273 lines
11 KiB
Go
273 lines
11 KiB
Go
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package basic
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import (
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"math"
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"sort"
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)
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const (
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schaeferNightSkyNanolambert = 180.0
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schaeferNanolambertToErg = 1.02e-15
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schaeferSunMagnitude = -26.74
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schaeferZeroMagnitudeRef = -11.05
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schaeferMinSeparationDeg = 0.1
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schaeferTwilightLowSunDeg = -3.0
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schaeferDaylightHighSunDeg = 4.0
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schaeferScotopicLimitNL = 1479.1
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)
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// HeliacalOptions 偕日可见计算参数；零值使用消光系数 0.25 星等/大气质量、目标最低高度 0.5° / heliacal visibility options.
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type HeliacalOptions struct {
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// ExtinctionCoefficient 大气消光系数（星等/大气质量）/ extinction in magnitudes per airmass.
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ExtinctionCoefficient float64
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// MinTargetAltitude 目标最低几何高度（度）/ minimum geometric target altitude in degrees.
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MinTargetAltitude float64
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// Moonlight 为 true 时计入月光散射（Krisciunas–Schaefer）；默认不计 / include scattered moonlight when true.
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Moonlight bool
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}
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func (options HeliacalOptions) normalized() HeliacalOptions {
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if !(options.ExtinctionCoefficient > 0) {
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options.ExtinctionCoefficient = 0.25
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}
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if !(options.MinTargetAltitude > 0) {
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options.MinTargetAltitude = 0.5
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}
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return options
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}
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func schaeferAirmass(altitudeDeg float64) float64 {
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z := math.Min(90, math.Max(0, 90-altitudeDeg)) * rad
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c := math.Cos(z)
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return 1 / (c + 0.025*math.Exp(-11*c))
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}
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func schaeferTransmission(k, airmass float64) float64 { return math.Pow(10, -0.4*k*airmass) }
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func schaeferPhase(separationDeg float64) float64 {
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s := math.Max(schaeferMinSeparationDeg, separationDeg)
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c := math.Cos(s * rad)
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return 6.2e7/(s*s) + math.Pow(10, 6.15-s/40) + math.Pow(10, 5.36)*(1.06+c*c)
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}
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func validExtinction(extinction float64) bool {
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return extinction > 0 && !math.IsInf(extinction, 0)
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}
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// SkyBrightnessNanolambert 无月夜晨昏天光亮度（nL，Schaefer 模型），消光系数须为正，否则返回 NaN / twilight sky brightness without moonlight, Schaefer model.
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func SkyBrightnessNanolambert(targetAltitude, sunAltitude, separation, extinction float64) float64 {
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if !validExtinction(extinction) {
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return math.NaN()
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}
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k := extinction
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targetT := schaeferTransmission(k, schaeferAirmass(targetAltitude))
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sunT := schaeferTransmission(k, schaeferAirmass(sunAltitude))
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targetZ := math.Min(90, math.Max(0, 90-targetAltitude))
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sunZ := math.Min(180, math.Max(0, 90-sunAltitude))
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sep := math.Max(schaeferMinSeparationDeg, separation)
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scale := math.Pow(10, -0.4*(schaeferSunMagnitude-schaeferZeroMagnitudeRef+43.27))
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day := scale * (1 - targetT) * (schaeferPhase(sep)*sunT + 440000*(1-sunT))
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twilight := math.Pow(10, -0.4*(schaeferSunMagnitude-schaeferZeroMagnitudeRef-57.5+sunZ-targetZ/(360*k))) *
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(1 - targetT) * 100 / sep
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sky := math.Min(day, twilight)
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switch {
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case sunAltitude < schaeferTwilightLowSunDeg:
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sky = twilight
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case sunAltitude > schaeferDaylightHighSunDeg:
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sky = day
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}
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sz := math.Sin(targetZ * rad)
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night := schaeferNightSkyNanolambert * (0.4 + 0.6/math.Sqrt(1-0.96*sz*sz)) * targetT
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return sky/schaeferNanolambertToErg + night
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}
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// LimitingMagnitude 肉眼极限星等（已扣除目标方向的大气消光），消光系数须为正，否则返回 NaN / naked-eye limiting magnitude after extinction at the target altitude.
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func LimitingMagnitude(targetAltitude, sunAltitude, separation, extinction float64) float64 {
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return limitingMagnitudeForSky(SkyBrightnessNanolambert(targetAltitude, sunAltitude, separation, extinction), targetAltitude, extinction)
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}
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// MoonlightNanolambert 月光在目标方向造成的天光亮度（nL，Krisciunas–Schaefer）；月在地平下为 0，消光系数非正为 NaN /
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// sky brightness from scattered moonlight; zero when the Moon is below the horizon.
