public static double ApparentGreenwichSiderealTime(double JD)
{
double MeanObliquity = CAANutation.MeanObliquityOfEcliptic(JD);
double TrueObliquity = MeanObliquity + CAANutation.NutationInObliquity(JD) / 3600;
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
double Value = MeanGreenwichSiderealTime(JD) + (NutationInLongitude * Math.Cos(CAACoordinateTransformation.DegreesToRadians(TrueObliquity)) / 54000);
return(CAACoordinateTransformation.MapTo0To24Range(Value));
}
public static double ApparentGreenwichSiderealTime(double JD)
{
double MeanObliquity = CAANutation.MeanObliquityOfEcliptic(JD);
double TrueObliquity = MeanObliquity + CAANutation.NutationInObliquity(JD) / 3600;
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
double Value = MeanGreenwichSiderealTime(JD) + (NutationInLongitude * Math.Cos(CT.D2R(TrueObliquity)) / 54000);
return(CT.M24(Value));
}
//////////////////////////////// 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);
}
//Static methods
//////////////////////////////// Implementation ///////////////////////////////
public static CAAPhysicalJupiterDetails Calculate(double JD)
{
//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 = CT.D2R(alpha0);
double delta0 = 64.50 - 0.0164 * T1;
double delta0rad = CT.D2R(delta0);
//Step 2
double W1 = CT.M360(17.710 + 877.90003539 * d);
double W2 = CT.M360(16.838 + 870.27003539 * d);
//Step 3
double l0 = CAAEarth.EclipticLongitude(JD);
double l0rad = CT.D2R(l0);
double b0 = CAAEarth.EclipticLatitude(JD);
double b0rad = CT.D2R(b0);
double R = CAAEarth.RadiusVector(JD);
//Step 4
double l = CAAJupiter.EclipticLongitude(JD);
double lrad = CT.D2R(l);
double b = CAAJupiter.EclipticLatitude(JD);
double brad = CT.D2R(b);
double r = CAAJupiter.RadiusVector(JD);
//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 = CT.D2R(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 = CAANutation.MeanObliquityOfEcliptic(JD);
double e0rad = CT.D2R(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 = CT.R2D(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 = CT.R2D(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = CT.R2D(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 = CT.R2D(Math.Asin(-Math.Sin(delta0rad) * Math.Sin(deltarad) - Math.Cos(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad)));
//Step 13
details.Geometricw1 = CT.M360(W1 - CT.R2D(xi) - 5.07033 * DELTA);
details.Geometricw2 = CT.M360(W2 - CT.R2D(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 = CT.M360(details.Geometricw1 + C);
details.Apparentw2 = CT.M360(details.Geometricw2 + C);
}
else
{
details.Apparentw1 = CT.M360(details.Geometricw1 - C);
details.Apparentw2 = CT.M360(details.Geometricw2 - C);
}
//Step 15
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
double NutationInObliquity = CAANutation.NutationInObliquity(JD);
e0 += NutationInObliquity / 3600;
e0rad = CT.D2R(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 = CT.M360(alpha);
alpharad = CT.D2R(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));
deltarad = CT.D2R(delta);
//Step 17
double NutationRA = CAANutation.NutationInRightAscension(alpha / 15, delta, e0, NutationInLongitude, NutationInObliquity);
double alphadash = alpha + NutationRA / 3600;
double alphadashrad = CT.D2R(alphadash);
double NutationDec = CAANutation.NutationInDeclination(alpha / 15, delta, e0, NutationInLongitude, NutationInObliquity);
double deltadash = delta + NutationDec / 3600;
double deltadashrad = CT.D2R(deltadash);
