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
510 lines
17 KiB
Go
510 lines
17 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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// 太阳中天时刻，通过均时差计算
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func CulminationTime(jd, lon, tz float64) float64 { //实际中天时间
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jd = math.Floor(jd)
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tmp := (tz*15 - lon) * 4 / 60
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return jd + tmp/24.0 - SunTime(jd)/24.0
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}
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func CulminationTimeN(jd, lon, tz float64, n int) float64 { //实际中天时间
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jd = math.Floor(jd)
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tmp := (tz*15 - lon) * 4 / 60
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return jd + tmp/24.0 - SunTimeN(jd, n)/24.0
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}
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/*
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* 昏朦影传入 当天0时时刻
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*/
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func EveningTwilight(jd, lon, lat, tz, targetAltitude float64) (float64, error) {
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jd = math.Floor(jd) + 1.5
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localTimeZone := math.Round(lon / 15)
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culminationTime := CulminationTime(jd, lon, localTimeZone)
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if SunHeight(culminationTime, lon, lat, localTimeZone) < targetAltitude {
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return 0, ErrNeverRise
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}
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if SunHeight(culminationTime+0.5, lon, lat, localTimeZone) > targetAltitude {
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return 0, ErrNeverSet
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}
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tmp := (Sin(targetAltitude) - Sin(HSunApparentDec(culminationTime))*Sin(lat)) / (Cos(HSunApparentDec(culminationTime)) * Cos(lat))
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var sundown float64
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if math.Abs(tmp) <= 1 && lat < 85 {
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hourOffset := ArcCos(tmp) / 15
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sundown = culminationTime + hourOffset/24.0 + 35.0/24.0/60.0
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} else {
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sundown = culminationTime
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i := 0
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for LowSunHeight(sundown, lon, lat, localTimeZone) > targetAltitude {
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i++
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sundown += 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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estimateJD := sundown - 5.00/24.00/60.00
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for {
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prevJD := estimateJD
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stDegree := SunHeight(prevJD, lon, lat, localTimeZone) - targetAltitude
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stDegreep := (SunHeight(prevJD+0.000005, lon, lat, localTimeZone) - SunHeight(prevJD-0.000005, lon, lat, localTimeZone)) / 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 - localTimeZone/24 + tz/24, nil
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}
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func EveningTwilightN(jd, lon, lat, tz, targetAltitude float64, n int) (float64, error) {
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jd = math.Floor(jd) + 1.5
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localTimeZone := math.Round(lon / 15)
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culminationTime := CulminationTimeN(jd, lon, localTimeZone, n)
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if SunHeightN(culminationTime, lon, lat, localTimeZone, n) < targetAltitude {
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return 0, ErrNeverRise
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}
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if SunHeightN(culminationTime+0.5, lon, lat, localTimeZone, n) > targetAltitude {
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return 0, ErrNeverSet
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}
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tmp := (Sin(targetAltitude) - Sin(HSunApparentDecN(culminationTime, n))*Sin(lat)) / (Cos(HSunApparentDecN(culminationTime, n)) * Cos(lat))
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var sundown float64
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if math.Abs(tmp) <= 1 && lat < 85 {
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hourOffset := ArcCos(tmp) / 15
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sundown = culminationTime + hourOffset/24.0 + 35.0/24.0/60.0
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} else {
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sundown = culminationTime
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i := 0
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for lowSunHeightForN(sundown, lon, lat, localTimeZone, n) > targetAltitude {
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i++
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sundown += 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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estimateJD := sundown - 5.00/24.00/60.00
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for {
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prevJD := estimateJD
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stDegree := SunHeightN(prevJD, lon, lat, localTimeZone, n) - targetAltitude
