b612
16c62a97d5
- 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
218 lines
7.5 KiB
Go
218 lines
7.5 KiB
Go
package basic
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import (
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. "b612.me/astro/tools"
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"math"
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)
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// StarHeight 星体的高度角
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// 传入 jde时间、瞬时赤经、瞬时赤纬、经度、纬度、时区，jde时间应为时区时间
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// 返回高度角，单位为度
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func StarHeight(localJD, ra, dec, lon, lat, timezone float64) float64 {
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// 转换为世界时
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utcJD := localJD - timezone/24.0
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// 计算视恒星时
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st := Limit360(ApparentSiderealTime(UTC2UT1(utcJD))*15 + lon)
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// 计算时角
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hourAngle := Limit360(st - ra)
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// 高度角、时角与天球座标三角转换公式
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// sin(h)=sin(lat)*sin(dec)+cos(dec)*cos(lat)*cos(hourAngle)
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sinHeight := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(hourAngle)
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return ArcSin(sinHeight)
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}
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// StarAzimuth 星体的方位角
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// 传入 jde时间、瞬时赤经、瞬时赤纬、经度、纬度、时区，jde时间应为时区时间
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// 返回方位角，单位为度，正北为0，度数顺时针增加，取值范围[0-360)
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func StarAzimuth(localJD, ra, dec, lon, lat, timezone float64) float64 {
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// 转换为世界时
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utcJD := localJD - timezone/24.0
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// 计算视恒星时
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st := Limit360(ApparentSiderealTime(UTC2UT1(utcJD))*15 + lon)
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// 计算时角
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hourAngle := Limit360(st - ra)
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// 三角转换公式
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tanAzimuth := Sin(hourAngle) / (Cos(hourAngle)*Sin(lat) - Tan(dec)*Cos(lat))
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azimuth := ArcTan(tanAzimuth)
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if azimuth < 0 {
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if hourAngle/15 < 12 {
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return azimuth + 360
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}
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return azimuth + 180
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}
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if hourAngle/15 < 12 {
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return azimuth + 180
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}
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return azimuth
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}
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// StarHourAngle 星体的时角
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// 传入 jde时间、瞬时赤经、瞬时赤纬、经度、时区，jde时间应为时区时间
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// 返回时角
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func StarHourAngle(localJD, ra, lon, timezone float64) float64 {
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// 转换为世界时
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utcJD := localJD - timezone/24.0
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// 计算视恒星时
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st := Limit360(ApparentSiderealTime(UTC2UT1(utcJD))*15 + lon)
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// 计算时角
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return Limit360(st - ra)
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}
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// MeanSiderealTime 平恒星时
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func MeanSiderealTime(jd float64) float64 {
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return MeanSiderealTime2006(jd)
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}
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// ApparentSiderealTime 视恒星时，计算章动
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func ApparentSiderealTime(jd float64) float64 {
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return ApparentSiderealTime2006(jd)
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}
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// MeanSiderealTime1982 不含章动下的恒星时
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func MeanSiderealTime1982(jd float64) float64 {
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t := (jd - 2451545) / 36525
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return (Limit360(280.46061837+360.98564736629*(jd-2451545.0)+0.000387933*t*t-t*t*t/38710000) / 15)
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}
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// ApparentSiderealTime1982 视恒星时，计算章动
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func ApparentSiderealTime1982(jd float64) float64 {
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tmp := MeanSiderealTime1982(jd)
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dpsi, deps := Nutation2000B(jd)
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return tmp + dpsi*math.Cos((Obliquity1980(jd)+deps)*math.Pi/180)/15
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}
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// EarthRotationAngle 计算地球自转角 (ERA)
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// jd_ut1: UT1 时间的儒略日
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// 返回值: 地球自转角 (弧度)
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func EarthRotationAngle(jd_ut1 float64) float64 {
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t := jd_ut1 - 2451545.0
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frac := math.Mod(jd_ut1, 1.0)
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era := math.Mod(math.Pi*2*(0.7790572732640+0.00273781191135448*t+frac), math.Pi*2)
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if era < 0 {
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era += math.Pi * 2
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}
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return era
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}
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// MeanSiderealTime2006 计算格林尼治平恒星时 (GMST)
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// jd_ut1: UT1 时间的儒略日
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// jd_tt: TT 时间的儒略日
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// 返回值: 格林尼治平恒星时 (弧度)
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func MeanSiderealTime2006(jd_ut1 float64) float64 {
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jd_tt := UT12TT(jd_ut1)
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t := (jd_tt - 2451545.0) / 36525.0
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era := EarthRotationAngle(jd_ut1)
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// 公式 2.12
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gmst := math.Mod(era+(0.014506+4612.15739966*t+1.39667721*t*t+
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-0.00009344*t*t*t+0.00001882*t*t*t*t)/60/60*math.Pi/180, math.Pi*2)
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if gmst < 0 {
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gmst += math.Pi * 2
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}
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return gmst * deg / 15
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}
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// ApparentSiderealTime2006 视恒星时，计算章动。
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// 一次求值只要一份 IAU2000B 章动（黄经与交角在同一次展开里同时得到），并走有界记忆表，
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// 避免月掩路径里的重复求值；ΔT 覆盖会使记忆表按世代失效。见 sidereal_memo.go。
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// ApparentSiderealTime2006 computes apparent sidereal time. One evaluation needs only a single
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// IAU2000B nutation expansion (longitude and obliquity come out of the same series) and is
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// memoized so repeated occultation-path queries do not rerun it; a ΔT override invalidates the
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// memo by generation. See sidereal_memo.go.
