public static double TrueLongitudeAscendingNode(double JD)
{
double TrueAscendingNode = MeanLongitudeAscendingNode(JD);
double D = MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = AASCoordinateTransformation.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(AASCoordinateTransformation.MapTo0To360Range(TrueAscendingNode));
}
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 double EclipticLongitude(double JD)
{
double Ldash = MeanLongitude(JD);
double LdashDegrees = Ldash;
Ldash = AASCoordinateTransformation.DegreesToRadians(Ldash);
double D = MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = AASCoordinateTransformation.DegreesToRadians(F);
double E = AASEarth.Eccentricity(JD);
double Esquared = E * E;
double T = (JD - 2451545) / 36525;
double A1 = AASCoordinateTransformation.MapTo0To360Range(119.75 + 131.849 * T);
A1 = AASCoordinateTransformation.DegreesToRadians(A1);
double A2 = AASCoordinateTransformation.MapTo0To360Range(53.09 + 479264.290 * T);
A2 = AASCoordinateTransformation.DegreesToRadians(A2);
int nLCoefficients = g_MoonCoefficients1.Length;
double SigmaL = 0;
for (int i = 0; i < nLCoefficients; i++)
{
double ThisSigma = g_MoonCoefficients2[i].A * Math.Sin(g_MoonCoefficients1[i].D * D + g_MoonCoefficients1[i].M * M +
g_MoonCoefficients1[i].Mdash * Mdash + g_MoonCoefficients1[i].F * F);
if ((g_MoonCoefficients1[i].M == 1) || (g_MoonCoefficients1[i].M == -1))
{
ThisSigma *= E;
}
else if ((g_MoonCoefficients1[i].M == 2) || (g_MoonCoefficients1[i].M == -2))
{
ThisSigma *= Esquared;
}
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 = AASNutation.NutationInLongitude(JD);
return(AASCoordinateTransformation.MapTo0To360Range(LdashDegrees + SigmaL / 1000000 + NutationInLong / 3600));
}
public static AASPhysicalSunDetails Calculate(double JD)
{
double theta = AASCoordinateTransformation.MapTo0To360Range((JD - 2398220) * 360 / 25.38);
double I = 7.25;
double K = 73.6667 + 1.3958333 * (JD - 2396758) / 36525;
//Calculate the apparent longitude of the sun (excluding the effect of nutation)
double L = AASEarth.EclipticLongitude(JD);
double R = AASEarth.RadiusVector(JD);
double SunLong = L + 180 - AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
double epsilon = AASNutation.TrueObliquityOfEcliptic(JD);
//Convert to radians
epsilon = AASCoordinateTransformation.DegreesToRadians(epsilon);
SunLong = AASCoordinateTransformation.DegreesToRadians(SunLong);
K = AASCoordinateTransformation.DegreesToRadians(K);
I = AASCoordinateTransformation.DegreesToRadians(I);
theta = AASCoordinateTransformation.DegreesToRadians(theta);
double x = Math.Atan(-Math.Cos(SunLong) * Math.Tan(epsilon));
double y = Math.Atan(-Math.Cos(SunLong - K) * Math.Tan(I));
AASPhysicalSunDetails details = new AASPhysicalSunDetails();
details.P = AASCoordinateTransformation.RadiansToDegrees(x + y);
details.B0 = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(SunLong - K) * Math.Sin(I)));
double eta = Math.Atan(Math.Tan(SunLong - K) * Math.Cos(I));
details.L0 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(eta - theta));
return(details);
}
public static double RadiusVector(double JD)
{
double D = MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = AASCoordinateTransformation.DegreesToRadians(F);
double E = AASEarth.Eccentricity(JD);
int nRCoefficients = g_MoonCoefficients1.Length;
double SigmaR = 0;
for (int i = 0; i < nRCoefficients; i++)
{
double ThisSigma = g_MoonCoefficients2[i].B * Math.Cos(g_MoonCoefficients1[i].D * D + g_MoonCoefficients1[i].M * M + g_MoonCoefficients1[i].Mdash * Mdash + g_MoonCoefficients1[i].F * F);
if (g_MoonCoefficients1[i].M == 1)
{
// in the C++, this was "if (g_MoonCoefficients1[i].M)", because 0 and 1 are used to represent false and true in C++
ThisSigma *= E;
}
SigmaR += ThisSigma;
}
return(385000.56 + SigmaR / 1000);
}
public static double EclipticLatitude(double JD)
{
double Ldash = MeanLongitude(JD);
Ldash = AASCoordinateTransformation.DegreesToRadians(Ldash);
double D = MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = AASCoordinateTransformation.DegreesToRadians(F);
double E = AASEarth.Eccentricity(JD);
double Esquared = E * E;
double T = (JD - 2451545) / 36525;
double A1 = AASCoordinateTransformation.MapTo0To360Range(119.75 + 131.849 * T);
