447 lines
11 KiB
Go
447 lines
11 KiB
Go
package basic
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import (
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"math"
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"b612.me/astro/planet"
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. "b612.me/astro/tools"
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)
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func SaturnL(JD float64) float64 {
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return planet.WherePlanet(5, 0, JD)
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}
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func SaturnB(JD float64) float64 {
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return planet.WherePlanet(5, 1, JD)
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}
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func SaturnR(JD float64) float64 {
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return planet.WherePlanet(5, 2, JD)
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}
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func ASaturnX(JD float64) float64 {
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l := SaturnL(JD)
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b := SaturnB(JD)
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r := SaturnR(JD)
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el := planet.WherePlanet(-1, 0, JD)
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eb := planet.WherePlanet(-1, 1, JD)
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er := planet.WherePlanet(-1, 2, JD)
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x := r*Cos(b)*Cos(l) - er*Cos(eb)*Cos(el)
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return x
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}
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func ASaturnY(JD float64) float64 {
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l := SaturnL(JD)
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b := SaturnB(JD)
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r := SaturnR(JD)
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el := planet.WherePlanet(-1, 0, JD)
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eb := planet.WherePlanet(-1, 1, JD)
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er := planet.WherePlanet(-1, 2, JD)
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y := r*Cos(b)*Sin(l) - er*Cos(eb)*Sin(el)
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return y
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}
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func ASaturnZ(JD float64) float64 {
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//l := SaturnL(JD)
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b := SaturnB(JD)
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r := SaturnR(JD)
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// el := planet.WherePlanet(-1, 0, JD)
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eb := planet.WherePlanet(-1, 1, JD)
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er := planet.WherePlanet(-1, 2, JD)
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z := r*Sin(b) - er*Sin(eb)
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return z
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}
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func ASaturnXYZ(JD float64) (float64, float64, float64) {
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l := SaturnL(JD)
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b := SaturnB(JD)
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r := SaturnR(JD)
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el := planet.WherePlanet(-1, 0, JD)
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eb := planet.WherePlanet(-1, 1, JD)
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er := planet.WherePlanet(-1, 2, JD)
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x := r*Cos(b)*Cos(l) - er*Cos(eb)*Cos(el)
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y := r*Cos(b)*Sin(l) - er*Cos(eb)*Sin(el)
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z := r*Sin(b) - er*Sin(eb)
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return x, y, z
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}
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func SaturnApparentRa(JD float64) float64 {
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lo, bo := SaturnApparentLoBo(JD)
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sita := Sita(JD)
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ra := math.Atan2((Sin(lo)*Cos(sita) - Tan(bo)*Sin(sita)), Cos(lo))
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ra = ra * 180 / math.Pi
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return Limit360(ra)
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}
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func SaturnApparentDec(JD float64) float64 {
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lo, bo := SaturnApparentLoBo(JD)
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sita := Sita(JD)
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dec := ArcSin(Sin(bo)*Cos(sita) + Cos(bo)*Sin(sita)*Sin(lo))
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return dec
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}
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func SaturnApparentRaDec(JD float64) (float64, float64) {
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lo, bo := SaturnApparentLoBo(JD)
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sita := Sita(JD)
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ra := math.Atan2((Sin(lo)*Cos(sita) - Tan(bo)*Sin(sita)), Cos(lo))
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ra = ra * 180 / math.Pi
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dec := ArcSin(Sin(bo)*Cos(sita) + Cos(bo)*Sin(sita)*Sin(lo))
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return Limit360(ra), dec
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}
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func EarthSaturnAway(JD float64) float64 {
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x, y, z := ASaturnXYZ(JD)
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to := math.Sqrt(x*x + y*y + z*z)
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return to
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}
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func SaturnApparentLo(JD float64) float64 {
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x, y, z := ASaturnXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = ASaturnXYZ(JD - to)
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lo := math.Atan2(y, x)
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bo := math.Atan2(z, math.Sqrt(x*x+y*y))
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lo = lo * 180 / math.Pi
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bo = bo * 180 / math.Pi
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lo = Limit360(lo)
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//lo-=GXCLo(lo,bo,JD)/3600;
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//bo+=GXCBo(lo,bo,JD);
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lo += Nutation2000Bi(JD)
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return lo
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}
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func SaturnApparentBo(JD float64) float64 {
