;var h=g.geo_eclip_lat;g=g.distance_au*e.KM_PER_AU;var 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g=0=c;)c+=360;for(;180Math.abs(q))break;g-=q/(-42.69778487239616*((k-n)/h-n*k*-.006694397995865464/(-42.69778487239616*p))+d*f+a*b)}g*=e.RAD2DEG;h=6378.1366/h;d=Math.abs(f)>Math.abs(b)?d/f-.9933056020041345*h:a/b-h}return new zb(g,c,1E3*d)};e.ObserverGravity=function(a,b){a=Math.sin(a*e.DEG2RAD);a*=a;return 9.7803253359* @@ -192,7 +192,7 @@ Math.atan2(d,a);for(var h,l=0;;){if(10<++l)throw"inverse_terra failed to converg a.x,this.y-a.y,this.z-a.z)};B.prototype.incr=function(a){this.x+=a.x;this.y+=a.y;this.z+=a.z};B.prototype.decr=function(a){this.x-=a.x;this.y-=a.y;this.z-=a.z};B.prototype.mul=function(a){return new B(a*this.x,a*this.y,a*this.z)};B.prototype.div=function(a){return new B(this.x/a,this.y/a,this.z/a)};B.prototype.mean=function(a){return new B((this.x+a.x)/2,(this.y+a.y)/2,(this.z+a.z)/2)};B.prototype.neg=function(){return new B(-this.x,-this.y,-this.z)};var X=function(a,b,c){this.tt=a;this.r=b;this.v= c};X.prototype.clone=function(){return new X(this.tt,this.r,this.v)};X.prototype.sub=function(a){return new X(this.tt,this.r.sub(a.r),this.v.sub(a.v))};var Da=function(a){var b=new X(a,new B(0,0,0),new B(0,0,0));this.Jupiter=R(b,a,m.Jupiter,2.825345909524226E-7);this.Saturn=R(b,a,m.Saturn,8.459715185680659E-8);this.Uranus=R(b,a,m.Uranus,1.292024916781969E-8);this.Neptune=R(b,a,m.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 X(a,b.r.mul(-1),b.v.mul(-1))};Da.prototype.Acceleration=function(a){var b=Ta(a,2.959122082855911E-4,this.Sun.r);b.incr(Ta(a,2.825345909524226E-7,this.Jupiter.r));b.incr(Ta(a,8.459715185680659E-8,this.Saturn.r));b.incr(Ta(a,1.292024916781969E-8,this.Uranus.r));b.incr(Ta(a,1.524358900784276E-8,this.Neptune.r));return b};var Ua=function(a,b,c,d){this.tt=a;this.r=b;this.v=c;this.a=d};Ua.prototype.clone= -function(){return new Ua(this.tt,this.r.clone(),this.v.clone(),this.a.clone())};var ic=function(a,b){this.bary=a;this.grav=b},Ib=[],pd=new J([[.999432765338654,-.0336771074697641,0],[.0303959428906285,.902057912352809,.430543388542295],[-.0144994559663353,-.430299169409101,.902569881273754]]),tb=[{mu:2.82489428433814E-7,al:[1.446213296021224,3.5515522861824],a:[[.0028210960212903,0,0]],l:[[-1.925258348666E-4,4.9369589722645,.01358483658305],[-9.70803596076E-5,4.3188796477322,.01303413843243],[-8.988174165E-5, +function(){return new Ua(this.tt,this.r.clone(),this.v.clone(),this.a.clone())};var ic=function(a,b){this.bary=a;this.grav=b},Ib=[],qd=new J([[.999432765338654,-.0336771074697641,0],[.0303959428906285,.902057912352809,.430543388542295],[-.0144994559663353,-.430299169409101,.902569881273754]]),tb=[{mu:2.82489428433814E-7,al:[1.446213296021224,3.5515522861824],a:[[.0028210960212903,0,0]],l:[[-1.925258348666E-4,4.9369589722645,.01358483658305],[-9.70803596076E-5,4.3188796477322,.01303413843243],[-8.988174165E-5, 1.9080016428617,.00305064867158],[-5.53101050262E-5,1.4936156681569,.01293892891155]],z:[[.0041510849668155,4.089939635545,-.01290686414666],[6.260521444113E-4,1.446188898627,3.5515522949802],[3.52747346169E-5,2.1256287034578,1.2727416567E-4]],zeta:[[3.142172466014E-4,2.7964219722923,-.002315096098],[9.04169207946E-5,1.0477061879627,-5.6920638196E-4]]},{mu:2.82483274392893E-7,al:[-.3735263437471362,1.76932271112347],a:[[.0044871037804314,0,0],[4.324367498E-7,1.819645606291,1.7822295777568]],l:[[8.576433172936E-4, 