public static CAA2DCoordinate 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 = CAACoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(GlobalMembersStdafx.g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
//Calculate the hour angle
double H = CAACoordinateTransformation.HoursToRadians(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);
CAA2DCoordinate Topocentric = new CAA2DCoordinate();
Topocentric.X = CAACoordinateTransformation.MapTo0To24Range(Alpha + CAACoordinateTransformation.RadiansToHours(DeltaAlpha));
Topocentric.Y = CAACoordinateTransformation.RadiansToDegrees(Math.Atan2((Math.Sin(Delta) - RhoSinThetaPrime * sinpi) * Math.Cos(DeltaAlpha), cosDelta - RhoCosThetaPrime * sinpi * cosH));
return(Topocentric);
}
//Conversion functions
public static CAA2DCoordinate 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 = CAACoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(GlobalMembersStdafx.g_AAParallax_C1 / Distance);
//Calculate the hour angle
double H = CAACoordinateTransformation.HoursToRadians(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
CAA2DCoordinate DeltaTopocentric = new CAA2DCoordinate();
DeltaTopocentric.X = CAACoordinateTransformation.RadiansToHours(-pi * RhoCosThetaPrime * sinH / cosDelta);
DeltaTopocentric.Y = CAACoordinateTransformation.RadiansToDegrees(-pi * (RhoSinThetaPrime * cosDelta - RhoCosThetaPrime * cosH * Math.Sin(Delta)));
return(DeltaTopocentric);
}
//Static methods
////////////////////// Implementation /////////////////////////////////////////
public static double ParallacticAngle(double HourAngle, double Latitude, double delta)
{
HourAngle = CAACoordinateTransformation.HoursToRadians(HourAngle);
Latitude = CAACoordinateTransformation.DegreesToRadians(Latitude);
delta = CAACoordinateTransformation.DegreesToRadians(delta);
return(CAACoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Sin(HourAngle), Math.Tan(Latitude) * Math.Cos(delta) - Math.Sin(delta) * Math.Cos(HourAngle))));
}
public static double NutationInDeclination(double Alpha, double Delta, double Obliquity, double NutationInLongitude, double NutationInObliquity)
{
//Convert to radians
Alpha = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta = CAACoordinateTransformation.DegreesToRadians(Delta);
Obliquity = CAACoordinateTransformation.DegreesToRadians(Obliquity);
return(Math.Sin(Obliquity) * Math.Cos(Alpha) * NutationInLongitude + Math.Sin(Alpha) * NutationInObliquity);
}
public static double PositionAngle(double Alpha0, double Delta0, double Alpha, double Delta)
{
//Convert to radians
Alpha0 = CAACoordinateTransformation.HoursToRadians(Alpha0);
Alpha = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta0 = CAACoordinateTransformation.DegreesToRadians(Delta0);
Delta = CAACoordinateTransformation.DegreesToRadians(Delta);
return(CAACoordinateTransformation.MapTo0To360Range(CAACoordinateTransformation.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)))));
}
public static double AngleBetweenEclipticAndHorizon(double LocalSiderealTime, double ObliquityOfEcliptic, double Latitude)
{
LocalSiderealTime = CAACoordinateTransformation.HoursToRadians(LocalSiderealTime);
Latitude = CAACoordinateTransformation.DegreesToRadians(Latitude);
ObliquityOfEcliptic = CAACoordinateTransformation.DegreesToRadians(ObliquityOfEcliptic);
double @value = CAACoordinateTransformation.RadiansToDegrees(Math.Acos(Math.Cos(ObliquityOfEcliptic) * Math.Sin(Latitude) - Math.Sin(ObliquityOfEcliptic) * Math.Cos(Latitude) * Math.Sin(LocalSiderealTime)));
return(CAACoordinateTransformation.MapTo0To360Range(@value));
}
public static double EclipticLongitudeOnHorizon(double LocalSiderealTime, double ObliquityOfEcliptic, double Latitude)
{
LocalSiderealTime = CAACoordinateTransformation.HoursToRadians(LocalSiderealTime);