A1 = AASCoordinateTransformation.DegreesToRadians(A1);
double A3 = AASCoordinateTransformation.MapTo0To360Range(313.45 + 481266.484 * T);
A3 = AASCoordinateTransformation.DegreesToRadians(A3);
int nBCoefficients = g_MoonCoefficients3.Length;
double SigmaB = 0;
for (int i = 0; i < nBCoefficients; i++)
{
double ThisSigma = g_MoonCoefficients4[i] * Math.Sin(g_MoonCoefficients3[i].D * D + g_MoonCoefficients3[i].M * M +
g_MoonCoefficients3[i].Mdash * Mdash + g_MoonCoefficients3[i].F * F);
if ((g_MoonCoefficients3[i].M == 1) || (g_MoonCoefficients3[i].M == -1))
{
ThisSigma *= E;
}
else if ((g_MoonCoefficients3[i].M == 2) || (g_MoonCoefficients3[i].M == -2))
{
ThisSigma *= Esquared;
}
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);
}
public static double ApparentEclipticLongitude(double JD)
{
double Longitude = GeometricFK5EclipticLongitude(JD);
//Apply the correction in longitude due to nutation
Longitude += AASCoordinateTransformation.DMSToDegrees(0, 0, AASNutation.NutationInLongitude(JD));
//Apply the correction in longitude due to aberration
double R = AASEarth.RadiusVector(JD);
Longitude -= AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
return(Longitude);
}
public static AAS3DCoordinate EquatorialRectangularCoordinatesMeanEquinox(double JD, bool bHighPrecision)
{
double Longitude = AASCoordinateTransformation.DegreesToRadians(GeometricFK5EclipticLongitude(JD, bHighPrecision));
double Latitude = AASCoordinateTransformation.DegreesToRadians(GeometricFK5EclipticLatitude(JD, bHighPrecision));
double R = AASEarth.RadiusVector(JD, bHighPrecision);
double epsilon = AASCoordinateTransformation.DegreesToRadians(AASNutation.MeanObliquityOfEcliptic(JD));
AAS3DCoordinate value = new AAS3DCoordinate
{
X = R * Math.Cos(Latitude) * Math.Cos(Longitude),
Y = R * (Math.Cos(Latitude) * Math.Sin(Longitude) * Math.Cos(epsilon) - Math.Sin(Latitude) * Math.Sin(epsilon)),
Z = R * (Math.Cos(Latitude) * Math.Sin(Longitude) * Math.Sin(epsilon) + Math.Sin(Latitude) * Math.Cos(epsilon))
};
return(value);
}
public static AAS3DCoordinate EclipticRectangularCoordinatesJ2000(double JD, bool bHighPrecision)
{
double Longitude = GeometricEclipticLongitudeJ2000(JD, bHighPrecision);
Longitude = AASCoordinateTransformation.DegreesToRadians(Longitude);
double Latitude = GeometricEclipticLatitudeJ2000(JD, bHighPrecision);
Latitude = AASCoordinateTransformation.DegreesToRadians(Latitude);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
double coslatitude = Math.Cos(Latitude);
AAS3DCoordinate value = new AAS3DCoordinate
{
X = R * coslatitude * Math.Cos(Longitude),
Y = R * coslatitude * Math.Sin(Longitude),
Z = R * Math.Sin(Latitude)
};
return(value);
}
public static double ApparentEclipticLongitude(double JD, bool bHighPrecision)
{
double Longitude = GeometricFK5EclipticLongitude(JD, bHighPrecision);
//Apply the correction in longitude due to nutation
Longitude += AASCoordinateTransformation.DMSToDegrees(0, 0, AASNutation.NutationInLongitude(JD));
//Apply the correction in longitude due to aberration
double R = AASEarth.RadiusVector(JD, bHighPrecision);
if (bHighPrecision)
{
Longitude -= (0.005775518 * R * AASCoordinateTransformation.DMSToDegrees(0, 0, VariationGeometricEclipticLongitude(JD)));
}
else
{
Longitude -= AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
}
return(Longitude);
}
public static double RadiusVector(double JD)
{
double D = MeanElongation(JD);
D = AASCoordinateTransformation.DegreesToRadians(D);
double M = AASEarth.SunMeanAnomaly(JD);
M = AASCoordinateTransformation.DegreesToRadians(M);
double Mdash = MeanAnomaly(JD);
Mdash = AASCoordinateTransformation.DegreesToRadians(Mdash);
double F = ArgumentOfLatitude(JD);
F = AASCoordinateTransformation.DegreesToRadians(F);
double E = AASEarth.Eccentricity(JD);
double Esquared = E * E;
int nRCoefficients = g_MoonCoefficients1.Length;
double SigmaR = 0;
for (int i = 0; i < nRCoefficients; i++)
{
double ThisSigma = g_MoonCoefficients2[i].B * Math.Cos(g_MoonCoefficients1[i].D * D + g_MoonCoefficients1[i].M * M +
g_MoonCoefficients1[i].Mdash * Mdash + g_MoonCoefficients1[i].F * F);
if ((g_MoonCoefficients1[i].M == 1) || (g_MoonCoefficients1[i].M == -1))
{
ThisSigma *= E;
}