4.3188693178264,.01303413830805],[4.549582875086E-4,1.4936531751079,.01293892881962],[3.248939825174E-4,1.8196494533458,1.7822295777568],[-3.074250079334E-4,4.9377037005911,.01358483286724],[1.982386144784E-4,1.907986905476,.00305101212869],[1.834063551804E-4,2.1402853388529,.00145009789338],[-1.434383188452E-4,5.622214036663,.89111478887838],[-7.71939140944E-5,4.300272437235,2.6733443704266]],z:[[-.0093589104136341,4.0899396509039,-.01290686414666],[2.988994545555E-4,5.9097265185595,1.7693227079462], [2.13903639035E-4,2.1256289300016,1.2727418407E-4],[1.980963564781E-4,2.743516829265,6.7797343009E-4],[1.210388158965E-4,5.5839943711203,3.20566149E-5],[8.37042048393E-5,1.6094538368039,-.90402165808846],[8.23525166369E-5,1.4461887708689,3.5515522949802]],zeta:[[.0040404917832303,1.0477063169425,-5.692064054E-4],[2.200421034564E-4,3.3368857864364,-1.2491307307E-4],[1.662544744719E-4,2.4134862374711,0],[5.90282470983E-5,5.9719930968366,-3.056160225E-5]]},{mu:2.82498184184723E-7,al:[.2874089391143348, @@ -204,38 +204,39 @@ z:[[.0014289811307319,2.1256295942739,1.2727413029E-4],[7.71093122676E-4,5.58363 oa;e.CorrectLightTravel=lc;var nc=function(a,b,c,d){this.observerBody=a;this.targetBody=b;this.aberration=c;this.observerPos=d};nc.prototype.Position=function(a){this.aberration&&(this.observerPos=Z(this.observerBody,a));var b=Z(this.targetBody,a);return new E(b.x-this.observerPos.x,b.y-this.observerPos.y,b.z-this.observerPos.z,a)};e.BackdatePosition=mc;e.GeoVector=W;e.BaryState=function(a,b){b=v(b);if(a===m.SSB)return new I(0,0,0,0,0,0,b);if(a===m.Pluto)return Hb(b,!1);var c=new Da(b.tt);switch(a){case m.Sun:return pa(c.Sun, b);case m.Jupiter:return pa(c.Jupiter,b);case m.Saturn:return pa(c.Saturn,b);case m.Uranus:return pa(c.Uranus,b);case m.Neptune:return pa(c.Neptune,b);case m.Moon:case m.EMB:var d=Sa(M[m.Earth],b.tt);a=a===m.Moon?Ra(b):Bb(b);return new I(a.x+c.Sun.r.x+d.r.x,a.y+c.Sun.r.y+d.r.y,a.z+c.Sun.r.z+d.r.z,a.vx+c.Sun.v.x+d.v.x,a.vy+c.Sun.v.y+d.v.y,a.vz+c.Sun.v.z+d.v.z,b)}if(a in M)return a=Sa(M[a],b.tt),new I(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.HelioState=mb;e.Search=K;e.SearchSunLongitude=oc;e.PairLongitude=Jb;e.AngleFromSun=Ha;e.EclipticLongitude=qa;var pc=function(a,b,c,d,f,g,h,l){this.time=a;this.mag=b;this.phase_angle=c;this.helio_dist=d;this.geo_dist=f;this.gc=g;this.hc=h;this.ring_tilt=l;this.phase_fraction=(1+Math.cos(e.DEG2RAD*c))/2};e.IlluminationInfo=pc;e.Illumination=nb;e.SearchRelativeLongitude=Ia;e.MoonPhase=Kb;e.SearchMoonPhase=Wa;var rc=function(a,b){this.quarter=a;this.time= -b};e.MoonQuarter=rc;e.SearchMoonQuarter=qc;e.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return qc(a)};e.SearchRiseSet=function(a,b,c,d,f){a:switch(a){case m.Sun:var g=Lc;break a;case m.Moon:g=Bd;break a;default:g=0}return sc(a,b,c,d,f,g,-Cd)};e.SearchAltitude=function(a,b,c,d,f,g){if(!Number.isFinite(g)||-90>g||90c||24<=c)throw"Invalid hour angle "+c;w(f);if(0===f)throw"Direction must be positive or negative.";for(;;){++g;var h=ca(d),l=Pa(a,d,b,!0,!0);h=(c+l.ra-b.longitude/15-h)%24;1===g?0h&&(h+=24):0h?h+=24:123600*Math.abs(h))return a=hb(d,b,l.ra,l.dec,"normal"),new ed(d,a);d=d.AddDays(h/24*.9972695717592592)}}; -e.HourAngle=function(a,b,c){var d=v(b);b=bc(d);a=Pa(a,d,c,!0,!0);c=(c.longitude/15+b-a.ra)%24;0>c&&(c+=24);return c};var fd=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=fd;e.Seasons=function(a){function b(h,l,k){l=new Date(Date.UTC(a,l-1,k));h=oc(h,l,20);if(!h)throw"Cannot find season change near "+l.toISOString();return h}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+ -a+" is neither a Date nor a safe integer.";var c=b(0,3,10),d=b(90,6,10),f=b(180,9,10),g=b(270,12,10);return new fd(c,d,f,g)};var uc=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=uc;e.Elongation=tc;e.SearchMaxElongation=function(a,b){function c(n){var p=n.AddDays(-.005);n=n.AddDays(.005);p=Ha(a,p);n=Ha(a,n);return(p-n)/.01}b=v(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only."; -for(var f=0;2>=++f;){var g=qa(a,b),h=qa(m.Earth,b),l=Fa(g-h),k=g=h=void 0;l>=-d.s1&&l<+d.s1?