NutationRA = CAANutation.NutationInRightAscension(alpha0 / 15, delta0, e0, NutationInLongitude, NutationInObliquity);
double alpha0dash = alpha0 + NutationRA / 3600;
double alpha0dashrad = CT.D2R(alpha0dash);
NutationDec = CAANutation.NutationInDeclination(alpha0 / 15, delta0, e0, NutationInLongitude, NutationInObliquity);
double delta0dash = delta0 + NutationDec / 3600;
double delta0dashrad = CT.D2R(delta0dash);
//Step 18
details.P = CT.M360(CT.R2D(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);
}
//Static methods
//////////////////////////////// Implementation ///////////////////////////////
public static CAAPhysicalMarsDetails Calculate(double JD)
{
//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 = CT.D2R(Lambda0);
double Beta0 = 63.2818 - 0.00394 * T;
double Beta0rad = CT.D2R(Beta0);
//Step 2
double l0 = CAAEarth.EclipticLongitude(JD);
double l0rad = CT.D2R(l0);
double b0 = CAAEarth.EclipticLatitude(JD);
double b0rad = CT.D2R(b0);
double R = CAAEarth.RadiusVector(JD);
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 brad = 0;
double r = 0;
while (bIterate)
{
double JD2 = JD - LightTravelTime;
//Step 3
l = CAAMars.EclipticLongitude(JD2);
lrad = CT.D2R(l);
b = CAAMars.EclipticLatitude(JD2);
brad = CT.D2R(b);
r = CAAMars.RadiusVector(JD2);
//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 = ELL.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 = CT.R2D(lambdarad);
double betarad = Math.Atan2(z, Math.Sqrt(x * x + y * y));
double beta = CT.R2D(betarad);
//Step 6
details.DE = CT.R2D(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 = CT.D2R(N);
double ldash = l - 0.00697 / r;
double ldashrad = CT.D2R(ldash);
double bdash = b - 0.000225 * (Math.Cos(lrad - Nrad) / r);
double bdashrad = CT.D2R(bdash);
//Step 8
details.DS = CT.R2D(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(bdashrad) - Math.Cos(Beta0rad) * Math.Cos(bdashrad) * Math.Cos(Lambda0rad - ldashrad)));
//Step 9
double W = CT.M360(11.504 + 350.89200025 * (JD - LightTravelTime - 2433282.5));
//Step 10
double e0 = CAANutation.MeanObliquityOfEcliptic(JD);
double e0rad = CT.D2R(e0);
COR PoleEquatorial = CT.Ec2Eq(Lambda0, Beta0, e0);
double alpha0rad = CT.H2R(PoleEquatorial.X);
double delta0rad = CT.D2R(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 = CT.R2H(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = CT.R2D(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 = CT.M360(W - CT.R2D(xi));
//Step 13
double NutationInLongitude = CAANutation.NutationInLongitude(JD);
double NutationInObliquity = CAANutation.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;
Lambda0rad = CT.D2R(Lambda0);
lambda += NutationInLongitude / 3600;
lambdarad = CT.D2R(lambda);
e0 += NutationInObliquity / 3600;
e0rad = CT.D2R(e0rad);
//Step 16
COR ApparentPoleEquatorial = CT.Ec2Eq(Lambda0, Beta0, e0);
double alpha0dash = CT.H2R(ApparentPoleEquatorial.X);
double delta0dash = CT.D2R(ApparentPoleEquatorial.Y);
COR ApparentMars = CT.Ec2Eq(lambda, beta, e0);
double alphadash = CT.H2R(ApparentMars.X);
double deltadash = CT.D2R(ApparentMars.Y);
//Step 17
details.P = CT.M360(CT.R2D(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 = CAASun.GeometricEclipticLongitude(JD);
double SunBeta = CAASun.GeometricEclipticLatitude(JD);
COR SunEquatorial = CT.Ec2Eq(SunLambda, SunBeta, e0);
details.X = MIFR.PositionAngle(SunEquatorial.X, SunEquatorial.Y, alpha, delta);
//Step 19
details.d = 9.36 / DELTA;
details.k = IFR.IlluminatedFraction2(r, R, DELTA);
details.q = (1 - details.k) * details.d;
return(details);
}