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stDegreep := (SunHeightN(prevJD+0.000005, lon, lat, localTimeZone, n) - SunHeightN(prevJD-0.000005, lon, lat, localTimeZone, n)) / 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 - localTimeZone/24 + tz/24, nil
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}
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func MorningTwilight(jd, lon, lat, tz, targetAltitude float64) (float64, error) {
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// 调整到中午12点
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jd = math.Floor(jd) + 1.5
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// 计算时区
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localTimeZone := math.Round(lon / 15)
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// 计算太阳上中天时间
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culminationTime := CulminationTime(jd, lon, localTimeZone)
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// 检查极夜和极昼条件
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if SunHeight(culminationTime, lon, lat, localTimeZone) < targetAltitude {
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return 0, ErrNeverRise
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}
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if SunHeight(culminationTime-0.5, lon, lat, localTimeZone) > targetAltitude {
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return 0, ErrNeverSet
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}
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// 计算日出时间
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sunDec := HSunApparentDec(culminationTime)
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tmp := (Sin(targetAltitude) - Sin(sunDec)*Sin(lat)) / (Cos(sunDec) * Cos(lat))
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var sunrise float64
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if math.Abs(tmp) <= 1 && lat < 85 {
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hourAngle := ArcCos(tmp) / 15
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sunrise = culminationTime - hourAngle/24 - 25.0/(24.0*60.0)
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} else {
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sunrise = culminationTime
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for i := 0; i < 48 && LowSunHeight(sunrise, lon, lat, localTimeZone) > targetAltitude; i++ {
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sunrise -= 15.0 / (60.0 * 24.0) // 每次减少15分钟
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}
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}
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estimateJD := sunrise - 5.0/(24.0*60.0)
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for {
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prevJD := estimateJD
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heightDiff := SunHeight(prevJD, lon, lat, localTimeZone) - targetAltitude
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heightDerivative := (SunHeight(prevJD+0.000005, lon, lat, localTimeZone) - SunHeight(prevJD-0.000005, lon, lat, localTimeZone)) / 0.00001
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estimateJD = prevJD - heightDiff/heightDerivative
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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 - localTimeZone/24 + tz/24, nil
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}
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func MorningTwilightN(jd, lon, lat, tz, targetAltitude float64, n int) (float64, error) {
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jd = math.Floor(jd) + 1.5
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localTimeZone := math.Round(lon / 15)
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culminationTime := CulminationTimeN(jd, lon, localTimeZone, n)
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if SunHeightN(culminationTime, lon, lat, localTimeZone, n) < targetAltitude {
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return 0, ErrNeverRise
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}
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if SunHeightN(culminationTime-0.5, lon, lat, localTimeZone, n) > targetAltitude {
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return 0, ErrNeverSet
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}
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sunDec := HSunApparentDecN(culminationTime, n)
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tmp := (Sin(targetAltitude) - Sin(sunDec)*Sin(lat)) / (Cos(sunDec) * Cos(lat))
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var sunrise float64
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if math.Abs(tmp) <= 1 && lat < 85 {
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hourAngle := ArcCos(tmp) / 15
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sunrise = culminationTime - hourAngle/24 - 25.0/(24.0*60.0)
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} else {
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sunrise = culminationTime
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for i := 0; i < 48 && lowSunHeightForN(sunrise, lon, lat, localTimeZone, n) > targetAltitude; i++ {
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sunrise -= 15.0 / (60.0 * 24.0)
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}
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}
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estimateJD := sunrise - 5.0/(24.0*60.0)
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for {
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prevJD := estimateJD
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heightDiff := SunHeightN(prevJD, lon, lat, localTimeZone, n) - targetAltitude
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heightDerivative := (SunHeightN(prevJD+0.000005, lon, lat, localTimeZone, n) - SunHeightN(prevJD-0.000005, lon, lat, localTimeZone, n)) / 0.00001
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estimateJD = prevJD - heightDiff/heightDerivative
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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 - localTimeZone/24 + tz/24, nil
