package basic import ( "math" . "b612.me/astro/tools" ) // 太阳中天时刻,通过均时差计算 func CulminationTime(jd, lon, tz float64) float64 { //实际中天时间 jd = math.Floor(jd) tmp := (tz*15 - lon) * 4 / 60 return jd + tmp/24.0 - SunTime(jd)/24.0 } func CulminationTimeN(jd, lon, tz float64, n int) float64 { //实际中天时间 jd = math.Floor(jd) tmp := (tz*15 - lon) * 4 / 60 return jd + tmp/24.0 - SunTimeN(jd, n)/24.0 } /* * 昏朦影传入 当天0时时刻 */ func EveningTwilight(jd, lon, lat, tz, targetAltitude float64) (float64, error) { jd = math.Floor(jd) + 1.5 localTimeZone := math.Round(lon / 15) culminationTime := CulminationTime(jd, lon, localTimeZone) if SunHeight(culminationTime, lon, lat, localTimeZone) < targetAltitude { return 0, ErrNeverRise } if SunHeight(culminationTime+0.5, lon, lat, localTimeZone) > targetAltitude { return 0, ErrNeverSet } tmp := (Sin(targetAltitude) - Sin(HSunApparentDec(culminationTime))*Sin(lat)) / (Cos(HSunApparentDec(culminationTime)) * Cos(lat)) var sundown float64 if math.Abs(tmp) <= 1 && lat < 85 { hourOffset := ArcCos(tmp) / 15 sundown = culminationTime + hourOffset/24.0 + 35.0/24.0/60.0 } else { sundown = culminationTime i := 0 for LowSunHeight(sundown, lon, lat, localTimeZone) > targetAltitude { i++ sundown += 15.0 / 60.0 / 24.0 if i > 48 { break } } } estimateJD := sundown - 5.00/24.00/60.00 var ok bool estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 { stDegree := SunHeight(prevJD, lon, lat, localTimeZone) - targetAltitude stDegreep := (SunHeight(prevJD+0.000005, lon, lat, localTimeZone) - SunHeight(prevJD-0.000005, lon, lat, localTimeZone)) / 0.00001 return stDegree / stDegreep }) if !ok { return 0, ErrInvalidObservationInput } return estimateJD - localTimeZone/24 + tz/24, nil } func EveningTwilightN(jd, lon, lat, tz, targetAltitude float64, n int) (float64, error) { jd = math.Floor(jd) + 1.5 localTimeZone := math.Round(lon / 15) culminationTime := CulminationTimeN(jd, lon, localTimeZone, n) if SunHeightN(culminationTime, lon, lat, localTimeZone, n) < targetAltitude { return 0, ErrNeverRise } if SunHeightN(culminationTime+0.5, lon, lat, localTimeZone, n) > targetAltitude { return 0, ErrNeverSet } tmp := (Sin(targetAltitude) - Sin(HSunApparentDecN(culminationTime, n))*Sin(lat)) / (Cos(HSunApparentDecN(culminationTime, n)) * Cos(lat)) var sundown float64 if math.Abs(tmp) <= 1 && lat < 85 { hourOffset := ArcCos(tmp) / 15 sundown = culminationTime + hourOffset/24.0 + 35.0/24.0/60.0 } else { sundown = culminationTime i := 0 for lowSunHeightForN(sundown, lon, lat, localTimeZone, n) > targetAltitude { i++ sundown += 15.0 / 60.0 / 24.0 if i > 48 { break } } } estimateJD := sundown - 5.00/24.00/60.00 var ok bool estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 { stDegree := SunHeightN(prevJD, lon, lat, localTimeZone, n) - targetAltitude stDegreep := (SunHeightN(prevJD+0.000005, lon, lat, localTimeZone, n) - SunHeightN(prevJD-0.000005, lon, lat, localTimeZone, n)) / 0.00001 return stDegree / stDegreep }) if !ok { return 0, ErrInvalidObservationInput } return estimateJD - localTimeZone/24 + tz/24, nil } func MorningTwilight(jd, lon, lat, tz, targetAltitude float64) (float64, error) { // 调整到中午12点 jd = math.Floor(jd) + 1.5 // 计算时区 localTimeZone := math.Round(lon / 15) // 计算太阳上中天时间 culminationTime := CulminationTime(jd, lon, localTimeZone) // 检查极夜和极昼条件 if SunHeight(culminationTime, lon, lat, localTimeZone) < targetAltitude { return 0, ErrNeverRise } if SunHeight(culminationTime-0.5, lon, lat, localTimeZone) > targetAltitude { return 0, ErrNeverSet } // 计算日出时间 sunDec := HSunApparentDec(culminationTime) tmp := (Sin(targetAltitude) - Sin(sunDec)*Sin(lat)) / (Cos(sunDec) * Cos(lat)) var sunrise float64 if math.Abs(tmp) <= 1 && lat < 85 { hourAngle := ArcCos(tmp) / 15 sunrise = culminationTime - hourAngle/24 - 25.0/(24.0*60.0) } else { sunrise = culminationTime for i := 0; i < 48 && LowSunHeight(sunrise, lon, lat, localTimeZone) > targetAltitude; i++ { sunrise -= 15.0 / (60.0 * 24.0) // 每次减少15分钟 } } estimateJD := sunrise - 5.0/(24.0*60.0) var ok bool estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 { heightDiff := SunHeight(prevJD, lon, lat, localTimeZone) - targetAltitude heightDerivative := (SunHeight(prevJD+0.000005, lon, lat, localTimeZone) - SunHeight(prevJD-0.000005, lon, lat, localTimeZone)) / 0.00001 return heightDiff / heightDerivative }) if !ok { return 0, ErrInvalidObservationInput } return estimateJD - localTimeZone/24 + tz/24, nil } func MorningTwilightN(jd, lon, lat, tz, targetAltitude float64, n int) (float64, error) { jd = math.Floor(jd) + 1.5 localTimeZone := math.Round(lon / 15) culminationTime := CulminationTimeN(jd, lon, localTimeZone, n) if SunHeightN(culminationTime, lon, lat, localTimeZone, n) < targetAltitude { return 0, ErrNeverRise } if SunHeightN(culminationTime-0.5, lon, lat, localTimeZone, n) > targetAltitude { return 0, ErrNeverSet } sunDec := HSunApparentDecN(culminationTime, n) tmp := (Sin(targetAltitude) - Sin(sunDec)*Sin(lat)) / (Cos(sunDec) * Cos(lat)) var sunrise float64 if math.Abs(tmp) <= 1 && lat < 85 { hourAngle := ArcCos(tmp) / 15 sunrise = culminationTime - hourAngle/24 - 25.0/(24.0*60.0) } else { sunrise = culminationTime for i := 0; i < 48 && lowSunHeightForN(sunrise, lon, lat, localTimeZone, n) > targetAltitude; i++ { sunrise -= 15.0 / (60.0 * 24.0) } } estimateJD := sunrise - 5.0/(24.0*60.0) var ok bool estimateJD, ok = eventNewtonRefine(estimateJD, 0.00001, func(prevJD float64) float64 { heightDiff := SunHeightN(prevJD, lon, lat, localTimeZone, n) - targetAltitude heightDerivative := (SunHeightN(prevJD+0.000005, lon, lat, localTimeZone, n) - SunHeightN(prevJD-0.000005, lon, lat, localTimeZone, n)) / 0.00001 return heightDiff / heightDerivative }) if !ok { return 0, ErrInvalidObservationInput } return estimateJD - localTimeZone/24 + tz/24, nil } /* * 太阳时角 */ func SunTimeAngle(jd, lon, lat, tz float64) float64 { startime := Limit360(ApparentSiderealTime(jd-tz/24)*15 + lon) timeangle := startime - HSunApparentRa(TD2UT(jd-tz/24, true)) if timeangle < 0 { timeangle += 360 } return timeangle } func SunTimeAngleN(jd, lon, lat, tz float64, n int) float64 { startime := Limit360(ApparentSiderealTime(jd-tz/24)*15 + lon) timeangle := startime - HSunApparentRaN(TD2UT(jd-tz/24, true), n) if timeangle < 0 { timeangle += 360 } return timeangle } type sunObservationState struct { altitude float64 distanceAU float64 } func sunObservationStateN(jd, lon, lat, tz float64, n int) sunObservationState { calculationJD := jd - tz/24.0 tt := TD2UT(calculationJD, true) siderealTime := Limit360(ApparentSiderealTime(calculationJD)*15 + lon) ra, dec, distanceAU := hSunApparentRaDecDistanceN(tt, n) hourAngle := Limit360(siderealTime - ra) altitudeSine := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(hourAngle) return sunObservationState{ altitude: ArcSin(altitudeSine), distanceAU: distanceAU, } } func sunRiseSetResidual(jd, longitude, latitude, timeZone, zenithShift, height float64, n int) float64 { state := sunObservationStateN(jd, longitude, latitude, timeZone, n) // 相对观测者下沉地平线的视上缘高度角 / Apparent upper-limb altitude relative to the observer's depressed horizon. residual := state.altitude + HeightDegreeByLat(height, latitude) if zenithShift != 0 { residual += RefractionFromTrueAltitude(state.altitude, refractionStandardPressureHPa, refractionStandardTemperatureC) residual += angularSemidiameterFromAU(sunEquatorialRadiusKM, state.distanceAU) / 3600 } return residual } func sunRiseSetOnCivilDay(candidate, slope, civilDayStart, longitude, latitude, requestedTimeZone, localTimeZone, zenithShift, height float64, isSunrise bool, n int, fallbackErr error) (float64, error) { if eventRiseSetCandidateValid(candidate, civilDayStart, slope, isSunrise) { return candidate, nil } return eventDirectionalRiseSetSearch(civilDayStart, isSunrise, fallbackErr, func(outputJD float64) float64 { localJD := outputJD + localTimeZone/24 - requestedTimeZone/24 return sunRiseSetResidual(localJD, longitude, latitude, localTimeZone, zenithShift, height, n) }) } // GetSunRiseTime 精确计算日出时间,传入当日0时JDE func GetSunRiseTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) { return calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height, true) } func GetSunRiseTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, n int) (float64, error) { return calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height, true, n) } // GetSunSetTime 精确计算日落时间,传入当日0时JDE func GetSunSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64) (float64, error) { return calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height, false) } func GetSunSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, n int) (float64, error) { return calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height, false, n) } // calculateSunRiseSetTime 统一的日出日落计算函数 func calculateSunRiseSetTime(julianDay, longitude, latitude, timeZone, zenithShift, height float64, isSunrise bool) (float64, error) { if !isFiniteFloat(julianDay) || !isFiniteFloat(longitude) || !isFiniteFloat(latitude) || !isFiniteFloat(timeZone) || !isFiniteFloat(zenithShift) || !isFiniteFloat(height) { return 0, ErrInvalidObservationInput } civilDayStart := math.Floor(julianDay) + 0.5 julianDay = math.Floor(julianDay) + 1.5 naturalTimeZone := math.Round(longitude / 15) sunAngle := StandardAltitudeSun(zenithShift, height, latitude) // 获取太阳上中天时间 solarNoonTime := CulminationTime(julianDay, longitude, naturalTimeZone) // 检查极夜极昼条件 if err := checkPolarConditions(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, isSunrise); err != nil { return sunRiseSetOnCivilDay(math.NaN(), math.NaN(), civilDayStart, longitude, latitude, timeZone, naturalTimeZone, zenithShift, height, isSunrise, -1, err) } // 计算初始估算时间 initialTime := calculateInitialSunTime(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, zenithShift, height, isSunrise) // 牛顿-拉夫逊迭代求精确解 result, slope := sunRiseSetNewtonRaphsonIteration(initialTime, longitude, latitude, naturalTimeZone, zenithShift, height, timeZone) return sunRiseSetOnCivilDay(result, slope, civilDayStart, longitude, latitude, timeZone, naturalTimeZone, zenithShift, height, isSunrise, -1, nil) } func calculateSunRiseSetTimeN(julianDay, longitude, latitude, timeZone, zenithShift, height