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func ApparentSiderealTime2006(jd float64) float64 {
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if value, ok := siderealMemoLoad(jd); ok {
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return value
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}
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generation := siderealMemoGeneration()
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tmp := MeanSiderealTime2006(jd)
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dpsi, deps := Nutation2000B(jd)
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value := tmp + dpsi*math.Cos((Obliquity1980(jd)+deps)*math.Pi/180)/15
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siderealMemoStore(jd, value, generation)
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return value
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}
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func StarRiseTime(localJD, ra, dec, lon, lat, height, timezone float64, aero bool) (float64, error) {
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return StarRiseSetTime(localJD, ra, dec, lon, lat, height, timezone, aero, true)
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}
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func StarSetTime(localJD, ra, dec, lon, lat, height, timezone float64, aero bool) (float64, error) {
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return StarRiseSetTime(localJD, ra, dec, lon, lat, height, timezone, aero, false)
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}
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func StarRiseSetTime(localJD, ra, dec, lon, lat, height, timezone float64, aero, isRise bool) (float64, error) {
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if !isFiniteFloat(localJD) || !isFiniteFloat(ra) || !isFiniteFloat(dec) || !isFiniteFloat(lon) || !isFiniteFloat(lat) || !isFiniteFloat(height) || !isFiniteFloat(timezone) {
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return 0, ErrInvalidObservationInput
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}
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// localJD 是本地民用日锚点（当地 0 时），不是力学时。
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//ra,dec 瞬时天球座标，非J2000等时间天球坐标
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localJD = math.Floor(localJD) + 0.5
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targetAltitude := StandardAltitudeStar(aero, height, lat)
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sct := StarCulminationTime(localJD, ra, lon, timezone)
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tmp := (Sin(targetAltitude) - Sin(dec)*Sin(lat)) / (Cos(dec) * Cos(lat))
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if math.Abs(tmp) > 1 {
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if StarHeight(sct, ra, dec, lon, lat, timezone) < 0 {
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return 0, ErrNeverRise
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}
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return 0, ErrNeverSet
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}
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var estimateJD float64
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if isRise {
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estimateJD = sct - ArcCos(tmp)/15.0/24.0
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} else {
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estimateJD = sct + ArcCos(tmp)/15.0/24.0
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}
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var ok bool
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estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 {
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stDegree := StarHeight(prevJD, ra, dec, lon, lat, timezone) - targetAltitude
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stDegreep := (StarHeight(prevJD+0.000005, ra, dec, lon, lat, timezone) - StarHeight(prevJD-0.000005, ra, dec, lon, lat, timezone)) / 0.00001
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return stDegree / stDegreep
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})
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if !ok {
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return 0, ErrInvalidObservationInput
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}
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return estimateJD, nil
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}
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func StarCulminationTime(localJD, ra, lon, timezone float64) float64 {
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if !isFiniteFloat(localJD) || !isFiniteFloat(ra) || !isFiniteFloat(lon) || !isFiniteFloat(timezone) {
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return math.NaN()
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}
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// localJD 是本地民用日锚点（当地 0 时），不是力学时。
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//ra,dec 瞬时天球座标，非J2000等时间天球坐标
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localJD = math.Floor(localJD) + 0.5
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estimateJD := localJD + Limit360(360-StarHourAngle(localJD, ra, lon, timezone))/15.0/24.0*0.99726851851851851851
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limitStarHA := func(localJD, ra, lon, timezone float64) float64 {
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ha := StarHourAngle(localJD, ra, lon, timezone)
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if ha < 180 {
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ha += 360
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}
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return ha
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}
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var ok bool
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estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 {
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stDegree := limitStarHA(prevJD, ra, lon, timezone) - 360
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stDegreep := (limitStarHA(prevJD+0.000005, ra, lon, timezone) - limitStarHA(prevJD-0.000005, ra, lon, timezone)) / 0.00001
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return stDegree / stDegreep
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})
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if !ok {
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return math.NaN()
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}
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return estimateJD
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}
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func StarAngularSeparation(ra1, dec1, ra2, dec2 float64) float64 {
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//cos(d)=sinδ1 sinδ2 + cosδ1 cosδ2 cos(α1-α2)
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d := Sin(dec1)*Sin(dec2) + Cos(dec1)*Cos(dec2)*Cos(ra1-ra2)
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if math.Abs(d) >= 0.999999997 {
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//d = √(Δα*cosδ)2+(Δδ)2
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tmp1 := ((ra1 - ra2) * Cos((dec1+dec2)/2))
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tmp2 := (dec1 - dec2)
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return math.Sqrt(tmp1*tmp1 + tmp2*tmp2)
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}
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return ArcCos(d)
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}
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