402 lines
13 KiB
Go
402 lines
13 KiB
Go
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package basic
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import "math"
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// LocalSolarEclipseResult 表示某个站点的一次站心日食几何结果。
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//
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// 所有时刻字段都使用力学时儒略日（JDE, TT）。
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// 输入 seedJDE 只需要落在目标朔月附近，允许相差数天。
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type LocalSolarEclipseResult struct {
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Model SolarEclipseRadiusModel
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Type SolarEclipseType
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// GreatestEclipse 是站心盘面中心角距最小的时刻。
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GreatestEclipse float64
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// PartialStart / PartialEnd 是站心偏食始 / 偏食终。
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PartialStart float64
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PartialEnd float64
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// CentralStart / CentralEnd 是站心中心食始 / 中心食终。
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//
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// 对全食对应食既 / 生光；
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// 对环食对应环食始 / 环食终。
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CentralStart float64
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CentralEnd float64
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// Magnitude 是站心食分。
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Magnitude float64
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// Obscuration 是食甚时太阳视圆面被月面遮蔽的面积比例，范围 [0, 1]。
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Obscuration float64
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// Separation 是食甚时日月中心的站心角距，单位为度。
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Separation float64
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// SunAltitude / SunAzimuth 是食甚时太阳的站心高度角 / 方位角，单位为度。
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SunAltitude float64
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SunAzimuth float64
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// VisibleAtGreatest 表示食甚时太阳中心在地平线上方。
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VisibleAtGreatest bool
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HasPartial bool
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HasCentral bool
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HasAnnular bool
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HasTotal bool
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}
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type localSolarEclipseState struct {
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separationRad float64
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separationSquared float64
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sunRadiusRad float64
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moonOuterRadiusRad float64
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moonInnerRadiusRad float64
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sunAltitudeRad float64
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sunAzimuthRad float64
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}
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const (
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localSolarEclipseGreatestWindowDays = 0.5
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localSolarEclipseGreatestTolerance = 1e-8
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localSolarEclipseContactStepDays = 10.0 / 1440.0
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localSolarEclipseContactSearchSteps = 72
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localSolarEclipseContactTolerance = 1e-8
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localSolarMoonRadiusScale = 1.0000036
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)
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// LocalSolarEclipse 计算给定近朔时刻附近的一次站心日食，默认使用 NASA bulletin Split-K 模型。
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//
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// seedJDE 为力学时儒略日（TT），只需落在目标朔月附近，允许相差数天。
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// lon 为经度，东正西负；lat 为纬度，北正南负；height 为海拔高度，单位米。
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func LocalSolarEclipse(seedJDE, lon, lat, height float64) LocalSolarEclipseResult {
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return LocalSolarEclipseNASABulletinSplitK(seedJDE, lon, lat, height)
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}
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// LocalSolarEclipseIAUSingleK 计算给定近朔时刻附近的一次站心日食，使用 IAU Single-K 模型。
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func LocalSolarEclipseIAUSingleK(seedJDE, lon, lat, height float64) LocalSolarEclipseResult {
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return localSolarEclipse(seedJDE, lon, lat, height, SolarEclipseModelIAUSingleK)
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}
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// LocalSolarEclipseNASABulletinSplitK 计算给定近朔时刻附近的一次站心日食，使用 NASA bulletin Split-K 模型。
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func LocalSolarEclipseNASABulletinSplitK(seedJDE, lon, lat, height float64) LocalSolarEclipseResult {
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return localSolarEclipse(seedJDE, lon, lat, height, SolarEclipseModelNASABulletinSplitK)
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}
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func localSolarEclipse(seedJDE, lonDeg, latDeg, heightMeters float64, model SolarEclipseRadiusModel) LocalSolarEclipseResult {
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newMoonJDE := CalcMoonSHByJDE(seedJDE, 0)
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lonRad := lonDeg * rad
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latRad := latDeg * rad
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heightKM := heightMeters / 1000.0
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params := solarEclipseModelParams(model)
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greatestEclipseJDE := localSolarEclipseGreatest(newMoonJDE, lonRad, latRad, heightKM, params)
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state := localSolarEclipseStateAt(greatestEclipseJDE, lonRad, latRad, heightKM, params)