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x, y, z := ASaturnXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = ASaturnXYZ(JD - to)
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//lo := math.Atan2(y, x)
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bo := math.Atan2(z, math.Sqrt(x*x+y*y))
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//lo = lo * 180 / math.Pi
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bo = bo * 180 / math.Pi
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//lo+=GXCLo(lo,bo,JD);
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//bo+=GXCBo(lo,bo,JD)/3600;
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//lo+=Nutation2000Bi(JD);
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return bo
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}
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func SaturnApparentLoBo(JD float64) (float64, float64) {
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x, y, z := ASaturnXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = ASaturnXYZ(JD - to)
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lo := math.Atan2(y, x)
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bo := math.Atan2(z, math.Sqrt(x*x+y*y))
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lo = lo * 180 / math.Pi
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bo = bo * 180 / math.Pi
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lo = Limit360(lo)
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//lo-=GXCLo(lo,bo,JD)/3600;
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//bo+=GXCBo(lo,bo,JD);
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lo += Nutation2000Bi(JD)
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return lo, bo
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}
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func SaturnMag(JD float64) float64 {
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AwaySun := SaturnR(JD)
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AwayEarth := EarthSaturnAway(JD)
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Away := planet.WherePlanet(-1, 2, JD)
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i := (AwaySun*AwaySun + AwayEarth*AwayEarth - Away*Away) / (2 * AwaySun * AwayEarth)
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i = ArcCos(i)
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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)))
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return FloatRound(Mag, 2)
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}
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func SaturnRingB(JD float64) float64 {
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T := (JD - 2451545) / 36525
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i := 28.075216 - 0.012998*T + 0.000004*T*T
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omi := 169.508470 + 1.394681*T + 0.000412*T*T
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lo, bo := SaturnApparentLoBo(JD)
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B := Sin(i)*Cos(bo)*Sin(lo-omi) - Cos(i)*Cos(bo)
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return ArcSin(B)
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}
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func SaturnHeight(jde, lon, lat, timezone float64) float64 {
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// 转换为世界时
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utcJde := jde - timezone/24.0
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// 计算视恒星时
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ra, dec := SaturnApparentRaDec(TD2UT(utcJde, true))
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st := Limit360(ApparentSiderealTime(utcJde)*15 + lon)
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// 计算时角
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H := Limit360(st - ra)
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// 高度角、时角与天球座标三角转换公式
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// sin(h)=sin(lat)*sin(dec)+cos(dec)*cos(lat)*cos(H)
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sinHeight := Sin(lat)*Sin(dec) + Cos(dec)*Cos(lat)*Cos(H)
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return ArcSin(sinHeight)
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}
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func SaturnAzimuth(jde, lon, lat, timezone float64) float64 {
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// 转换为世界时
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utcJde := jde - timezone/24.0
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// 计算视恒星时
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ra, dec := SaturnApparentRaDec(TD2UT(utcJde, true))
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st := Limit360(ApparentSiderealTime(utcJde)*15 + lon)
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// 计算时角
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H := Limit360(st - ra)
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// 三角转换公式
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tanAzimuth := Sin(H) / (Cos(H)*Sin(lat) - Tan(dec)*Cos(lat))
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Azimuth := ArcTan(tanAzimuth)
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if Azimuth < 0 {
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if H/15 < 12 {
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return Azimuth + 360
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}
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return Azimuth + 180
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}
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if H/15 < 12 {
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return Azimuth + 180
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}
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return Azimuth
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}
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func SaturnHourAngle(JD, Lon, TZ float64) float64 {
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startime := Limit360(ApparentSiderealTime(JD-TZ/24)*15 + Lon)
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timeangle := startime - SaturnApparentRa(TD2UT(JD-TZ/24.0, 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 SaturnCulminationTime(jde, lon, 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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JD1 := jde + Limit360(360-SaturnHourAngle(jde, lon, timezone))/15.0/24.0*0.99726851851851851851
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limitHA := func(jde, lon, timezone float64) float64 {
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ha := SaturnHourAngle(jde, lon, 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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JD0 := JD1
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stDegree := limitHA(JD0, lon, timezone) - 360
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stDegreep := (limitHA(JD0+0.000005, lon, timezone) - limitHA(JD0-0.000005, lon, timezone)) / 0.00001
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JD1 = JD0 - stDegree/stDegreep
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if math.Abs(JD1-JD0) <= 0.00001 {
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break
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}
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}
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return JD1