else if ((g_MoonCoefficients1[i].M == 2) || (g_MoonCoefficients1[i].M == -2))
{
ThisSigma *= Esquared;
}
SigmaR += ThisSigma;
}
return(385000.56 + SigmaR / 1000);
}
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);
}
public static CAAPhysicalMarsDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
CAAPhysicalMarsDetails details = new CAAPhysicalMarsDetails();
//Step 1
double T = (JD - 2451545) / 36525;
double Lambda0 = 352.9065 + 1.17330 * T;
double Lambda0rad = AASCoordinateTransformation.DegreesToRadians(Lambda0);
double Beta0 = 63.2818 - 0.00394 * T;
double Beta0rad = AASCoordinateTransformation.DegreesToRadians(Beta0);
//Step 2
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
double PreviousLightTravelTime = 0;
double LightTravelTime = 0;
double x = 0;
double y = 0;
double z = 0;
bool bIterate = true;
double DELTA = 0;
double l = 0;
double lrad = 0;
double b = 0;
double r = 0;
while (bIterate)
{
double JD2 = JD - LightTravelTime;
//Step 3
l = AASMars.EclipticLongitude(JD2, bHighPrecision);
lrad = AASCoordinateTransformation.DegreesToRadians(l);
b = AASMars.EclipticLatitude(JD2, bHighPrecision);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASMars.RadiusVector(JD2, bHighPrecision);
//Step 4
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
LightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(LightTravelTime - PreviousLightTravelTime) > 2E-6); //2E-6 correponds to 0.17 of a second
if (bIterate)
{
PreviousLightTravelTime = LightTravelTime;
}
}
//Step 5
double lambdarad = Math.Atan2(y, x);
double lambda = AASCoordinateTransformation.RadiansToDegrees(lambdarad);
double betarad = Math.Atan2(z, Math.Sqrt(x * x + y * y));
double beta = AASCoordinateTransformation.RadiansToDegrees(betarad);
//Step 6
details.DE = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(betarad) - Math.Cos(Beta0rad) * Math.Cos(betarad) * Math.Cos(Lambda0rad - lambdarad)));
//Step 7
double N = 49.5581 + 0.7721 * T;
double Nrad = AASCoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.00697 / r;
double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000225 * (Math.Cos(lrad - Nrad) / r);
double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash);
//Step 8
details.DS = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(bdashrad) - Math.Cos(Beta0rad) * Math.Cos(bdashrad) * Math.Cos(Lambda0rad - ldashrad)));
//Step 9
double W = AASCoordinateTransformation.MapTo0To360Range(11.504 + 350.89200025 * (JD - LightTravelTime - 2433282.5));
//Step 10
double e0 = AASNutation.MeanObliquityOfEcliptic(JD);
double e0rad = AASCoordinateTransformation.DegreesToRadians(e0);
AAS2DCoordinate PoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0rad = AASCoordinateTransformation.HoursToRadians(PoleEquatorial.X);
double delta0rad = AASCoordinateTransformation.DegreesToRadians(PoleEquatorial.Y);
//Step 11
double u = y * Math.Cos(e0rad) - z * Math.Sin(e0rad);
double v = y * Math.Sin(e0rad) + z * Math.Cos(e0rad);
double alpharad = Math.Atan2(u, x);
double alpha = AASCoordinateTransformation.RadiansToHours(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = AASCoordinateTransformation.RadiansToDegrees(deltarad);
double xi = Math.Atan2(Math.Sin(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad) - Math.Sin(deltarad) * Math.Cos(delta0rad), Math.Cos(deltarad) * Math.Sin(alpha0rad - alpharad));
//Step 12
details.w = AASCoordinateTransformation.MapTo0To360Range(W - AASCoordinateTransformation.RadiansToDegrees(xi));
//Step 13
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
double NutationInObliquity = AASNutation.NutationInObliquity(JD);
//Step 14
lambda += 0.005693 * Math.Cos(l0rad - lambdarad) / Math.Cos(betarad);
beta += 0.005693 * Math.Sin(l0rad - lambdarad) * Math.Sin(betarad);
//Step 15
Lambda0 += NutationInLongitude / 3600;
lambda += NutationInLongitude / 3600;
e0 += NutationInObliquity / 3600;
//Step 16
AAS2DCoordinate ApparentPoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0dash = AASCoordinateTransformation.HoursToRadians(ApparentPoleEquatorial.X);
double delta0dash = AASCoordinateTransformation.DegreesToRadians(ApparentPoleEquatorial.Y);
AAS2DCoordinate ApparentMars = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, e0);