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func MoonlightNanolambert(targetAltitude, moonAltitude, moonSeparation, moonPhaseAngle, extinction float64) float64 {
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if !validExtinction(extinction) {
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return math.NaN()
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}
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if moonAltitude <= 0 || targetAltitude <= 0 {
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return 0
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}
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alpha := math.Abs(moonPhaseAngle)
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mag := -12.73 + 0.026*alpha + 4e-9*math.Pow(alpha, 4)
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illuminance := math.Pow(10, -0.4*(mag+16.57))
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rho := math.Max(schaeferMinSeparationDeg, moonSeparation)
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c := math.Cos(rho * rad)
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scatter := math.Pow(10, 5.36)*(1.06+c*c) + math.Pow(10, 6.15-rho/40)
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airmass := func(alt float64) float64 {
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s := math.Sin((90 - alt) * rad)
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return 1 / math.Sqrt(1-0.96*s*s)
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}
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return scatter * illuminance * math.Pow(10, -0.4*extinction*airmass(moonAltitude)) *
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(1 - math.Pow(10, -0.4*extinction*airmass(targetAltitude)))
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}
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func limitingMagnitudeForSky(b, targetAltitude, extinction float64) float64 {
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c, k := 4.4668359215096e-9, 1.2589254117942e-6
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if b < schaeferScotopicLimitNL {
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c, k = 1.5848931924611e-10, 0.012589254117942
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}
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threshold := c * math.Pow(1+math.Sqrt(k*b), 2)
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return -16.57 - 2.5*math.Log10(threshold) - extinction*schaeferAirmass(targetAltitude)
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}
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// HeliacalEventKind 偕日事件类型 / heliacal event kind.
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type HeliacalEventKind int
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const (
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// HeliacalMorningFirst 晨始见（偕日升）/ morning first visibility.
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HeliacalMorningFirst HeliacalEventKind = iota
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// HeliacalMorningLast 晨末见 / morning last visibility.
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HeliacalMorningLast
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// HeliacalEveningFirst 昏始见 / evening first visibility.
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HeliacalEveningFirst
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// HeliacalEveningLast 昏末见（偕日落）/ evening last visibility.
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HeliacalEveningLast
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)
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// HeliacalEvent 偕日事件：JD 为当天最佳可见时刻（UT 儒略日），Margin 为极限星等减目标星等 / heliacal event at the best moment of that twilight.
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type HeliacalEvent struct {
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Kind HeliacalEventKind
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JD float64
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Margin float64
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TargetAltitude float64
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SunAltitude float64
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}
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// heliacalTarget 返回 TT 时刻目标的视赤经、赤纬（度）与视星等。
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type heliacalTarget func(jde float64) (ra, dec, magnitude float64)
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type heliacalBest struct {
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jd, margin, targetAlt, sunAlt float64
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visible bool
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}
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func heliacalAltitude(ra, dec, lst, lat float64) float64 {
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h := (lst - ra) * rad
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d, p := dec*rad, lat*rad
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return math.Asin(math.Sin(p)*math.Sin(d)+math.Cos(p)*math.Cos(d)*math.Cos(h)) / rad
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}
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// heliacalTwilight 扫描一次晨（morning）或昏的太阳高度 −18°..0° 时段，取可见余量最大的样本。
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// 日月位置在窗口中点取一次，窗口不足两小时，引入的高度误差远小于模型本身。
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func heliacalTwilight(dayJD, lon, lat float64, morning bool, target heliacalTarget, options HeliacalOptions, inst *Instance) heliacalBest {
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center := dayJD - lon/360 + 0.5
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if morning {
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center -= 0.25
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} else {
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center += 0.25
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}
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jde := UTC2TT(center)
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sunRA, sunDec := HSunApparentRaDecWithInstance(jde, inst)
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ra, dec, mag := target(jde)
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sep := skyAngularDistance(ra, dec, sunRA, sunDec)
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best := heliacalBest{margin: math.Inf(-1)}
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if math.IsNaN(ra) || math.IsNaN(mag) {
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return best
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}
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var moonRA, moonDec, moonSep, moonPhase float64
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if options.Moonlight {
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lo, bo := SkyBodyApparentLoBoWithInstance(SkyMoon, jde, inst)
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moonRA, moonDec = LoBoToRaDec(jde, lo, bo)
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moonSep = skyAngularDistance(ra, dec, moonRA, moonDec)
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moonPhase = 180 - skyAngularDistance(moonRA, moonDec, sunRA, sunDec)
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}
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lst0 := ApparentSiderealTime(UTC2UT1(center))*15 + lon
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const step = 2.0 / 1440
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for dt := -0.25; dt <= 0.25; dt += step {
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lst := lst0 + dt*360.98564736629
