153 lines
6.9 KiB
Go
153 lines
6.9 KiB
Go
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package eclipse
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import (
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"math"
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"time"
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"b612.me/astro/basic"
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)
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const (
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// brownLunationEpochJDE 是布朗月序数 0 号朔的儒略日（1923-01-17）。
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brownLunationEpochJDE = 2423436.0
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// brownLunationSynodicMonth 是平均朔望月长度，用于把朔的儒略日换算成月序数。
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brownLunationSynodicMonth = 29.530588853
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// 视半径换算地平视差用的半径比：地球赤道半径除以天体半径。
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horizontalParallaxMoonRatio = 6378.137 / 1737.4
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horizontalParallaxSunRatio = 6378.137 / 696000.0
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)
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// SolarEclipseGeocentricPanel 汇总 详细版式面板所需的食甚时刻地心量。
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// SolarEclipseGeocentricPanel carries the geocentric quantities that detailed panels print.
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type SolarEclipseGeocentricPanel struct {
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// Conjunction 是本次朔，即地心视黄经相等的时刻；与 NASA 全球图上的 Geocentric Conjunction 不是同一个量。
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// Conjunction is the new moon, the instant of equal geocentric apparent ecliptic longitude. It is not
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// the same quantity as the Geocentric Conjunction printed on NASA world maps.
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Conjunction time.Time
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ConjunctionJDE float64
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// RightAscensionConjunction 是地心视赤经相等的时刻，也就是 NASA 全球图上 Geocentric Conjunction 的口径；
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// 2009-07-22 两者相差约 90 s（视黄经相等在 02:34:34 UT，视赤经相等在 02:33:04 UT）。
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// RightAscensionConjunction is the instant of equal geocentric apparent right ascension, the quantity NASA
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// world maps print as Geocentric Conjunction. For 2009-07-22 the two differ by about 90 s.
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RightAscensionConjunction time.Time
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RightAscensionConjunctionJDE float64
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// RightAscensionConjunctionJD 是同一时刻的世界时儒略日，NASA 全球图上印的就是它。
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// RightAscensionConjunctionJD is the universal-time Julian day of that instant, the value NASA maps print.
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RightAscensionConjunctionJD float64
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// DeltaTSeconds 是食甚时刻实际使用的 ΔT。
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// DeltaTSeconds is the ΔT used at greatest eclipse.
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DeltaTSeconds float64
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SunRightAscensionDeg float64
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SunDeclinationDeg float64
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SunSemidiameterArcsec float64
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SunParallaxArcsec float64
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MoonRightAscensionDeg float64
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MoonDeclinationDeg float64
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MoonSemidiameterArcsec float64
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MoonParallaxArcsec float64
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LibrationLongitudeDeg float64
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LibrationLatitudeDeg float64
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LibrationPositionAngleDeg float64
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BrownLunationNumber int
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// PenumbralK 与 UmbralK 是月地半径比 k1/k2。
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PenumbralK float64
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UmbralK float64
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// BodyShiftLongitudeArcsec 与 BodyShiftLatitudeArcsec 是星历表里的 Δl/Δb；本库模型不做月面位置平移，恒为零。
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BodyShiftLongitudeArcsec float64
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BodyShiftLatitudeArcsec float64
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// Ephemeris 是所用模型名称。
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Ephemeris string
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// SingleK 表示使用的是 IAU Single-K（k1 同时用于半影与本影）。
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SingleK bool
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}
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// horizontalParallaxArcsec 由视半径换算地平视差：sin(HP) = sin(SD) × R⊕ / R天体。
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func horizontalParallaxArcsec(semidiameterArcsec, radiusRatio float64) float64 {
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sine := math.Sin(semidiameterArcsec / 3600 * math.Pi / 180)
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return math.Asin(math.Max(-1, math.Min(1, sine*radiusRatio))) * 180 / math.Pi * 3600
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}
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// SolarEclipseGeocentricPanelAt 计算给定日食在食甚时刻的地心量面板。
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// SolarEclipseGeocentricPanelAt computes the geocentric panel of one eclipse at greatest eclipse.
