348 lines
12 KiB
Go
348 lines
12 KiB
Go
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package basic
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import "math"
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// LunarEclipseType 表示月食类型。
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type LunarEclipseType string
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const (
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// LunarEclipseNone 表示该次望月没有发生月食。
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LunarEclipseNone LunarEclipseType = "none"
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// LunarEclipsePenumbral 表示半影月食。
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LunarEclipsePenumbral LunarEclipseType = "penumbral"
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// LunarEclipsePartial 表示月偏食。
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LunarEclipsePartial LunarEclipseType = "partial"
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// LunarEclipseTotal 表示月全食。
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LunarEclipseTotal LunarEclipseType = "total"
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)
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// LunarEclipseResult 表示一次望月附近的月食几何结果。
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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 只需要落在目标望月附近，允许相差数天。
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type LunarEclipseResult struct {
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Type LunarEclipseType
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// Maximum 是食甚时刻；即使最终没有月食，也会返回该次望月附近
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// “月面中心最接近地影中心”的几何极值时刻。
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Maximum float64
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// Magnitude 是本影食分。纯半影月食时可为负值；无月食时为 0。
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Magnitude float64
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// PenumbralMagnitude 是半影食分。无半影接触时为 0。
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PenumbralMagnitude float64
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// MinimumDistance 是食甚时月心到地影中心的最小角距离，单位为弧度。
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MinimumDistance float64
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// Contact times:
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// PenumbralStart / PenumbralEnd: 半影食始 / 半影食终
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// PartialStart / PartialEnd: 初亏 / 复圆
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// TotalStart / TotalEnd: 食既 / 生光
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PenumbralStart float64
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PenumbralEnd float64
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PartialStart float64
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PartialEnd float64
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TotalStart float64
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TotalEnd float64
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HasPenumbral bool
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HasPartial bool
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HasTotal bool
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}
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type lunarShadowState struct {
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jde float64
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x float64
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y float64
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moonRadiusRad float64
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umbraRadiusRad float64
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penumbraRadiusRad float64
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}
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type lunarEclipseShadowModel int
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const (
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lunarEclipseShadowDanjon lunarEclipseShadowModel = iota
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lunarEclipseShadowChauvenet
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)
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const (
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lunarEarthEquatorialRadiusKM = 6378.1366
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lunarAstronomicalUnitKM = 1.49597870691e8
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// 沿用月食常量：
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// - 0.2725076 用于月亮视半径和半影几何
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// - 959.63 / 8.794 分别为太阳视半径与太阳视差的常用角秒常量
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lunarMoonRadiusRatio = 0.2725076
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lunarMoonRadiusScale = lunarMoonRadiusRatio * lunarEarthEquatorialRadiusKM * 1.0000036
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lunarSolarRadiusArcsec = 959.63
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lunarSolarParallaxArcsec = 8.794
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lunarLongitudeAberration = -3.4e-6
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lunarFiniteDifferenceStep = 60.0 / 86400.0
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// Chauvenet 体系：
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// - 地球有效半径取 0.99834 * 赤道半径
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// - 再统一乘 51/50 的大气放大因子
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lunarChauvenetEarthScale = 0.99834
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lunarChauvenetShadowGain = 51.0 / 50.0
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// Danjon 体系：
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// - 影半径只对月球水平视差项乘 1.01
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// - 太阳视半径与太阳视差项不再统一乘 1.02
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lunarDanjonParallaxScale = 1.01
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)
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var lunarArcsecPerRadian = 180.0 * 3600.0 / math.Pi