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sunAlt := heliacalAltitude(sunRA, sunDec, lst, lat)
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if sunAlt > 0 || sunAlt < -18 {
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continue
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}
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alt := heliacalAltitude(ra, dec, lst, lat)
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if alt < options.MinTargetAltitude {
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continue
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}
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sky := SkyBrightnessNanolambert(alt, sunAlt, sep, options.ExtinctionCoefficient)
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if options.Moonlight {
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sky += MoonlightNanolambert(alt, heliacalAltitude(moonRA, moonDec, lst, lat), moonSep, moonPhase, options.ExtinctionCoefficient)
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}
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margin := limitingMagnitudeForSky(sky, alt, options.ExtinctionCoefficient) - mag
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if margin > best.margin {
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best = heliacalBest{center + dt, margin, alt, sunAlt, margin >= 0}
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}
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}
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return best
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}
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// heliacalMaxDays 逐日扫描的天数上限（约 2.3 万年），挡住非法跨度造成的近乎无界扫描。
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const heliacalMaxDays = 1 << 23
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// findHeliacalEvents 逐日扫描晨、昏可见性，从不可见变为可见记“始见”，反之记“末见”（取末个可见日）。
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func findHeliacalEvents(startJD, endJD, lon, lat float64, target heliacalTarget, options HeliacalOptions, inst *Instance) []HeliacalEvent {
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options = options.normalized()
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if !finite(startJD) || !finite(endJD) || !(endJD > startJD) || math.Abs(lat) >= 90 {
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return nil
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}
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day0 := math.Floor(startJD-0.5) + 0.5
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span := math.Floor(endJD - day0)
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if !(span < heliacalMaxDays) {
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return nil
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}
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days := int(span)
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var out []HeliacalEvent
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for _, morning := range []bool{true, false} {
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first, last := HeliacalEveningFirst, HeliacalEveningLast
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if morning {
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first, last = HeliacalMorningFirst, HeliacalMorningLast
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}
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prev := heliacalTwilight(day0-1, lon, lat, morning, target, options, inst)
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for i := 0; i <= days; i++ {
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cur := heliacalTwilight(day0+float64(i), lon, lat, morning, target, options, inst)
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// 事件时刻是采样日内的细化值，可能越过 endJD，所以上界按事件时刻判断，不能按采样日判断。
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switch {
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case cur.visible && !prev.visible && cur.jd >= startJD && cur.jd <= endJD:
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out = append(out, HeliacalEvent{first, cur.jd, cur.margin, cur.targetAlt, cur.sunAlt})
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case !cur.visible && prev.visible && prev.jd >= startJD && prev.jd <= endJD:
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out = append(out, HeliacalEvent{last, prev.jd, prev.margin, prev.targetAlt, prev.sunAlt})
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}
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prev = cur
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}
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}
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sortHeliacalEvents(out)
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return out
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}
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func sortHeliacalEvents(events []HeliacalEvent) {
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sort.SliceStable(events, func(i, j int) bool { return events[i].JD < events[j].JD })
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}
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// FindPlanetHeliacalEventsWithInstance 行星偕日事件（UT 儒略日范围，经度东正）/ planet heliacal events in a UT JD range.
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func FindPlanetHeliacalEventsWithInstance(body SkyBody, startJD, endJD, lon, lat float64, options HeliacalOptions, inst *Instance) []HeliacalEvent {
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if body < SkyMercury || body > SkyNeptune {
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return nil
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}
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index := int(body-SkyMercury) + 1
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target := func(jde float64) (float64, float64, float64) {
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lo, bo := SkyBodyApparentLoBoWithInstance(body, jde, inst)
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ra, dec := LoBoToRaDec(jde, lo, bo)
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return ra, dec, planetMagnitude2018(index, jde, inst)
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}
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return findHeliacalEvents(startJD, endJD, lon, lat, target, options, inst)
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}
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// FindStarHeliacalEventsWithInstance 恒星偕日事件；magnitude 为恒星 V 星等 / star heliacal events with the star's V magnitude.
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func FindStarHeliacalEventsWithInstance(star StarCoordinate, magnitude, startJD, endJD, lon, lat float64, options HeliacalOptions, inst *Instance) []HeliacalEvent {
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if math.IsNaN(magnitude) || math.IsInf(magnitude, 0) {
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return nil
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}
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target := func(jde float64) (float64, float64, float64) {
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ra, dec := starApparentRaDecGeocentric(jde, star, inst)
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return ra, dec, magnitude
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}
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return findHeliacalEvents(startJD, endJD, lon, lat, target, options, inst)
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}
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