double alphadash = AASCoordinateTransformation.HoursToRadians(ApparentMars.X);
double deltadash = AASCoordinateTransformation.DegreesToRadians(ApparentMars.Y);
//Step 17
details.P = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0dash) * Math.Sin(alpha0dash - alphadash), Math.Sin(delta0dash) * Math.Cos(deltadash) - Math.Cos(delta0dash) * Math.Sin(deltadash) * Math.Cos(alpha0dash - alphadash))));
//Step 18
double SunLambda = AASSun.GeometricEclipticLongitude(JD, bHighPrecision);
double SunBeta = AASSun.GeometricEclipticLatitude(JD, bHighPrecision);
AAS2DCoordinate SunEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(SunLambda, SunBeta, e0);
details.X = AASMoonIlluminatedFraction.PositionAngle(SunEquatorial.X, SunEquatorial.Y, alpha, delta);
//Step 19
details.d = 9.36 / DELTA;
details.k = AASIlluminatedFraction.IlluminatedFraction(r, R, DELTA);
details.q = (1 - details.k) * details.d;
return(details);
}
public static AASGalileanMoonsDetails Calculate(double JD, bool bHighPrecision)
{
//Calculate the position of the Sun
double sunlong = AASSun.GeometricEclipticLongitude(JD, bHighPrecision);
double sunlongrad = AASCoordinateTransformation.DegreesToRadians(sunlong);
double beta = AASSun.GeometricEclipticLatitude(JD, bHighPrecision);
double betarad = AASCoordinateTransformation.DegreesToRadians(beta);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
//Calculate the the light travel time from Jupiter to the Earth
double DELTA = 5;
double PreviousEarthLightTravelTime = 0;
double EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
double JD1 = JD - EarthLightTravelTime;
bool bIterate = true;
double x;
double y;
double z;
double l;
double lrad;
double b;
double brad;
double r;
while (bIterate)
{
//Calculate the position of Jupiter
l = AASJupiter.EclipticLongitude(JD1, bHighPrecision);
lrad = AASCoordinateTransformation.DegreesToRadians(l);
b = AASJupiter.EclipticLatitude(JD1, bHighPrecision);
brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASJupiter.RadiusVector(JD1, bHighPrecision);
x = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
y = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
z = r * Math.Sin(brad) + R * Math.Sin(betarad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(EarthLightTravelTime - PreviousEarthLightTravelTime) > 2e-6); //2e-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - EarthLightTravelTime;
PreviousEarthLightTravelTime = EarthLightTravelTime;
}
}
//Calculate the details as seen from the earth
AASGalileanMoonsDetails details1 = CalculateHelper(JD, sunlongrad, betarad, R, bHighPrecision);
AASGalileanMoonDetail details1Satellite1 = details1.Satellite1;
AASGalileanMoonDetail details1Satellite2 = details1.Satellite2;
AASGalileanMoonDetail details1Satellite3 = details1.Satellite3;
AASGalileanMoonDetail details1Satellite4 = details1.Satellite4;
FillInPhenomenaDetails(ref details1Satellite1);
FillInPhenomenaDetails(ref details1Satellite2);
FillInPhenomenaDetails(ref details1Satellite3);
FillInPhenomenaDetails(ref details1Satellite4);
//Calculate the the light travel time from Jupiter to the Sun
JD1 = JD - EarthLightTravelTime;
l = AASJupiter.EclipticLongitude(JD1, bHighPrecision);
lrad = AASCoordinateTransformation.DegreesToRadians(l);
b = AASJupiter.EclipticLatitude(JD1, bHighPrecision);
brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASJupiter.RadiusVector(JD1, bHighPrecision);
x = r * Math.Cos(brad) * Math.Cos(lrad);
y = r * Math.Cos(brad) * Math.Sin(lrad);
z = r * Math.Sin(brad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
double SunLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Calculate the details as seen from the Sun
AASGalileanMoonsDetails details2 = CalculateHelper(JD + SunLightTravelTime - EarthLightTravelTime, sunlongrad, betarad, 0, bHighPrecision);
AASGalileanMoonDetail details2Satellite1 = details2.Satellite1;
AASGalileanMoonDetail details2Satellite2 = details2.Satellite2;
AASGalileanMoonDetail details2Satellite3 = details2.Satellite3;
AASGalileanMoonDetail details2Satellite4 = details2.Satellite4;
FillInPhenomenaDetails(ref details2Satellite1);
FillInPhenomenaDetails(ref details2Satellite2);
FillInPhenomenaDetails(ref details2Satellite3);
FillInPhenomenaDetails(ref details2Satellite4);