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func SolarEclipseGeocentricPanelAt(date time.Time) (SolarEclipseGeocentricPanel, bool) {
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info, ok := SolarEclipseOnDateNASABulletinSplitK(date)
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if !ok {
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return SolarEclipseGeocentricPanel{}, false
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}
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panel := solarEclipseGeocentricPanelAt(info)
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panel.Ephemeris = "NASA bulletin Split-K"
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panel.PenumbralK = basic.SolarEclipsePenumbralK
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panel.UmbralK = basic.SolarEclipseUmbralK
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return panel, true
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}
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// SolarEclipseGeocentricPanelIAUSingleK 使用 IAU Single-K 计算地心量面板。
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// SolarEclipseGeocentricPanelIAUSingleK computes the geocentric panel with the IAU Single-K model.
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func SolarEclipseGeocentricPanelIAUSingleK(date time.Time) (SolarEclipseGeocentricPanel, bool) {
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info, ok := SolarEclipseOnDateIAUSingleK(date)
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if !ok {
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return SolarEclipseGeocentricPanel{}, false
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}
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panel := solarEclipseGeocentricPanelAt(info)
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panel.Ephemeris = "IAU Single-K"
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panel.PenumbralK = basic.SolarEclipsePenumbralK
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panel.UmbralK = basic.SolarEclipsePenumbralK
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panel.SingleK = true
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return panel, true
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}
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func solarEclipseGeocentricPanelAt(info SolarEclipseInfo) SolarEclipseGeocentricPanel {
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tt := solarEclipseTimeToTTJDE(info.GreatestEclipse)
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conjunctionJDE := basic.CalcMoonSHByJDE(tt, 0)
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rightAscensionJDE := solarEclipseRightAscensionConjunction(tt)
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panel := SolarEclipseGeocentricPanel{
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Conjunction: solarEclipseTTJDEToTime(conjunctionJDE, info.GreatestEclipse.Location()),
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ConjunctionJDE: conjunctionJDE,
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RightAscensionConjunction: solarEclipseTTJDEToTime(rightAscensionJDE, info.GreatestEclipse.Location()),
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RightAscensionConjunctionJDE: rightAscensionJDE,
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RightAscensionConjunctionJD: rightAscensionJDE - basic.DeltaT(tt, true)/86400,
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DeltaTSeconds: basic.DeltaT(tt, true),
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}
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panel.SunRightAscensionDeg, panel.SunDeclinationDeg = basic.SunApparentRaDec(tt)
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panel.MoonRightAscensionDeg, panel.MoonDeclinationDeg = basic.HMoonTrueRaDec(tt)
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panel.SunSemidiameterArcsec = basic.SunSemidiameter(tt)
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panel.MoonSemidiameterArcsec = basic.MoonSemidiameter(tt)
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panel.SunParallaxArcsec = horizontalParallaxArcsec(panel.SunSemidiameterArcsec, horizontalParallaxSunRatio)
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panel.MoonParallaxArcsec = horizontalParallaxArcsec(panel.MoonSemidiameterArcsec, horizontalParallaxMoonRatio)
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physical := basic.MoonPhysical(tt)
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panel.LibrationLongitudeDeg = physical.LibrationLongitude
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panel.LibrationLatitudeDeg = physical.LibrationLatitude
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panel.LibrationPositionAngleDeg = physical.PositionAngle
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panel.BrownLunationNumber = int(math.Floor((panel.ConjunctionJDE-brownLunationEpochJDE)/brownLunationSynodicMonth)) + 1
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return panel
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}
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// solarEclipseRightAscensionGap 返回月亮与太阳的地心视赤经差，单位弧度。
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func solarEclipseRightAscensionGap(tt float64) float64 {
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sunRightAscension, _ := basic.SunApparentRaDec(tt)
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moonRightAscension, _ := basic.HMoonTrueRaDec(tt)
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return math.Remainder(moonRightAscension-sunRightAscension, 360) * math.Pi / 180
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}
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// solarEclipseRightAscensionConjunction 求地心视赤经相等的时刻。
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// 赤经差在合附近单调，用牛顿法从食甚时刻收敛即可，不需要预先求朔。
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func solarEclipseRightAscensionConjunction(tt float64) float64 {
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estimate := tt
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for iteration := 0; iteration < 40; iteration++ {
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value := solarEclipseRightAscensionGap(estimate)
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if math.Abs(value) < 1e-10 {
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break
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}
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derivative := (solarEclipseRightAscensionGap(estimate+1e-5) - solarEclipseRightAscensionGap(estimate-1e-5)) / 2e-5
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if derivative == 0 || math.IsNaN(derivative) || math.IsInf(derivative, 0) {
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break
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}
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estimate -= value / derivative
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}
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return estimate
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}
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