462 lines
19 KiB
Go
462 lines
19 KiB
Go
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package basic
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import (
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"fmt"
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"math"
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"sort"
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"time"
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)
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const (
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starOccultationLimbDefaultStep = 200 * time.Millisecond
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starOccultationLimbMinimumStep = 10 * time.Millisecond
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starOccultationLimbMaxSamples = 20000
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starOccultationLimbMinSamples = 64
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starOccultationLimbBoundStep = 60.0 / 86400.0
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starOccultationLimbBoundSpan = 3.5 / 24.0
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starOccultationLimbNodeDays = 10.0 / 1440.0
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starOccultationLimbNodeSpan = 4.0 / 24.0
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starOccultationLimbRootDays = 1e-3 / 86400.0
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starOccultationLimbUnrangedPadKM = 1.0
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)
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// StarOccultationLimbProfileOptions 控制精密恒星月掩的星迹采样 / sampling of a precise stellar occultation.
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type StarOccultationLimbProfileOptions struct {
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// Step 是星迹采样步长；零值 200 ms，小于 10 ms 提升到 10 ms；每段至少 64 个样本、总数不超过 20000，越界时自动调整。短于步长的遮挡或复现可能漏检 / track sampling step.
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Step time.Duration
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}
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// StarOccultationLimbSample 星迹上一个时刻的月缘几何，角量均为角秒、度 / limb geometry at one instant on the star track.
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type StarOccultationLimbSample struct {
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Time time.Time
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// SeparationArcsec 恒星到站心月心的角距 / star–Moon-centre separation.
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SeparationArcsec float64
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// LimbRadiusArcsec 恒星方向上的月缘角半径 / limb radius toward the star.
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LimbRadiusArcsec float64
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// MeanRadiusArcsec 参考圆月面角半径 / circular reference radius.
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MeanRadiusArcsec float64
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// PositionAngleDeg 恒星相对月心的位置角，自天北向东 / position angle of the star.
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PositionAngleDeg float64
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// Hidden 恒星位于月缘以内 / star is behind the limb.
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Hidden bool
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}
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// OccultationInterval 一段连续遮挡 / one continuous hidden interval.
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type OccultationInterval struct {
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Start time.Time
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End time.Time
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}
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// StarOccultationLimbProfileResult 一次恒星月掩沿星迹的月缘剖面与全部遮挡区间 / limb profile and every hidden interval of a stellar occultation.
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type StarOccultationLimbProfileResult struct {
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// Occultation 按同一剖面求得的标准结果，掩始、掩终为首次遮挡与最后复现 / standard result on the same profile.
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Occultation StarOccultationInfo
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// Segments 月缘起伏带内的采样段，按时间排序；深掩时为掩入侧与复现侧两段，掠掩时通常为一段 / samples inside the limb relief band.
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Segments [][]StarOccultationLimbSample
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// Hidden 全部遮挡区间，按时间排序 / every hidden interval.
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Hidden []OccultationInterval
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// ReferenceRadiusKM 样本 MeanRadiusArcsec 对应的参考月球半径 / reference lunar radius behind MeanRadiusArcsec.
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ReferenceRadiusKM float64
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// ReliefMinKM / ReliefMaxKM 判定所用的月缘半径范围 / limb radius range used for gating.
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ReliefMinKM float64
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ReliefMaxKM float64
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// Step 实际采用的采样步长 / effective step.