//Finally transfer the required values from details2 to details1
details1.Satellite1.bInEclipse = details2.Satellite1.bInOccultation;
details1.Satellite2.bInEclipse = details2.Satellite2.bInOccultation;
details1.Satellite3.bInEclipse = details2.Satellite3.bInOccultation;
details1.Satellite4.bInEclipse = details2.Satellite4.bInOccultation;
details1.Satellite1.bInShadowTransit = details2.Satellite1.bInTransit;
details1.Satellite2.bInShadowTransit = details2.Satellite2.bInTransit;
details1.Satellite3.bInShadowTransit = details2.Satellite3.bInTransit;
details1.Satellite4.bInShadowTransit = details2.Satellite4.bInTransit;
return(details1);
}
public static AASEllipticalPlanetaryDetails Calculate(double JD, AASEllipticalObject ellipticalObject, bool bHighPrecision)
{
//What will the the return value
AASEllipticalPlanetaryDetails details = new AASEllipticalPlanetaryDetails();
//Calculate the position of the earth first
double JD0 = JD;
double L0 = AASEarth.EclipticLongitude(JD0, bHighPrecision);
double B0 = AASEarth.EclipticLatitude(JD0, bHighPrecision);
double R0 = AASEarth.RadiusVector(JD0, bHighPrecision);
L0 = AASCoordinateTransformation.DegreesToRadians(L0);
B0 = AASCoordinateTransformation.DegreesToRadians(B0);
double cosB0 = Math.Cos(B0);
//Iterate to find the positions adjusting for light-time correction if required
double L = 0;
double B = 0;
double R = 0;
if (ellipticalObject != AASEllipticalObject.SUN)
{
bool bRecalc = true;
bool bFirstRecalc = true;
double LPrevious = 0;
double BPrevious = 0;
double RPrevious = 0;
while (bRecalc)
{
switch (ellipticalObject)
{
case AASEllipticalObject.SUN:
L = AASSun.GeometricEclipticLongitude(JD0, bHighPrecision);
B = AASSun.GeometricEclipticLatitude(JD0, bHighPrecision);
R = AASEarth.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.MERCURY:
L = AASMercury.EclipticLongitude(JD0, bHighPrecision);
B = AASMercury.EclipticLatitude(JD0, bHighPrecision);
R = AASMercury.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.VENUS:
L = AASVenus.EclipticLongitude(JD0, bHighPrecision);
B = AASVenus.EclipticLatitude(JD0, bHighPrecision);
R = AASVenus.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.MARS:
L = AASMars.EclipticLongitude(JD0, bHighPrecision);
B = AASMars.EclipticLatitude(JD0, bHighPrecision);
R = AASMars.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.JUPITER:
L = AASJupiter.EclipticLongitude(JD0, bHighPrecision);
B = AASJupiter.EclipticLatitude(JD0, bHighPrecision);
R = AASJupiter.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.SATURN:
L = AASSaturn.EclipticLongitude(JD0, bHighPrecision);
B = AASSaturn.EclipticLatitude(JD0, bHighPrecision);
R = AASSaturn.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.URANUS:
L = AASUranus.EclipticLongitude(JD0, bHighPrecision);
B = AASUranus.EclipticLatitude(JD0, bHighPrecision);
R = AASUranus.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.NEPTUNE:
L = AASNeptune.EclipticLongitude(JD0, bHighPrecision);
B = AASNeptune.EclipticLatitude(JD0, bHighPrecision);
R = AASNeptune.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.PLUTO:
L = AASPluto.EclipticLongitude(JD0);
B = AASPluto.EclipticLatitude(JD0);
R = AASPluto.RadiusVector(JD0);
break;
default:
break;
}
if (!bFirstRecalc)
{
bRecalc = ((Math.Abs(L - LPrevious) > 0.00001) || (Math.Abs(B - BPrevious) > 0.00001) || (Math.Abs(R - RPrevious) > 0.000001));
LPrevious = L;
BPrevious = B;
RPrevious = R;
}
else
{
bFirstRecalc = false;
}
//Calculate the new value
if (bRecalc)
{
double Lrad = AASCoordinateTransformation.DegreesToRadians(L);
double Brad = AASCoordinateTransformation.DegreesToRadians(B);
double cosB = Math.Cos(Brad);
double cosL = Math.Cos(Lrad);
double x1 = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
double y1 = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
double z1 = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
double distance = Math.Sqrt(x1 * x1 + y1 * y1 + z1 * z1);
//Prepare for the next loop around
JD0 = JD - AASElliptical.DistanceToLightTime(distance);
}
}
}
double x = 0;
double y = 0;
double z = 0;
if (ellipticalObject != AASEllipticalObject.SUN)
{
double Lrad = AASCoordinateTransformation.DegreesToRadians(L);