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}
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func SaturnRiseTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 {
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return saturnRiseDown(JD, Lon, Lat, TZ, ZS, HEI, true)
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}
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func SaturnDownTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 {
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return saturnRiseDown(JD, Lon, Lat, TZ, ZS, HEI, false)
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}
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func saturnRiseDown(JD, Lon, Lat, TZ, ZS, HEI float64, isRise bool) float64 {
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var An float64
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JD = math.Floor(JD) + 0.5
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ntz := math.Round(Lon / 15)
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if ZS != 0 {
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An = -0.8333
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}
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An = An - HeightDegreeByLat(HEI, Lat)
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tztime := SaturnCulminationTime(JD, Lon, ntz)
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if SaturnHeight(tztime, Lon, Lat, ntz) < An {
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return -2 //极夜
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}
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if SaturnHeight(tztime-0.5, Lon, Lat, ntz) > An {
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return -1 //极昼
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}
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dec := HSunApparentDec(TD2UT(tztime-ntz/24, true))
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//(sin(ho)-sin(φ)*sin(δ2))/(cos(φ)*cos(δ2))
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tmp := (Sin(An) - Sin(dec)*Sin(Lat)) / (Cos(dec) * Cos(Lat))
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var rise float64
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if math.Abs(tmp) <= 1 {
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rzsc := ArcCos(tmp) / 15
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if isRise {
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rise = tztime - rzsc/24 - 25.0/24.0/60.0
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} else {
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rise = tztime + rzsc/24 - 25.0/24.0/60.0
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}
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} else {
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rise = tztime
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i := 0
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//TODO:使用二分法计算
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for SaturnHeight(rise, Lon, Lat, ntz) > An {
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i++
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if isRise {
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rise -= 15.0 / 60.0 / 24.0
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} else {
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rise += 15.0 / 60.0 / 24.0
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}
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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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JD1 := rise
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for {
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JD0 := JD1
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stDegree := SaturnHeight(JD0, Lon, Lat, ntz) - An
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stDegreep := (SaturnHeight(JD0+0.000005, Lon, Lat, ntz) - SaturnHeight(JD0-0.000005, Lon, Lat, ntz)) / 0.00001
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JD1 = JD0 - stDegree/stDegreep
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if math.Abs(JD1-JD0) <= 0.00001 {
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break
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}
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}
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return JD1 - ntz/24 + TZ/24
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}
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// Pos
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const SATURN_S_PERIOD = 1 / ((1 / 365.256363004) - (1 / 10759.0))
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func saturnConjunction(jde, degree float64, next uint8) float64 {
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//0=last 1=next
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decSub := func(jde float64, degree float64, filter bool) float64 {
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sub := Limit360(Limit360(SaturnApparentLo(jde)-HSunApparentLo(jde)) - degree)
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if filter {
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if sub > 180 {
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sub -= 360
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}
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if sub < -180 {
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sub += 360
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}
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}
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return sub
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}
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dayCost := SATURN_S_PERIOD / 360
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nowSub := decSub(jde, degree, false)
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if next == 0 {
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jde -= (360 - nowSub) * dayCost
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} else {
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jde += dayCost * nowSub
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}
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JD1 := jde
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for {
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JD0 := JD1
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stDegree := decSub(JD0, degree, true)
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stDegreep := (decSub(JD0+0.000005, degree, true) - decSub(JD0-0.000005, degree, true)) / 0.00001
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JD1 = JD0 - stDegree/stDegreep
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if math.Abs(JD1-JD0) <= 0.00001 {
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break
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}
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}
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return TD2UT(JD1, false)
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}
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func LastSaturnConjunction(jde float64) float64 {
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return saturnConjunction(jde, 0, 0)
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}
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func NextSaturnConjunction(jde float64) float64 {
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return saturnConjunction(jde, 0, 1)
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}
