public static double TrueLongitudeAscendingNode(double JD)
{
double TrueAscendingNode = MeanLongitudeAscendingNode(JD);
double D = MeanElongation(JD);
D = CT.D2R(D);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CT.D2R(M);
double Mdash = MeanAnomaly(JD);
Mdash = CT.D2R(Mdash);
double F = ArgumentOfLatitude(JD);
F = CT.D2R(F);
//Add the principal additive terms
TrueAscendingNode -= 1.4979 * Math.Sin(2 * (D - F));
TrueAscendingNode -= 0.1500 * Math.Sin(M);
TrueAscendingNode -= 0.1226 * Math.Sin(2 * D);
TrueAscendingNode += 0.1176 * Math.Sin(2 * F);
TrueAscendingNode -= 0.0801 * Math.Sin(2 * (Mdash - F));
return(CT.M360(TrueAscendingNode));
}
public static double TrueLongitudeAscendingNode(double JD)
{
double TrueAscendingNode = MeanLongitudeAscendingNode(JD);
double D = MeanElongation(JD);
D = CAACoordinateTransformation.DegreesToRadians(D);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CAACoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = CAACoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = CAACoordinateTransformation.DegreesToRadians(F);
//Add the principal additive terms
TrueAscendingNode -= 1.4979 * Math.Sin(2 * (D - F));
TrueAscendingNode -= 0.1500 * Math.Sin(M);
TrueAscendingNode -= 0.1226 * Math.Sin(2 * D);
TrueAscendingNode += 0.1176 * Math.Sin(2 * F);
TrueAscendingNode -= 0.0801 * Math.Sin(2 * (Mdash - F));
return(CAACoordinateTransformation.MapTo0To360Range(TrueAscendingNode));
}
public static double EclipticLongitude(double JD)
{
double Ldash = MeanLongitude(JD);
double LdashDegrees = Ldash;
Ldash = CT.D2R(Ldash);
double D = MeanElongation(JD);
D = CT.D2R(D);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CT.D2R(M);
double Mdash = MeanAnomaly(JD);
Mdash = CT.D2R(Mdash);
double F = ArgumentOfLatitude(JD);
F = CT.D2R(F);
double E = CAAEarth.Eccentricity(JD);
double T = (JD - 2451545) / 36525;
double A1 = CT.M360(119.75 + 131.849 * T);
A1 = CT.D2R(A1);
double A2 = CT.M360(53.09 + 479264.290 * T);
A2 = CT.D2R(A2);
double A3 = CT.M360(313.45 + 481266.484 * T);
A3 = CT.D2R(A3);
int nLCoefficients = GFX.g_MoonCoefficients1.Length;
Debug.Assert(GFX.g_MoonCoefficients2.Length == nLCoefficients);
double SigmaL = 0;
for (int i = 0; i < nLCoefficients; i++)
{
double ThisSigma = GFX.g_MoonCoefficients2[i].A * Math.Sin(GFX.g_MoonCoefficients1[i].D * D + GFX.g_MoonCoefficients1[i].M * M + GFX.g_MoonCoefficients1[i].Mdash * Mdash + GFX.g_MoonCoefficients1[i].F * F);
if (GFX.g_MoonCoefficients1[i].M != 0)
{
ThisSigma *= E;
}
SigmaL += ThisSigma;
}
//Finally the additive terms
SigmaL += 3958 * Math.Sin(A1);
SigmaL += 1962 * Math.Sin(Ldash - F);
SigmaL += 318 * Math.Sin(A2);
//And finally apply the nutation in longitude
double NutationInLong = CAANutation.NutationInLongitude(JD);
return(CT.M360(LdashDegrees + SigmaL / 1000000 + NutationInLong / 3600));
}
public static double EclipticLatitude(double JD)
{
double Ldash = MeanLongitude(JD);
Ldash = CT.D2R(Ldash);
double D = MeanElongation(JD);
