starainrt
3ffdbe0034
- 新增日食、月食、本地可见性、中心线、半影区域、SVG 图示与沙罗周期信息 - 新增行星冲合、留、方照、物理星历、视直径、相位、亮肢角、轨道节点等计算 - 新增木星伽利略卫星位置、现象与接触事件计算 - 新增恒星星表、星座判定、自行修正与观测辅助能力 - 新增 coord、formula、orbit、sundial、lite/sun、lite/moon 等扩展包 - 完善农历年号、月相英文别名、视差角、大气质量、折射、日晷与双星计算 - 增加 NASA、JPL Horizons、IMCCE 等回归测试数据与基线测试 - 重构基础算法文件组织，补充大量公开 API 注释和语义回归测试 - 更新中文和英文 README，补充示例、精度说明、SVG 配图
348 lines
11 KiB
Go
348 lines
11 KiB
Go
package basic
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import (
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"math"
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. "b612.me/astro/tools"
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)
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/*
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* 月球方位角
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*/
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func MoonAzimuth(jd, lon, lat, tz float64) float64 {
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//tmp := (tz*15 - lon) * 4 / 60
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calcjd := TD2UT(jd-tz/24, true)
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ra := MoonTrueRa(calcjd)
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dec := MoonTrueDec(calcjd)
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away := MoonAway(calcjd) / 149597870.7
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ndec := TopocentricDec(ra, dec, lat, lon, jd-tz/24, away, 0)
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nra := TopocentricRa(ra, dec, lat, lon, jd-tz/24, away, 0)
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calcjd = jd - tz/24
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st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
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hourAngle := Limit360(st - nra)
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tmp2 := Sin(hourAngle) / (Cos(hourAngle)*Sin(lat) - Tan(ndec)*Cos(lat))
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azimuth := ArcTan(tmp2)
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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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} else {
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return azimuth + 180
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}
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} else {
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if hourAngle/15 < 12 {
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return azimuth + 180
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} else {
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return azimuth
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}
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}
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}
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func MoonHeight(jd, lon, lat, tz float64) float64 {
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// tmp := (tz*15 - lon) * 4 / 60
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//truejd=jd-tmp/24;
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calcjd := TD2UT(jd-tz/24, true)
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ra := MoonTrueRa(calcjd)
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dec := MoonTrueDec(calcjd)
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away := MoonAway(calcjd) / 149597870.7
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ndec := TopocentricDec(ra, dec, lat, lon, jd-tz/24, away, 0)
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nra := TopocentricRa(ra, dec, lat, lon, jd-tz/24, away, 0)
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calcjd = jd - tz/24
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st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
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hourAngle := Limit360(st - nra)
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tmp2 := Sin(lat)*Sin(ndec) + Cos(ndec)*Cos(lat)*Cos(hourAngle)
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return ArcSin(tmp2)
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}
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func HMoonAzimuth(jd, lon, lat, tz float64) float64 {
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return HMoonAzimuthN(jd, lon, lat, tz, -1)
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}
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func HMoonAzimuthN(jd, lon, lat, tz float64, n int) float64 {
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calcjd := TD2UT(jd-tz/24, true)
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ra := HMoonTrueRaN(calcjd, n)
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dec := HMoonTrueDecN(calcjd, n)
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away := HMoonAwayN(calcjd, n) / 149597870.7
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ndec := TopocentricDec(ra, dec, lat, lon, jd-tz/24, away, 0)
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nra := TopocentricRa(ra, dec, lat, lon, jd-tz/24, away, 0)
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calcjd = jd - tz/24
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st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
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hourAngle := Limit360(st - nra)
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tmp2 := Sin(hourAngle) / (Cos(hourAngle)*Sin(lat) - Tan(ndec)*Cos(lat))
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azimuth := ArcTan(tmp2)
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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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} else {
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return azimuth + 180
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}
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} else {
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if hourAngle/15 < 12 {
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return azimuth + 180
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} else {
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return azimuth
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}
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}
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}
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func HMoonHeight(jd, lon, lat, tz float64) float64 {
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return HMoonHeightN(jd, lon, lat, tz, -1)
