361 lines
15 KiB
Go
361 lines
15 KiB
Go
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package basic
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import (
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"math"
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"time"
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)
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// occultationLimbTarget 给出某时刻目标的地心视赤经、赤纬（度）与地心距（km，恒星为 0）及站心角半径（角秒）。
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type occultationLimbTarget func(tt float64) (ra, dec, distanceKM, radiusArcsec float64, ok bool)
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func planetOccultationLimbTarget(config planetOccultationConfig, observer Observer) occultationLimbTarget {
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return func(tt float64) (float64, float64, float64, float64, bool) {
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ra, dec := config.apparentRaDecN(tt, -1)
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distanceKM := config.earthDistanceN(tt, -1) * angularDiameterAstronomicalUnitKM
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radius := planetTopocentricSemidiameterN(tt, config, observer, -1)
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return ra, dec, distanceKM, radius, finite(ra) && finite(dec) && finite(distanceKM) && finite(radius)
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}
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}
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const (
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occultationLimbCrossingStepDays = 60.0 / 86400.0
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occultationLimbCrossingSpanDays = 3.5 / 24.0
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occultationLimbRootDays = 1e-3 / 86400.0
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occultationLimbMinSamples = 64
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occultationLimbMaxSamples = 4000
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occultationLimbBandPadArcsec = 0.05
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occultationLimbUnrangedPadKM = 1.0
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planetOccultationLimbStepDays = 0.25 / 86400.0
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)
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// occultationLimbRangeKM 返回剖面半径范围；剖面不报告范围时在 tt 时刻朝目标扫一圈并外扩 1 km。
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func occultationLimbRangeKM(tt float64, limb LunarLimb, observer Observer, target occultationLimbTarget, inst *Instance) (float64, float64, bool) {
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geoRA, geoDec := HMoonGeocentricApparentRaDecNWithInstance(tt, -1, inst)
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geoDistance := HMoonAwayNWithInstance(tt, -1, inst)
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frame := newLunarLimbFrame(limb, tt, lunarEclipseLimbVector(geoRA, geoDec, geoDistance), inst)
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if !frame.valid {
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return 0, 0, false
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}
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if frame.ranged {
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return frame.minKM, frame.maxKM, true
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}
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ra, dec, _, _, ok := target(tt)
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if !ok {
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return 0, 0, false
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}
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topoRA, topoDec := moonTopocentricApparentRaDec(tt, observer, -1, inst)
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view, ok := frame.viewToward(lunarEclipseLimbVector(topoRA, topoDec, 1), lunarEclipseLimbVector(ra, dec, 1))
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if !ok {
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return 0, 0, false
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}
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low, high := math.Inf(1), math.Inf(-1)
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for offset := 0.0; offset < 360; offset += frame.stepDeg {
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radius, ok := frame.radiusAt(view, offset)
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if !ok {
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return 0, 0, false
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}
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low, high = math.Min(low, radius), math.Max(high, radius)
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}
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return low - occultationLimbUnrangedPadKM, high + occultationLimbUnrangedPadKM, true
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}
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// occultationLimbCrossing 自 greatestTT 向 direction 一侧求圆月面间隙升到 level 的时刻；间隙自掩甚单调增大，起点已不低于 level 时返回起点。
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func occultationLimbCrossing(greatestTT, direction, level float64, circular func(float64) (float64, bool)) (float64, bool) {
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near := greatestTT
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value, ok := circular(near)
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if !ok {
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return 0, false
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}
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if value >= level {
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return greatestTT, true
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}
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for step := 1; float64(step)*occultationLimbCrossingStepDays <= occultationLimbCrossingSpanDays; step++ {
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far := greatestTT + direction*float64(step)*occultationLimbCrossingStepDays
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farValue, ok := circular(far)
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if !ok {
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return 0, false
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}
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if farValue < level {
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near = far
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continue
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}
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for i := 0; i < 64 && math.Abs(far-near) > occultationLimbRootDays; i++ {
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mid := (near + far) / 2
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midValue, ok := circular(mid)
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if !ok {
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return 0, false
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}
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if midValue < level {