D = CT.D2R(D);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CT.D2R(M);
double Mdash = MeanAnomaly(JD);
Mdash = CT.D2R(Mdash);
double F = ArgumentOfLatitude(JD);
F = CT.D2R(F);
double E = CAAEarth.Eccentricity(JD);
double T = (JD - 2451545) / 36525;
double A1 = CT.M360(119.75 + 131.849 * T);
A1 = CT.D2R(A1);
double A2 = CT.M360(53.09 + 479264.290 * T);
A2 = CT.D2R(A2);
double A3 = CT.M360(313.45 + 481266.484 * T);
A3 = CT.D2R(A3);
int nBCoefficients = GFX.g_MoonCoefficients3.Length;
Debug.Assert(GFX.g_MoonCoefficients4.Length == nBCoefficients);
double SigmaB = 0;
for (int i = 0; i < nBCoefficients; i++)
{
double ThisSigma = GFX.g_MoonCoefficients4[i] * Math.Sin(GFX.g_MoonCoefficients3[i].D * D + GFX.g_MoonCoefficients3[i].M * M + GFX.g_MoonCoefficients3[i].Mdash * Mdash + GFX.g_MoonCoefficients3[i].F * F);
if (GFX.g_MoonCoefficients3[i].M != 0)
{
ThisSigma *= E;
}
SigmaB += ThisSigma;
}
//Finally the additive terms
SigmaB -= 2235 * Math.Sin(Ldash);
SigmaB += 382 * Math.Sin(A3);
SigmaB += 175 * Math.Sin(A1 - F);
SigmaB += 175 * Math.Sin(A1 + F);
SigmaB += 127 * Math.Sin(Ldash - Mdash);
SigmaB -= 115 * Math.Sin(Ldash + Mdash);
return(SigmaB / 1000000);
}
//////////////////////////////// Implementation ///////////////////////////////
protected static void CalculateOpticalLibration(double JD, double Lambda, double Beta, ref double ldash, ref double bdash, ref double ldash2, ref double bdash2, ref double epsilon, ref double omega, ref double DeltaU, ref double sigma, ref double I, ref double rho)
{
//Calculate the initial quantities
double Lambdarad = CAACoordinateTransformation.DegreesToRadians(Lambda);
double Betarad = CAACoordinateTransformation.DegreesToRadians(Beta);
I = CAACoordinateTransformation.DegreesToRadians(1.54242);
DeltaU = CAACoordinateTransformation.DegreesToRadians(CAANutation.NutationInLongitude(JD) / 3600);
double F = CAACoordinateTransformation.DegreesToRadians(CAAMoon.ArgumentOfLatitude(JD));
omega = CAACoordinateTransformation.DegreesToRadians(CAAMoon.MeanLongitudeAscendingNode(JD));
epsilon = CAANutation.MeanObliquityOfEcliptic(JD) + CAANutation.NutationInObliquity(JD) / 3600;
//Calculate the optical librations
double W = Lambdarad - DeltaU / 3600 - omega;
double A = Math.Atan2(Math.Sin(W) * Math.Cos(Betarad) * Math.Cos(I) - Math.Sin(Betarad) * Math.Sin(I), Math.Cos(W) * Math.Cos(Betarad));
ldash = CAACoordinateTransformation.MapTo0To360Range(CAACoordinateTransformation.RadiansToDegrees(A) - CAACoordinateTransformation.RadiansToDegrees(F));
if (ldash > 180)
{
ldash -= 360;
}
bdash = Math.Asin(-Math.Sin(W) * Math.Cos(Betarad) * Math.Sin(I) - Math.Sin(Betarad) * Math.Cos(I));
//Calculate the physical librations
double T = (JD - 2451545.0) / 36525;
double K1 = 119.75 + 131.849 * T;
K1 = CAACoordinateTransformation.DegreesToRadians(K1);
double K2 = 72.56 + 20.186 * T;
K2 = CAACoordinateTransformation.DegreesToRadians(K2);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CAACoordinateTransformation.DegreesToRadians(M);
