//Conversion functions
public static COR Equatorial2TopocentricDelta(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = CAAGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = CAAGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = CAASidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = CT.D2R(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(GFX.g_AAParallax_C1 / Distance);
//Calculate the hour angle
double H = CT.H2R(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
COR DeltaTopocentric = new COR();
DeltaTopocentric.X = CT.R2H(-pi * RhoCosThetaPrime * sinH / cosDelta);
DeltaTopocentric.Y = CT.R2D(-pi * (RhoSinThetaPrime * cosDelta - RhoCosThetaPrime * cosH * Math.Sin(Delta)));
return(DeltaTopocentric);
}
//Static methods
//Tangible Process Only End
////////////////////////////////// Implementation /////////////////////////////
public static CAABinaryStarDetails Calculate(double t, double P, double T, double e, double a, double i, double omega, double w)
{
double n = 360 / P;
double M = CT.M360(n * (t - T));
double E = CAAKepler.Calculate(M, e);
E = CT.D2R(E);
i = CT.D2R(i);
w = CT.D2R(w);
omega = CT.D2R(omega);
CAABinaryStarDetails details = new CAABinaryStarDetails();
details.r = a * (1 - e * Math.Cos(E));
double v = Math.Atan(Math.Sqrt((1 + e) / (1 - e)) * Math.Tan(E / 2)) * 2;
details.Theta = Math.Atan2(Math.Sin(v + w) * Math.Cos(i), Math.Cos(v + w)) + omega;
details.Theta = CT.M360(CT.R2D(details.Theta));
double sinvw = Math.Sin(v + w);
double cosvw = Math.Cos(v + w);
double cosi = Math.Cos(i);
details.Rho = details.r * Math.Sqrt((sinvw * sinvw * cosi * cosi) + (cosvw * cosvw));
return(details);
}
public static COR Equatorial2Topocentric(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = CAAGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = CAAGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = CAASidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = CT.D2R(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(GFX.g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
//Calculate the hour angle
double H = CT.H2R(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
//Calculate the adjustment in right ascension
double DeltaAlpha = Math.Atan2(-RhoCosThetaPrime * sinpi * sinH, cosDelta - RhoCosThetaPrime * sinpi * cosH);
COR Topocentric = new COR();
Topocentric.X = CT.M24(Alpha + CT.R2H(DeltaAlpha));
Topocentric.Y = CT.R2D(Math.Atan2((Math.Sin(Delta) - RhoSinThetaPrime * sinpi) * Math.Cos(DeltaAlpha), cosDelta - RhoCosThetaPrime * sinpi * cosH));
return(Topocentric);
}
public static CAAEclipticalElementDetails FK4B1950ToFK5J2000(double i0, double w0, double omega0)
{
//convert to radians
double L = CT.D2R(5.19856209);
double J = CT.D2R(0.00651966);
double i0rad = CT.D2R(i0);
double omega0rad = CT.D2R(omega0);
double sini0rad = Math.Sin(i0rad);
double cosi0rad = Math.Cos(i0rad);
//Calculate some values used later
double cosJ = Math.Cos(J);
double sinJ = Math.Sin(J);
double W = L + omega0rad;
double cosW = Math.Cos(W);
double sinW = Math.Sin(W);
double A = sinJ * sinW;
double B = sini0rad * cosJ + cosi0rad * sinJ * cosW;