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near = mid
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} else {
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far = mid
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}
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}
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return (near + far) / 2, true
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}
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return 0, false
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}
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// occultationLimbOuterRoots 在 [start, end] 上采样月缘间隙，返回首个由正转负与最后一个由负转正的零点；
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// 端点状态由调用方保证（hiddenAtStart、hiddenAtEnd），ok 为假表示剖面无值或星历失败。
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func occultationLimbOuterRoots(start, end float64, hiddenAtStart, hiddenAtEnd bool, gap func(float64) (float64, bool)) (first, last float64, found, ok bool) {
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if end <= start {
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return 0, 0, false, true
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}
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count := int(math.Ceil((end - start) / planetOccultationLimbStepDays))
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if count < occultationLimbMinSamples {
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count = occultationLimbMinSamples
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}
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if count > occultationLimbMaxSamples {
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count = occultationLimbMaxSamples
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}
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first, last = math.NaN(), math.NaN()
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previousTT, previousHidden := start, hiddenAtStart
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for index := 0; index <= count; index++ {
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tt := start + (end-start)*float64(index)/float64(count)
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value, valueOK := gap(tt)
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if !valueOK {
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return 0, 0, false, false
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}
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hidden := value < 0
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if index == 0 {
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hidden = hiddenAtStart
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} else if index == count {
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hidden = hiddenAtEnd
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}
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if index > 0 && hidden != previousHidden {
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root := occultationLimbBisect(previousTT, tt, previousHidden, gap)
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if hidden && math.IsNaN(first) {
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first = root
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}
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if !hidden {
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last = root
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}
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}
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previousTT, previousHidden = tt, hidden
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}
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return first, last, !math.IsNaN(first) || !math.IsNaN(last), true
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}
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// occultationLimbBisect 在相邻样本间求遮挡状态翻转的时刻；leftHidden 是左端的遮挡状态。
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func occultationLimbBisect(left, right float64, leftHidden bool, gap func(float64) (float64, bool)) float64 {
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for i := 0; i < 64 && right-left > occultationLimbRootDays; i++ {
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mid := (left + right) / 2
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value, ok := gap(mid)
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if !ok {
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break
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}
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if (value < 0) == leftHidden {
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left = mid
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} else {
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right = mid
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}
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}
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return (left + right) / 2
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}
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// planetOccultationInfoWithLimb 有月缘时按剖面判定行星月掩：只在圆月面间隙落进月缘起伏带的时段采样全方向月缘间隙，
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// 取最外侧的外切与内切；月缘可新增或取消圆月面的掠掩与全掩，有正持续时间的接触一律按偏掩或全掩上报。剖面无值时退回圆月面结果。
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func planetOccultationInfoWithLimb(greatestTT float64, config planetOccultationConfig, observer Observer, safetyMarginArcsec float64, location *time.Location, limb LunarLimb, inst *Instance) (PlanetOccultationInfo, bool) {
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circularInfo, circularOK := planetOccultationInfoAtGreatest(greatestTT, config, observer, safetyMarginArcsec, location, inst)
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if limb == nil {
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return circularInfo, circularOK
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}
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info, state, ok := planetOccultationGreatestInfo(greatestTT, config, observer, safetyMarginArcsec, location, inst)
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if !ok {
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return circularInfo, circularOK
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}
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target := planetOccultationLimbTarget(config, observer)
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lowKM, highKM, ok := occultationLimbRangeKM(greatestTT, limb, observer, target, inst)
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if !ok {
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return circularInfo, circularOK
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}
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ephemeris, ok := newPlanetLimbEphemeris(greatestTT, config, limb, inst)
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if !ok {
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return circularInfo, circularOK
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}