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// LunarEclipse 计算给定近望时刻附近的一次月食，默认使用 Danjon 影半径模型。
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//
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// seedJDE 为力学时儒略日（TT），只需落在目标望月附近，允许相差数天。
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// 返回值中的所有接触时刻也都是力学时儒略日。
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func LunarEclipse(seedJDE float64) LunarEclipseResult {
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return LunarEclipseDanjon(seedJDE)
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}
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// LunarEclipseDanjon 计算给定近望时刻附近的一次月食，使用 Danjon 影半径模型。
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func LunarEclipseDanjon(seedJDE float64) LunarEclipseResult {
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return lunarEclipse(seedJDE, lunarEclipseShadowDanjon)
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}
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// LunarEclipseChauvenet 计算给定近望时刻附近的一次月食，使用 Chauvenet 影半径模型。
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func LunarEclipseChauvenet(seedJDE float64) LunarEclipseResult {
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return lunarEclipse(seedJDE, lunarEclipseShadowChauvenet)
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}
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func lunarEclipse(seedJDE float64, shadowModel lunarEclipseShadowModel) LunarEclipseResult {
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fullMoonJDE := CalcMoonSHByJDE(seedJDE, 1)
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maximumJDE, state, dxdt, dydt, minimumDistance := refineLunarEclipseMaximum(fullMoonJDE, shadowModel)
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result := LunarEclipseResult{
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Type: LunarEclipseNone,
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Maximum: maximumJDE,
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MinimumDistance: minimumDistance,
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PenumbralMagnitude: (state.moonRadiusRad + state.penumbraRadiusRad - minimumDistance) / (2 * state.moonRadiusRad),
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}
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rawUmbralMagnitude := (state.moonRadiusRad + state.umbraRadiusRad - minimumDistance) / (2 * state.moonRadiusRad)
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if result.PenumbralMagnitude < 0 {
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result.PenumbralMagnitude = 0
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}
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if minimumDistance <= state.moonRadiusRad+state.penumbraRadiusRad {
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result.Type = LunarEclipsePenumbral
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result.HasPenumbral = true
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result.Magnitude = rawUmbralMagnitude
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result.PenumbralStart = refineLunarEclipseContact(
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state, dxdt, dydt, state.moonRadiusRad+state.penumbraRadiusRad, false, shadowModel,
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)
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result.PenumbralEnd = refineLunarEclipseContact(
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state, dxdt, dydt, state.moonRadiusRad+state.penumbraRadiusRad, true, shadowModel,
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)
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}
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if minimumDistance <= state.moonRadiusRad+state.umbraRadiusRad {
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result.Type = LunarEclipsePartial
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result.HasPartial = true
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result.Magnitude = rawUmbralMagnitude
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result.PartialStart = refineLunarEclipseContact(
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state, dxdt, dydt, state.moonRadiusRad+state.umbraRadiusRad, false, shadowModel,
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)
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result.PartialEnd = refineLunarEclipseContact(
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state, dxdt, dydt, state.moonRadiusRad+state.umbraRadiusRad, true, shadowModel,
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)
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}
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if minimumDistance <= state.umbraRadiusRad-state.moonRadiusRad {
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result.Type = LunarEclipseTotal
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result.HasTotal = true
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result.TotalStart = refineLunarEclipseContact(
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state, dxdt, dydt, state.umbraRadiusRad-state.moonRadiusRad, false, shadowModel,
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)
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result.TotalEnd = refineLunarEclipseContact(
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state, dxdt, dydt, state.umbraRadiusRad-state.moonRadiusRad, true, shadowModel,
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)
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}
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return result
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}
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// refineLunarEclipseMaximum 从近望初值出发，用有限差分速度做两轮几何极值修正。
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//
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// 这里直接在月心相对地影中心的二维平面上求 |r| 的极小值，
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func refineLunarEclipseMaximum(
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seedJDE float64,
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shadowModel lunarEclipseShadowModel,