//Calculate the values
CAAEclipticalElementDetails details = new CAAEclipticalElementDetails();
details.i = CT.R2D(Math.Asin(Math.Sqrt(A * A + B * B)));
double cosi = cosi0rad * cosJ - sini0rad * sinJ * cosW;
if (cosi < 0)
{
details.i = 180 - details.i;
}
details.w = CT.M360(w0 + CT.R2D(Math.Atan2(A, B)));
details.omega = CT.M360(CT.R2D(Math.Atan2(sini0rad * sinW, cosi0rad * sinJ + sini0rad * cosJ * cosW)) - 4.50001688);
return(details);
}
//Static methods
/////////////////////////////// Implementation ////////////////////////////////
public static double EclipticLongitude(double JD)
{
double rho = (JD - 2451545) / 365250;
double rhosquared = rho * rho;
double rhocubed = rhosquared * rho;
double rho4 = rhocubed * rho;
//Calculate L0
int nL0Coefficients = GFX.g_L0UranusCoefficients.Length;
double L0 = 0;
int i;
for (i = 0; i < nL0Coefficients; i++)
{
L0 += GFX.g_L0UranusCoefficients[i].A * Math.Cos(GFX.g_L0UranusCoefficients[i].B + GFX.g_L0UranusCoefficients[i].C * rho);
}
//Calculate L1
int nL1Coefficients = GFX.g_L1UranusCoefficients.Length;
double L1 = 0;
for (i = 0; i < nL1Coefficients; i++)
{
L1 += GFX.g_L1UranusCoefficients[i].A * Math.Cos(GFX.g_L1UranusCoefficients[i].B + GFX.g_L1UranusCoefficients[i].C * rho);
}
//Calculate L2
int nL2Coefficients = GFX.g_L2UranusCoefficients.Length;
double L2 = 0;
for (i = 0; i < nL2Coefficients; i++)
{
L2 += GFX.g_L2UranusCoefficients[i].A * Math.Cos(GFX.g_L2UranusCoefficients[i].B + GFX.g_L2UranusCoefficients[i].C * rho);
}
//Calculate L3
int nL3Coefficients = GFX.g_L3UranusCoefficients.Length;
double L3 = 0;
for (i = 0; i < nL3Coefficients; i++)
{
L3 += GFX.g_L3UranusCoefficients[i].A * Math.Cos(GFX.g_L3UranusCoefficients[i].B + GFX.g_L3UranusCoefficients[i].C * rho);
}
//Calculate L4
int nL4Coefficients = GFX.g_L4UranusCoefficients.Length;
double L4 = 0;
for (i = 0; i < nL4Coefficients; i++)
{
L4 += GFX.g_L4UranusCoefficients[i].A * Math.Cos(GFX.g_L4UranusCoefficients[i].B + GFX.g_L4UranusCoefficients[i].C * rho);
}
double @value = (L0 + L1 * rho + L2 * rhosquared + L3 * rhocubed + L4 * rho4) / 100000000;
//convert results back to degrees
@value = CT.M360(CT.R2D(@value));
return(@value);
}
public static double EclipticLatitude(double JD)
{
double rho = (JD - 2451545) / 365250;
double rhosquared = rho * rho;
double rhocubed = rhosquared * rho;
double rho4 = rhocubed * rho;
//Calculate B0
int nB0Coefficients = GFX.g_B0VenusCoefficients.Length;
double B0 = 0;
int i;
for (i = 0; i < nB0Coefficients; i++)
{
B0 += GFX.g_B0VenusCoefficients[i].A * Math.Cos(GFX.g_B0VenusCoefficients[i].B + GFX.g_B0VenusCoefficients[i].C * rho);
}
//Calculate B1
int nB1Coefficients = GFX.g_B1VenusCoefficients.Length;
double B1 = 0;
for (i = 0; i < nB1Coefficients; i++)
{
B1 += GFX.g_B1VenusCoefficients[i].A * Math.Cos(GFX.g_B1VenusCoefficients[i].B + GFX.g_B1VenusCoefficients[i].C * rho);
}
//Calculate B2
int nB2Coefficients = GFX.g_B2VenusCoefficients.Length;
double B2 = 0;
for (i = 0; i < nB2Coefficients; i++)
{
B2 += GFX.g_B2VenusCoefficients[i].A * Math.Cos(GFX.g_B2VenusCoefficients[i].B + GFX.g_B2VenusCoefficients[i].C * rho);