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Step time.Duration
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}
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type starLimbState struct {
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separation, limbRadius, meanRadius, positionAngle float64
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distanceKM float64
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}
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// starLimbEphemeris 掩甚前后 ±4 h 的地心月球、恒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 starLimbEphemeris struct {
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bodies []localEphemerisVectorNode
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axes []localEphemerisVectorNode
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base lunarLimbFrame
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hasDistance bool
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}
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func newStarLimbEphemeris(greatestTT float64, star StarCoordinate, limb LunarLimb, inst *Instance) (*starLimbEphemeris, bool) {
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half := int(math.Round(starOccultationLimbNodeSpan / starOccultationLimbNodeDays))
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ephemeris := &starLimbEphemeris{
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bodies: make([]localEphemerisVectorNode, 2*half+1),
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axes: make([]localEphemerisVectorNode, 2*half+1),
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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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starRA, starDec, distanceAU := starApparentRaDecDistanceGeocentric(tt, star, inst)
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if distanceAU <= 0 {
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distanceAU = 1
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} else {
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ephemeris.hasDistance = true
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}
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frame := newLunarLimbFrame(limb, tt, moon, inst)
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if !frame.valid || !finiteVector3(moon) {
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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: lunarEclipseLimbVector(starRA, starDec, distanceAU)}
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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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func (ephemeris *starLimbEphemeris) stateAt(tt float64, observer Observer) (starLimbState, bool) {
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moon, starVector, ok := interpolateLocalEphemerisVectors(ephemeris.bodies, tt)
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if !ok {
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return starLimbState{}, 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 starLimbState{}, false
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}
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geoDistance := math.Sqrt(lunarLimbDot(moon, moon))
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geoRA := normalizeRA(math.Atan2(moon[1], moon[0]) / rad)
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geoDec := math.Asin(clampUnit(moon[2]/geoDistance)) / rad
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ut := TT2UTC(tt)
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topoRA, topoDec := TopocentricRaDec(geoRA, geoDec, observer.Latitude, observer.Longitude, ut, geoDistance/149597870.7, observer.Height)
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topoRA = normalizeRA(topoRA)
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topoDistance := topocentricDistanceKM(geoRA, geoDec, geoDistance, observer, ut)
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starDistance := math.Sqrt(lunarLimbDot(starVector, starVector))
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starRA := normalizeRA(math.Atan2(starVector[1], starVector[0]) / rad)
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starDec := math.Asin(clampUnit(starVector[2]/starDistance)) / rad
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if ephemeris.hasDistance {
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starRA, starDec = TopocentricRaDec(starRA, starDec, observer.Latitude, observer.Longitude, ut, starDistance, observer.Height)
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starRA = normalizeRA(starRA)
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}
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if !finite(topoRA) || !finite(topoDec) || !finite(topoDistance) || topoDistance <= 0 || !finite(starRA) || !finite(starDec) {
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return starLimbState{}, false
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}
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frame := ephemeris.base
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if frame.axisX, ok = lunarLimbNormalize(axisX); !ok {
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return starLimbState{}, false
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}
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if frame.axisZ, ok = lunarLimbNormalize(axisZ); !ok {
