package basic import ( "math" "b612.me/astro/planet" . "b612.me/astro/tools" ) func MercuryL(JD float64) float64 { return planet.WherePlanet(1, 0, JD) } func MercuryB(JD float64) float64 { return planet.WherePlanet(1, 1, JD) } func MercuryR(JD float64) float64 { return planet.WherePlanet(1, 2, JD) } func AMercuryX(JD float64) float64 { l := MercuryL(JD) b := MercuryB(JD) r := MercuryR(JD) el := planet.WherePlanet(-1, 0, JD) eb := planet.WherePlanet(-1, 1, JD) er := planet.WherePlanet(-1, 2, JD) x := r*Cos(b)*Cos(l) - er*Cos(eb)*Cos(el) return x } func AMercuryY(JD float64) float64 { l := MercuryL(JD) b := MercuryB(JD) r := MercuryR(JD) el := planet.WherePlanet(-1, 0, JD) eb := planet.WherePlanet(-1, 1, JD) er := planet.WherePlanet(-1, 2, JD) y := r*Cos(b)*Sin(l) - er*Cos(eb)*Sin(el) return y } func AMercuryZ(JD float64) float64 { //l := MercuryL(JD) b := MercuryB(JD) r := MercuryR(JD) // el := planet.WherePlanet(-1, 0, JD) eb := planet.WherePlanet(-1, 1, JD) er := planet.WherePlanet(-1, 2, JD) z := r*Sin(b) - er*Sin(eb) return z } func AMercuryXYZ(JD float64) (float64, float64, float64) { l := MercuryL(JD) b := MercuryB(JD) r := MercuryR(JD) el := planet.WherePlanet(-1, 0, JD) eb := planet.WherePlanet(-1, 1, JD) er := planet.WherePlanet(-1, 2, JD) x := r*Cos(b)*Cos(l) - er*Cos(eb)*Cos(el) y := r*Cos(b)*Sin(l) - er*Cos(eb)*Sin(el) z := r*Sin(b) - er*Sin(eb) return x, y, z } func MercuryApparentRa(JD float64) float64 { lo, bo := MercuryApparentLoBo(JD) return LoToRa(JD, lo, bo) } func MercuryApparentDec(JD float64) float64 { lo, bo := MercuryApparentLoBo(JD) sita := Sita(JD) dec := ArcSin(Sin(bo)*Cos(sita) + Cos(bo)*Sin(sita)*Sin(lo)) return dec } func MercuryApparentRaDec(JD float64) (float64, float64) { lo, bo := MercuryApparentLoBo(JD) return LoBoToRaDec(JD, lo, bo) } func EarthMercuryAway(JD float64) float64 { x, y, z := AMercuryXYZ(JD) to := math.Sqrt(x*x + y*y + z*z) return to } func MercuryApparentLo(JD float64) float64 { x, y, z := AMercuryXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = AMercuryXYZ(JD - to) lo := math.Atan2(y, x) bo := math.Atan2(z, math.Sqrt(x*x+y*y)) lo = lo * 180 / math.Pi bo = bo * 180 / math.Pi lo = Limit360(lo) //lo-=GXCLo(lo,bo,JD)/3600; //bo+=GXCBo(lo,bo,JD); lo += HJZD(JD) return lo } func MercuryApparentBo(JD float64) float64 { x, y, z := AMercuryXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = AMercuryXYZ(JD - to) //lo := math.Atan2(y, x) bo := math.Atan2(z, math.Sqrt(x*x+y*y)) //lo = lo * 180 / math.Pi bo = bo * 180 / math.Pi //lo+=GXCLo(lo,bo,JD); //bo+=GXCBo(lo,bo,JD)/3600; //lo+=HJZD(JD); return bo } func MercuryApparentLoBo(JD float64) (float64, float64) { x, y, z := AMercuryXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = AMercuryXYZ(JD - to) lo := math.Atan2(y, x) bo := math.Atan2(z, math.Sqrt(x*x+y*y)) lo = lo * 180 / math.Pi bo = bo * 180 / math.Pi lo = Limit360(lo) + HJZD(JD) //lo-=GXCLo(lo,bo,JD)/3600; //bo+=GXCBo(lo,bo,JD); return lo, bo } func MercuryMag(JD float64) float64 { AwaySun := MercuryR(JD) AwayEarth := EarthMercuryAway(JD) Away := planet.WherePlanet(-1, 2, JD) i := (AwaySun*AwaySun + AwayEarth*AwayEarth - Away*Away) / (2 * AwaySun * AwayEarth) i = ArcCos(i) Mag := -0.42 + 5*math.Log10(AwaySun*AwayEarth) + 0.0380*i - 0.000273*i*i + 0.000002*i*i*i return FloatRound(Mag, 2) } func MercuryHeight(jde, lon, lat, timezone float64) float64 { // 转换为世界时 utcJde := jde - timezone/24.0 // 计算视恒星时 ra, dec := MercuryApparentRaDec(TD2UT(utcJde, true)) st := Limit360(ApparentSiderealTime(utcJde)*15 + lon) // 计算时角 H := Limit360(st - ra) // 高度角、时角与天球座标三角转换公式 // sin(h)=sin(lat)*sin(dec)+cos(dec)*cos(lat)*cos(H) sinHeight := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(H) return ArcSin(sinHeight) } func MercuryAzimuth(jde, lon, lat, timezone float64) float64 { // 转换为世界时 utcJde := jde - timezone/24.0 // 计算视恒星时 ra, dec := MercuryApparentRaDec(TD2UT(utcJde, true)) st := Limit360(ApparentSiderealTime(utcJde)*15 + lon) // 计算时角 H := Limit360(st - ra) // 三角转换公式 tanAzimuth := Sin(H) / (Cos(H)*Sin(lat) - Tan(dec)*Cos(lat)) Azimuth := ArcTan(tanAzimuth) if Azimuth < 0 { if H/15 < 12 { return Azimuth + 360 } return Azimuth + 180 } if H/15 < 12 { return Azimuth + 180 } return Azimuth } func MercuryHourAngle(JD, Lon, TZ float64) float64 { startime := Limit360(ApparentSiderealTime(JD-TZ/24)*15 + Lon) timeangle := startime - MercuryApparentRa(TD2UT(JD-TZ/24.0, true)) if timeangle < 0 { timeangle += 360 } return timeangle } func MercuryCulminationTime(jde, lon, timezone float64) float64 { //jde 世界时,非力学时,当地时区 0时,无需转换力学时 //ra,dec 瞬时天球座标,非J2000等时间天球坐标 jde = math.Floor(jde) + 0.5 JD1 := jde + Limit360(360-MercuryHourAngle(jde, lon, timezone))/15.0/24.0*0.99726851851851851851 limitHA := func(jde, lon, timezone float64) float64 { ha := MercuryHourAngle(jde, lon, timezone) if ha < 180 { ha += 360 } return ha } for { JD0 := JD1 stDegree := limitHA(JD0, lon, timezone) - 360 stDegreep := (limitHA(JD0+0.000005, lon, timezone) - limitHA(JD0-0.000005, lon, timezone)) / 0.00001 JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 0.00001 { break } } return JD1 } func MercuryRiseTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 { return mercuryRiseDown(JD, Lon, Lat, TZ, ZS, HEI, true) } func MercuryDownTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 { return mercuryRiseDown(JD, Lon, Lat, TZ, ZS, HEI, false) } func mercuryRiseDown(JD, Lon, Lat, TZ, ZS, HEI float64, isRise bool) float64 { var An float64 JD = math.Floor(JD) + 0.5 ntz := math.Round(Lon / 15) if ZS != 0 { An = -0.8333 } An = An - HeightDegreeByLat(HEI, Lat) tztime := MercuryCulminationTime(JD, Lon, ntz) if MercuryHeight(tztime, Lon, Lat, ntz) < An { return -2 //极夜 } if MercuryHeight(tztime-0.5, Lon, Lat, ntz) > An { return -1 //极昼 } dec := HSunApparentDec(TD2UT(tztime-ntz/24, true)) //(sin(ho)-sin(φ)*sin(δ2))/(cos(φ)*cos(δ2)) tmp := (Sin(An) - Sin(dec)*Sin(Lat)) / (Cos(dec) * Cos(Lat)) var rise float64 if math.Abs(tmp) <= 1 { rzsc := ArcCos(tmp) / 15 if isRise { rise = tztime - rzsc/24 - 25.0/24.0/60.0 } else { rise = tztime + rzsc/24 - 25.0/24.0/60.0 } } else { rise = tztime i := 0 //TODO:使用二分法计算 for MercuryHeight(rise, Lon, Lat, ntz) > An { i++ if isRise { rise -= 15.0 / 60.0 / 24.0 } else { rise += 15.0 / 60.0 / 24.0 } if i > 48 { break } } } JD1 := rise for { JD0 := JD1 stDegree := MercuryHeight(JD0, Lon, Lat, ntz) - An stDegreep := (MercuryHeight(JD0+0.000005, Lon, Lat, ntz) - MercuryHeight(JD0-0.000005, Lon, Lat, ntz)) / 0.00001 JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 0.00001 { break } } return JD1 - ntz/24 + TZ/24 } // Pos const MERCURY_S_PERIOD = 1 / ((1 / 87.9691) - (1 / 365.256363004)) func mercuryConjunction(jde float64, next uint8) float64 { //0=last 1=next decSub := func(jde float64) float64 { sub := Limit360(MercuryApparentLo(jde) - HSunApparentLo(jde)) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub } nowSub := decSub(jde) // pos 大于0:远离太阳 小于0:靠近太阳 pos := math.Abs(decSub(jde+1/86400.0)) - math.Abs(nowSub) if pos >= 0 && next == 1 && nowSub > 0 { jde += MERCURY_S_PERIOD/8.0 + 2 } if pos >= 0 && next == 1 && nowSub < 0 { jde += MERCURY_S_PERIOD/6.0 + 2 } if pos <= 0 && next == 0 && nowSub < 0 { jde -= MERCURY_S_PERIOD/8.0 + 2 } if pos <= 0 && next == 0 && nowSub > 0 { jde -= MERCURY_S_PERIOD/6.0 + 2 } for { nowSub := decSub(jde) pos := math.Abs(decSub(jde+1/86400.0)) - math.Abs(nowSub) if math.Abs(nowSub) > 12 || (pos > 0 && next == 1) || (pos < 0 && next == 0) { if next == 1 { jde += 2 } else { jde -= 2 } continue } break } JD1 := jde for { JD0 := JD1 stDegree := decSub(JD0) stDegreep := (decSub(JD0+0.000005) - decSub(JD0-0.000005)) / 0.00001 JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 0.00001 { break } } return TD2UT(JD1, false) } func LastMercuryConjunction(jde float64) float64 { return mercuryConjunction(jde, 0) } func NextMercuryConjunction(jde float64) float64 { return mercuryConjunction(jde, 1) } func NextMercuryInferiorConjunction(jde float64) float64 { date := NextMercuryConjunction(jde) if EarthMercuryAway(date) > EarthAway(date) { return NextMercuryConjunction(date + 2) } return date } func NextMercurySuperiorConjunction(jde float64) float64 { date := NextMercuryConjunction(jde) if EarthMercuryAway(date) < EarthAway(date) { return NextMercuryConjunction(date + 2) } return date } func LastMercuryInferiorConjunction(jde float64) float64 { date := LastMercuryConjunction(jde) if EarthMercuryAway(date) > EarthAway(date) { return LastMercuryConjunction(date - 2) } return date } func LastMercurySuperiorConjunction(jde float64) float64 { date := LastMercuryConjunction(jde) if EarthMercuryAway(date) < EarthAway(date) { return LastMercuryConjunction(date - 2) } return date } func mercuryRetrograde(jde float64) float64 { //0=last 1=next decSunSub := func(jde float64) float64 { sub := Limit360(MercuryApparentRa(jde) - SunApparentRa(jde)) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub } decSub := func(jde float64, val float64) float64 { sub := MercuryApparentRa(jde+val) - MercuryApparentRa(jde-val) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub / (2 * val) } lastHe := LastMercuryConjunction(jde) nextHe := NextMercuryConjunction(jde) nowSub := decSunSub(jde) if nowSub > 0 { jde = lastHe + ((nextHe - lastHe) / 5.0 * 3.5) } else { jde = lastHe + ((nextHe - lastHe) / 5.5) } for { nowSub := decSub(jde, 1.0/86400.0) if math.Abs(nowSub) > 0.55 { jde += 2 continue } break } JD1 := jde for { JD0 := JD1 stDegree := decSub(JD0, 2.0/86400.0) stDegreep := (decSub(JD0+15.0/86400.0, 2.0/86400.0) - decSub(JD0-15.0/86400.0, 2.0/86400.0)) / (30.0 / 86400.0) JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 30.0/86400.0 { break } } JD1 = JD1 - 15.0/86400.0 min := JD1 minRa := 100.0 for i := 0.0; i < 60.0; i++ { tmp := decSub(JD1+i*0.5/86400.0, 0.5/86400.0) if math.Abs(tmp) < math.Abs(minRa) { minRa = tmp min = JD1 + i*0.5/86400.0 } } //fmt.Println((min - lastHe) / (nextHe - lastHe)) return TD2UT(min, false) } func NextMercuryRetrograde(jde float64) float64 { date := mercuryRetrograde(jde) if date < jde { nextHe := NextMercuryConjunction(jde) return mercuryRetrograde(nextHe + 2) } return date } func LastMercuryRetrograde(jde float64) float64 { lastHe := LastMercuryConjunction(jde) date := mercuryRetrograde(lastHe + 2) if date > jde { lastLastHe := LastMercuryConjunction(lastHe - 2) return mercuryRetrograde(lastLastHe + 2) } return date } func NextMercuryProgradeToRetrograde(jde float64) float64 { date := NextMercuryRetrograde(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub > 180 { return NextMercuryRetrograde(date + MERCURY_S_PERIOD/2) } return date } func NextMercuryRetrogradeToPrograde(jde float64) float64 { date := NextMercuryRetrograde(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub < 180 { return NextMercuryRetrograde(date + 12) } return date } func LastMercuryProgradeToRetrograde(jde float64) float64 { date := LastMercuryRetrograde(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub > 180 { return LastMercuryRetrograde(date - 12) } return date } func LastMercuryRetrogradeToPrograde(jde float64) float64 { date := LastMercuryRetrograde(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub < 180 { return LastMercuryRetrograde(date - MERCURY_S_PERIOD/2) } return date } func MercurySunElongation(jde float64) float64 { lo1, bo1 := MercuryApparentLoBo(jde) lo2 := SunApparentLo(jde) bo2 := HSunTrueBo(jde) return StarAngularSeparation(lo1, bo1, lo2, bo2) } func mercuryGreatestElongation(jde float64) float64 { decSunSub := func(jde float64) float64 { sub := Limit360(MercuryApparentRa(jde) - SunApparentRa(jde)) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub } decSub := func(jde float64, val float64) float64 { sub := MercurySunElongation(jde+val) - MercurySunElongation(jde-val) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub / (2 * val) } lastHe := LastMercuryConjunction(jde) nextHe := NextMercuryConjunction(jde) nowSub := decSunSub(jde) if nowSub > 0 { jde = lastHe + ((nextHe - lastHe) / 5.0 * 2.0) } else { jde = lastHe + ((nextHe - lastHe) / 6.0) } for { nowSub := decSub(jde, 1.0/86400.0) if math.Abs(nowSub) > 0.4 { jde += 2 continue } break } JD1 := jde for { JD0 := JD1 stDegree := decSub(JD0, 2.0/86400.0) stDegreep := (decSub(JD0+15.0/86400.0, 2.0/86400.0) - decSub(JD0-15.0/86400.0, 2.0/86400.0)) / (30.0 / 86400.0) JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 30.0/86400.0 { break } } JD1 = JD1 - 15.0/86400.0 min := JD1 minRa := 100.0 for i := 0.0; i < 60.0; i++ { tmp := decSub(JD1+i*0.5/86400.0, 0.5/86400.0) if math.Abs(tmp) < math.Abs(minRa) { minRa = tmp min = JD1 + i*0.5/86400.0 } } //fmt.Println((min - lastHe) / (nextHe - lastHe)) return TD2UT(min, false) } func NextMercuryGreatestElongation(jde float64) float64 { date := mercuryGreatestElongation(jde) if date < jde { nextHe := NextMercuryConjunction(jde) return mercuryGreatestElongation(nextHe + 2) } return date } func LastMercuryGreatestElongation(jde float64) float64 { lastHe := LastMercuryConjunction(jde) date := mercuryGreatestElongation(lastHe + 2) if date > jde { lastLastHe := LastMercuryConjunction(lastHe - 2) return mercuryGreatestElongation(lastLastHe + 2) } return date } func NextMercuryGreatestElongationEast(jde float64) float64 { date := NextMercuryGreatestElongation(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub > 180 { return NextMercuryGreatestElongation(date + 1) } return date } func NextMercuryGreatestElongationWest(jde float64) float64 { date := NextMercuryGreatestElongation(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub < 180 { return NextMercuryGreatestElongation(date + 1) } return date } func LastMercuryGreatestElongationEast(jde float64) float64 { date := LastMercuryGreatestElongation(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub > 180 { return LastMercuryGreatestElongation(date - 1) } return date } func LastMercuryGreatestElongationWest(jde float64) float64 { date := LastMercuryGreatestElongation(jde) sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date)) if sub < 180 { return LastMercuryGreatestElongation(date - 1) } return date }