}
//Calculate B3
int nB3Coefficients = GFX.g_B3VenusCoefficients.Length;
double B3 = 0;
for (i = 0; i < nB3Coefficients; i++)
{
B3 += GFX.g_B3VenusCoefficients[i].A * Math.Cos(GFX.g_B3VenusCoefficients[i].B + GFX.g_B3VenusCoefficients[i].C * rho);
}
//Calculate B4
int nB4Coefficients = GFX.g_B4VenusCoefficients.Length;
double B4 = 0;
for (i = 0; i < nB4Coefficients; i++)
{
B4 += GFX.g_B4VenusCoefficients[i].A * Math.Cos(GFX.g_B4VenusCoefficients[i].B + GFX.g_B4VenusCoefficients[i].C * rho);
}
double @value = (B0 + B1 * rho + B2 * rhosquared + B3 * rhocubed + B4 * rho4) / 100000000;
//convert results back to degrees
@value = CT.R2D(@value);
return(@value);
}
public static double PhaseAngle(double GeocentricElongation, double EarthObjectDistance, double EarthSunDistance)
{
//Convert from degrees to radians
GeocentricElongation = CT.D2R(GeocentricElongation);
//Return the result
return(CT.M360(CT.R2D(Math.Atan2(EarthSunDistance * Math.Sin(GeocentricElongation), EarthObjectDistance - EarthSunDistance * Math.Cos(GeocentricElongation)))));
}
//Static methods
////////////////////// Implementation /////////////////////////////////////////
public static double ParallacticAngle(double HourAngle, double Latitude, double delta)
{
HourAngle = CT.H2R(HourAngle);
Latitude = CT.D2R(Latitude);
delta = CT.D2R(delta);
return(CT.R2D(Math.Atan2(Math.Sin(HourAngle), Math.Tan(Latitude) * Math.Cos(delta) - Math.Sin(delta) * Math.Cos(HourAngle))));
}
//Static methods
/////////////////////////// Implementation ////////////////////////////////////
public static CAAEclipticalElementDetails Calculate(double i0, double w0, double omega0, double JD0, double JD)
{
double T = (JD0 - 2451545.0) / 36525;
double Tsquared = T * T;
double t = (JD - JD0) / 36525;
double tsquared = t * t;
double tcubed = tsquared * t;
//Now convert to radians
double i0rad = CT.D2R(i0);
double omega0rad = CT.D2R(omega0);
double eta = (47.0029 - 0.06603 * T + 0.000598 * Tsquared) * t + (-0.03302 + 0.000598 * T) * tsquared + 0.00006 * tcubed;
eta = CT.D2R(CT.DMS2D(0, 0, eta));
double pi = 174.876384 * 3600 + 3289.4789 * T + 0.60622 * Tsquared - (869.8089 + 0.50491 * T) * t + 0.03536 * tsquared;
pi = CT.D2R(CT.DMS2D(0, 0, pi));
double p = (5029.0966 + 2.22226 * T - 0.000042 * Tsquared) * t + (1.11113 - 0.000042 * T) * tsquared - 0.000006 * tcubed;
p = CT.D2R(CT.DMS2D(0, 0, p));
double sini0rad = Math.Sin(i0rad);
double cosi0rad = Math.Cos(i0rad);
double sinomega0rad_pi = Math.Sin(omega0rad - pi);
double cosomega0rad_pi = Math.Cos(omega0rad - pi);
double sineta = Math.Sin(eta);
double coseta = Math.Cos(eta);
double A = sini0rad * sinomega0rad_pi;
double B = -sineta * cosi0rad + coseta * sini0rad * cosomega0rad_pi;
double irad = Math.Asin(Math.Sqrt(A * A + B * B));
CAAEclipticalElementDetails details = new CAAEclipticalElementDetails();
details.i = CT.R2D(irad);
double cosi = cosi0rad * coseta + sini0rad * sineta * cosomega0rad_pi;
if (cosi < 0)
{
details.i = 180 - details.i;
}
double phi = pi + p;
details.omega = CT.M360(CT.R2D(Math.Atan2(A, B) + phi));
A = -sineta * sinomega0rad_pi;