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}
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/*
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* 太阳时角
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*/
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func SunTimeAngle(jd, lon, lat, tz float64) float64 {
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startime := Limit360(ApparentSiderealTime(jd-tz/24)*15 + lon)
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timeangle := startime - HSunApparentRa(TD2UT(jd-tz/24, true))
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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 SunTimeAngleN(jd, lon, lat, tz float64, n int) float64 {
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startime := Limit360(ApparentSiderealTime(jd-tz/24)*15 + lon)
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timeangle := startime - HSunApparentRaN(TD2UT(jd-tz/24, true), n)
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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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// GetSunRiseTime 精确计算日出时间，传入当日0时JDE
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func GetSunRiseTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) {
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return calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height, true)
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}
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func GetSunRiseTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, n int) (float64, error) {
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return calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height, true, n)
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}
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// GetSunSetTime 精确计算日落时间，传入当日0时JDE
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func GetSunSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) {
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return calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height, false)
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}
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func GetSunSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, n int) (float64, error) {
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return calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height, false, n)
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}
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// calculateSunRiseSetTime 统一的日出日落计算函数
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func calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64, isSunrise bool) (float64, error) {
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julianDay = math.Floor(julianDay) + 1.5
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naturalTimeZone := math.Round(longitude / 15)
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sunAngle := StandardAltitudeSun(zenithShift, height, latitude)
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// 获取太阳上中天时间
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solarNoonTime := CulminationTime(julianDay, longitude, naturalTimeZone)
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// 检查极夜极昼条件
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if err := checkPolarConditions(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise); err != nil {
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return 0, err
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}
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// 计算初始估算时间
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initialTime := calculateInitialSunTime(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise)
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// 牛顿-拉夫逊迭代求精确解
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return sunRiseSetNewtonRaphsonIteration(initialTime, longitude, latitude, naturalTimeZone, sunAngle, timeZone), nil
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}
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func calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, isSunrise bool, n int) (float64, error) {
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julianDay = math.Floor(julianDay) + 1.5
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naturalTimeZone := math.Round(longitude / 15)
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sunAngle := StandardAltitudeSun(zenithShift, height, latitude)
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solarNoonTime := CulminationTimeN(julianDay, longitude, naturalTimeZone, n)
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if err := checkPolarConditionsN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise, n); err != nil {
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return 0, err
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}
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initialTime := calculateInitialSunTimeN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise, n)
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return sunRiseSetNewtonRaphsonIterationN(initialTime, longitude, latitude, naturalTimeZone, sunAngle, timeZone, n), nil
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}
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// checkPolarConditions 检查极夜极昼条件
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func checkPolarConditions(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool) error {
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if SunHeight(solarNoonTime, longitude, latitude, naturalTimeZone) < sunAngle {
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return ErrNeverRise
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}
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checkTime := solarNoonTime + 0.5
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if isSunrise {
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checkTime = solarNoonTime - 0.5
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}
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if SunHeight(checkTime, longitude, latitude, naturalTimeZone) > sunAngle {