(k=0,h=+d.s1,g=+d.s2):l>=+d.s2||l<-d.s2?(k=0,h=-d.s2,g=-d.s1):0<=l?(k=-Va(a)/4,h=+d.s1,g=+d.s2):(k=-Va(a)/4,h=-d.s2,g=-d.s1);l=b.AddDays(k);h=Ia(a,h,l);g=Ia(a,g,h);l=c(h);if(0<=l)throw"SearchMaxElongation: internal error: m1 = "+l;k=c(g);if(0>=k)throw"SearchMaxElongation: internal error: m2 = "+k;l=K(c,h,g,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchMaxElongation: failed search iter "+ -f+" (t1="+h.toString()+", t2="+g.toString()+")";if(l.tt>=b.tt)return tc(a,l);b=g.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};e.SearchPeakMagnitude=function(a,b){function c(k){var n=k.AddDays(-.005);k=k.AddDays(.005);n=nb(a,n).mag;return(nb(a,k).mag-n)/.01}if(a!==m.Venus)throw"SearchPeakMagnitude currently works for Venus only.";b=v(b);for(var d=0;2>=++d;){var f=qa(a,b),g=qa(m.Earth,b),h=Fa(f-g),l=f=g=void 0;-10<=h&&10>h?(l=0,g=10,f=30):30<=h||-30>h?(l=0,g=-30,f=-10): -0<=h?(l=-Va(a)/4,g=10,f=30):(l=-Va(a)/4,g=-30,f=-10);h=b.AddDays(l);g=Ia(a,g,h);f=Ia(a,f,g);h=c(g);if(0<=h)throw"SearchPeakMagnitude: internal error: m1 = "+h;l=c(f);if(0>=l)throw"SearchPeakMagnitude: internal error: m2 = "+l;h=K(c,g,f,{init_f1:h,init_f2:l,dt_tolerance_seconds:10});if(!h)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+g.toString()+", t2="+f.toString()+")";if(h.tt>=b.tt)return nb(a,h);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Ja; -(function(a){a[a.Pericenter=0]="Pericenter";a[a.Apocenter=1]="Apocenter"})(Ja=e.ApsisKind||(e.ApsisKind={}));var Xa=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Xa;e.SearchLunarApsis=vc;e.NextLunarApsis=function(a){var b=vc(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=xc; -e.NextPlanetApsis=function(a,b){if(b.kind!==Ja.Pericenter&&b.kind!==Ja.Apocenter)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*aa[a].OrbitalPeriod);a=xc(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=Ka;e.CombineRotation=ja;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= -w(c)*e.DEG2RAD;c=Math.cos(d);d=Math.sin(d);var f=(b+1)%3,g=(b+2)%3,h=[[0,0,0],[0,0,0],[0,0,0]];h[f][f]=c*a.rot[f][f]-d*a.rot[f][g];h[f][g]=d*a.rot[f][f]+c*a.rot[f][g];h[f][b]=a.rot[f][b];h[g][f]=c*a.rot[g][f]-d*a.rot[g][g];h[g][g]=d*a.rot[g][f]+c*a.rot[g][g];h[g][b]=a.rot[g][b];h[b][f]=c*a.rot[b][f]-d*a.rot[b][g];h[b][g]=d*a.rot[b][f]+c*a.rot[b][g];h[b][b]=a.rot[b][b];return new J(h)};e.VectorFromSphere=lb;e.EquatorFromVector=Mb;e.SphereFromVector=Nb;e.HorizonFromVector=function(a,b){a=Nb(a);a.lon= -yc(a.lon);a.lat+=Oa(b,a.lat);return a};e.VectorFromHorizon=function(a,b,c){b=v(b);var d=yc(a.lon);c=a.lat+zc(c,a.lat);a=new Ba(c,d,a.dist);return lb(a,b)};e.Refraction=Oa;e.InverseRefraction=zc;e.RotateVector=Ya;e.RotateState=Ea;e.Rotation_EQJ_ECL=Ac;e.Rotation_ECL_EQJ=function(){return new J([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=ob;e.Rotation_EQJ_ECT=function(a){var b=v(a);a=ob(b);b=Hc(b);return ja(a,b)};e.Rotation_ECT_EQJ= -function(a){var b=v(a);a=Gc(b);b=pb(b);return ja(a,b)};e.Rotation_EQD_EQJ=pb;e.Rotation_EQD_HOR=Ob;e.Rotation_HOR_EQD=Bc;e.Rotation_HOR_EQJ=Cc;e.Rotation_EQJ_HOR=function(a,b){a=Cc(a,b);return Ka(a)};e.Rotation_EQD_ECL=Dc;e.Rotation_ECL_EQD=Ec;e.Rotation_ECL_HOR=Fc;e.Rotation_HOR_ECL=function(a,b){a=Fc(a,b);return