B = sini0rad * coseta - cosi0rad * sineta * cosomega0rad_pi;
double deltaw = CT.R2D(Math.Atan2(A, B));
details.w = CT.M360(w0 + deltaw);
return(details);
}
public static double AngleBetweenEclipticAndHorizon(double LocalSiderealTime, double ObliquityOfEcliptic, double Latitude)
{
LocalSiderealTime = CT.H2R(LocalSiderealTime);
Latitude = CT.D2R(Latitude);
ObliquityOfEcliptic = CT.D2R(ObliquityOfEcliptic);
double @value = CT.R2D(Math.Acos(Math.Cos(ObliquityOfEcliptic) * Math.Sin(Latitude) - Math.Sin(ObliquityOfEcliptic) * Math.Cos(Latitude) * Math.Sin(LocalSiderealTime)));
return(CT.M360(@value));
}
public static double EclipticLongitudeOnHorizon(double LocalSiderealTime, double ObliquityOfEcliptic, double Latitude)
{
LocalSiderealTime = CT.H2R(LocalSiderealTime);
Latitude = CT.D2R(Latitude);
ObliquityOfEcliptic = CT.D2R(ObliquityOfEcliptic);
double @value = CT.R2D(Math.Atan2(-Math.Cos(LocalSiderealTime), Math.Sin(ObliquityOfEcliptic) * Math.Tan(Latitude) + Math.Cos(ObliquityOfEcliptic) * Math.Sin(LocalSiderealTime)));
return(CT.M360(@value));
}
public static double PhaseAngle2(double R, double R0, double B, double L, double L0, double Delta)
{
//Convert from degrees to radians
B = CT.D2R(B);
L = CT.D2R(L);
L0 = CT.D2R(L0);
//Return the result
return(CT.M360(CT.R2D(Math.Acos((R - R0 * Math.Cos(B) * Math.Cos(L - L0)) / Delta))));
}
public static double PhaseAngleRectangular(double x, double y, double z, double B, double L, double Delta)
{
//Convert from degrees to radians
B = CT.D2R(B);
L = CT.D2R(L);
double cosB = Math.Cos(B);
//Return the result
return(CT.M360(CT.R2D(Math.Acos((x * cosB * Math.Cos(L) + y * cosB * Math.Sin(L) + z * Math.Sin(B)) / Delta))));
}
public static double PositionAngle(double Alpha0, double Delta0, double Alpha, double Delta)
{
//Convert to radians
Alpha0 = CT.H2R(Alpha0);
Alpha = CT.H2R(Alpha);
Delta0 = CT.D2R(Delta0);
Delta = CT.D2R(Delta);
return(CT.M360(CT.R2D(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)))));
}
public static double AngleBetweenNorthCelestialPoleAndNorthPoleOfEcliptic(double Lambda, double Beta, double ObliquityOfEcliptic)
{
Lambda = CT.D2R(Lambda);
Beta = CT.D2R(Beta);
ObliquityOfEcliptic = CT.D2R(ObliquityOfEcliptic);
double @value = CT.R2D(Math.Atan2(Math.Cos(Lambda) * Math.Tan(ObliquityOfEcliptic), Math.Sin(Beta) * Math.Sin(Lambda) * Math.Tan(ObliquityOfEcliptic) - Math.Cos(Beta)));
return(CT.M360(@value));
}
//Static methods
//////////////////// Implementation ///////////////////////////////////////////
public static double GeocentricElongation(double ObjectAlpha, double ObjectDelta, double SunAlpha, double SunDelta)
{
//Convert the RA's to radians
ObjectAlpha = CT.D2R(ObjectAlpha * 15);
SunAlpha = CT.D2R(SunAlpha * 15);
//Convert the declinations to radians
ObjectDelta = CT.D2R(ObjectDelta);
SunDelta = CT.D2R(SunDelta);
//Return the result
return(CT.R2D(Math.Acos(Math.Sin(SunDelta) * Math.Sin(ObjectDelta) + Math.Cos(SunDelta) * Math.Cos(ObjectDelta) * Math.Cos(SunAlpha - ObjectAlpha))));
}
//C++ TO C# CONVERTER NOTE: C# does not allow default values for parameters. Overloaded methods are inserted above.