double Brad = AASCoordinateTransformation.DegreesToRadians(B);
double cosB = Math.Cos(Brad);
double cosL = Math.Cos(Lrad);
x = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
y = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
z = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
}
else
{
x = -R0 *cosB0 *Math.Cos(L0);
y = -R0 *cosB0 *Math.Sin(L0);
z = -R0 *Math.Sin(B0);
}
double x2 = x * x;
double y2 = y * y;
details.ApparentGeocentricLatitude = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(z, Math.Sqrt(x2 + y2)));
details.ApparentGeocentricDistance = Math.Sqrt(x2 + y2 + z * z);
details.ApparentGeocentricLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(y, x)));
details.ApparentLightTime = AASElliptical.DistanceToLightTime(details.ApparentGeocentricDistance);
//Adjust for Aberration
AAS2DCoordinate Aberration = AASAberration.EclipticAberration(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD, bHighPrecision);
details.ApparentGeocentricLongitude += Aberration.X;
details.ApparentGeocentricLatitude += Aberration.Y;
//convert to the FK5 system
double DeltaLong = AASFK5.CorrectionInLongitude(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD);
details.ApparentGeocentricLatitude += AASFK5.CorrectionInLatitude(details.ApparentGeocentricLongitude, JD);
details.ApparentGeocentricLongitude += DeltaLong;
//Correct for nutation
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
double Epsilon = AASNutation.TrueObliquityOfEcliptic(JD);
details.ApparentGeocentricLongitude += AASCoordinateTransformation.DMSToDegrees(0, 0, NutationInLongitude);
//Convert to RA and Dec
AAS2DCoordinate ApparentEqu = AASCoordinateTransformation.Ecliptic2Equatorial(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, Epsilon);
details.ApparentGeocentricRA = ApparentEqu.X;
details.ApparentGeocentricDeclination = ApparentEqu.Y;
return(details);
}
public static double GeometricEclipticLongitude(double JD, bool bHighPrecision)
{
return(AASCoordinateTransformation.MapTo0To360Range(AASEarth.EclipticLongitude(JD, bHighPrecision) + 180));
}
public static double GeometricEclipticLatitudeJ2000(double JD, bool bHighPrecision)
{
return(-AASEarth.EclipticLatitudeJ2000(JD, bHighPrecision));
}
public static CAAPhysicalJupiterDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
CAAPhysicalJupiterDetails details = new CAAPhysicalJupiterDetails();
//Step 1
double d = JD - 2433282.5;
double T1 = d / 36525;
double alpha0 = 268.00 + 0.1061 * T1;
double alpha0rad = AASCoordinateTransformation.DegreesToRadians(alpha0);
double delta0 = 64.50 - 0.0164 * T1;
double delta0rad = AASCoordinateTransformation.DegreesToRadians(delta0);
//Step 2
double W1 = AASCoordinateTransformation.MapTo0To360Range(17.710 + 877.90003539 * d);
double W2 = AASCoordinateTransformation.MapTo0To360Range(16.838 + 870.27003539 * d);
//Step 3
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
//Step 4
double l = AASJupiter.EclipticLongitude(JD, bHighPrecision);
double lrad = AASCoordinateTransformation.DegreesToRadians(l);
double b = AASJupiter.EclipticLatitude(JD, bHighPrecision);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
double r = AASJupiter.RadiusVector(JD, bHighPrecision);
//Step 5
double x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
double y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
double z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
double DELTA = Math.Sqrt(x * x + y * y + z * z);
//Step 6
l -= 0.012990 * DELTA / (r * r);
lrad = AASCoordinateTransformation.DegreesToRadians(l);
//Step 7
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
//Step 8
double e0 = AASNutation.MeanObliquityOfEcliptic(JD);
double e0rad = AASCoordinateTransformation.DegreesToRadians(e0);
//Step 9
double alphas = Math.Atan2(Math.Cos(e0rad) * Math.Sin(lrad) - Math.Sin(e0rad) * Math.Tan(brad), Math.Cos(lrad));
double deltas = Math.Asin(Math.Cos(e0rad) * Math.Sin(brad) + Math.Sin(e0rad) * Math.Cos(brad) * Math.Sin(lrad));
//Step 10
details.DS = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(delta0rad) * Math.Sin(deltas) - Math.Cos(delta0rad) * Math.Cos(deltas) * Math.Cos(alpha0rad - alphas)));
//Step 11
double u = y * Math.Cos(e0rad) - z * Math.Sin(e0rad);
double v = y * Math.Sin(e0rad) + z * Math.Cos(e0rad);