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return starLimbState{}, false
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}
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// 两轴分别插值后不再严格正交，按 z 轴重新正交化 x 轴。
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if frame.axisX, ok = lunarLimbNormalize(lunarLimbReject(frame.axisX, frame.axisZ)); !ok {
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return starLimbState{}, false
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}
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frame.axisY = lunarLimbCross(frame.axisZ, frame.axisX)
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radiusKM, ok := frame.radiusKM(lunarEclipseLimbVector(topoRA, topoDec, topoDistance), lunarEclipseLimbVector(starRA, starDec, 1), false)
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if !ok {
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return starLimbState{}, false
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}
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return starLimbState{
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separation: angularSeparationDegrees(topoRA, topoDec, starRA, starDec) * 3600,
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limbRadius: angularSemidiameterArcsec(radiusKM, topoDistance),
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meanRadius: angularSemidiameterArcsec(moonEquatorialRadiusKM, topoDistance),
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positionAngle: occultationPositionAngle(topoRA, topoDec, starRA, starDec),
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distanceKM: topoDistance,
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}, true
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}
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// starOccultationLimbRange 返回剖面半径范围；剖面不报告范围时在掩甚扫一圈并外扩 1 km。
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func starOccultationLimbRange(tt float64, star StarCoordinate, observer Observer, limb LunarLimb, 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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topoRA, topoDec := moonTopocentricApparentRaDec(tt, observer, -1, inst)
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starRA, starDec := starApparentRaDec(tt, star, observer, inst)
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view, ok := frame.viewToward(lunarEclipseLimbVector(topoRA, topoDec, 1), lunarEclipseLimbVector(starRA, starDec, 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 - starOccultationLimbUnrangedPadKM, high + starOccultationLimbUnrangedPadKM, true
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}
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// starOccultationSeparationCrossing 自掩甚向 direction 一侧求角距升到 radiusKM 对应角半径的时刻；角距自掩甚单调增大。
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func starOccultationSeparationCrossing(greatestTT float64, direction float64, radiusKM float64, ephemeris *starLimbEphemeris, observer Observer) (float64, bool) {
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value := func(tt float64) float64 {
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state, ok := ephemeris.stateAt(tt, observer)
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if !ok {
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return math.NaN()
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}
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return state.separation - angularSemidiameterArcsec(radiusKM, state.distanceKM)
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}
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near, nearValue := greatestTT, value(greatestTT)
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if !finite(nearValue) {
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return 0, false
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}
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if nearValue >= 0 {
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return greatestTT, true
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}
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for step := 1; float64(step)*starOccultationLimbBoundStep <= starOccultationLimbBoundSpan; step++ {
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far := greatestTT + direction*float64(step)*starOccultationLimbBoundStep
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farValue := value(far)
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if !finite(farValue) {
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return 0, false
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}
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if farValue < 0 {
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near, nearValue = far, farValue
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continue
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}
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for i := 0; i < 64 && math.Abs(far-near) > starOccultationLimbRootDays; i++ {
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mid := (near + far) / 2
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if v := value(mid); v < 0 {
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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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type starLimbRoot struct {