//ORIGINAL LINE: static double Calculate(double M, double e, int nIterations = 53)
public static double CalculateIter(double M, double e, int nIterations)
{
//Convert from degrees to radians
M = CT.D2R(M);
double PI = CT.PI();
double F = 1;
if (M < 0)
{
F = -1;
}
M = Math.Abs(M) / (2 * PI);
M = (M - (int)(M)) * 2 * PI * F;
if (M < 0)
{
M += 2 * PI;
}
F = 1;
if (M > PI)
{
F = -1;
}
if (M > PI)
{
M = 2 * PI - M;
}
double E = PI / 2;
double scale = PI / 4;
for (int i = 0; i < nIterations; i++)
{
double R = E - e * Math.Sin(E);
if (M > R)
{
E += scale;
}
else
{
E -= scale;
}
scale /= 2;
}
//Convert the result back to degrees
return(CT.R2D(E) * F);
}
public static double TopocentricMoonSemidiameter(double DistanceDelta, double Delta, double H, double Latitude, double Height)
{
//Convert to radians
H = CT.H2R(H);
Delta = CT.D2R(Delta);
double pi = Math.Asin(6378.14 / DistanceDelta);
double A = Math.Cos(Delta) * Math.Sin(H);
double B = Math.Cos(Delta) * Math.Cos(H) - CAAGlobe.RhoCosThetaPrime(Latitude, Height) * Math.Sin(pi);
double C = Math.Sin(Delta) - CAAGlobe.RhoSinThetaPrime(Latitude, Height) * Math.Sin(pi);
double q = Math.Sqrt(A * A + B * B + C * C);
double s = CT.D2R(GeocentricMoonSemidiameter(DistanceDelta) / 3600);
return(CT.R2D(Math.Asin(Math.Sin(s) / q)) * 3600);
}
public static CAATopocentricEclipticDetails Ecliptic2Topocentric(double Lambda, double Beta, double Semidiameter, double Distance, double Epsilon, double Longitude, double Latitude, double Height, double JD)
{
double S = CAAGlobe.RhoSinThetaPrime(Latitude, Height);
double C = CAAGlobe.RhoCosThetaPrime(Latitude, Height);
//Convert to radians
Lambda = CT.D2R(Lambda);
Beta = CT.D2R(Beta);
Epsilon = CT.D2R(Epsilon);
Longitude = CT.D2R(Longitude);
Latitude = CT.D2R(Latitude);
Semidiameter = CT.D2R(Semidiameter);
double sine = Math.Sin(Epsilon);
double cose = Math.Cos(Epsilon);
double cosBeta = Math.Cos(Beta);
double sinBeta = Math.Sin(Beta);
//Calculate the Sidereal time
double theta = CAASidereal.ApparentGreenwichSiderealTime(JD);
theta = CT.H2R(theta);
double sintheta = Math.Sin(theta);
//Calculate the Parallax
double pi = Math.Asin(GFX.g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
double N = Math.Cos(Lambda) * cosBeta - C * sinpi * Math.Cos(theta);
CAATopocentricEclipticDetails Topocentric = new CAATopocentricEclipticDetails();
Topocentric.Lambda = Math.Atan2(Math.Sin(Lambda) * cosBeta - sinpi * (S * sine + C * cose * sintheta), N);
double cosTopocentricLambda = Math.Cos(Topocentric.Lambda);
Topocentric.Beta = Math.Atan(cosTopocentricLambda * (sinBeta - sinpi * (S * cose - C * sine * sintheta)) / N);
Topocentric.Semidiameter = Math.Asin(cosTopocentricLambda * Math.Cos(Topocentric.Beta) * Math.Sin(Semidiameter) / N);
//Convert back to degrees
Topocentric.Semidiameter = CT.R2D(Topocentric.Semidiameter);
Topocentric.Lambda = CT.M360(CT.R2D(Topocentric.Lambda));
Topocentric.Beta = CT.R2D(Topocentric.Beta);
return(Topocentric);
}
public static COR EquatorialAberration(double Alpha, double Delta, double JD)
{
//Convert to radians
Alpha = CT.D2R(Alpha * 15);
Delta = CT.D2R(Delta);
double cosAlpha = Math.Cos(Alpha);
double sinAlpha = Math.Sin(Alpha);
double cosDelta = Math.Cos(Delta);
double sinDelta = Math.Sin(Delta);
C3D velocity = EarthVelocity(JD);
//What is the return value
COR aberration = new COR();
aberration.X = CT.R2H((velocity.Y * cosAlpha - velocity.X * sinAlpha) / (17314463350.0 * cosDelta));
aberration.Y = CT.R2D(-(((velocity.X * cosAlpha + velocity.Y * sinAlpha) * sinDelta - velocity.Z * cosDelta) / 17314463350.0));