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return ErrNeverSet
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}
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return nil
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}
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func checkPolarConditionsN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool, n int) error {
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if SunHeightN(solarNoonTime, longitude, latitude, naturalTimeZone, n) < sunAngle {
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return ErrNeverRise
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}
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checkTime := solarNoonTime + 0.5
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if isSunrise {
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checkTime = solarNoonTime - 0.5
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}
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if SunHeightN(checkTime, longitude, latitude, naturalTimeZone, n) > sunAngle {
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return ErrNeverSet
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}
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return nil
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}
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// calculateInitialSunTime 计算日出日落的初始估算时间
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func calculateInitialSunTime(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool) float64 {
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// 使用球面三角法计算: (sin(ho)-sin(φ)*sin(δ))/(cos(φ)*cos(δ))
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apparentDeclination := HSunApparentDec(solarNoonTime)
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cosHourAngle := (Sin(sunAngle) - Sin(apparentDeclination)*Sin(latitude)) / (Cos(apparentDeclination) * Cos(latitude))
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if math.Abs(cosHourAngle) <= 1 && latitude < 85 {
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// 使用解析解
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hourAngle := ArcCos(cosHourAngle) / 15
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timeOffset := 25.0 / 24.0 / 60.0 // 日出偏移
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if !isSunrise {
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timeOffset = 35.0 / 24.0 / 60.0 // 日落偏移
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}
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if isSunrise {
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return solarNoonTime - hourAngle/24 - timeOffset
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} else {
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return solarNoonTime + hourAngle/24 + timeOffset
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}
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} else {
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// 使用迭代逼近法（极地条件）
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return iterativeApproach(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise)
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}
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}
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func calculateInitialSunTimeN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool, n int) float64 {
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apparentDeclination := HSunApparentDecN(solarNoonTime, n)
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cosHourAngle := (Sin(sunAngle) - Sin(apparentDeclination)*Sin(latitude)) / (Cos(apparentDeclination) * Cos(latitude))
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if math.Abs(cosHourAngle) <= 1 && latitude < 85 {
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hourAngle := ArcCos(cosHourAngle) / 15
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timeOffset := 25.0 / 24.0 / 60.0
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if !isSunrise {
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timeOffset = 35.0 / 24.0 / 60.0
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}
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if isSunrise {
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return solarNoonTime - hourAngle/24 - timeOffset
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}
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return solarNoonTime + hourAngle/24 + timeOffset
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}
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return iterativeApproachN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, isSunrise, n)
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}
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// iterativeApproach 迭代逼近法计算（用于极地等特殊条件）
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func iterativeApproach(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool) float64 {
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estimatedTime := solarNoonTime
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stepSize := 15.0 / 60.0 / 24.0 // 15分钟步长
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if isSunrise {
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stepSize = -stepSize
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}
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const maxIterations = 48
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for i := 0; i < maxIterations && LowSunHeight(estimatedTime, longitude, latitude, naturalTimeZone) > sunAngle; i++ {
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estimatedTime += stepSize
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}
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return estimatedTime
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}
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func iterativeApproachN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle float64, isSunrise bool, n int) float64 {
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estimatedTime := solarNoonTime
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stepSize := 15.0 / 60.0 / 24.0