Ka(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]])};e.Rotation_ECT_EQD=Gc;e.Rotation_EQD_ECT=Hc;var Dd=[["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"]],Ed=[[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]],Tb,gd,hd=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};e.ConstellationInfo=hd;e.Constellation=function(a,b){w(a);w(b);if(-90>b||90a&&(a+=24);Tb||(Tb=ob(new O(-45655.74141261017)),gd=new O(0));a=new Ba(b,15*a,1);a=lb(a,gd);a=Ya(Tb,a);a=Mb(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Ed),f=d.next();!f.done;f=d.next()){f=f.value;var g=f[1]*c,h=f[2]*c;if(f[3]*b<=a.dec&&g<=a.ra&&a.raa||1E5=a){var b=288.15-.0065*a;a=101325*Math.pow(288.15/b,-5.25577)}else 2E4>=a?(b=216.65,a=22632*Math.exp(-1.5768832E-4*(a-11E3))):(b=216.65+.001*(a-2E4),a=5474.87*Math.pow(216.65/b,34.16319)); +return new ed(a,b,a/b/(101325/288.15))};e.SearchRiseSet=function(a,b,c,d,f){a:switch(a){case m.Sun:var g=Lc;break a;case m.Moon:g=Cd;break a;default:g=0}return sc(a,b,c,d,f,g,-Dd)};e.SearchAltitude=function(a,b,c,d,f,g){if(!Number.isFinite(g)||-90>g||90c||24<=c)throw"Invalid hour angle "+c;w(f);if(0===f)throw"Direction must be positive or negative.";for(;;){++g;var h=ca(d),l=Pa(a,d,b,!0,!0);h=(c+l.ra-b.longitude/15-h)%24;1===g?0h&&(h+=24):0h?h+=24:123600*Math.abs(h))return a=hb(d,b,l.ra,l.dec,"normal"),new fd(d,a);d=d.AddDays(h/24*.9972695717592592)}};e.HourAngle=function(a,b,c){var d=v(b);b=bc(d);a=Pa(a,d,c,!0,!0);c= +(c.longitude/15+b-a.ra)%24;0>c&&(c+=24);return c};var gd=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};e.SeasonInfo=gd;e.Seasons=function(a){function b(h,l,k){l=new Date(Date.UTC(a,l-1,k));h=oc(h,l,20);if(!h)throw"Cannot find season change near "+l.toISOString();return h}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+a+" is neither a Date nor a safe integer."; +var c=b(0,3,10),d=b(90,6,10),f=b(180,9,10),g=b(270,12,10);return new gd(c,d,f,g)};var uc=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};e.ElongationEvent=uc;e.Elongation=tc;e.SearchMaxElongation=function(a,b){function c(n){var p=n.AddDays(-.005);n=n.AddDays(.005);p=Ha(a,p);n=Ha(a,n);return(p-n)/.01}b=v(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only.";for(var f=0;2>=++f;){var g= +qa(a,b),h=qa(m.Earth,b),l=Fa(g-h),k=g=h=void 0;l>=-d.s1&&l<+d.s1?(k=0,h=+d.s1,g=+d.s2):l>=+d.s2||l<-d.s2?(k=0,h=-d.s2,g=-d.s1):0<=l?(k=-Va(a)/4,h=+d.s1,g=+d.s2):(k=-Va(a)/4,h=-d.s2,g=-d.s1);l=b.AddDays(k);h=Ia(a,h,l);g=Ia(a,g,h);l=c(h);if(0<=l)throw"SearchMaxElongation: internal error: m1 = "+l;k=c(g);if(0>=k)throw"SearchMaxElongation: internal error: m2 = "+k;l=K(c,h,g,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchMaxElongation: failed search iter "+f+" (t1="+h.toString()+", t2="+ +g.toString()+")";if(l.tt>=b.tt)return tc(a,l);b=g.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};e.SearchPeakMagnitude=function(a,b){function c(k){var n=k.AddDays(-.005);k=k.AddDays(.005);n=nb(a,n).mag;return(nb(a,k).mag-n)/.01}if(a!==m.Venus)throw"SearchPeakMagnitude currently works for Venus only.";b=v(b);for(var d=0;2>=++d;){var f=qa(a,b),g=qa(m.Earth,b),h=Fa(f-g),l=f=g=void 0;-10<=h&&10>h?(l=0,g=10,f=30):30<=h||-30>h?(l=0,g=-30,f=-10):0<=h?(l=-Va(a)/4,g=10,f=30): +(l=-Va(a)/4,g=-30,f=-10);h=b.AddDays(l);g=Ia(a,g,h);f=Ia(a,f,g);h=c(g);if(0<=h)throw"SearchPeakMagnitude: internal error: m1 = "+h;l=c(f);if(0>=l)throw"SearchPeakMagnitude: internal error: m2 = "+l;h=K(c,g,f,{init_f1:h,init_f2:l,dt_tolerance_seconds:10});if(!h)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+g.toString()+", t2="+f.toString()+")";if(h.tt>=b.tt)return nb(a,h);b=f.