return(aberration);
}
public static COR AdjustPositionUsingMotionInSpace(double r, double DeltaR, double t, double Alpha, double Delta, double PMAlpha, double PMDelta)
{
//Convert DeltaR from km/s to Parsecs / Year
DeltaR /= 977792;
//Convert from seconds of time to Radians / Year
PMAlpha /= 13751;
//Convert from seconds of arc to Radians / Year
PMDelta /= 206265;
//Now convert to radians
Alpha = CT.H2R(Alpha);
Delta = CT.D2R(Delta);
double x = r * Math.Cos(Delta) * Math.Cos(Alpha);
double y = r * Math.Cos(Delta) * Math.Sin(Alpha);
double z = r * Math.Sin(Delta);
double DeltaX = x / r * DeltaR - z * PMDelta * Math.Cos(Alpha) - y * PMAlpha;
double DeltaY = y / r * DeltaR - z * PMDelta * Math.Sin(Alpha) + x * PMAlpha;
double DeltaZ = z / r * DeltaR + r * PMDelta * Math.Cos(Delta);
x += t * DeltaX;
y += t * DeltaY;
z += t * DeltaZ;
COR @value = new COR();
@value.X = CT.R2H(Math.Atan2(y, x));
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CT.R2D(Math.Atan2(z, Math.Sqrt(x * x + y * y)));
return(@value);
}
public static COR PrecessEcliptic(double Lambda, double Beta, double JD0, double JD)
{
double T = (JD0 - 2451545.0) / 36525;
double Tsquared = T * T;
double t = (JD - JD0) / 36525;
double tsquared = t * t;
double tcubed = tsquared * t;
//Now convert to radians
Lambda = CT.D2R(Lambda);
Beta = CT.D2R(Beta);
double eta = (47.0029 - 0.06603 * T + 0.000598 * Tsquared) * t + (-0.03302 + 0.000598 * T) * tsquared + 0.00006 * tcubed;
eta = CT.D2R(CT.DMS2D(0, 0, eta));
double pi = 174.876384 * 3600 + 3289.4789 * T + 0.60622 * Tsquared - (869.8089 + 0.50491 * T) * t + 0.03536 * tsquared;
pi = CT.D2R(CT.DMS2D(0, 0, pi));
double p = (5029.0966 + 2.22226 * T - 0.000042 * Tsquared) * t + (1.11113 - 0.000042 * T) * tsquared - 0.000006 * tcubed;
p = CT.D2R(CT.DMS2D(0, 0, p));
double A = Math.Cos(eta) * Math.Cos(Beta) * Math.Sin(pi - Lambda) - Math.Sin(eta) * Math.Sin(Beta);
double B = Math.Cos(Beta) * Math.Cos(pi - Lambda);
double C = Math.Cos(eta) * Math.Sin(Beta) + Math.Sin(eta) * Math.Cos(Beta) * Math.Sin(pi - Lambda);
COR @value = new COR();
@value.X = CT.R2D(p + pi - Math.Atan2(A, B));
if (@value.X < 0)
{
@value.X += 360;
}
@value.Y = CT.R2D(Math.Asin(C));
return(@value);
}
//Static methods
public static COR PrecessEquatorial(double Alpha, double Delta, double JD0, double JD)
{
double T = (JD0 - 2451545.0) / 36525;
double Tsquared = T * T;
double t = (JD - JD0) / 36525;
double tsquared = t * t;
double tcubed = tsquared * t;
//Now convert to radians
Alpha = CT.H2R(Alpha);
Delta = CT.D2R(Delta);
double sigma = (2306.2181 + 1.39656 * T - 0.000139 * Tsquared) * t + (0.30188 - 0.0000344 * T) * tsquared + 0.017988 * tcubed;
sigma = CT.D2R(CT.DMS2D(0, 0, sigma));
double zeta = (2306.2181 + 1.39656 * T - 0.000138 * Tsquared) * t + (1.09468 + 0.000066 * T) * tsquared + 0.018203 * tcubed;
zeta = CT.D2R(CT.DMS2D(0, 0, zeta));
double phi = (2004.3109 - 0.8533 * T - 0.000217 * Tsquared) * t - (0.42665 + 0.000217 * T) * tsquared - 0.041833 * tcubed;
phi = CT.D2R(CT.DMS2D(0, 0, phi));
double A = Math.Cos(Delta) * Math.Sin(Alpha + sigma);
double B = Math.Cos(phi) * Math.Cos(Delta) * Math.Cos(Alpha + sigma) - Math.Sin(phi) * Math.Sin(Delta);
double C = Math.Sin(phi) * Math.Cos(Delta) * Math.Cos(Alpha + sigma) + Math.Cos(phi) * Math.Sin(Delta);
COR @value = new COR();
@value.X = CT.R2H(Math.Atan2(A, B) + zeta);
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CT.R2D(Math.Asin(C));
return(@value);
}
public static COR PrecessEquatorialFK4(double Alpha, double Delta, double JD0, double JD)