float64, isSunrise bool, n int) (float64, error) { if !isFiniteFloat(julianDay) || !isFiniteFloat(longitude) || !isFiniteFloat(latitude) || !isFiniteFloat(timeZone) || !isFiniteFloat(zenithShift) || !isFiniteFloat(height) { return 0, ErrInvalidObservationInput } civilDayStart := math.Floor(julianDay) + 0.5 julianDay = math.Floor(julianDay) + 1.5 naturalTimeZone := math.Round(longitude / 15) sunAngle := StandardAltitudeSun(zenithShift, height, latitude) solarNoonTime := CulminationTimeN(julianDay, longitude, naturalTimeZone, n) if err := checkPolarConditionsN(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, isSunrise, n); err != nil { return sunRiseSetOnCivilDay(math.NaN(), math.NaN(), civilDayStart, longitude, latitude, timeZone, naturalTimeZone, zenithShift, height, isSunrise, n, err) } initialTime := calculateInitialSunTimeN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, zenithShift, height, isSunrise, n) result, slope := sunRiseSetNewtonRaphsonIterationN(initialTime, longitude, latitude, naturalTimeZone, zenithShift, height, timeZone, n) return sunRiseSetOnCivilDay(result, slope, civilDayStart, longitude, latitude, timeZone, naturalTimeZone, zenithShift, height, isSunrise, n, nil) } // checkPolarConditions 检查极夜极昼条件 func checkPolarConditions(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height float64, isSunrise bool) error { if sunRiseSetResidual(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, -1) < 0 { return ErrNeverRise } checkTime := solarNoonTime + 0.5 if isSunrise { checkTime = solarNoonTime - 0.5 } if sunRiseSetResidual(checkTime, longitude, latitude, naturalTimeZone, zenithShift, height, -1) > 0 { return ErrNeverSet } return nil } func checkPolarConditionsN(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height float64, isSunrise bool, n int) error { if sunRiseSetResidual(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, n) < 0 { return ErrNeverRise } checkTime := solarNoonTime + 0.5 if isSunrise { checkTime = solarNoonTime - 0.5 } if sunRiseSetResidual(checkTime, longitude, latitude, naturalTimeZone, zenithShift, height, n) > 0 { return ErrNeverSet } return nil } // calculateInitialSunTime 计算日出日落的初始估算时间 func calculateInitialSunTime(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, zenithShift, height float64, isSunrise bool) float64 { // 使用球面三角法计算: (sin(ho)-sin(φ)*sin(δ))/(cos(φ)*cos(δ)) apparentDeclination := HSunApparentDec(solarNoonTime) cosHourAngle := (Sin(sunAngle) - Sin(apparentDeclination)*Sin(latitude)) / (Cos(apparentDeclination) * Cos(latitude)) if math.Abs(cosHourAngle) <= 1 && latitude < 85 { // 使用解析解 hourAngle := ArcCos(cosHourAngle) / 15 timeOffset := 25.0 / 24.0 / 60.0 // 日出偏移 if !isSunrise { timeOffset = 35.0 / 24.0 / 60.0 // 日落偏移 } if isSunrise { return solarNoonTime - hourAngle/24 - timeOffset } else { return solarNoonTime + hourAngle/24 + timeOffset } } else { // 使用迭代逼近法(极地条件) return iterativeApproach(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, isSunrise) } } func calculateInitialSunTimeN(solarNoonTime, longitude, latitude, naturalTimeZone, sunAngle, zenithShift, height float64, isSunrise bool, n int) float64 { apparentDeclination := HSunApparentDecN(solarNoonTime, n) cosHourAngle := (Sin(sunAngle) - Sin(apparentDeclination)*Sin(latitude)) / (Cos(apparentDeclination) * Cos(latitude)) if math.Abs(cosHourAngle) <= 1 && latitude < 85 { hourAngle := ArcCos(cosHourAngle) / 15 timeOffset := 25.0 / 24.0 / 60.0 if !isSunrise { timeOffset = 35.0 / 24.0 / 60.0 } if isSunrise { return solarNoonTime - hourAngle/24 - timeOffset } return solarNoonTime + hourAngle/24 + timeOffset } return iterativeApproachN(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height, isSunrise, n) } // iterativeApproach 迭代逼近法计算(用于极地等特殊条件) func iterativeApproach(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height float64, isSunrise bool) float64 { estimatedTime := solarNoonTime stepSize := 15.0 / 60.0 / 24.0 // 15分钟步长 if isSunrise { stepSize = -stepSize } const maxIterations = 48 for i := 0; i < maxIterations && sunRiseSetResidual(estimatedTime, longitude, latitude, naturalTimeZone, zenithShift, height, -1) > 0; i++ { estimatedTime += stepSize } return estimatedTime } func iterativeApproachN(solarNoonTime, longitude, latitude, naturalTimeZone, zenithShift, height float64, isSunrise bool, n int) float64 { estimatedTime := solarNoonTime stepSize := 15.0 / 60.0 / 24.0 if isSunrise { stepSize = -stepSize } const maxIterations = 48 for i := 0; i < maxIterations && sunRiseSetResidual(estimatedTime, longitude, latitude, naturalTimeZone, zenithShift, height, n) > 0; i++ { estimatedTime += stepSize } return estimatedTime } // sunRiseSetNewtonRaphsonIteration 牛顿-拉夫逊迭代法求精确解 func sunRiseSetNewtonRaphsonIteration(initialTime, longitude, latitude, naturalTimeZone, zenithShift, height, timeZone float64) (float64, float64) { const ( convergenceThreshold = 0.00001 derivativeStep = 0.000005 ) currentTime := initialTime slope := math.NaN() var ok bool currentTime, ok = eventNewtonRefine(currentTime, convergenceThreshold, func(previousTime float64) float64 { functionValue := sunRiseSetResidual(previousTime, longitude, latitude, naturalTimeZone, zenithShift, height, -1) slope = (sunRiseSetResidual(previousTime+derivativeStep, longitude, latitude, naturalTimeZone, zenithShift, height, -1) - sunRiseSetResidual(previousTime-derivativeStep, longitude, latitude, naturalTimeZone, zenithShift, height, -1)) / (2 * derivativeStep) return functionValue / slope }) if !ok { return math.NaN(), math.NaN() } // 转换为指定时区 return currentTime - naturalTimeZone/24 + timeZone/24, slope } func sunRiseSetNewtonRaphsonIterationN(initialTime, longitude, latitude, naturalTimeZone, zenithShift, height, timeZone float64, n int) (float64, float64) { const ( convergenceThreshold = 0.00001 derivativeStep = 0.000005 ) currentTime := initialTime slope := math.NaN() var ok bool currentTime, ok = eventNewtonRefine(currentTime, convergenceThreshold, func(previousTime float64) float64 { functionValue := sunRiseSetResidual(previousTime, longitude, latitude, naturalTimeZone, zenithShift, height, n) slope = (sunRiseSetResidual(previousTime+derivativeStep, longitude, latitude, naturalTimeZone, zenithShift, height, n) - sunRiseSetResidual(previousTime-derivativeStep, longitude, latitude, naturalTimeZone, zenithShift, height, n)) / (2 * derivativeStep) return functionValue / slope }) if !ok { return math.NaN(), math.NaN() } return currentTime - naturalTimeZone/24 + timeZone/24, slope } /* * 太阳高度角 世界时 */ func SunHeight(jd, lon, lat, tz float64) float64 { return SunHeightN(jd, lon, lat, tz, -1) } func SunHeightN(jd, lon, lat, tz float64, n int) float64 { return sunObservationStateN(jd, lon, lat, tz, n).altitude } 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 }