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var Ja;(function(a){a[a.Pericenter= +0]="Pericenter";a[a.Apocenter=1]="Apocenter"})(Ja=e.ApsisKind||(e.ApsisKind={}));var Xa=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=c*e.KM_PER_AU};e.Apsis=Xa;e.SearchLunarApsis=vc;e.NextLunarApsis=function(a){var b=vc(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=xc;e.NextPlanetApsis=function(a, +b){if(b.kind!==Ja.Pericenter&&b.kind!==Ja.Apocenter)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*aa[a].OrbitalPeriod);a=xc(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=Ka;e.CombineRotation=ja;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=w(c)*e.DEG2RAD;c=Math.cos(d); +d=Math.sin(d);var f=(b+1)%3,g=(b+2)%3,h=[[0,0,0],[0,0,0],[0,0,0]];h[f][f]=c*a.rot[f][f]-d*a.rot[f][g];h[f][g]=d*a.rot[f][f]+c*a.rot[f][g];h[f][b]=a.rot[f][b];h[g][f]=c*a.rot[g][f]-d*a.rot[g][g];h[g][g]=d*a.rot[g][f]+c*a.rot[g][g];h[g][b]=a.rot[g][b];h[b][f]=c*a.rot[b][f]-d*a.rot[b][g];h[b][g]=d*a.rot[b][f]+c*a.rot[b][g];h[b][b]=a.rot[b][b];return new J(h)};e.VectorFromSphere=lb;e.EquatorFromVector=Mb;e.SphereFromVector=Nb;e.HorizonFromVector=function(a,b){a=Nb(a);a.lon=yc(a.lon);a.lat+=Oa(b,a.lat); +return a};e.VectorFromHorizon=function(a,b,c){b=v(b);var d=yc(a.lon);c=a.lat+zc(c,a.lat);a=new Ba(c,d,a.dist);return lb(a,b)};e.Refraction=Oa;e.InverseRefraction=zc;e.RotateVector=Ya;e.RotateState=Ea;e.Rotation_EQJ_ECL=Ac;e.Rotation_ECL_EQJ=function(){return new J([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};e.Rotation_EQJ_EQD=ob;e.Rotation_EQJ_ECT=function(a){var b=v(a);a=ob(b);b=Hc(b);return ja(a,b)};e.Rotation_ECT_EQJ=function(a){var b=v(a);a=Gc(b); +b=pb(b);return ja(a,b)};e.Rotation_EQD_EQJ=pb;e.Rotation_EQD_HOR=Ob;e.Rotation_HOR_EQD=Bc;e.Rotation_HOR_EQJ=Cc;e.Rotation_EQJ_HOR=function(a,b){a=Cc(a,b);return Ka(a)};e.Rotation_EQD_ECL=Dc;e.Rotation_ECL_EQD=Ec;e.Rotation_ECL_HOR=Fc;e.Rotation_HOR_ECL=function(a,b){a=Fc(a,b);return Ka(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]])};e.Rotation_ECT_EQD=Gc;e.Rotation_EQD_ECT=Hc;var Ed=[["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"]],Fd=[[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]],Tb,hd,id=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};e.ConstellationInfo=id;e.Constellation=function(a,b){w(a);w(b);if(-90>b||90a&&(a+=24);Tb||(Tb= +ob(new O(-45655.74141261017)),hd=new O(0));a=new Ba(b,15*a,1);a=lb(a,hd);a=Ya(Tb,a);a=Mb(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Fd),f=d.next();!f.done;f=d.next()){f=f.value;var g=f[1]*c,h=f[2]*c;if(f[3]*b<=a.dec&&g<=a.ra&&a.ra 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + let temperature; + let pressure; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065 * elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } + else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } + else { + temperature = T1 + 0.001 * (elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} +exports.Atmosphere = Atmosphere; function BodyRadiusAu(body) { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/source/js/astronomy.min.js b/source/js/astronomy.min.js index d7719a86..531fea84 100644 --- a/source/js/astronomy.min.js +++ b/source/js/astronomy.min.js @@ -40,13 +40,13 @@ $jscomp.polyfill("Math.cbrt",function(a){return a?a:function(b){if(0===b)return