double alpharad = Math.Atan2(u, x);
double alpha = AASCoordinateTransformation.RadiansToDegrees(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = AASCoordinateTransformation.RadiansToDegrees(deltarad);
double xi = Math.Atan2(Math.Sin(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad) - Math.Sin(deltarad) * Math.Cos(delta0rad), Math.Cos(deltarad) * Math.Sin(alpha0rad - alpharad));
//Step 12
details.DE = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(delta0rad) * Math.Sin(deltarad) - Math.Cos(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad)));
//Step 13
details.Geometricw1 = AASCoordinateTransformation.MapTo0To360Range(W1 - AASCoordinateTransformation.RadiansToDegrees(xi) - 5.07033 * DELTA);
details.Geometricw2 = AASCoordinateTransformation.MapTo0To360Range(W2 - AASCoordinateTransformation.RadiansToDegrees(xi) - 5.02626 * DELTA);
//Step 14
double C = 57.2958 * (2 * r * DELTA + R * R - r * r - DELTA * DELTA) / (4 * r * DELTA);
if (Math.Sin(lrad - l0rad) > 0)
{
details.Apparentw1 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw1 + C);
details.Apparentw2 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw2 + C);
}
else
{
details.Apparentw1 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw1 - C);
details.Apparentw2 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw2 - C);
}
//Step 15
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
double NutationInObliquity = AASNutation.NutationInObliquity(JD);
e0 += NutationInObliquity / 3600;
e0rad = AASCoordinateTransformation.DegreesToRadians(e0);
//Step 16
alpha += 0.005693 * (Math.Cos(alpharad) * Math.Cos(l0rad) * Math.Cos(e0rad) + Math.Sin(alpharad) * Math.Sin(l0rad)) / Math.Cos(deltarad);
alpha = AASCoordinateTransformation.MapTo0To360Range(alpha);
alpharad = AASCoordinateTransformation.DegreesToRadians(alpha);
delta += 0.005693 * (Math.Cos(l0rad) * Math.Cos(e0rad) * (Math.Tan(e0rad) * Math.Cos(deltarad) - Math.Sin(alpharad) * Math.Sin(deltarad)) + Math.Cos(alpharad) * Math.Sin(deltarad) * Math.Sin(l0rad));
//Step 17
double NutationRA = AASNutation.NutationInRightAscension(alpha / 15, delta, e0, NutationInLongitude, NutationInObliquity);
double alphadash = alpha + NutationRA / 3600;
double alphadashrad = AASCoordinateTransformation.DegreesToRadians(alphadash);
double NutationDec = AASNutation.NutationInDeclination(alpha / 15, e0, NutationInLongitude, NutationInObliquity);
double deltadash = delta + NutationDec / 3600;
double deltadashrad = AASCoordinateTransformation.DegreesToRadians(deltadash);
NutationRA = AASNutation.NutationInRightAscension(alpha0 / 15, delta0, e0, NutationInLongitude, NutationInObliquity);
double alpha0dash = alpha0 + NutationRA / 3600;
double alpha0dashrad = AASCoordinateTransformation.DegreesToRadians(alpha0dash);
NutationDec = AASNutation.NutationInDeclination(alpha0 / 15, e0, NutationInLongitude, NutationInObliquity);
double delta0dash = delta0 + NutationDec / 3600;
double delta0dashrad = AASCoordinateTransformation.DegreesToRadians(delta0dash);
//Step 18
details.P = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0dashrad) * Math.Sin(alpha0dashrad - alphadashrad), Math.Sin(delta0dashrad) * Math.Cos(deltadashrad) - Math.Cos(delta0dashrad) * Math.Sin(deltadashrad) * Math.Cos(alpha0dashrad - alphadashrad))));
return(details);
}
public static double GeometricEclipticLatitudeJ2000(double JD)
{
return(AASEarth.EclipticLatitudeJ2000(JD));
}
public static double GeometricEclipticLongitudeJ2000(double JD)
{
return(AASCoordinateTransformation.MapTo0To360Range(AASEarth.EclipticLongitudeJ2000(JD) + 180));
}
public static AASSaturnRingDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
AASSaturnRingDetails details = new AASSaturnRingDetails();
double T = (JD - 2451545) / 36525;
double T2 = T * T;
//Step 1. Calculate the inclination of the plane of the ring and the longitude of the ascending node referred to the ecliptic and mean equinox of the date
double i = 28.075216 - 0.012998 * T + 0.000004 * T2;
double irad = AASCoordinateTransformation.DegreesToRadians(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = AASCoordinateTransformation.DegreesToRadians(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