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visibleThresholdRad := 0.0
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if heightMeters > 0 {
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visibleThresholdRad = -HeightDegreeByLat(heightMeters, latDeg) * rad
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}
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result := LocalSolarEclipseResult{
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Model: model,
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Type: SolarEclipseNone,
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GreatestEclipse: greatestEclipseJDE,
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Separation: state.separationRad / rad,
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SunAltitude: state.sunAltitudeRad / rad,
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SunAzimuth: state.sunAzimuthRad / rad,
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VisibleAtGreatest: state.sunAltitudeRad > visibleThresholdRad,
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}
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partialBoundary := state.sunRadiusRad + state.moonOuterRadiusRad
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partialGap := state.separationRad - partialBoundary
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if partialGap > 0 {
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return result
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}
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result.Type = SolarEclipsePartial
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result.HasPartial = true
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result.Magnitude = (state.moonOuterRadiusRad + state.sunRadiusRad - state.separationRad) / (2 * state.sunRadiusRad)
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if result.Magnitude < 0 {
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result.Magnitude = 0
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}
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result.Obscuration = localSolarEclipseObscuration(
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state.sunRadiusRad,
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state.moonOuterRadiusRad,
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state.separationRad,
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)
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if partialStart, ok := localSolarEclipseContact(greatestEclipseJDE, lonRad, latRad, heightKM, params, false, true); ok {
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result.PartialStart = partialStart
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}
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if partialEnd, ok := localSolarEclipseContact(greatestEclipseJDE, lonRad, latRad, heightKM, params, false, false); ok {
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result.PartialEnd = partialEnd
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}
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centralBoundary := math.Abs(state.sunRadiusRad - state.moonInnerRadiusRad)
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if state.separationRad > centralBoundary {
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return result
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}
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result.HasCentral = true
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if state.moonInnerRadiusRad >= state.sunRadiusRad {
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result.Type = SolarEclipseTotal
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result.HasTotal = true
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} else {
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result.Type = SolarEclipseAnnular
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result.HasAnnular = true
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}
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result.Magnitude = state.moonInnerRadiusRad / state.sunRadiusRad
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if centralStart, ok := localSolarEclipseContact(greatestEclipseJDE, lonRad, latRad, heightKM, params, true, true); ok {
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result.CentralStart = centralStart
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}
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if centralEnd, ok := localSolarEclipseContact(greatestEclipseJDE, lonRad, latRad, heightKM, params, true, false); ok {
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result.CentralEnd = centralEnd
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}
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return result
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}
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func solarEclipseModelParams(model SolarEclipseRadiusModel) solarEclipseModelParameters {
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params := solarEclipseModelParameters{
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penumbralK: solarEclipsePenumbralK,
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umbralK: solarEclipsePenumbralK,
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}
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if model == SolarEclipseModelNASABulletinSplitK {
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params.umbralK = solarEclipseUmbralK
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}
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return params
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}
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func localSolarEclipseGreatest(
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newMoonJDE, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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) float64 {
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left := newMoonJDE - localSolarEclipseGreatestWindowDays
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right := newMoonJDE + localSolarEclipseGreatestWindowDays
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goldenRatio := (math.Sqrt(5) - 1) / 2
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x1 := right - goldenRatio*(right-left)
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x2 := left + goldenRatio*(right-left)
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f1 := localSolarEclipseStateAt(x1, lonRad, latRad, heightKM, params).separationSquared
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f2 := localSolarEclipseStateAt(x2, lonRad, latRad, heightKM, params).separationSquared