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if isSunrise {
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stepSize = -stepSize
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}
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const maxIterations = 48
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for i := 0; i < maxIterations && lowSunHeightForN(estimatedTime, longitude, latitude, naturalTimeZone, n) > sunAngle; i++ {
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estimatedTime += stepSize
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}
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return estimatedTime
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}
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// sunRiseSetNewtonRaphsonIteration 牛顿-拉夫逊迭代法求精确解
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func sunRiseSetNewtonRaphsonIteration(initialTime, longitude, latitude, naturalTimeZone, sunAngle, timeZone float64) float64 {
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const (
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convergenceThreshold = 0.00001
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derivativeStep = 0.000005
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)
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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) = SunHeight(t) - targetAngle
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functionValue := SunHeight(previousTime, longitude, latitude, naturalTimeZone) - sunAngle
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// 计算导数：f'(t) ≈ (f(t+h) - f(t-h)) / (2h)
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derivative := (SunHeight(previousTime+derivativeStep, longitude, latitude, naturalTimeZone) -
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SunHeight(previousTime-derivativeStep, longitude, latitude, naturalTimeZone)) / (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) <= convergenceThreshold {
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break
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}
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}
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// 转换为指定时区
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return currentTime - naturalTimeZone/24 + timeZone/24
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}
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func sunRiseSetNewtonRaphsonIterationN(initialTime, longitude, latitude, naturalTimeZone, sunAngle, timeZone float64, n int) float64 {
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const (
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convergenceThreshold = 0.00001
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derivativeStep = 0.000005
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)
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currentTime := initialTime
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for {
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previousTime := currentTime
|
||
functionValue := SunHeightN(previousTime, longitude, latitude, naturalTimeZone, n) - sunAngle
|
||
derivative := (SunHeightN(previousTime+derivativeStep, longitude, latitude, naturalTimeZone, n) -
|
||
SunHeightN(previousTime-derivativeStep, longitude, latitude, naturalTimeZone, n)) / (2 * derivativeStep)
|
||
currentTime = previousTime - functionValue/derivative
|
||
if math.Abs(currentTime-previousTime) <= convergenceThreshold {
|
||
break
|
||
}
|
||
}
|
||
|
||
return currentTime - naturalTimeZone/24 + timeZone/24
|
||
}
|
||
|
||
/*
|
||
* 太阳高度角 世界时
|
||
*/
|
||
func SunHeight(jd, lon, lat, tz float64) float64 {
|
||
//tmp := (tz*15 - lon) * 4 / 60
|
||
//truejd := jd - tmp/24
|
||
calcjd := jd - tz/24.0
|
||
tjde := TD2UT(calcjd, true)
|
||
st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
|
||
ra, dec := HSunApparentRaDec(tjde)
|
||
hourAngle := Limit360(st - ra)
|
||
tmp2 := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(hourAngle)
|
||
return ArcSin(tmp2)
|
||
}
|
||
|
||
func SunHeightN(jd, lon, lat, tz float64, n int) float64 {
|
||
calcjd := jd - tz/24.0
|
||
tjde := TD2UT(calcjd, true)
|
||
st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
|
||
ra, dec := HSunApparentRaDecN(tjde, n)
|
||
hourAngle := Limit360(st - ra)
|
||
tmp2 := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(hourAngle)
|
||
return ArcSin(tmp2)
|
||
}
|
||
|
||
func LowSunHeight(jd, lon, lat, tz float64) float64 {
|
||
//tmp := (tz*15 - lon) * 4 / 60
|
||
//truejd := jd - tmp/24
|
||
calcjd := jd - tz/24
|
||
st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
|
||
hourAngle := Limit360(st - SunApparentRa(TD2UT(calcjd, true)))
|
||
dec := SunApparentDec(TD2UT(calcjd, true))
|
||
tmp2 := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(hourAngle)
|
||
return ArcSin(tmp2)
|
||
}
|
||
|
||
func lowSunHeightForN(jd, lon, lat, tz float64, n int) float64 {
|
||
if n < 0 {
|
||
return LowSunHeight(jd, lon, lat, tz)
|
||
}
|
||
return SunHeightN(jd, lon, lat, tz, n)
|
||
}
|
||
|
||
func SunAzimuth(jd, lon, lat, tz float64) float64 {
|
||
//tmp := (tz*15 - lon) * 4 / 60
|
||
//truejd := jd - tmp/24
|
||
calcjd := jd - tz/24
|
||
st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
|
||
hourAngle := Limit360(st - HSunApparentRa(TD2UT(calcjd, true)))
|
||
tmp2 := Sin(hourAngle) / (Cos(hourAngle)*Sin(lat) - Tan(HSunApparentDec(TD2UT(calcjd, true)))*Cos(lat))
|
||
azimuth := ArcTan(tmp2)
|
||
if azimuth < 0 {
|
||
if hourAngle/15 < 12 {
|
||
return azimuth + 360
|
||
}
|
||
return azimuth + 180
|
||
}
|
||
if hourAngle/15 < 12 {
|
||
return azimuth + 180
|
||
}
|
||
return azimuth
|
||
}
|
||
|
||
func SunAzimuthN(jd, lon, lat, tz float64, n int) float64 {
|
||
calcjd := jd - tz/24
|
||
st := Limit360(ApparentSiderealTime(calcjd)*15 + lon)
|
||
hourAngle := Limit360(st - HSunApparentRaN(TD2UT(calcjd, true), n))
|
||
tmp2 := Sin(hourAngle) / (Cos(hourAngle)*Sin(lat) - Tan(HSunApparentDecN(TD2UT(calcjd, true), n))*Cos(lat))
|
||
azimuth := ArcTan(tmp2)
|
||
if azimuth < 0 {
|
||
if hourAngle/15 < 12 {
|
||
return azimuth + 360
|
||
}
|
||
return azimuth + 180
|
||
}
|
||
if hourAngle/15 < 12 {
|
||
return azimuth + 180
|
||
}
|
||
return azimuth
|
||
}
|