{
double T = (JD0 - 2415020.3135) / 36524.2199;
double t = (JD - JD0) / 36524.2199;
double tsquared = t * t;
double tcubed = tsquared * t;
//Now convert to radians
Alpha = CT.H2R(Alpha);
Delta = CT.D2R(Delta);
double sigma = (2304.250 + 1.396 * T) * t + 0.302 * tsquared + 0.018 * tcubed;
sigma = CT.D2R(CT.DMS2D(0, 0, sigma));
double zeta = 0.791 * tsquared + 0.001 * tcubed;
zeta = CT.D2R(CT.DMS2D(0, 0, zeta));
zeta += sigma;
double phi = (2004.682 - 0.853 * T) * t - 0.426 * tsquared - 0.042 * tcubed;
phi = CT.D2R(CT.DMS2D(0, 0, phi));
double A = Math.Cos(Delta) * Math.Sin(Alpha + sigma);
double B = Math.Cos(phi) * Math.Cos(Delta) * Math.Cos(Alpha + sigma) - Math.Sin(phi) * Math.Sin(Delta);
double C = Math.Sin(phi) * Math.Cos(Delta) * Math.Cos(Alpha + sigma) + Math.Cos(phi) * Math.Sin(Delta);
COR @value = new COR();
@value.X = CT.R2H(Math.Atan2(A, B) + zeta);
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CT.R2D(Math.Asin(C));
return(@value);
}
//Static methods
//////////////////////////// Implementation ///////////////////////////////////
public static double Separation(double Alpha1, double Delta1, double Alpha2, double Delta2)
{
Delta1 = CT.D2R(Delta1);
Delta2 = CT.D2R(Delta2);
Alpha1 = CT.H2R(Alpha1);
Alpha2 = CT.H2R(Alpha2);
double x = Math.Cos(Delta1) * Math.Sin(Delta2) - Math.Sin(Delta1) * Math.Cos(Delta2) * Math.Cos(Alpha2 - Alpha1);
double y = Math.Cos(Delta2) * Math.Sin(Alpha2 - Alpha1);
double z = Math.Sin(Delta1) * Math.Sin(Delta2) + Math.Cos(Delta1) * Math.Cos(Delta2) * Math.Cos(Alpha2 - Alpha1);
double @value = Math.Atan2(Math.Sqrt(x * x + y * y), z);
@value = CT.R2D(@value);
if (@value < 0)
{
@value += 180;
}
return(@value);
}
public static double PositionAngle(double alpha1, double delta1, double alpha2, double delta2)
{
double Alpha1;
double Delta1;
double Alpha2;
double Delta2;
Delta1 = CT.D2R(delta1);
Delta2 = CT.D2R(delta2);
Alpha1 = CT.H2R(alpha1);
Alpha2 = CT.H2R(alpha2);
double DeltaAlpha = Alpha1 - Alpha2;
double demoninator = Math.Cos(Delta2) * Math.Tan(Delta1) - Math.Sin(Delta2) * Math.Cos(DeltaAlpha);
double numerator = Math.Sin(DeltaAlpha);
double @value = Math.Atan2(numerator, demoninator);
@value = CT.R2D(@value);
return(@value);
}
public static double DistanceFromGreatArc(double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3)
{
Delta1 = CT.D2R(Delta1);
Delta2 = CT.D2R(Delta2);
Delta3 = CT.D2R(Delta3);
Alpha1 = CT.H2R(Alpha1);
Alpha2 = CT.H2R(Alpha2);
Alpha3 = CT.H2R(Alpha3);
double X1 = Math.Cos(Delta1) * Math.Cos(Alpha1);
double X2 = Math.Cos(Delta2) * Math.Cos(Alpha2);
double Y1 = Math.Cos(Delta1) * Math.Sin(Alpha1);
double Y2 = Math.Cos(Delta2) * Math.Sin(Alpha2);
double Z1 = Math.Sin(Delta1);
double Z2 = Math.Sin(Delta2);
double A = Y1 * Z2 - Z1 * Y2;
double B = Z1 * X2 - X1 * Z2;
double C = X1 * Y2 - Y1 * X2;
double m = Math.Tan(Alpha3);
double n = Math.Tan(Delta3) / Math.Cos(Alpha3);
double @value = Math.Asin((A + B * m + C * n) / (Math.Sqrt(A * A + B * B + C * C) * Math.Sqrt(1 + m * m + n * n)));
@value = CT.R2D(@value);
if (@value < 0)
{
@value = Math.Abs(@value);
}
return(@value);
}
//Static methods
//////////////////////////////// Implementation ///////////////////////////////
public static CAAPhysicalSunDetails Calculate(double JD)
{
double theta = CT.M360((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 = CAAEarth.EclipticLongitude(JD);
double R = CAAEarth.RadiusVector(JD);
double SunLong = L + 180 - CT.DMS2D(0, 0, 20.4898 / R);
double SunLongDash = SunLong + CT.DMS2D(0, 0, CAANutation.NutationInLongitude(JD));
