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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 MercuryL(JD float64) float64 {
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return planet.WherePlanet(1, 0, JD)
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}
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func MercuryB(JD float64) float64 {
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return planet.WherePlanet(1, 1, JD)
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}
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func MercuryR(JD float64) float64 {
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return planet.WherePlanet(1, 2, JD)
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}
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func AMercuryX(JD float64) float64 {
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l := MercuryL(JD)
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b := MercuryB(JD)
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r := MercuryR(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 AMercuryY(JD float64) float64 {
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l := MercuryL(JD)
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b := MercuryB(JD)
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r := MercuryR(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 AMercuryZ(JD float64) float64 {
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//l := MercuryL(JD)
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b := MercuryB(JD)
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r := MercuryR(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 AMercuryXYZ(JD float64) (float64, float64, float64) {
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l := MercuryL(JD)
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b := MercuryB(JD)
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r := MercuryR(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 MercuryApparentRa(JD float64) float64 {
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lo, bo := MercuryApparentLoBo(JD)
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return LoToRa(JD, lo, bo)
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}
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func MercuryApparentDec(JD float64) float64 {
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lo, bo := MercuryApparentLoBo(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 MercuryApparentRaDec(JD float64) (float64, float64) {
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lo, bo := MercuryApparentLoBo(JD)
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return LoBoToRaDec(JD, lo, bo)
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}
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func EarthMercuryAway(JD float64) float64 {
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x, y, z := AMercuryXYZ(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 MercuryApparentLo(JD float64) float64 {
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x, y, z := AMercuryXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = AMercuryXYZ(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 += HJZD(JD)
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return lo
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}
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func MercuryApparentBo(JD float64) float64 {
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x, y, z := AMercuryXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = AMercuryXYZ(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+=HJZD(JD);
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return bo
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}
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func MercuryApparentLoBo(JD float64) (float64, float64) {
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x, y, z := AMercuryXYZ(JD)
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to := 0.0057755183 * math.Sqrt(x*x+y*y+z*z)
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x, y, z = AMercuryXYZ(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) + HJZD(JD)
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//lo-=GXCLo(lo,bo,JD)/3600;
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//bo+=GXCBo(lo,bo,JD);
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return lo, bo
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}
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func MercuryMag(JD float64) float64 {
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AwaySun := MercuryR(JD)
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AwayEarth := EarthMercuryAway(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 := -0.42 + 5*math.Log10(AwaySun*AwayEarth) + 0.0380*i - 0.000273*i*i + 0.000002*i*i*i
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return FloatRound(Mag, 2)
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}
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func MercuryHeight(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 := MercuryApparentRaDec(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 MercuryAzimuth(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 := MercuryApparentRaDec(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 MercuryHourAngle(JD, Lon, TZ float64) float64 {
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startime := Limit360(ApparentSiderealTime(JD-TZ/24)*15 + Lon)
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timeangle := startime - MercuryApparentRa(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 MercuryCulminationTime(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-MercuryHourAngle(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 := MercuryHourAngle(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 MercuryRiseTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 {
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return mercuryRiseDown(JD, Lon, Lat, TZ, ZS, HEI, true)
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}
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func MercuryDownTime(JD, Lon, Lat, TZ, ZS, HEI float64) float64 {
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return mercuryRiseDown(JD, Lon, Lat, TZ, ZS, HEI, false)
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}
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func mercuryRiseDown(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 := MercuryCulminationTime(JD, Lon, ntz)
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if MercuryHeight(tztime, Lon, Lat, ntz) < An {
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return -2 //极夜
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}
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if MercuryHeight(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 MercuryHeight(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 := MercuryHeight(JD0, Lon, Lat, ntz) - An
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stDegreep := (MercuryHeight(JD0+0.000005, Lon, Lat, ntz) - MercuryHeight(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 MERCURY_S_PERIOD = 1 / ((1 / 87.9691) - (1 / 365.256363004))
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func mercuryConjunction(jde float64, next uint8) float64 {
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//0=last 1=next
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decSub := func(jde float64) float64 {
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sub := Limit360(MercuryApparentLo(jde) - HSunApparentLo(jde))
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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
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}
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nowSub := decSub(jde)
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// pos 大于0:远离太阳 小于0:靠近太阳
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pos := math.Abs(decSub(jde+1/86400.0)) - math.Abs(nowSub)
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if pos >= 0 && next == 1 && nowSub > 0 {
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jde += MERCURY_S_PERIOD/8.0 + 2
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}
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if pos >= 0 && next == 1 && nowSub < 0 {
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jde += MERCURY_S_PERIOD/6.0 + 2
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}
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if pos <= 0 && next == 0 && nowSub < 0 {
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jde -= MERCURY_S_PERIOD/8.0 + 2
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}
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if pos <= 0 && next == 0 && nowSub > 0 {
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jde -= MERCURY_S_PERIOD/6.0 + 2
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}
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for {
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nowSub := decSub(jde)
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pos := math.Abs(decSub(jde+1/86400.0)) - math.Abs(nowSub)
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if math.Abs(nowSub) > 12 || (pos > 0 && next == 1) || (pos < 0 && next == 0) {
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if next == 1 {
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jde += 2
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} else {
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jde -= 2
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}
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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)
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stDegreep := (decSub(JD0+0.000005) - decSub(JD0-0.000005)) / 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 LastMercuryConjunction(jde float64) float64 {
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return mercuryConjunction(jde, 0)
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}
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func NextMercuryConjunction(jde float64) float64 {
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return mercuryConjunction(jde, 1)
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}
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func NextMercuryInferiorConjunction(jde float64) float64 {
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date := NextMercuryConjunction(jde)
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if EarthMercuryAway(date) > EarthAway(date) {
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return NextMercuryConjunction(date + 2)
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}
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return date
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}
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func NextMercurySuperiorConjunction(jde float64) float64 {
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date := NextMercuryConjunction(jde)
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if EarthMercuryAway(date) < EarthAway(date) {
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return NextMercuryConjunction(date + 2)
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}
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return date
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}
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func LastMercuryInferiorConjunction(jde float64) float64 {
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date := LastMercuryConjunction(jde)
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if EarthMercuryAway(date) > EarthAway(date) {
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return LastMercuryConjunction(date - 2)
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}
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return date
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}
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func LastMercurySuperiorConjunction(jde float64) float64 {
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date := LastMercuryConjunction(jde)
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if EarthMercuryAway(date) < EarthAway(date) {
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return LastMercuryConjunction(date - 2)
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}
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return date
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}
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func mercuryRetrograde(jde float64) float64 {
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//0=last 1=next
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decSunSub := func(jde float64) float64 {
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sub := Limit360(MercuryApparentRa(jde) - SunApparentRa(jde))
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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
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}
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decSub := func(jde float64, val float64) float64 {
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sub := MercuryApparentRa(jde+val) - MercuryApparentRa(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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lastHe := LastMercuryConjunction(jde)
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nextHe := NextMercuryConjunction(jde)
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nowSub := decSunSub(jde)
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if nowSub > 0 {
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jde = lastHe + ((nextHe - lastHe) / 5.0 * 3.5)
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} else {
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jde = lastHe + ((nextHe - lastHe) / 5.5)
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}
|
|
|
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
|
|
|
}
|