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) (float64, lunarShadowState, float64, float64, float64) {
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currentJDE := seedJDE
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for i := 0; i < 2; i++ {
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state := computeLunarShadowState(currentJDE, shadowModel)
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nextState := computeLunarShadowState(currentJDE+lunarFiniteDifferenceStep, shadowModel)
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dxdt := (nextState.x - state.x) / lunarFiniteDifferenceStep
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dydt := (nextState.y - state.y) / lunarFiniteDifferenceStep
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denominator := dxdt*dxdt + dydt*dydt
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if denominator == 0 {
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finalState := computeLunarShadowState(currentJDE, shadowModel)
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return currentJDE, finalState, 0, 0, math.Hypot(finalState.x, finalState.y)
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}
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correction := -(state.x*dxdt + state.y*dydt) / denominator
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currentJDE += correction
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}
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linearState := computeLunarShadowState(currentJDE, shadowModel)
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nextLinearState := computeLunarShadowState(currentJDE+lunarFiniteDifferenceStep, shadowModel)
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dxdt := (nextLinearState.x - linearState.x) / lunarFiniteDifferenceStep
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dydt := (nextLinearState.y - linearState.y) / lunarFiniteDifferenceStep
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denominator := dxdt*dxdt + dydt*dydt
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if denominator == 0 {
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return currentJDE, linearState, dxdt, dydt, math.Hypot(linearState.x, linearState.y)
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}
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correction := -(linearState.x*dxdt + linearState.y*dydt) / denominator
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maximumJDE := currentJDE + correction
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finalState := computeLunarShadowState(maximumJDE, shadowModel)
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nextState := computeLunarShadowState(maximumJDE+lunarFiniteDifferenceStep, shadowModel)
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dxdt = (nextState.x - finalState.x) / lunarFiniteDifferenceStep
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dydt = (nextState.y - finalState.y) / lunarFiniteDifferenceStep
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return maximumJDE, finalState, dxdt, dydt, math.Hypot(finalState.x, finalState.y)
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}
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// refineLunarEclipseContact 先用固定速度近似求一次接触时刻，
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// 再在接触点重算半径并修正一次。
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func refineLunarEclipseContact(
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maximumState lunarShadowState,
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dxdt, dydt, boundaryRadius float64,
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afterMaximum bool,
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shadowModel lunarEclipseShadowModel,
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) float64 {
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firstGuess, ok := solveLineCircleContact(maximumState, dxdt, dydt, boundaryRadius, afterMaximum)
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if !ok {
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return 0
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}
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contactState := computeLunarShadowState(firstGuess, shadowModel)
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refinedRadius := boundaryRadius
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switch {
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case math.Abs(boundaryRadius-(maximumState.moonRadiusRad+maximumState.umbraRadiusRad)) < 1e-18:
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refinedRadius = contactState.moonRadiusRad + contactState.umbraRadiusRad
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case math.Abs(boundaryRadius-(maximumState.moonRadiusRad+maximumState.penumbraRadiusRad)) < 1e-18:
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refinedRadius = contactState.moonRadiusRad + contactState.penumbraRadiusRad
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case math.Abs(boundaryRadius-(maximumState.umbraRadiusRad-maximumState.moonRadiusRad)) < 1e-18:
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refinedRadius = contactState.umbraRadiusRad - contactState.moonRadiusRad
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}
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refinedGuess, ok := solveLineCircleContact(contactState, dxdt, dydt, refinedRadius, afterMaximum)
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if !ok {
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return firstGuess
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}
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return refinedGuess
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}
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// solveLineCircleContact 求月心轨迹与某个影界圆的交点时刻。
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func solveLineCircleContact(
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state lunarShadowState,
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dxdt, dydt, radius float64,