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for i := 0; i < 80 && right-left > localSolarEclipseGreatestTolerance; i++ {
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if f1 <= f2 {
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right = x2
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x2 = x1
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f2 = f1
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x1 = right - goldenRatio*(right-left)
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f1 = localSolarEclipseStateAt(x1, lonRad, latRad, heightKM, params).separationSquared
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continue
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}
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left = x1
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x1 = x2
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f1 = f2
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x2 = left + goldenRatio*(right-left)
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f2 = localSolarEclipseStateAt(x2, lonRad, latRad, heightKM, params).separationSquared
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}
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return (left + right) / 2
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}
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func localSolarEclipseContact(
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greatestEclipseJDE, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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central bool,
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beforeGreatest bool,
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) (float64, bool) {
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centerGap := localSolarEclipseGap(greatestEclipseJDE, lonRad, latRad, heightKM, params, central)
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if centerGap > 0 {
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return 0, false
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}
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if math.Abs(centerGap) <= 1e-14 {
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return greatestEclipseJDE, true
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}
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direction := 1.0
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if beforeGreatest {
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direction = -1.0
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}
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previousJDE := greatestEclipseJDE
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for i := 1; i <= localSolarEclipseContactSearchSteps; i++ {
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currentJDE := greatestEclipseJDE + direction*localSolarEclipseContactStepDays*float64(i)
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currentGap := localSolarEclipseGap(currentJDE, lonRad, latRad, heightKM, params, central)
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if currentGap >= 0 {
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left := previousJDE
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right := currentJDE
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if beforeGreatest {
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left = currentJDE
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right = previousJDE
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}
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return localSolarEclipseContactBisection(left, right, lonRad, latRad, heightKM, params, central)
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}
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previousJDE = currentJDE
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}
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return 0, false
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}
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func localSolarEclipseContactBisection(
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leftJDE, rightJDE, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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central bool,
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) (float64, bool) {
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leftGap := localSolarEclipseGap(leftJDE, lonRad, latRad, heightKM, params, central)
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rightGap := localSolarEclipseGap(rightJDE, lonRad, latRad, heightKM, params, central)
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if leftGap == 0 {
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return leftJDE, true
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}
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if rightGap == 0 {
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return rightJDE, true
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}
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if leftGap*rightGap > 0 {
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return 0, false
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}
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for i := 0; i < 80 && rightJDE-leftJDE > localSolarEclipseContactTolerance; i++ {
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midJDE := (leftJDE + rightJDE) / 2
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midGap := localSolarEclipseGap(midJDE, lonRad, latRad, heightKM, params, central)
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if leftGap*midGap > 0 {
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leftJDE = midJDE
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leftGap = midGap
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continue
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}
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rightJDE = midJDE
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rightGap = midGap
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}
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return (leftJDE + rightJDE) / 2, true
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}
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func localSolarEclipseGap(
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jdTT, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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central bool,
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) float64 {
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state := localSolarEclipseStateAt(jdTT, lonRad, latRad, heightKM, params)
