package basic import ( "math" "b612.me/astro/planet" . "b612.me/astro/tools" ) func SaturnL(JD float64) float64 { return planet.WherePlanet(5, 0, JD) } func SaturnB(JD float64) float64 { return planet.WherePlanet(5, 1, JD) } func SaturnR(JD float64) float64 { return planet.WherePlanet(5, 2, JD) } func ASaturnX(JD float64) float64 { l := SaturnL(JD) b := SaturnB(JD) r := SaturnR(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 ASaturnY(JD float64) float64 { l := SaturnL(JD) b := SaturnB(JD) r := SaturnR(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 ASaturnZ(JD float64) float64 { //l := SaturnL(JD) b := SaturnB(JD) r := SaturnR(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 ASaturnXYZ(JD float64) (float64, float64, float64) { l := SaturnL(JD) b := SaturnB(JD) r := SaturnR(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 SaturnApparentRa(JD float64) float64 { lo, bo := SaturnApparentLoBo(JD) sita := Sita(JD) ra := math.Atan2((Sin(lo)*Cos(sita) - Tan(bo)*Sin(sita)), Cos(lo)) ra = ra * 180 / math.Pi return Limit360(ra) } func SaturnApparentDec(JD float64) float64 { lo, bo := SaturnApparentLoBo(JD) sita := Sita(JD) dec := ArcSin(Sin(bo)*Cos(sita) + Cos(bo)*Sin(sita)*Sin(lo)) return dec } func SaturnApparentRaDec(JD float64) (float64, float64) { lo, bo := SaturnApparentLoBo(JD) sita := Sita(JD) ra := math.Atan2((Sin(lo)*Cos(sita) - Tan(bo)*Sin(sita)), Cos(lo)) ra = ra * 180 / math.Pi dec := ArcSin(Sin(bo)*Cos(sita) + Cos(bo)*Sin(sita)*Sin(lo)) return Limit360(ra), dec } func EarthSaturnAway(JD float64) float64 { x, y, z := ASaturnXYZ(JD) to := math.Sqrt(x*x + y*y + z*z) return to } func SaturnApparentLo(JD float64) float64 { x, y, z := ASaturnXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = ASaturnXYZ(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 SaturnApparentBo(JD float64) float64 { x, y, z := ASaturnXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = ASaturnXYZ(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 SaturnApparentLoBo(JD float64) (float64, float64) { x, y, z := ASaturnXYZ(JD) to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z) x, y, z = ASaturnXYZ(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, bo } func SaturnMag(JD float64) float64 { AwaySun := SaturnR(JD) AwayEarth := EarthSaturnAway(JD) Away := planet.WherePlanet(-1, 2, JD) i := (AwaySun*AwaySun + AwayEarth*AwayEarth - Away*Away) / (2 * AwaySun * AwayEarth) i = ArcCos(i) Mag := -8.68 + 5*math.Log10(AwaySun*AwayEarth) + 0.044*i - 2.6*Sin(math.Abs(SaturnRingB(JD))) + 1.25*Sin(math.Abs(SaturnRingB(JD)))*Sin(math.Abs(SaturnRingB(JD))) return FloatRound(Mag, 2) } func SaturnRingB(JD float64) float64 { T := (JD - 2451545) / 36525 i := 28.075216 - 0.012998*T + 0.000004*T*T omi := 169.508470 + 1.394681*T + 0.000412*T*T lo, bo := SaturnApparentLoBo(JD) B := Sin(i)*Cos(bo)*Sin(lo-omi) - Cos(i)*Cos(bo) return ArcSin(B) } func SaturnHeight(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 := SaturnApparentRaDec(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 SaturnAzimuth(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 := SaturnApparentRaDec(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 SaturnHourAngle(JD, Lon, TZ float64) float64 { startime := Limit360(ApparentSiderealTime(JD-TZ/24)*15 + Lon) timeangle := startime - SaturnApparentRa(TD2UT(JD-TZ/24.0, true)) if timeangle < 0 { timeangle += 360 } return timeangle } func SaturnCulminationTime(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-SaturnHourAngle(jde, lon, timezone))/15.0/24.0*0.99726851851851851851 limitHA := func(jde, lon, timezone float64) float64 { ha := SaturnHourAngle(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 SaturnRiseTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 { return saturnRiseDown(JD, Lon, Lat, TZ, ZS, HEI, true) } func SaturnDownTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 { return saturnRiseDown(JD, Lon, Lat, TZ, ZS, HEI, false) } func saturnRiseDown(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 := SaturnCulminationTime(JD, Lon, ntz) if SaturnHeight(tztime, Lon, Lat, ntz) < An { return -2 //极夜 } if SaturnHeight(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 SaturnHeight(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 := SaturnHeight(JD0, Lon, Lat, ntz) - An stDegreep := (SaturnHeight(JD0+0.000005, Lon, Lat, ntz) - SaturnHeight(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 SATURN_S_PERIOD = 1 / ((1 / 365.256363004) - (1 / 10759.0)) func saturnConjunction(jde, degree float64, next uint8) float64 { //0=last 1=next decSub := func(jde float64, degree float64, filter bool) float64 { sub := Limit360(Limit360(SaturnApparentLo(jde)-HSunApparentLo(jde)) - degree) if filter { if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } } return sub } dayCost := SATURN_S_PERIOD / 360 nowSub := decSub(jde, degree, false) if next == 0 { jde -= (360 - nowSub) * dayCost } else { jde += dayCost * nowSub } JD1 := jde for { JD0 := JD1 stDegree := decSub(JD0, degree, true) stDegreep := (decSub(JD0+0.000005, degree, true) - decSub(JD0-0.000005, degree, true)) / 0.00001 JD1 = JD0 - stDegree/stDegreep if math.Abs(JD1-JD0) <= 0.00001 { break } } return TD2UT(JD1, false) } func LastSaturnConjunction(jde float64) float64 { return saturnConjunction(jde, 0, 0) } func NextSaturnConjunction(jde float64) float64 { return saturnConjunction(jde, 0, 1) } func LastSaturnOpposition(jde float64) float64 { return saturnConjunction(jde, 180, 0) } func NextSaturnOpposition(jde float64) float64 { return saturnConjunction(jde, 180, 1) } func NextSaturnEasternQuadrature(jde float64) float64 { return saturnConjunction(jde, 90, 1) } func LastSaturnEasternQuadrature(jde float64) float64 { return saturnConjunction(jde, 90, 0) } func NextSaturnWesternQuadrature(jde float64) float64 { return saturnConjunction(jde, 270, 1) } func LastSaturnWesternQuadrature(jde float64) float64 { return saturnConjunction(jde, 270, 0) } func saturnRetrograde(jde float64, isLeft bool) float64 { //0=last 1=next decSub := func(jde float64, val float64) float64 { sub := SaturnApparentRa(jde+val) - SaturnApparentRa(jde-val) if sub > 180 { sub -= 360 } if sub < -180 { sub += 360 } return sub / (2 * val) } jde = NextSaturnOpposition(jde) if isLeft { jde -= 60 } else { jde += 60 } 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 } } return TD2UT(min, false) } func NextSaturnRetrogradeToPrograde(jde float64) float64 { date := saturnRetrograde(jde, false) if date < jde { op := NextSaturnOpposition(jde) return saturnRetrograde(op+10, false) } return date } func LastSaturnRetrogradeToPrograde(jde float64) float64 { jde = LastSaturnOpposition(jde) - 10 date := saturnRetrograde(jde, false) if date > jde { op := LastSaturnOpposition(jde) return saturnRetrograde(op-10, false) } return date } func NextSaturnProgradeToRetrograde(jde float64) float64 { date := saturnRetrograde(jde, true) if date < jde { op := NextSaturnOpposition(jde) return saturnRetrograde(op+10, true) } return date } func LastSaturnProgradeToRetrograde(jde float64) float64 { jde = LastSaturnOpposition(jde) - 10 date := saturnRetrograde(jde, true) if date > jde { op := LastSaturnOpposition(jde) return saturnRetrograde(op-10, true) } return date }