exports.GeoEmbState=exports.GeoMoonState=exports.EclipticGeoMoon=exports.GeoMoon=exports.Ecliptic=exports.ObserverGravity=exports.VectorObserver=exports.ObserverState=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.SiderealTime=exports.Libration=exports.LibrationInfo= exports.CalcMoonCount=exports.e_tilt=exports.MakeTime=exports.AstroTime=exports.SetDeltaTFunction=exports.DeltaT_JplHorizons=exports.DeltaT_EspenakMeeus=exports.PlanetOrbitalPeriod=exports.DefineStar=exports.Body=exports.AngleBetween=exports.MassProduct=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.AU_PER_LY=exports.KM_PER_AU=exports.C_AUDAY=void 0; -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.ApsisKind=exports.SearchPeakMagnitude=exports.SearchMaxElongation=exports.Elongation=exports.ElongationEvent=exports.Seasons= -exports.SeasonInfo=exports.HourAngle=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=exports.AngleFromSun=exports.PairLongitude=exports.SearchSunLongitude=exports.Search=exports.HelioState=exports.BaryState=exports.GeoVector=exports.BackdatePosition= -exports.CorrectLightTravel=exports.HelioDistance=exports.HelioVector=exports.JupiterMoons=exports.JupiterMoonsInfo=void 0; +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.ApsisKind=exports.SearchPeakMagnitude=exports.SearchMaxElongation=exports.Elongation=exports.ElongationEvent=exports.Seasons=exports.SeasonInfo=exports.HourAngle=exports.SearchHourAngle= +exports.HourAngleEvent=exports.SearchAltitude=exports.SearchRiseSet=exports.Atmosphere=exports.AtmosphereInfo=exports.NextMoonQuarter=exports.SearchMoonQuarter=exports.MoonQuarter=exports.SearchMoonPhase=exports.MoonPhase=exports.SearchRelativeLongitude=exports.Illumination=exports.IlluminationInfo=exports.EclipticLongitude=exports.AngleFromSun=exports.PairLongitude=exports.SearchSunLongitude=exports.Search=exports.HelioState=exports.BaryState=exports.GeoVector=exports.BackdatePosition=exports.CorrectLightTravel= +exports.HelioDistance=exports.HelioVector=exports.JupiterMoons=exports.JupiterMoonsInfo=void 0; exports.GravitySimulator=exports.LagrangePointFast=exports.LagrangePoint=exports.RotationAxis=exports.AxisInfo=exports.NextMoonNode=exports.SearchMoonNode=exports.NodeEventInfo=exports.NodeEventKind=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.EclipseKind=exports.Constellation=exports.ConstellationInfo=exports.Rotation_EQD_ECT=exports.Rotation_ECT_EQD=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_ECT_EQJ=exports.Rotation_EQJ_ECT=exports.Rotation_EQJ_EQD=exports.Rotation_ECL_EQJ= -exports.Rotation_EQJ_ECL=exports.RotateState=exports.RotateVector=void 0;exports.C_AUDAY=173.1446326846693;exports.KM_PER_AU=1.4959787069098932E8;exports.AU_PER_LY=63241.07708807546;exports.DEG2RAD=.017453292519943295;exports.HOUR2RAD=.26179938779914946;exports.RAD2DEG=57.29577951308232;exports.RAD2HOUR=3.819718634205488;exports.JUPITER_EQUATORIAL_RADIUS_KM=71492;exports.JUPITER_POLAR_RADIUS_KM=66854;exports.JUPITER_MEAN_RADIUS_KM=69911;exports.IO_RADIUS_KM=1821.6;exports.EUROPA_RADIUS_KM=1560.8; -exports.GANYMEDE_RADIUS_KM=2631.2;exports.CALLISTO_RADIUS_KM=2410.3; +exports.Rotation_EQJ_ECL=exports.RotateState=exports.RotateVector=exports.InverseRefraction=exports.Refraction=void 0;exports.C_AUDAY=173.1446326846693;exports.KM_PER_AU=1.4959787069098932E8;exports.AU_PER_LY=63241.07708807546;exports.DEG2RAD=.017453292519943295;exports.HOUR2RAD=.26179938779914946;exports.RAD2DEG=57.29577951308232;exports.RAD2HOUR=3.819718634205488;exports.JUPITER_EQUATORIAL_RADIUS_KM=71492;exports.JUPITER_POLAR_RADIUS_KM=66854;exports.JUPITER_MEAN_RADIUS_KM=69911; +exports.IO_RADIUS_KM=1821.6;exports.EUROPA_RADIUS_KM=1560.8;exports.GANYMEDE_RADIUS_KM=2631.2;exports.CALLISTO_RADIUS_KM=2410.3; var