public static AASSelenographicMoonDetails CalculateSelenographicPositionOfSun(double JD, bool bHighPrecision)
{
double R = AASEarth.RadiusVector(JD, bHighPrecision) * 149597970;
double Delta = AASMoon.RadiusVector(JD);
double lambda0 = AASSun.ApparentEclipticLongitude(JD, bHighPrecision);
double lambda = AASMoon.EclipticLongitude(JD);
double beta = AASMoon.EclipticLatitude(JD);
double lambdah = AASCoordinateTransformation.MapTo0To360Range(lambda0 + 180 + Delta / R * 57.296 * Math.Cos(AASCoordinateTransformation.DegreesToRadians(beta)) * Math.Sin(AASCoordinateTransformation.DegreesToRadians(lambda0 - lambda)));
double betah = Delta / R * beta;
//What will be the return value
AASSelenographicMoonDetails details = new AASSelenographicMoonDetails();
//Calculate the optical libration
double omega = 0;
double DeltaU = 0;
double sigma = 0;
double I = 0;
double rho = 0;
double ldash0 = 0;
double bdash0 = 0;
double ldash20 = 0;
double bdash20 = 0;
double epsilon = 0;
CalculateOpticalLibration(JD, lambdah, betah, ref ldash0, ref bdash0, ref ldash20, ref bdash20, ref epsilon, ref omega, ref DeltaU, ref sigma, ref I, ref rho);
details.l0 = ldash0 + ldash20;
details.b0 = bdash0 + bdash20;
details.c0 = AASCoordinateTransformation.MapTo0To360Range(450 - details.l0);
return(details);
}
public static AASPhysicalMoonDetails CalculateHelper(double JD, ref double Lambda, ref double Beta, ref double epsilon, ref AAS2DCoordinate Equatorial)
{
//What will be the return value
AASPhysicalMoonDetails details = new AASPhysicalMoonDetails();
//Calculate the initial quantities
Lambda = AASMoon.EclipticLongitude(JD);
Beta = AASMoon.EclipticLatitude(JD);
//Calculate the optical libration
double omega = 0;
double DeltaU = 0;
double sigma = 0;
double I = 0;
double rho = 0;
double ldash = 0;
double bdash = 0;
double ldash2 = 0;
double bdash2 = 0;
CalculateOpticalLibration(JD, Lambda, Beta, ref ldash, ref bdash, ref ldash2, ref bdash2, ref epsilon, ref omega, ref DeltaU, ref sigma, ref I, ref rho);
details.ldash = ldash;
details.bdash = bdash;
details.ldash2 = ldash2;
details.bdash2 = bdash2;
double epsilonrad = AASCoordinateTransformation.DegreesToRadians(epsilon);
//Calculate the total libration
details.l = details.ldash + details.ldash2;
details.b = details.bdash + details.bdash2;
double b = AASCoordinateTransformation.DegreesToRadians(details.b);
//Calculate the position angle
double V = omega + DeltaU + AASCoordinateTransformation.DegreesToRadians(sigma) / Math.Sin(I);
double I_rho = I + AASCoordinateTransformation.DegreesToRadians(rho);
double X = Math.Sin(I_rho) * Math.Sin(V);
double Y = Math.Sin(I_rho) * Math.Cos(V) * Math.Cos(epsilonrad) - Math.Cos(I_rho) * Math.Sin(epsilonrad);
double w = Math.Atan2(X, Y);
Equatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda, Beta, epsilon);
double Alpha = AASCoordinateTransformation.HoursToRadians(Equatorial.X);
details.P = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sqrt(X * X + Y * Y) * Math.Cos(Alpha - w) / (Math.Cos(b))));
return(details);
}
public static AASPhysicalMoonDetails CalculateTopocentric(double JD, double Longitude, double Latitude)
{
//First convert to radians
Longitude = AASCoordinateTransformation.DegreesToRadians(Longitude);
Latitude = AASCoordinateTransformation.DegreesToRadians(Latitude);
double Lambda = 0;
double Beta = 0;
double epsilon = 0;
AAS2DCoordinate Equatorial = new AAS2DCoordinate();
AASPhysicalMoonDetails details = CalculateHelper(JD, ref Lambda, ref Beta, ref epsilon, ref Equatorial);
double R = AASMoon.RadiusVector(JD);
double pi = AASMoon.RadiusVectorToHorizontalParallax(R);
double Alpha = AASCoordinateTransformation.HoursToRadians(Equatorial.X);
double Delta = AASCoordinateTransformation.DegreesToRadians(Equatorial.Y);
double AST = AASSidereal.ApparentGreenwichSiderealTime(JD);
double H = AASCoordinateTransformation.HoursToRadians(AST) - Longitude - Alpha;
double Q = Math.Atan2(Math.Cos(Latitude) * Math.Sin(H), Math.Cos(Delta) * Math.Sin(Latitude) - Math.Sin(Delta) * Math.Cos(Latitude) * Math.Cos(H));
double Z = Math.Acos(Math.Sin(Delta) * Math.Sin(Latitude) + Math.Cos(Delta) * Math.Cos(Latitude) * Math.Cos(H));
double pidash = pi * (Math.Sin(Z) + 0.0084 * Math.Sin(2 * Z));
double Prad = AASCoordinateTransformation.DegreesToRadians(details.P);
double DeltaL = -pidash *Math.Sin(Q - Prad) / Math.Cos(AASCoordinateTransformation.DegreesToRadians(details.b));
details.l += DeltaL;
double DeltaB = pidash * Math.Cos(Q - Prad);
details.b += DeltaB;
double DeltaP = DeltaL * Math.Sin(AASCoordinateTransformation.DegreesToRadians(details.b)) - pidash * Math.Sin(Q) * Math.Tan(Delta);
details.P += DeltaP;
return(details);
}
public 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 = AASCoordinateTransformation.DegreesToRadians(Lambda);
double Betarad = AASCoordinateTransformation.DegreesToRadians(Beta);
I = AASCoordinateTransformation.DegreesToRadians(1.54242);
DeltaU = AASCoordinateTransformation.DegreesToRadians(AASNutation.NutationInLongitude(JD) / 3600);
double F = AASCoordinateTransformation.DegreesToRadians(AASMoon.ArgumentOfLatitude(JD));
omega = AASCoordinateTransformation.DegreesToRadians(AASMoon.MeanLongitudeAscendingNode(JD));
epsilon = AASNutation.MeanObliquityOfEcliptic(JD) + AASNutation.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 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(A) - AASCoordinateTransformation.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 = AASCoordinateTransformation.DegreesToRadians(K1);
double K2 = 72.56 + 20.186 * T;
K2 = AASCoordinateTransformation.DegreesToRadians(K2);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = AASMoon.MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double D = AASMoon.MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double E = AASEarth.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 = AASCoordinateTransformation.RadiansToDegrees(bdash);
bdash2 = sigma * Math.Cos(A) - rho * Math.Sin(A);
}