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boundary := state.sunRadiusRad + state.moonOuterRadiusRad
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if central {
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boundary = math.Abs(state.sunRadiusRad - state.moonInnerRadiusRad)
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}
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return state.separationRad - boundary
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}
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func localSolarEclipseStateAt(
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jdTT, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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) localSolarEclipseState {
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sunEquatorial, moonEquatorial := solarEclipseSunMoonEquatorial(jdTT)
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sunXYZ := solarEclipseLLRToXYZ(sunEquatorial[0], sunEquatorial[1], sunEquatorial[2])
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moonXYZ := solarEclipseLLRToXYZ(moonEquatorial[0], moonEquatorial[1], moonEquatorial[2])
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utJDE := TD2UT(jdTT, false)
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gst := ApparentSiderealTime(utJDE) * 15 * rad
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observerXYZ := localSolarEclipseObserverXYZ(gst, lonRad, latRad, heightKM)
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sunTopocentric := solarEclipseXYZToLLR(
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sunXYZ[0]-observerXYZ[0],
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sunXYZ[1]-observerXYZ[1],
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sunXYZ[2]-observerXYZ[2],
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)
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moonTopocentric := solarEclipseXYZToLLR(
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moonXYZ[0]-observerXYZ[0],
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moonXYZ[1]-observerXYZ[1],
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moonXYZ[2]-observerXYZ[2],
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)
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sunUnit := solarEclipseLLRToXYZ(sunTopocentric[0], sunTopocentric[1], 1)
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moonUnit := solarEclipseLLRToXYZ(moonTopocentric[0], moonTopocentric[1], 1)
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dot := sunUnit[0]*moonUnit[0] + sunUnit[1]*moonUnit[1] + sunUnit[2]*moonUnit[2]
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if dot > 1 {
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dot = 1
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}
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if dot < -1 {
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dot = -1
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}
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sunRadiusRad := math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * solarEclipseSolarRadiusRatio / sunTopocentric[2],
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))
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moonOuterRadiusRad := math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * solarEclipsePenumbralK * localSolarMoonRadiusScale / moonTopocentric[2],
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))
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moonInnerRadiusRad := math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * params.umbralK * localSolarMoonRadiusScale / moonTopocentric[2],
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))
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|
sunHorizontal := solarEclipseEquatorialToHorizontal(
|
|||
|
|
sunTopocentric[0],
|
|||
|
|
sunTopocentric[1],
|
|||
|
|
sunTopocentric[2],
|
|||
|
|
lonRad,
|
|||
|
|
latRad,
|
|||
|
|
gst,
|
|||
|
|
)
|
|||
|
|
|
|||
|
|
return localSolarEclipseState{
|
|||
|
|
separationRad: math.Acos(dot),
|
|||
|
|
separationSquared: 2 - 2*dot,
|
|||
|
|
sunRadiusRad: sunRadiusRad,
|
|||
|
|
moonOuterRadiusRad: moonOuterRadiusRad,
|
|||
|
|
moonInnerRadiusRad: moonInnerRadiusRad,
|
|||
|
|
sunAltitudeRad: sunHorizontal[1],
|
|||
|
|
sunAzimuthRad: solarEclipseNormalizeRadians(sunHorizontal[0] + math.Pi),
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func localSolarEclipseObserverXYZ(gst, lonRad, latRad, heightKM float64) [3]float64 {
|
|||
|
|
equatorialRadius := solarEclipseEarthEquatorialRadiusKM
|
|||
|
|
polarRadius := solarEclipseEarthEquatorialRadiusKM * solarEclipseEarthPolarRatio
|
|||
|
|
|
|||
|
|
u := math.Atan((polarRadius / equatorialRadius) * math.Tan(latRad))
|
|||
|
|
radiusXY := equatorialRadius*math.Cos(u) + heightKM*math.Cos(latRad)
|
|||
|
|
radiusZ := polarRadius*math.Sin(u) + heightKM*math.Sin(latRad)
|
|||
|
|
angle := gst + lonRad
|
|||
|
|
|
|||
|
|
return [3]float64{
|
|||
|
|
radiusXY * math.Cos(angle),
|
|||
|
|
radiusXY * math.Sin(angle),
|
|||
|
|
radiusZ,
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func localSolarEclipseObscuration(sunRadius, moonRadius, separation float64) float64 {
|
|||
|
|
if separation >= sunRadius+moonRadius {
|
|||
|
|
return 0
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
sunArea := math.Pi * sunRadius * sunRadius
|
|||
|
|
if separation <= math.Abs(sunRadius-moonRadius) {
|
|||
|
|
if moonRadius >= sunRadius {
|
|||
|
|
return 1
|
|||
|
|
}
|
|||
|
|
return moonRadius * moonRadius / (sunRadius * sunRadius)
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
partSun := localSolarEclipseClampUnit((separation*separation + sunRadius*sunRadius - moonRadius*moonRadius) / (2 * separation * sunRadius))
|
|||
|
|
partMoon := localSolarEclipseClampUnit((separation*separation + moonRadius*moonRadius - sunRadius*sunRadius) / (2 * separation * moonRadius))
|
|||
|
|
term := (-separation + sunRadius + moonRadius) *
|
|||
|
|
(separation + sunRadius - moonRadius) *
|
|||
|
|
(separation - sunRadius + moonRadius) *
|
|||
|
|
(separation + sunRadius + moonRadius)
|
|||
|
|
if term < 0 {
|
|||
|
|
term = 0
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
overlapArea := sunRadius*sunRadius*math.Acos(partSun) +
|
|||
|
|
moonRadius*moonRadius*math.Acos(partMoon) -
|
|||
|
|
0.5*math.Sqrt(term)
|
|||
|
|
|
|||
|
|
return overlapArea / sunArea
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func localSolarEclipseClampUnit(value float64) float64 {
|
|||
|
|
if value > 1 {
|
|||
|
|
return 1
|
|||
|
|
}
|
|||
|
|
if value < -1 {
|
|||
|
|
return -1
|
|||
|
|
}
|
|||
|
|
return value
|
|||
|
|
}
|