feat: 完善时标与天象几何计算并扩展输出接口
- 新增时标、ΔT 模型、质心时间与 UT1 支持 - 改进日月食、月掩、行星事件及路径边界计算 - 完善恒星三维自行与动态距离传播 - 扩展 SVG、GeoJSON、KML 输出与底层距离换算工具 - 整理中英文手册、示例资源及回归测试
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@@ -217,7 +217,7 @@ func newOccultationRiseSetContext(
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target := newOccultationRiseSetBody(targetRA, targetDec, targetDistanceKM)
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return occultationRiseSetContext{
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tt: tt,
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siderealDegrees: ApparentSiderealTime(TD2UT(tt, false)) * 15,
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siderealDegrees: ApparentSiderealTime(TT2UT1(tt)) * 15,
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moonRA: moonRA,
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moonDec: moonDec,
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moon: moon,
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@@ -245,7 +245,7 @@ func newOccultationRiseSetContextFromVectors(
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target, _, _, targetOK := occultationRiseSetBodyFromVector(targetXYZ, targetAtFiniteDistance)
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return occultationRiseSetContext{
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tt: tt,
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siderealDegrees: ApparentSiderealTime(TD2UT(tt, false)) * 15,
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siderealDegrees: ApparentSiderealTime(TT2UT1(tt)) * 15,
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moonRA: moonRA,
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moonDec: moonDec,
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moon: moon,
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@@ -635,7 +635,7 @@ func (evaluation occultationRiseSetEvaluation) pointsAt(
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if !evaluation.center.valid || !evaluation.before.valid || !evaluation.after.valid {
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return result
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}
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gst := ApparentSiderealTime(TD2UT(evaluation.tt, false)) * 15
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gst := ApparentSiderealTime(TT2UT1(evaluation.tt)) * 15
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centerLongitude := normalizeLongitude(evaluation.center.moonRA - gst)
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centerLatitude := evaluation.center.moonDec
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appendRoots := func(greatest bool) {
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@@ -776,6 +776,130 @@ func (evaluation occultationRiseSetEvaluation) classify(
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}, occultationRiseSetCurveKey{phase: phase, direction: direction}, true
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}
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// occultationSiderealRatePerDay 是视恒星时的角速率（弧度/日），用于观测者与天顶矢量的时间导数。
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const occultationSiderealRatePerDay = 2 * math.Pi * 1.00273790935
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// occultationRiseSetBodyVelocity 由前后时刻的体位置给出速度（千米/日）；点源（距离为零）返回零。
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func occultationRiseSetBodyVelocity(before, after occultationRiseSetBody, stepDays float64) occultationPathVector {
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if stepDays <= 0 || before.distanceKM <= 0 || after.distanceKM <= 0 {
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return occultationPathVector{}
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}
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return occultationPathScale(occultationPathSub(after.positionKM, before.positionKM), 1/(2*stepDays))
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}
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// occultationRiseSetDirectionRate 给出单位方向的时间导数 du/dt = (v − u(u·v))/|p|。
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func occultationRiseSetDirectionRate(position, velocity, direction occultationPathVector) occultationPathVector {
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norm := occultationPathNorm(position)
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if norm <= 0 {
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return occultationPathVector{}
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}
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radial := occultationPathScale(direction, occultationPathDot(direction, velocity))
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return occultationPathScale(occultationPathSub(velocity, radial), 1/norm)
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}
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// occultationRiseSetRadiusRate 给出视半径 asin(R/d) 的解析时间导数（度/日），d 为站心距离。
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func occultationRiseSetRadiusRate(
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body occultationRiseSetBody,
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observer, direction, velocity occultationPathVector,
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radiusKM float64,
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) (float64, float64, bool) {
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if body.distanceKM <= 0 || radiusKM <= 0 {
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return 0, 0, true
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}
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position := occultationPathSub(body.positionKM, observer)
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distance := occultationPathNorm(position)
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if distance <= radiusKM {
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return 0, 0, false
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}
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ratio := radiusKM / distance
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sinRadius := math.Max(-1, math.Min(1, ratio))
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cosRadius := math.Sqrt(math.Max(0, 1-sinRadius*sinRadius))
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if cosRadius <= 1e-12 {
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return 0, 0, false
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}
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return math.Asin(sinRadius) / rad,
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-(ratio / distance) * occultationPathDot(velocity, direction) / cosRadius / rad, true
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}
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// contactRateAt 用体位置的前后差分给出接触度量的解析时间导数（度/日）：与 contactDerivative 的中心差分同口径，
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// 但没有差分噪声，且不需要为前后时刻各求一次站心几何。
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func (evaluation occultationRiseSetEvaluation) contactRateAt(longitude, latitude float64) float64 {
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center := evaluation.center
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observer, observerDistance, _ := occultationRiseSetObserverVectors(center.siderealDegrees, longitude, latitude)
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observerVelocity := occultationPathCross(occultationPathVector{z: occultationSiderealRatePerDay}, observer)