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// 月缘间隙 ≈ 圆月面间隙 −（月缘半径 − 参考半径），所以圆月面间隙不低于 bandHigh 必不接触、不高于 bandLow 必已接触。
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// 起伏带以角秒计，外扩一点容差覆盖月心距在事件内的变化。
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scale := state.moonSemidiameter / moonEquatorialRadiusKM
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bandLow := (lowKM-moonEquatorialRadiusKM)*scale - occultationLimbBandPadArcsec
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bandHigh := (highKM-moonEquatorialRadiusKM)*scale + occultationLimbBandPadArcsec
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circular := func(internal bool) func(float64) (float64, bool) {
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return func(tt float64) (float64, bool) { return ephemeris.circularGap(tt, observer, internal) }
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}
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limbGap := func(internal bool) func(float64) (float64, bool) {
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return func(tt float64) (float64, bool) { return ephemeris.limbGap(tt, observer, internal) }
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}
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// solve 求一种接触的最外侧掩入、复现：圆月面间隙在 [bandLow, bandHigh] 之外的两端遮挡状态已知，只在带内采样。
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solve := func(internal bool, circularMinimum float64) (float64, float64, bool, bool) {
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if circularMinimum >= bandHigh {
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return 0, 0, false, true
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}
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outerLeft, okLeft := occultationLimbCrossing(greatestTT, -1, bandHigh, circular(internal))
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outerRight, okRight := occultationLimbCrossing(greatestTT, 1, bandHigh, circular(internal))
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if !okLeft || !okRight {
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return 0, 0, false, false
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}
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if circularMinimum > bandLow {
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first, last, found, ok := occultationLimbOuterRoots(outerLeft, outerRight, false, false, limbGap(internal))
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return first, last, found && !math.IsNaN(first) && !math.IsNaN(last), ok
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}
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innerLeft, okLeft := occultationLimbCrossing(greatestTT, -1, bandLow, circular(internal))
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innerRight, okRight := occultationLimbCrossing(greatestTT, 1, bandLow, circular(internal))
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if !okLeft || !okRight {
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return 0, 0, false, false
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}
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first, _, foundLeft, okLeftRoots := occultationLimbOuterRoots(outerLeft, innerLeft, false, true, limbGap(internal))
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_, last, foundRight, okRightRoots := occultationLimbOuterRoots(innerRight, outerRight, true, false, limbGap(internal))
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return first, last, foundLeft && foundRight && !math.IsNaN(first) && !math.IsNaN(last), okLeftRoots && okRightRoots
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}
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externalImmersion, externalEmersion, external, ok := solve(false, state.externalContactMetric)
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if !ok {
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return circularInfo, circularOK
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}
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if !external {
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return PlanetOccultationInfo{}, false
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}
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internalImmersion, internalEmersion, internal, ok := solve(true, state.internalContactMetric)
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if !ok {
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return circularInfo, circularOK
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}
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info.Type = OccultationPartial
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info.ExternalImmersion = occultationTTToLocation(externalImmersion, location)
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info.ExternalEmersion = occultationTTToLocation(externalEmersion, location)
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if internal && internalImmersion > externalImmersion && internalEmersion < externalEmersion && internalImmersion < internalEmersion {
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info.Type = OccultationTotal
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info.HasInternalContacts = true
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info.InternalImmersion = occultationTTToLocation(internalImmersion, location)
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info.InternalEmersion = occultationTTToLocation(internalEmersion, location)
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}
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info.ContactsComplete = true
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info.LunarLimbApplied = true
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return info, true
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}
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// planetLimbEphemeris 掩甚前后 ±4 h 的地心月球、行星视位置与月球本体坐标架插值表；站心换算逐点精确计算。
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type planetLimbEphemeris struct {
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bodies []localEphemerisVectorNode
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axes []localEphemerisVectorNode
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base lunarLimbFrame
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radiusKM float64
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}
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func newPlanetLimbEphemeris(greatestTT float64, config planetOccultationConfig, limb LunarLimb, inst *Instance) (*planetLimbEphemeris, bool) {
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half := int(math.Round(starOccultationLimbNodeSpan / starOccultationLimbNodeDays))
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ephemeris := &planetLimbEphemeris{
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bodies: make([]localEphemerisVectorNode, 2*half+1),
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axes: make([]localEphemerisVectorNode, 2*half+1),
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radiusKM: config.equatorialRadiusKM,
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}
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for index := range ephemeris.bodies {