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}
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func HMoonHeightN(jd, lon, lat, tz float64, n int) float64 {
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calcjd := TD2UT(jd-tz/24, true)
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ra, dec := HMoonTrueRaDecN(calcjd, n)
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away := HMoonAwayN(calcjd, n) / 149597870.7
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nra, ndec := TopocentricRaDec(ra, dec, lat, lon, calcjd, away, 0)
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calcjd = jd - tz/24
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st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
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hourAngle := Limit360(st - nra)
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tmp2 := Sin(lat)*Sin(ndec) + Cos(ndec)*Cos(lat)*Cos(hourAngle)
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return ArcSin(tmp2)
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}
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// 废弃
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func GetMoonTZTime(jd, lon, lat, tz float64) float64 { //实际中天时间{
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jd = math.Floor(jd) + 0.5
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ttm := MoonTimeAngle(jd, lon, lat, tz)
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if ttm > 0 && ttm < 180 {
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jd += 0.5
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}
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estimateJD := jd
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for {
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prevJD := estimateJD
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stDegree := MoonTimeAngle(prevJD, lon, lat, tz) - 359.599
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stDegreep := (MoonTimeAngle(prevJD+0.000005, lon, lat, tz) - MoonTimeAngle(prevJD-0.000005, lon, lat, tz)) / 0.00001
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estimateJD = prevJD - stDegree/stDegreep
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if math.Abs(estimateJD-prevJD) <= 0.00001 {
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break
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}
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}
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return estimateJD
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}
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func MoonCulminationTime(jde, lon, lat, timezone float64) float64 {
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//jde 世界时，非力学时，当地时区 0时，无需转换力学时
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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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jde = math.Floor(jde) + 0.5
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estimateJD := jde + Limit360(360-MoonTimeAngle(jde, lon, lat, timezone))/15.0/24.0/0.9
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limitHA := func(jde, lon, timezone float64) float64 {
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ha := MoonTimeAngle(jde, lon, lat, 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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for {
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prevJD := estimateJD
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stDegree := limitHA(prevJD, lon, timezone) - 360
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stDegreep := (limitHA(prevJD+0.000005, lon, timezone) - limitHA(prevJD-0.000005, lon, timezone)) / 0.00001
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estimateJD = prevJD - stDegree/stDegreep
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if math.Abs(estimateJD-prevJD) <= 0.00001 {
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break
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}
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}
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return estimateJD
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}
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func MoonTimeAngle(jd, lon, lat, tz float64) float64 {
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startime := Limit360(ApparentSiderealTime(jd-tz/24)*15 + lon)
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timeangle := startime - HMoonApparentRa(jd, lon, lat, tz)
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if timeangle < 0 {
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timeangle += 360
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}
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return timeangle
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}
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func GetMoonRiseTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) {
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originalTimeZone := timeZone
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timeZone = longitude / 15
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var timeToMeridian float64
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julianDayZero := math.Floor(julianDay) + 0.5
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//julianDay = math.Floor(julianDay) + 0.5 - originalTimeZone/24 + timeZone/24 // 求0时JDE
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//fix:这里时间分界线应当以传入的时区为准，不应当使用当地时区，否则在0时的判断会出错
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julianDay = math.Floor(julianDay) + 0.5
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estimatedTime := julianDay
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moonHeight := MoonHeight(julianDay, longitude, latitude, originalTimeZone) // 求此时月亮高度
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moonAngle := StandardAltitudeMoon(zenithShift, height, latitude)
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moonAngleTime := MoonTimeAngle(julianDay, longitude, latitude, originalTimeZone)
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if moonHeight-moonAngle > 0 { // 月亮在地平线上或在落下与下中天之间
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if moonAngleTime > 180 {
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timeToMeridian = (180 + 360 - moonAngleTime) / 15
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} else {