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moonPosition := occultationPathSub(center.moon.positionKM, observer)
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targetPosition := occultationPathSub(center.target.positionKM, observer)
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moonDirection := occultationRiseSetTopocentricDirection(center.moon, observer)
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targetDirection := occultationRiseSetTopocentricDirection(center.target, observer)
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moonVelocity := occultationPathSub(
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occultationRiseSetBodyVelocity(evaluation.before.moon, evaluation.after.moon, occultationRiseSetDerivativeStepDays),
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observerVelocity,
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)
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targetVelocity := occultationPathSub(
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occultationRiseSetBodyVelocity(evaluation.before.target, evaluation.after.target, occultationRiseSetDerivativeStepDays),
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observerVelocity,
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)
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if center.target.distanceKM <= 0 {
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// 点源目标没有站心视差：视线方向就是地心视方向，速率取单位矢量的前后差分。
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// 零位置减观测者会得到日尺度的虚假速率，掩带边界因此无法加密。
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targetPosition = targetDirection
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targetVelocity = occultationPathScale(
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occultationPathSub(evaluation.after.target.direction, evaluation.before.target.direction),
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1/(2*occultationRiseSetDerivativeStepDays),
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)
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}
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moonDirectionRate := occultationRiseSetDirectionRate(moonPosition, moonVelocity, moonDirection)
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targetDirectionRate := occultationRiseSetDirectionRate(targetPosition, targetVelocity, targetDirection)
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cosSeparation := math.Max(-1, math.Min(1, occultationPathDot(moonDirection, targetDirection)))
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sinSeparation := math.Sqrt(math.Max(0, 1-cosSeparation*cosSeparation))
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if sinSeparation <= 1e-12 {
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return math.NaN()
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}
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separationRate := -(occultationPathDot(moonDirectionRate, targetDirection) +
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occultationPathDot(moonDirection, targetDirectionRate)) / sinSeparation / rad
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if occultationRiseSetTopocentricDistance(center.moon, observerDistance) <= 0 {
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return math.NaN()
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}
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moonRadius, moonRadiusRate, moonOK := occultationRiseSetRadiusRate(
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center.moon, observer, moonDirection, moonVelocity, moonEquatorialRadiusKM,
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)
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targetRadius, targetRadiusRate, targetOK := occultationRiseSetRadiusRate(
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center.target, observer, targetDirection, targetVelocity, center.targetRadiusKM,
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)
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if !moonOK || !targetOK {
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return math.NaN()
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}
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if center.internalContact {
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if moonRadius >= targetRadius {
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return separationRate - (moonRadiusRate - targetRadiusRate)
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}
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return separationRate + (moonRadiusRate - targetRadiusRate)
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}
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return separationRate - moonRadiusRate - targetRadiusRate
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}
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// moonAltitudeRateAt 给出月球几何高度角的解析时间导数（度/日）。
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func (evaluation occultationRiseSetEvaluation) moonAltitudeRateAt(longitude, latitude float64) float64 {
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center := evaluation.center
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observer, _, zenith := occultationRiseSetObserverVectors(center.siderealDegrees, longitude, latitude)
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spin := occultationPathVector{z: occultationSiderealRatePerDay}
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observerVelocity := occultationPathCross(spin, observer)
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moonPosition := occultationPathSub(center.moon.positionKM, observer)
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moonDirection := occultationRiseSetTopocentricDirection(center.moon, observer)
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moonVelocity := occultationPathSub(
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occultationRiseSetBodyVelocity(evaluation.before.moon, evaluation.after.moon, occultationRiseSetDerivativeStepDays),
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observerVelocity,
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)
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moonDirectionRate := occultationRiseSetDirectionRate(moonPosition, moonVelocity, moonDirection)
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sinAltitude := math.Max(-1, math.Min(1, occultationPathDot(moonDirection, zenith)))
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cosAltitude := math.Sqrt(math.Max(0, 1-sinAltitude*sinAltitude))
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if cosAltitude <= 1e-12 {
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return math.NaN()
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}
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return (occultationPathDot(moonDirectionRate, zenith) +
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occultationPathDot(moonDirection, occultationPathCross(spin, zenith))) / cosAltitude / rad
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}
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func (evaluation occultationRiseSetEvaluation) contactDerivative(longitude, latitude float64) float64 {
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before := evaluation.before.stateAt(longitude, latitude)
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after := evaluation.after.stateAt(longitude, latitude)
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