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tt := greatestTT + float64(index-half)*starOccultationLimbNodeDays
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moonRA, moonDec := HMoonGeocentricApparentRaDecNWithInstance(tt, -1, inst)
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moon := lunarEclipseLimbVector(moonRA, moonDec, HMoonAwayNWithInstance(tt, -1, inst))
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planetRA, planetDec := config.apparentRaDecN(tt, -1)
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planet := lunarEclipseLimbVector(planetRA, planetDec, config.earthDistanceN(tt, -1)*angularDiameterAstronomicalUnitKM)
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frame := newLunarLimbFrame(limb, tt, moon, inst)
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if !frame.valid || !finiteVector3(moon) || !finiteVector3(planet) {
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return nil, false
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}
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if index == half {
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ephemeris.base = frame
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}
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ephemeris.bodies[index] = localEphemerisVectorNode{tt: tt, first: moon, next: planet}
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ephemeris.axes[index] = localEphemerisVectorNode{tt: tt, first: frame.axisX, next: frame.axisZ}
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}
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return ephemeris, true
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}
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// planetLimbTopocentric 是插值得到的站心月球、行星方向与距离（km），以及该时刻的月球本体坐标架。
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type planetLimbTopocentric struct {
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moon, planet [3]float64
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moonDistance, planetRadius float64
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frame lunarLimbFrame
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}
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func (ephemeris *planetLimbEphemeris) topocentricAt(tt float64, observer Observer) (planetLimbTopocentric, bool) {
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moon, planet, ok := interpolateLocalEphemerisVectors(ephemeris.bodies, tt)
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if !ok {
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return planetLimbTopocentric{}, false
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}
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axisX, axisZ, ok := interpolateLocalEphemerisVectors(ephemeris.axes, tt)
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if !ok {
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return planetLimbTopocentric{}, false
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}
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ut := TT2UTC(tt)
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toTopocentric := func(vector [3]float64) (float64, float64, float64, bool) {
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distance := math.Sqrt(lunarLimbDot(vector, vector))
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ra := normalizeRA(math.Atan2(vector[1], vector[0]) / rad)
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dec := math.Asin(clampUnit(vector[2]/distance)) / rad
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topoRA, topoDec := TopocentricRaDec(ra, dec, observer.Latitude, observer.Longitude, ut, distance/angularDiameterAstronomicalUnitKM, observer.Height)
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topoDistance := topocentricDistanceKM(ra, dec, distance, observer, ut)
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return normalizeRA(topoRA), topoDec, topoDistance, finite(topoRA) && finite(topoDec) && finite(topoDistance) && topoDistance > 0
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}
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moonRA, moonDec, moonDistance, okMoon := toTopocentric(moon)
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planetRA, planetDec, planetDistance, okPlanet := toTopocentric(planet)
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if !okMoon || !okPlanet || planetDistance <= ephemeris.radiusKM {
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return planetLimbTopocentric{}, false
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}
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|
frame := ephemeris.base
|
||
|
|
if frame.axisZ, ok = lunarLimbNormalize(axisZ); !ok {
|
||
|
|
return planetLimbTopocentric{}, false
|
||
|
|
}
|
||
|
|
if frame.axisX, ok = lunarLimbNormalize(lunarLimbReject(axisX, frame.axisZ)); !ok {
|
||
|
|
return planetLimbTopocentric{}, false
|
||
|
|
}
|
||
|
|
frame.axisY = lunarLimbCross(frame.axisZ, frame.axisX)
|
||
|
|
return planetLimbTopocentric{
|
||
|
|
moon: lunarEclipseLimbVector(moonRA, moonDec, moonDistance),
|
||
|
|
planet: lunarEclipseLimbVector(planetRA, planetDec, 1),
|
||
|
|
moonDistance: moonDistance,
|
||
|
|
planetRadius: math.Asin(ephemeris.radiusKM / planetDistance),
|
||
|
|
frame: frame,
|
||
|
|
}, true
|
||
|
|
}
|
||
|
|
|
||
|
|
// circularGap 圆月面外切或内切间隙（角秒），与 planetOccultationStateAt 同口径。
|
||
|
|
func (ephemeris *planetLimbEphemeris) circularGap(tt float64, observer Observer, internal bool) (float64, bool) {
|
||
|
|
state, ok := ephemeris.topocentricAt(tt, observer)
|
||
|
|
if !ok {
|
||
|
|
return 0, false
|
||
|
|
}
|
||
|
|
separation := math.Acos(clampUnit(lunarLimbDot(state.moon, state.planet) / state.moonDistance))
|
||
|
|
moonRadius := math.Asin(moonEquatorialRadiusKM / state.moonDistance)
|
||
|
|
if internal {
|
||
|
|
return (separation - moonRadius + state.planetRadius) * angularDiameterArcsecPerRadian, true
|
||
|
|
}
|
||
|
|
return (separation - moonRadius - state.planetRadius) * angularDiameterArcsecPerRadian, true
|
||
|
|
}
|
||
|
|
|
||
|
|
// limbGap 全方向月缘外切或内切间隙（角秒）。
|
||
|
|
func (ephemeris *planetLimbEphemeris) limbGap(tt float64, observer Observer, internal bool) (float64, bool) {
|
||
|
|
state, ok := ephemeris.topocentricAt(tt, observer)
|
||
|
|
if !ok {
|
||
|
|
return 0, false
|
||
|
|
}
|
||
|
|
view, ok := state.frame.viewToward(state.moon, state.planet)
|
||
|
|
if !ok {
|
||
|
|
return 0, false
|
||
|
|
}
|
||
|
|
contact := lunarLimbContact{
|
||
|
|
frame: &state.frame,
|
||
|
|
view: view,
|
||
|
|
distanceKM: state.moonDistance,
|
||
|
|
separation: math.Acos(clampUnit(lunarLimbDot(state.moon, state.planet) / state.moonDistance)),
|
||
|
|
targetRadius: state.planetRadius,
|
||
|
|
}
|
||
|
|
if internal {
|
||
|
|
inner, ok := contact.innerRadius(true)
|
||
|
|
if !ok {
|
||
|
|
return 0, false
|
||
|
|
}
|
||
|
|
return (contact.separation - math.Abs(inner-contact.targetRadius)) * angularDiameterArcsecPerRadian, true
|
||
|
|
}
|
||
|
|
outer, ok := contact.outerRadius()
|
||
|
|
if !ok {
|
||
|
|
return 0, false
|
||
|
|
}
|
||
|
|
return (contact.separation - outer - contact.targetRadius) * angularDiameterArcsecPerRadian, true
|
||
|
|
}
|