l0 += AASFK5.CorrectionInLongitude(l0, b0, JD);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
b0 += AASFK5.CorrectionInLatitude(l0, JD);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
//Step 3. Calculate the corresponding coordinates l,b,r for Saturn but for the instance t-lightraveltime
double DELTA = 9;
double PreviousEarthLightTravelTime = 0;
double EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
double JD1 = JD - EarthLightTravelTime;
bool bIterate = true;
double x = 0;
double y = 0;
double z = 0;
double l = 0;
double b = 0;
double r = 0;
while (bIterate)
{
//Calculate the position of Saturn
l = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
b = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
l += AASFK5.CorrectionInLongitude(l, b, JD1);
b += AASFK5.CorrectionInLatitude(l, JD1);
double lrad = AASCoordinateTransformation.DegreesToRadians(l);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASSaturn.RadiusVector(JD1, bHighPrecision);
//Step 4
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(EarthLightTravelTime - PreviousEarthLightTravelTime) > 2e-6); //2e-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - EarthLightTravelTime;
PreviousEarthLightTravelTime = EarthLightTravelTime;
}
}
//Step 5. Calculate Saturn's geocentric Longitude and Latitude
double lambda = Math.Atan2(y, x);
double beta = Math.Atan2(z, Math.Sqrt(x * x + y * y));
//Step 6. Calculate B, a and b
details.B = Math.Asin(Math.Sin(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad) - Math.Cos(irad) * Math.Sin(beta));
details.a = 375.35 / DELTA;
details.b = details.a * Math.Sin(Math.Abs(details.B));
details.B = AASCoordinateTransformation.RadiansToDegrees(details.B);
//Step 7. Calculate the longitude of the ascending node of Saturn's orbit
double N = 113.6655 + 0.8771 * T;
double Nrad = AASCoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.01759 / r;
double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash);
//Step 8. Calculate Bdash
details.Bdash = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad) - Math.Cos(irad) * Math.Sin(bdashrad)));
//Step 9. Calculate DeltaU
details.U1 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Sin(irad) * Math.Sin(bdashrad) + Math.Cos(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad), Math.Cos(bdashrad) * Math.Cos(ldashrad - omegarad))));
details.U2 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Sin(irad) * Math.Sin(beta) + Math.Cos(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad), Math.Cos(beta) * Math.Cos(lambda - omegarad))));
details.DeltaU = Math.Abs(details.U1 - details.U2);
if (details.DeltaU > 180)
{
details.DeltaU = 360 - details.DeltaU;
}
//Step 10. Calculate the Nutations
double Obliquity = AASNutation.TrueObliquityOfEcliptic(JD);
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
//Step 11. Calculate the Ecliptical longitude and latitude of the northern pole of the ring plane
double lambda0 = omega - 90;
double beta0 = 90 - i;
//Step 12. Correct lambda and beta for the aberration of Saturn
lambda += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Sin(l0rad - lambda) * Math.Sin(beta));
//Step 13. Add nutation in longitude to lambda0 and lambda
lambda = AASCoordinateTransformation.RadiansToDegrees(lambda);
lambda += NutationInLongitude / 3600;
lambda = AASCoordinateTransformation.MapTo0To360Range(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = AASCoordinateTransformation.MapTo0To360Range(lambda0);
//Step 14. Convert to equatorial coordinates
beta = AASCoordinateTransformation.RadiansToDegrees(beta);
AAS2DCoordinate GeocentricEclipticSaturn = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, Obliquity);
double alpha = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticSaturn.X);
double delta = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticSaturn.Y);
AAS2DCoordinate GeocentricEclipticNorthPole = AASCoordinateTransformation.Ecliptic2Equatorial(lambda0, beta0, Obliquity);
double alpha0 = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticNorthPole.X);
double delta0 = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0) * Math.Sin(alpha0 - alpha), Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(alpha0 - alpha)));
return(details);
}