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timeToMeridian = (180 - moonAngleTime) / 15
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}
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estimatedTime += (timeToMeridian/24 + (timeToMeridian/24*12.0)/15.0/24.0)
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}
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if moonHeight-moonAngle < 0 && moonAngleTime > 180 {
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timeToMeridian = (180 - moonAngleTime) / 15
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estimatedTime += (timeToMeridian/24 + (timeToMeridian/24*12.0)/15.0/24.0)
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} else if moonHeight-moonAngle < 0 && moonAngleTime < 180 {
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timeToMeridian = (180 - moonAngleTime) / 15
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estimatedTime += (timeToMeridian/24 + (timeToMeridian/24*12.0)/15.0/24.0)
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}
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currentAngle := MoonTimeAngle(estimatedTime, longitude, latitude, timeZone)
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if math.Abs(currentAngle-180) > 0.5 {
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estimatedTime += (180 - currentAngle) * 4.0 / 60.0 / 24.0
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}
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currentHeight := HMoonHeight(estimatedTime, longitude, latitude, timeZone)
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if !(currentHeight < -10 && math.Abs(latitude) < 60) {
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if currentHeight > moonAngle {
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return 0, ErrNeverSet
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}
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checkTime := estimatedTime + 12.0/24.0 + 6.0/15.0/24.0
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checkAngle := MoonTimeAngle(checkTime, longitude, latitude, timeZone)
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if checkAngle < 90 {
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checkAngle += 360
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}
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checkTime += (360 - checkAngle) * 4.0 / 60.0 / 24.0
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if HMoonHeight(checkTime, longitude, latitude, timeZone) < moonAngle {
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return 0, ErrNeverRise
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}
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}
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moonDeclination := MoonApparentDec(estimatedTime, longitude, latitude, timeZone)
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tmp := (Sin(moonAngle) - Sin(moonDeclination)*Sin(latitude)) / (Cos(moonDeclination) * Cos(latitude))
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if math.Abs(tmp) <= 1 && latitude < 85 {
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hourAngle := (180 - ArcCos(tmp)) / 15
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estimatedTime += hourAngle/24.00 + hourAngle/33.00/15.00
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} else {
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i := 0
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for MoonHeight(estimatedTime, longitude, latitude, timeZone) < moonAngle {
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i++
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estimatedTime += 15.0 / 60.0 / 24.0
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if i > 48 {
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break
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}
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}
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}
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// 使用牛顿迭代法求精确解
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estimatedTime = moonRiseSetNewtonRaphsonIteration(estimatedTime, longitude, latitude, timeZone, moonAngle, HMoonHeight, 0.00002)
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estimatedTime = estimatedTime - timeZone/24 + originalTimeZone/24
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if estimatedTime > julianDayZero+1 || estimatedTime < julianDayZero {
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return 0, ErrNotOnThisDate
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}
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return estimatedTime, nil
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}
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func GetMoonSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) {
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originalTimeZone := timeZone
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timeZone = longitude / 15
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var timeToMeridian float64
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julianDayZero := math.Floor(julianDay) + 0.5
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//julianDay = math.Floor(julianDay) + 0.5 - originalTimeZone/24 + timeZone/24 // 求0时JDE
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//fix:这里时间分界线应当以传入的时区为准，不应当使用当地时区，否则在0时的判断会出错
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julianDay = math.Floor(julianDay) + 0.5
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estimatedTime := julianDay
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moonHeight := MoonHeight(julianDay, longitude, latitude, originalTimeZone) // 求此时月亮高度
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moonAngle := StandardAltitudeMoon(zenithShift, height, latitude)
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moonAngleTime := MoonTimeAngle(julianDay, longitude, latitude, originalTimeZone)
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if moonHeight-moonAngle < 0 {
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timeToMeridian = (360 - moonAngleTime) / 15
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estimatedTime += (timeToMeridian/24 + (timeToMeridian/24.0*12.0)/15.0/24.0)
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}
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// 月亮在地平线上或在落下与下中天之间
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if moonHeight-moonAngle > 0 && moonAngleTime < 180 {