double epsilon = CAANutation.TrueObliquityOfEcliptic(JD);
//Convert to radians
epsilon = CT.D2R(epsilon);
SunLong = CT.D2R(SunLong);
SunLongDash = CT.D2R(SunLongDash);
K = CT.D2R(K);
I = CT.D2R(I);
theta = CT.D2R(theta);
double x = Math.Atan(-Math.Cos(SunLong) * Math.Tan(epsilon));
double y = Math.Atan(-Math.Cos(SunLong - K) * Math.Tan(I));
CAAPhysicalSunDetails details = new CAAPhysicalSunDetails();
details.P = CT.R2D(x + y);
details.B0 = CT.R2D(Math.Asin(Math.Sin(SunLong - K) * Math.Sin(I)));
double eta = Math.Atan(Math.Tan(SunLong - K) * Math.Cos(I));
details.L0 = CT.M360(CT.R2D(eta - theta));
return(details);
}
//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 CAASaturnRingDetails Calculate(double JD)
{
//What will be the return value
CAASaturnRingDetails details = new CAASaturnRingDetails();
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 = CT.D2R(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = CT.D2R(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
double l0 = CAAEarth.EclipticLongitude(JD);
double b0 = CAAEarth.EclipticLatitude(JD);
l0 += CAAFK5.CorrectionInLongitude(l0, b0, JD);
double l0rad = CT.D2R(l0);
b0 += CAAFK5.CorrectionInLatitude(l0, JD);
double b0rad = CT.D2R(b0);
double R = CAAEarth.RadiusVector(JD);
//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 = ELL.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 = CAASaturn.EclipticLongitude(JD1);
b = CAASaturn.EclipticLatitude(JD1);
l += CAAFK5.CorrectionInLongitude(l, b, JD1);
b += CAAFK5.CorrectionInLatitude(l, JD1);
double lrad = CT.D2R(l);
double brad = CT.D2R(b);
r = CAASaturn.RadiusVector(JD1);
//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 = ELL.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 = CT.R2D(details.B);
//Step 7. Calculate the longitude of the ascending node of Saturn's orbit
double N = 113.6655 + 0.8771 * T;
double Nrad = CT.D2R(N);
double ldash = l - 0.01759 / r;
double ldashrad = CT.D2R(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = CT.D2R(bdash);
//Step 8. Calculate Bdash
details.Bdash = CT.R2D(Math.Asin(Math.Sin(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad) - Math.Cos(irad) * Math.Sin(bdashrad)));
//Step 9. Calculate DeltaU
double U1 = 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));
double U2 = 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 = CT.R2D(Math.Abs(U1 - U2));
//Step 10. Calculate the Nutations
double Obliquity = CAANutation.TrueObliquityOfEcliptic(JD);
double NutationInLongitude = CAANutation.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 += CT.D2R(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += CT.D2R(0.005693 * Math.Sin(l0rad - lambda) * Math.Sin(beta));
//Step 13. Add nutation in longitude to lambda0 and lambda
//double NLrad = CAACoordinateTransformation::DegreesToRadians(NutationInLongitude/3600);
lambda = CT.R2D(lambda);
lambda += NutationInLongitude / 3600;
lambda = CT.M360(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = CT.M360(lambda0);
//Step 14. Convert to equatorial coordinates
beta = CT.R2D(beta);
COR GeocentricEclipticSaturn = CT.Ec2Eq(lambda, beta, Obliquity);
double alpha = CT.H2R(GeocentricEclipticSaturn.X);
double delta = CT.D2R(GeocentricEclipticSaturn.Y);
COR GeocentricEclipticNorthPole = CT.Ec2Eq(lambda0, beta0, Obliquity);
double alpha0 = CT.H2R(GeocentricEclipticNorthPole.X);
double delta0 = CT.D2R(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = CT.R2D(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);
}