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tt float64
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disappear bool
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}
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type starLimbScan struct {
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segments [][]StarOccultationLimbSample
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hidden [][2]float64
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lowKM float64
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highKM float64
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stepDays float64
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// grazing 为真表示星迹始终在月缘起伏带内（单段采样）。
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grazing bool
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}
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// starOccultationLimbScanAt 按剖面起伏带把星迹分必见、必掩与带内三段，带外两端遮挡状态由构造保证；ok 为假表示剖面无值或星历失败。
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func starOccultationLimbScanAt(greatestTT float64, star StarCoordinate, observer Observer, limb LunarLimb, stepDays float64, location *time.Location, inst *Instance) (starLimbScan, bool) {
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lowKM, highKM, ok := starOccultationLimbRange(greatestTT, star, observer, limb, inst)
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if !ok {
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return starLimbScan{}, false
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}
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scan := starLimbScan{lowKM: lowKM, highKM: highKM, stepDays: stepDays}
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ephemeris, ok := newStarLimbEphemeris(greatestTT, star, limb, inst)
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if !ok {
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return starLimbScan{}, false
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}
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outerLeft, okLeft := starOccultationSeparationCrossing(greatestTT, -1, highKM, ephemeris, observer)
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outerRight, okRight := starOccultationSeparationCrossing(greatestTT, 1, highKM, ephemeris, observer)
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if !okLeft || !okRight {
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return starLimbScan{}, false
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}
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if outerLeft == greatestTT && outerRight == greatestTT {
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return scan, true
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}
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innerLeft, okLeft := starOccultationSeparationCrossing(greatestTT, -1, lowKM, ephemeris, observer)
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innerRight, okRight := starOccultationSeparationCrossing(greatestTT, 1, lowKM, ephemeris, observer)
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if !okLeft || !okRight {
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return starLimbScan{}, false
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}
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type span struct {
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start, end float64
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hiddenAtStart bool
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hiddenAtEnd bool
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forceStart, forceEnd bool
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}
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spans := []span{{outerLeft, innerLeft, false, true, true, true}, {innerRight, outerRight, true, false, true, true}}
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if innerLeft == greatestTT && innerRight == greatestTT {
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spans = []span{{outerLeft, outerRight, false, false, true, true}}
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}
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total, shortest := 0.0, math.Inf(1)
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for _, item := range spans {
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total += item.end - item.start
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shortest = math.Min(shortest, item.end-item.start)
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}
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// 步长过大时掠掩两端都可见、中间的遮挡会整段漏掉，所以每段至少保留 64 个样本。
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if limit := shortest / starOccultationLimbMinSamples; shortest > 0 && stepDays > limit {
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stepDays = math.Max(limit, starOccultationLimbMinimumStep.Hours()/24)
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}
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if total/stepDays > starOccultationLimbMaxSamples {
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stepDays = total / starOccultationLimbMaxSamples
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}
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scan.stepDays = stepDays
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scan.grazing = len(spans) == 1
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gapAt := func(tt float64) (starLimbState, float64, bool) {