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timeToMeridian = (-moonAngleTime) / 15
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estimatedTime += (timeToMeridian/24.0 + (timeToMeridian/24.0*12.0)/15.0/24.0)
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} else if moonHeight-moonAngle > 0 {
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timeToMeridian = (360 - moonAngleTime) / 15
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estimatedTime += (timeToMeridian/24.0 + (timeToMeridian/24.0*12.0)/15.0/24.0)
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}
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currentAngle := MoonTimeAngle(estimatedTime, longitude, latitude, timeZone)
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if currentAngle < 180 {
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currentAngle += 360
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}
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if math.Abs(currentAngle-360) > 0.5 {
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estimatedTime += (360 - currentAngle) * 4.0 / 60.0 / 24.0
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}
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// estimatedTime = 月球中天时间
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currentHeight := HMoonHeight(estimatedTime, longitude, latitude, timeZone)
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if !(currentHeight > 10 && math.Abs(latitude) < 60) {
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if currentHeight < moonAngle {
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return 0, ErrNeverRise
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}
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checkTime := estimatedTime + 12.0/24.0 + 6.0/15.0/24.0
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angleSubtraction := 180 - MoonTimeAngle(checkTime, longitude, latitude, timeZone)
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checkTime += angleSubtraction * 4.0 / 60.0 / 24.0
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if HMoonHeight(checkTime, longitude, latitude, timeZone) > moonAngle {
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return 0, ErrNeverSet
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}
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}
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moonDeclination := MoonApparentDec(estimatedTime, longitude, latitude, timeZone)
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tmp := (Sin(moonAngle) - Sin(moonDeclination)*Sin(latitude)) / (Cos(moonDeclination) * Cos(latitude))
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if math.Abs(tmp) <= 1 && latitude < 85 {
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hourAngle := (ArcCos(tmp)) / 15.0
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estimatedTime += hourAngle/24 + hourAngle/33.0/15.0
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} else {
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i := 0
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for MoonHeight(estimatedTime, longitude, latitude, timeZone) > moonAngle {
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i++
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estimatedTime += 15.0 / 60.0 / 24.0
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if i > 48 {
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break
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}
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}
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}
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// 使用牛顿迭代法求精确解
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estimatedTime = moonRiseSetNewtonRaphsonIteration(estimatedTime, longitude, latitude, timeZone, moonAngle, HMoonHeight, 0.00002)
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estimatedTime = estimatedTime - timeZone/24 + originalTimeZone/24
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if estimatedTime > julianDayZero+1 || estimatedTime < julianDayZero {
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return 0, ErrNotOnThisDate
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}
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return estimatedTime, nil
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}
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// heightFunction 高度函数类型定义，用于牛顿迭代法
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type heightFunction func(time, longitude, latitude, timeZone float64) float64
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// moonRiseSetNewtonRaphsonIteration 牛顿-拉夫逊迭代法求解天体高度方程
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func moonRiseSetNewtonRaphsonIteration(initialTime, longitude, latitude, timeZone, targetAngle float64,
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heightFunc heightFunction, tolerance float64) float64 {
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const derivativeStep = 0.000005
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currentTime := initialTime
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for {
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previousTime := currentTime
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// 计算函数值：f(t) = height(t) - targetAngle
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functionValue := heightFunc(previousTime, longitude, latitude, timeZone) - targetAngle
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// 计算导数：f'(t) ≈ (f(t+h) - f(t-h)) / (2h)
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derivative := (heightFunc(previousTime+derivativeStep, longitude, latitude, timeZone) -
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heightFunc(previousTime-derivativeStep, longitude, latitude, timeZone)) / (2 * derivativeStep)
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// 牛顿-拉夫逊公式：t_new = t_old - f(t) / f'(t)
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currentTime = previousTime - functionValue/derivative
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// 检查收敛
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if math.Abs(currentTime-previousTime) <= tolerance {
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break
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}
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}
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return currentTime
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}
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