DAYS_PER_TROPICAL_YEAR=365.24217,J2000=new Date("2000-01-01T12:00:00Z"),PI2=2*Math.PI,ARC=180/Math.PI*3600,ASEC2RAD=4.84813681109536E-6,ASEC180=648E3,ASEC360=2*ASEC180,ANGVEL=7.292115E-5,AU_PER_PARSEC=ASEC180/Math.PI,SUN_MAG_1AU=-.17-5*Math.log10(AU_PER_PARSEC),MEAN_SYNODIC_MONTH=29.530588,SECONDS_PER_DAY=86400,MILLIS_PER_DAY=1E3*SECONDS_PER_DAY,SOLAR_DAYS_PER_SIDEREAL_DAY=.9972695717592592,SUN_RADIUS_KM=695700,SUN_RADIUS_AU=SUN_RADIUS_KM/exports.KM_PER_AU,EARTH_FLATTENING=.996647180302104,EARTH_FLATTENING_SQUARED= EARTH_FLATTENING*EARTH_FLATTENING,EARTH_EQUATORIAL_RADIUS_KM=6378.1366,EARTH_EQUATORIAL_RADIUS_AU=EARTH_EQUATORIAL_RADIUS_KM/exports.KM_PER_AU,EARTH_POLAR_RADIUS_KM=EARTH_EQUATORIAL_RADIUS_KM*EARTH_FLATTENING,EARTH_MEAN_RADIUS_KM=6371,EARTH_ATMOSPHERE_KM=88,EARTH_ECLIPSE_RADIUS_KM=EARTH_MEAN_RADIUS_KM+EARTH_ATMOSPHERE_KM,MOON_EQUATORIAL_RADIUS_KM=1738.1,MOON_EQUATORIAL_RADIUS_AU=MOON_EQUATORIAL_RADIUS_KM/exports.KM_PER_AU,MOON_MEAN_RADIUS_KM=1737.4,MOON_POLAR_RADIUS_KM=1736,MOON_POLAR_RADIUS_AU=MOON_POLAR_RADIUS_KM/ exports.KM_PER_AU,REFRACTION_NEAR_HORIZON=34/60,EARTH_MOON_MASS_RATIO=81.30056,SUN_GM=2.959122082855911E-4,MERCURY_GM=4.912547451450812E-11,VENUS_GM=7.243452486162703E-10,EARTH_GM=8.887692390113509E-10,MARS_GM=9.549535105779258E-11,JUPITER_GM=2.825345909524226E-7,SATURN_GM=8.459715185680659E-8,URANUS_GM=1.292024916781969E-8,NEPTUNE_GM=1.524358900784276E-8,PLUTO_GM=2.18869976542597E-12,MOON_GM=EARTH_GM/EARTH_MOON_MASS_RATIO; @@ -218,6 +218,7 @@ function SearchRelativeLongitude(a,b,c){function d(l){var m=EclipticLongitude(a, c=c.AddDays(h);if(1>Math.abs(h)*SECONDS_PER_DAY)return c;h=g;g=d(c);30>Math.abs(h)&&h!==g&&(h/=h-g,.5h&&(e*=h))}throw"Relative longitude search failed to converge for "+a+" near "+c.toString()+" (error_angle = "+g+").";}exports.SearchRelativeLongitude=SearchRelativeLongitude;function MoonPhase(a){return PairLongitude(Body.Moon,Body.Sun,a)}exports.MoonPhase=MoonPhase; function SearchMoonPhase(a,b,c){function d(k){k=MoonPhase(k);return LongitudeOffset(k-a)}VerifyNumber(a);VerifyNumber(c);b=MakeTime(b);var e=d(b);if(0>c){0>e&&(e+=360);var f=-(MEAN_SYNODIC_MONTH*e)/360;e=f+1.5;if(ec)return null;e=Math.min(c,f+1.5)}c=b.AddDays(g);b=b.AddDays(e);return Search(d,c,b,{dt_tolerance_seconds:.1})}exports.SearchMoonPhase=SearchMoonPhase; var MoonQuarter=function(a,b){this.quarter=a;this.time=b};exports.MoonQuarter=MoonQuarter;function SearchMoonQuarter(a){var b=MoonPhase(a);b=(Math.floor(b/90)+1)%4;a=SearchMoonPhase(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new MoonQuarter(b,a)}exports.SearchMoonQuarter=SearchMoonQuarter;function NextMoonQuarter(a){a=new Date(a.time.date.getTime()+6*MILLIS_PER_DAY);return SearchMoonQuarter(a)}exports.NextMoonQuarter=NextMoonQuarter; +var AtmosphereInfo=function(a,b,c){this.pressure=a;this.temperature=b;this.density=c};exports.AtmosphereInfo=AtmosphereInfo;function Atmosphere(a){if(!Number.isFinite(a)||-500>a||1E5=a){var b=288.15-.0065*a;a=101325*Math.pow(288.15/b,-5.25577)}else 2E4>=a?