|
|||
|
|
state, ok := ephemeris.stateAt(tt, observer)
|
|||
|
|
return state, state.separation - state.limbRadius, ok
|
|||
|
|
}
|
|||
|
|
var roots []starLimbRoot
|
|||
|
|
for _, item := range spans {
|
|||
|
|
// 剖面范围零宽时带也零长，遮挡状态在该点翻转；不产样本，避免同刻样本。
|
|||
|
|
if item.end-item.start < starOccultationLimbRootDays {
|
|||
|
|
if item.hiddenAtStart != item.hiddenAtEnd {
|
|||
|
|
roots = append(roots, starLimbRoot{tt: item.start, disappear: item.hiddenAtEnd})
|
|||
|
|
}
|
|||
|
|
continue
|
|||
|
|
}
|
|||
|
|
count := int(math.Ceil((item.end - item.start) / stepDays))
|
|||
|
|
if count < 1 {
|
|||
|
|
count = 1
|
|||
|
|
}
|
|||
|
|
samples := make([]StarOccultationLimbSample, 0, count+1)
|
|||
|
|
previousTT, previousHidden := 0.0, false
|
|||
|
|
var previousGap float64
|
|||
|
|
for index := 0; index <= count; index++ {
|
|||
|
|
tt := item.start + (item.end-item.start)*float64(index)/float64(count)
|
|||
|
|
state, gap, ok := gapAt(tt)
|
|||
|
|
if !ok {
|
|||
|
|
return starLimbScan{}, false
|
|||
|
|
}
|
|||
|
|
hidden := gap < 0
|
|||
|
|
// 带两端的遮挡状态由角距保证，消除端点上的舍入抖动。
|
|||
|
|
if index == 0 && item.forceStart {
|
|||
|
|
hidden = item.hiddenAtStart
|
|||
|
|
}
|
|||
|
|
if index == count && item.forceEnd {
|
|||
|
|
hidden = item.hiddenAtEnd
|
|||
|
|
}
|
|||
|
|
samples = append(samples, StarOccultationLimbSample{
|
|||
|
|
Time: occultationTTToLocation(tt, location),
|
|||
|
|
SeparationArcsec: state.separation,
|
|||
|
|
LimbRadiusArcsec: state.limbRadius,
|
|||
|
|
MeanRadiusArcsec: state.meanRadius,
|
|||
|
|
PositionAngleDeg: state.positionAngle,
|
|||
|
|
Hidden: hidden,
|
|||
|
|
})
|
|||
|
|
if index > 0 && hidden != previousHidden {
|
|||
|
|
root := starOccultationLimbBisect(previousTT, tt, previousGap, gap, gapAt)
|
|||
|
|
roots = append(roots, starLimbRoot{tt: root, disappear: hidden})
|
|||
|
|
}
|
|||
|
|
previousTT, previousHidden, previousGap = tt, hidden, gap
|
|||
|
|
}
|
|||
|
|
scan.segments = append(scan.segments, samples)
|
|||
|
|
}
|
|||
|
|
sort.SliceStable(roots, func(i, j int) bool { return roots[i].tt < roots[j].tt })
|
|||
|
|
start := math.NaN()
|
|||
|
|
for _, root := range roots {
|
|||
|
|
if root.disappear {
|
|||
|
|
start = root.tt
|
|||
|
|
} else if !math.IsNaN(start) {
|
|||
|
|
scan.hidden = append(scan.hidden, [2]float64{start, root.tt})
|
|||
|
|
start = math.NaN()
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return scan, true
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// starOccultationLimbBisect 在相邻样本间求月缘间隙零点；端点被强制定号时零点可能落在端点上。
|
|||
|
|
func starOccultationLimbBisect(left, right, leftGap, rightGap float64, gapAt func(float64) (starLimbState, float64, bool)) float64 {
|
|||
|
|
if leftGap*rightGap > 0 {
|
|||
|
|
if math.Abs(leftGap) < math.Abs(rightGap) {
|
|||
|
|
return left
|
|||
|
|
}
|
|||
|
|
return right
|
|||
|
|
}
|
|||
|
|
for i := 0; i < 64 && right-left > starOccultationLimbRootDays; i++ {
|
|||
|
|
mid := (left + right) / 2
|
|||
|
|
_, gap, ok := gapAt(mid)
|
|||
|
|
if !ok {
|
|||
|
|
break
|
|||
|
|
}
|
|||
|
|
if (gap < 0) == (leftGap < 0) {
|
|||
|
|
left, leftGap = mid, gap
|
|||
|
|
} else {
|
|||
|
|
right = mid
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return (left + right) / 2
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// starOccultationInfoWithLimb 有月缘时按剖面判定是否成掩，掩始、掩终取首次遮挡与最后复现；剖面无值时退回圆月面。
|
|||
|
|
func starOccultationInfoWithLimb(greatestTT float64, star StarCoordinate, observer Observer, safetyMarginArcsec float64, location *time.Location, limb LunarLimb, inst *Instance) (StarOccultationInfo, bool) {
|
|||
|
|
if limb == nil {
|
|||
|
|
return starOccultationInfoAtGreatest(greatestTT, star, observer, safetyMarginArcsec, location, inst)
|
|||
|
|
}
|
|||
|
|
info, ok := starOccultationGreatestInfo(greatestTT, star, observer, safetyMarginArcsec, location, inst)
|
|||
|
|
if !ok {
|
|||
|
|
return StarOccultationInfo{}, false
|
|||
|
|
}
|
|||
|
|
scan, ok := starOccultationLimbScanAt(greatestTT, star, observer, limb, starOccultationLimbDefaultStep.Hours()/24, location, inst)
|
|||
|
|
if !ok {
|
|||
|
|
return starOccultationInfoAtGreatest(greatestTT, star, observer, safetyMarginArcsec, location, inst)
|
|||
|
|
}
|
|||
|
|
return starOccultationInfoFromScan(info, scan, location), len(scan.hidden) > 0
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func starOccultationInfoFromScan(info StarOccultationInfo, scan starLimbScan, location *time.Location) StarOccultationInfo {
|
|||
|
|
if len(scan.hidden) == 0 {
|
|||
|
|
info.Type = OccultationNone
|
|||
|
|
info.Immersion, info.Emersion = time.Time{}, time.Time{}
|
|||
|
|
info.ContactsComplete = false
|
|||
|
|
info.LunarLimbApplied = true
|
|||
|
|
return info
|
|||
|
|
}
|
|||
|
|
info.Type = OccultationTotal
|
|||
|
|
if scan.grazing {
|
|||
|
|
info.Type = OccultationGrazing
|
|||
|
|
}
|
|||
|
|
info.Immersion = occultationTTToLocation(scan.hidden[0][0], location)
|
|||
|
|
info.Emersion = occultationTTToLocation(scan.hidden[len(scan.hidden)-1][1], location)
|
|||
|
|
info.ContactsComplete = true
|
|||
|
|
info.LunarLimbApplied = true
|
|||
|
|
return info
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// StarOccultationLimbProfileWithInstance 沿星迹按月缘剖面精密求解一次恒星月掩，返回全部遮挡区间与带内采样；info 只取掩甚时刻与观测者，须为 UTC 口径结果（不能传 UT1 标注副本），恒星未被遮挡时 Occultation.Type 为 OccultationNone / precise stellar occultation along the track with a lunar limb profile.