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func LastSaturnOpposition(jde float64) float64 {
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return saturnConjunction(jde, 180, 0)
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}
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func NextSaturnOpposition(jde float64) float64 {
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return saturnConjunction(jde, 180, 1)
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}
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func NextSaturnEasternQuadrature(jde float64) float64 {
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return saturnConjunction(jde, 90, 1)
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}
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func LastSaturnEasternQuadrature(jde float64) float64 {
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return saturnConjunction(jde, 90, 0)
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}
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func NextSaturnWesternQuadrature(jde float64) float64 {
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return saturnConjunction(jde, 270, 1)
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}
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func LastSaturnWesternQuadrature(jde float64) float64 {
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return saturnConjunction(jde, 270, 0)
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}
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func saturnRetrograde(jde float64, isLeft bool) float64 {
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//0=last 1=next
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decSub := func(jde float64, val float64) float64 {
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sub := SaturnApparentRa(jde+val) - SaturnApparentRa(jde-val)
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if sub > 180 {
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sub -= 360
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}
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if sub < -180 {
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sub += 360
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}
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return sub / (2 * val)
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}
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jde = NextSaturnOpposition(jde)
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if isLeft {
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jde -= 60
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} else {
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jde += 60
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}
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for {
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nowSub := decSub(jde, 1.0/86400.0)
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if math.Abs(nowSub) > 0.55 {
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jde += 2
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continue
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}
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break
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}
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JD1 := jde
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for {
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JD0 := JD1
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stDegree := decSub(JD0, 2.0/86400.0)
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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)
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JD1 = JD0 - stDegree/stDegreep
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if math.Abs(JD1-JD0) <= 30.0/86400.0 {
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break
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}
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}
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JD1 = JD1 - 15.0/86400.0
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min := JD1
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minRa := 100.0
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for i := 0.0; i < 60.0; i++ {
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tmp := decSub(JD1+i*0.5/86400.0, 0.5/86400.0)
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if math.Abs(tmp) < math.Abs(minRa) {
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minRa = tmp
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min = JD1 + i*0.5/86400.0
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}
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}
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return TD2UT(min, false)
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}
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func NextSaturnRetrogradeToPrograde(jde float64) float64 {
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date := saturnRetrograde(jde, false)
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if date < jde {
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op := NextSaturnOpposition(jde)
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return saturnRetrograde(op+10, false)
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}
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return date
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}
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func LastSaturnRetrogradeToPrograde(jde float64) float64 {
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jde = LastSaturnOpposition(jde) - 10
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date := saturnRetrograde(jde, false)
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if date > jde {
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op := LastSaturnOpposition(jde)
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return saturnRetrograde(op-10, false)
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}
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return date
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}
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func NextSaturnProgradeToRetrograde(jde float64) float64 {
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date := saturnRetrograde(jde, true)
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if date < jde {
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op := NextSaturnOpposition(jde)
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return saturnRetrograde(op+10, true)
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}
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return date
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}
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func LastSaturnProgradeToRetrograde(jde float64) float64 {
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jde = LastSaturnOpposition(jde) - 10
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date := saturnRetrograde(jde, true)
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if date > jde {
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op := LastSaturnOpposition(jde)
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return saturnRetrograde(op-10, true)
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}
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return date
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}
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