double Mdash = CAAMoon.MeanAnomaly(JD);
Mdash = CAACoordinateTransformation.DegreesToRadians(Mdash);
double D = CAAMoon.MeanElongation(JD);
D = CAACoordinateTransformation.DegreesToRadians(D);
double E = CAAEarth.Eccentricity(JD);
rho = -0.02752 * Math.Cos(Mdash) + -0.02245 * Math.Sin(F) + 0.00684 * Math.Cos(Mdash - 2 * F) + -0.00293 * Math.Cos(2 * F) + -0.00085 * Math.Cos(2 * F - 2 * D) + -0.00054 * Math.Cos(Mdash - 2 * D) + -0.00020 * Math.Sin(Mdash + F) + -0.00020 * Math.Cos(Mdash + 2 * F) + -0.00020 * Math.Cos(Mdash - F) + 0.00014 * Math.Cos(Mdash + 2 * F - 2 * D);
sigma = -0.02816 * Math.Sin(Mdash) + 0.02244 * Math.Cos(F) + -0.00682 * Math.Sin(Mdash - 2 * F) + -0.00279 * Math.Sin(2 * F) + -0.00083 * Math.Sin(2 * F - 2 * D) + 0.00069 * Math.Sin(Mdash - 2 * D) + 0.00040 * Math.Cos(Mdash + F) + -0.00025 * Math.Sin(2 * Mdash) + -0.00023 * Math.Sin(Mdash + 2 * F) + 0.00020 * Math.Cos(Mdash - F) + 0.00019 * Math.Sin(Mdash - F) + 0.00013 * Math.Sin(Mdash + 2 * F - 2 * D) + -0.00010 * Math.Cos(Mdash - 3 * F);
double tau = 0.02520 * E * Math.Sin(M) + 0.00473 * Math.Sin(2 * Mdash - 2 * F) + -0.00467 * Math.Sin(Mdash) + 0.00396 * Math.Sin(K1) + 0.00276 * Math.Sin(2 * Mdash - 2 * D) + 0.00196 * Math.Sin(omega) + -0.00183 * Math.Cos(Mdash - F) + 0.00115 * Math.Sin(Mdash - 2 * D) + -0.00096 * Math.Sin(Mdash - D) + 0.00046 * Math.Sin(2 * F - 2 * D) + -0.00039 * Math.Sin(Mdash - F) + -0.00032 * Math.Sin(Mdash - M - D) + 0.00027 * Math.Sin(2 * Mdash - M - 2 * D) + 0.00023 * Math.Sin(K2) + -0.00014 * Math.Sin(2 * D) + 0.00014 * Math.Cos(2 * Mdash - 2 * F) + -0.00012 * Math.Sin(Mdash - 2 * F) + -0.00012 * Math.Sin(2 * Mdash) + 0.00011 * Math.Sin(2 * Mdash - 2 * M - 2 * D);
ldash2 = -tau + (rho * Math.Cos(A) + sigma * Math.Sin(A)) * Math.Tan(bdash);
bdash = CAACoordinateTransformation.RadiansToDegrees(bdash);
bdash2 = sigma * Math.Cos(A) - rho * Math.Sin(A);
}
public static double RadiusVector(double JD)
{
double Ldash = MeanLongitude(JD);
Ldash = CT.D2R(Ldash);
double D = MeanElongation(JD);
D = CT.D2R(D);
double M = CAAEarth.SunMeanAnomaly(JD);
M = CT.D2R(M);
double Mdash = MeanAnomaly(JD);
Mdash = CT.D2R(Mdash);
double F = ArgumentOfLatitude(JD);
F = CT.D2R(F);
double E = CAAEarth.Eccentricity(JD);
double T = (JD - 2451545) / 36525;
double A1 = CT.M360(119.75 + 131.849 * T);
A1 = CT.D2R(A1);
double A2 = CT.M360(53.09 + 479264.290 * T);
A2 = CT.D2R(A2);
double A3 = CT.M360(313.45 + 481266.484 * T);
A3 = CT.D2R(A3);
int nRCoefficients = GFX.g_MoonCoefficients1.Length;
Debug.Assert(GFX.g_MoonCoefficients2.Length == nRCoefficients);
double SigmaR = 0;
for (int i = 0; i < nRCoefficients; i++)
{
double ThisSigma = GFX.g_MoonCoefficients2[i].B * Math.Cos(GFX.g_MoonCoefficients1[i].D * D + GFX.g_MoonCoefficients1[i].M * M + GFX.g_MoonCoefficients1[i].Mdash * Mdash + GFX.g_MoonCoefficients1[i].F * F);
if (GFX.g_MoonCoefficients1[i].M != 0)
{
ThisSigma *= E;
}
SigmaR += ThisSigma;
}
return(385000.56 + SigmaR / 1000);
}