|
|||
|
|
func StarOccultationLimbProfileWithInstance(info StarOccultationInfo, star StarCoordinate, limb LunarLimb, options StarOccultationLimbProfileOptions, inst *Instance) (StarOccultationLimbProfileResult, error) {
|
|||
|
|
if limb == nil {
|
|||
|
|
return StarOccultationLimbProfileResult{}, fmt.Errorf("%w: lunar limb profile is required", ErrInvalidOccultationInput)
|
|||
|
|
}
|
|||
|
|
if err := star.Validate(); err != nil {
|
|||
|
|
return StarOccultationLimbProfileResult{}, err
|
|||
|
|
}
|
|||
|
|
if err := info.Observer.Validate(); err != nil {
|
|||
|
|
return StarOccultationLimbProfileResult{}, err
|
|||
|
|
}
|
|||
|
|
if info.Greatest.IsZero() {
|
|||
|
|
return StarOccultationLimbProfileResult{}, fmt.Errorf("%w: greatest occultation time is required", ErrInvalidOccultationInput)
|
|||
|
|
}
|
|||
|
|
if options.Step < 0 {
|
|||
|
|
return StarOccultationLimbProfileResult{}, fmt.Errorf("%w: profile step cannot be negative", ErrInvalidOccultationInput)
|
|||
|
|
}
|
|||
|
|
step := options.Step
|
|||
|
|
if step == 0 {
|
|||
|
|
step = starOccultationLimbDefaultStep
|
|||
|
|
}
|
|||
|
|
if step < starOccultationLimbMinimumStep {
|
|||
|
|
step = starOccultationLimbMinimumStep
|
|||
|
|
}
|
|||
|
|
location := info.Greatest.Location()
|
|||
|
|
greatestTT := occultationTimeToTT(info.Greatest)
|
|||
|
|
base, ok := starOccultationGreatestInfo(greatestTT, star, info.Observer, math.Inf(1), location, inst)
|
|||
|
|
if !ok {
|
|||
|
|
return StarOccultationLimbProfileResult{}, fmt.Errorf("%w: geometry is unavailable at greatest occultation", ErrInvalidOccultationInput)
|
|||
|
|
}
|
|||
|
|
base.TargetID = star.ID
|
|||
|
|
scan, ok := starOccultationLimbScanAt(greatestTT, star, info.Observer, limb, step.Hours()/24, location, inst)
|
|||
|
|
if !ok {
|
|||
|
|
return StarOccultationLimbProfileResult{}, fmt.Errorf("%w: lunar limb profile has no value along the track", ErrInvalidOccultationInput)
|
|||
|
|
}
|
|||
|
|
profile := StarOccultationLimbProfileResult{
|
|||
|
|
Occultation: starOccultationInfoFromScan(base, scan, location),
|
|||
|
|
Segments: scan.segments,
|
|||
|
|
ReferenceRadiusKM: moonEquatorialRadiusKM,
|
|||
|
|
ReliefMinKM: scan.lowKM,
|
|||
|
|
ReliefMaxKM: scan.highKM,
|
|||
|
|
Step: time.Duration(math.Round(scan.stepDays * 86400 * float64(time.Second))),
|
|||
|
|
}
|
|||
|
|
for _, interval := range scan.hidden {
|
|||
|
|
profile.Hidden = append(profile.Hidden, OccultationInterval{
|
|||
|
|
Start: occultationTTToLocation(interval[0], location),
|
|||
|
|
End: occultationTTToLocation(interval[1], location),
|
|||
|
|
})
|
|||
|
|
}
|
|||
|
|
return profile, nil
|
|||
|
|
}
|