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afterMaximum bool,
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) (float64, bool) {
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a := dxdt*dxdt + dydt*dydt
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if a == 0 {
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return 0, false
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}
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b := 2 * (state.x*dxdt + state.y*dydt)
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c := state.x*state.x + state.y*state.y - radius*radius
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discriminant := b*b - 4*a*c
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if discriminant < 0 {
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return 0, false
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}
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root := math.Sqrt(discriminant)
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delta := (-b - root) / (2 * a)
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if afterMaximum {
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delta = (-b + root) / (2 * a)
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}
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return state.jde + delta, true
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}
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// computeLunarShadowState 计算某一力学时刻下，月心相对地影中心的二维几何状态。
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//
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// 所有内部角量统一使用弧度。影半径模型允许在 Danjon 与 Chauvenet 之间切换，
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// 其余月心轨迹与几何求交框架保持一致。
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func computeLunarShadowState(jde float64, shadowModel lunarEclipseShadowModel) lunarShadowState {
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julianCentury := (jde - 2451545.0) / 36525.0
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sunLongitude := HSunTrueLo(jde)*rad + sunLongitudeAberrationRad(julianCentury)
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sunLatitude := HSunTrueBo(jde) * rad
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moonLongitude := HMoonTrueLo(jde)*rad + lunarLongitudeAberration
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moonLatitude := HMoonTrueBo(jde)*rad + moonLatitudeAberrationRad(julianCentury)
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moonDistanceKM := HMoonAway(jde)
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sunDistanceAU := EarthAway(jde)
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moonRadiusArcsec := lunarMoonRadiusScale * lunarArcsecPerRadian / moonDistanceKM
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earthParallaxArcsec := lunarEarthEquatorialRadiusKM / moonDistanceKM * lunarArcsecPerRadian
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solarRadiusArcsec := lunarSolarRadiusArcsec / sunDistanceAU
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solarParallaxArcsec := lunarSolarParallaxArcsec / sunDistanceAU
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umbraRadiusArcsec, penumbraRadiusArcsec := lunarEclipseShadowRadiiArcsec(
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earthParallaxArcsec,
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solarRadiusArcsec,
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solarParallaxArcsec,
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shadowModel,
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)
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return lunarShadowState{
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jde: jde,
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x: normalizeRadians(moonLongitude+math.Pi-sunLongitude) * math.Cos((moonLatitude-sunLatitude)/2),
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y: moonLatitude + sunLatitude,
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moonRadiusRad: moonRadiusArcsec / lunarArcsecPerRadian,
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umbraRadiusRad: umbraRadiusArcsec / lunarArcsecPerRadian,
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penumbraRadiusRad: penumbraRadiusArcsec / lunarArcsecPerRadian,
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}
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}
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func lunarEclipseShadowRadiiArcsec(
|
|||
|
|
earthParallaxArcsec, solarRadiusArcsec, solarParallaxArcsec float64,
|
|||
|
|
shadowModel lunarEclipseShadowModel,
|
|||
|
|
) (float64, float64) {
|
|||
|
|
switch shadowModel {
|
|||
|
|
case lunarEclipseShadowDanjon:
|
|||
|
|
earthTerm := lunarDanjonParallaxScale * earthParallaxArcsec
|
|||
|
|
return earthTerm - solarRadiusArcsec + solarParallaxArcsec,
|
|||
|
|
earthTerm + solarRadiusArcsec + solarParallaxArcsec
|
|||
|
|
default:
|
|||
|
|
earthTerm := lunarChauvenetEarthScale * earthParallaxArcsec
|
|||
|
|
return (earthTerm - solarRadiusArcsec + solarParallaxArcsec) * lunarChauvenetShadowGain,
|
|||
|
|
(earthTerm + solarRadiusArcsec + solarParallaxArcsec) * lunarChauvenetShadowGain
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func normalizeRadians(angle float64) float64 {
|
|||
|
|
angle = math.Mod(angle, 2*math.Pi)
|
|||
|
|
if angle > math.Pi {
|
|||
|
|
angle -= 2 * math.Pi
|
|||
|
|
}
|
|||
|
|
if angle <= -math.Pi {
|
|||
|
|
angle += 2 * math.Pi
|
|||
|
|
}
|
|||
|
|
return angle
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func sunLongitudeAberrationRad(julianCentury float64) float64 {
|
|||
|
|
meanAnomaly := -0.043126 + 628.301955*julianCentury - 0.000002732*julianCentury*julianCentury
|
|||
|
|
eccentricity := 0.016708634 - 0.000042037*julianCentury - 0.0000001267*julianCentury*julianCentury
|
|||
|
|
return -20.49552 * (1 + eccentricity*math.Cos(meanAnomaly)) / lunarArcsecPerRadian
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func moonLatitudeAberrationRad(julianCentury float64) float64 {
|
|||
|
|
argument := 0.057 + 8433.4662*julianCentury + 0.000064*julianCentury*julianCentury
|
|||
|
|
return 0.063 * math.Sin(argument) / lunarArcsecPerRadian
|
|||
|
|
}
|