(b=216.65,a=22632*Math.exp(-1.5768832E-4*(a-11E3))):(b=216.65+.001*(a-2E4),a=5474.87*Math.pow(216.65/b,34.16319));return new AtmosphereInfo(a,b,a/b/(101325/288.15))}exports.Atmosphere=Atmosphere; function BodyRadiusAu(a){switch(a){case Body.Sun:return SUN_RADIUS_AU;case Body.Moon:return MOON_EQUATORIAL_RADIUS_AU;default:return 0}}function SearchRiseSet(a,b,c,d,e){var f=BodyRadiusAu(a);return InternalSearchAltitude(a,b,c,d,e,f,-REFRACTION_NEAR_HORIZON)}exports.SearchRiseSet=SearchRiseSet;function SearchAltitude(a,b,c,d,e,f){if(!Number.isFinite(f)||-90>f||90f&&0<=g)return new AscentInfo(d,e,f,g);if(0<=f&&0>g)return null;if(17k*SECONDS_PER_DAY||Math.min(Math.abs(f),Math.abs(g))>k/2*c)return null;k=new AstroTime((d.ut+e.ut)/2);var h=b(k);return FindAscent(1+a,b,c,d,k,f,h)||FindAscent(1+a,b,c,k,e,h,g)} function MaxAltitudeSlope(a,b){if(-90>b||90 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + + let temperature: number; + let pressure: number; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065*elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } else { + temperature = T1 + 0.001*(elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} + + function BodyRadiusAu(body: Body): number { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer diff --git a/source/js/esm/astronomy.js b/source/js/esm/astronomy.js index ae480765..6a1fc45c 100644 --- a/source/js/esm/astronomy.js +++ b/source/js/esm/astronomy.js @@ -4765,6 +4765,68 @@ export function NextMoonQuarter(mq) { let date = new Date(mq.time.date.getTime() + 6 * MILLIS_PER_DAY); return SearchMoonQuarter(date); } +/** + * @brief Information about idealized atmospheric variables at a given elevation. + * + * @property {number} pressure + * Atmospheric pressure in pascals. + * + * @property {number} temperature + * Atmospheric temperature in kelvins. + * + * @property {number} density + * Atmospheric density relative to sea level. + */ +export class AtmosphereInfo { + constructor(pressure, temperature, density) { + this.pressure = pressure; + this.temperature = temperature; + this.density = density; + } +} +/** + * @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation. + * + * This function calculates idealized values of pressure, temperature, and density + * using the U.S. Standard Atmosphere (1976) model. + * 1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976. + * 2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985. + * See: + * https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml + * https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf + * https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf + * + * @param {number} elevationMeters + * The elevation above sea level at which to calculate atmospheric variables. + * Must be in the range -500 to +100000, or an exception will occur. + * + * @returns {AtmosphereInfo} + */ +export function Atmosphere(elevationMeters) { + const P0 = 101325.0; // pressure at sea level [pascals] + const T0 = 288.15; // temperature at sea level [kelvins] + const T1 = 216.65; // temperature between 20 km and 32 km [kelvins] + if (!Number.isFinite(elevationMeters) || elevationMeters < -500.0 || elevationMeters > 100000.0) + throw `Invalid elevation: ${elevationMeters}`; + let temperature; + let pressure; + if (elevationMeters <= 11000.0) { + temperature = T0 - 0.0065 * elevationMeters; + pressure = P0 * Math.pow(T0 / temperature, -5.25577); + } + else if (elevationMeters <= 20000.0) { + temperature = T1; + pressure = 22632.0 * Math.exp(-0.00015768832 * (elevationMeters - 11000.0)); + } + else { + temperature = T1 + 0.001 * (elevationMeters - 20000.0); + pressure = 5474.87 * Math.pow(T1 / temperature, 34.16319); + } + // The density is calculated relative to the sea level value. + // Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. + const density = (pressure / temperature) / (P0 / T0); + return new AtmosphereInfo(pressure, temperature, density); +} function BodyRadiusAu(body) { // For the purposes of calculating rise/set times, // only the Sun and Moon appear large enough to an observer