Latitude = CAACoordinateTransformation.DegreesToRadians(Latitude);
ObliquityOfEcliptic = CAACoordinateTransformation.DegreesToRadians(ObliquityOfEcliptic);
double @value = CAACoordinateTransformation.RadiansToDegrees(Math.Atan2(-Math.Cos(LocalSiderealTime), Math.Sin(ObliquityOfEcliptic) * Math.Tan(Latitude) + Math.Cos(ObliquityOfEcliptic) * Math.Sin(LocalSiderealTime)));
return(CAACoordinateTransformation.MapTo0To360Range(@value));
}
public static double TopocentricMoonSemidiameter(double DistanceDelta, double Delta, double H, double Latitude, double Height)
{
//Convert to radians
H = CAACoordinateTransformation.HoursToRadians(H);
Delta = CAACoordinateTransformation.DegreesToRadians(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 = CAACoordinateTransformation.DegreesToRadians(GeocentricMoonSemidiameter(DistanceDelta) / 3600);
return(CAACoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(s) / q)) * 3600);
}
public static CAA2DCoordinate EquatorialPMToEcliptic(double Alpha, double Delta, double Beta, double PMAlpha, double PMDelta, double Epsilon)
{
//Convert to radians
Epsilon = CAACoordinateTransformation.DegreesToRadians(Epsilon);
Alpha = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta = CAACoordinateTransformation.DegreesToRadians(Delta);
Beta = CAACoordinateTransformation.DegreesToRadians(Beta);
double cosb = Math.Cos(Beta);
double sinEpsilon = Math.Sin(Epsilon);
CAA2DCoordinate @value = new CAA2DCoordinate();
@value.X = (PMDelta * sinEpsilon * Math.Cos(Alpha) + PMAlpha * Math.Cos(Delta) * (Math.Cos(Epsilon) * Math.Cos(Delta) + sinEpsilon * Math.Sin(Delta) * Math.Sin(Alpha))) / (cosb * cosb);
@value.Y = (PMDelta * (Math.Cos(Epsilon) * Math.Cos(Delta) + sinEpsilon * Math.Sin(Delta) * Math.Sin(Alpha)) - PMAlpha * sinEpsilon * Math.Cos(Alpha) * Math.Cos(Delta)) / cosb;
return(@value);
}
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 = CAACoordinateTransformation.DegreesToRadians(Lambda);
Beta = CAACoordinateTransformation.DegreesToRadians(Beta);
Epsilon = CAACoordinateTransformation.DegreesToRadians(Epsilon);
Longitude = CAACoordinateTransformation.DegreesToRadians(Longitude);
Latitude = CAACoordinateTransformation.DegreesToRadians(Latitude);
Semidiameter = CAACoordinateTransformation.DegreesToRadians(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 = CAACoordinateTransformation.HoursToRadians(theta);
double sintheta = Math.Sin(theta);
//Calculate the Parallax
double pi = Math.Asin(GlobalMembersStdafx.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 = CAACoordinateTransformation.RadiansToDegrees(Topocentric.Semidiameter);
Topocentric.Lambda = CAACoordinateTransformation.MapTo0To360Range(CAACoordinateTransformation.RadiansToDegrees(Topocentric.Lambda));
Topocentric.Beta = CAACoordinateTransformation.RadiansToDegrees(Topocentric.Beta);
return(Topocentric);
}
public static CAA2DCoordinate 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 = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta = CAACoordinateTransformation.DegreesToRadians(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;
CAA2DCoordinate @value = new CAA2DCoordinate();
@value.X = CAACoordinateTransformation.RadiansToHours(Math.Atan2(y, x));
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CAACoordinateTransformation.RadiansToDegrees(Math.Atan2(z, Math.Sqrt(x * x + y * y)));
return(@value);
}
//Static methods
//////////////////////////// Implementation ///////////////////////////////////
public static double Separation(double Alpha1, double Delta1, double Alpha2, double Delta2)
{
Delta1 = CAACoordinateTransformation.DegreesToRadians(Delta1);
Delta2 = CAACoordinateTransformation.DegreesToRadians(Delta2);
Alpha1 = CAACoordinateTransformation.HoursToRadians(Alpha1);
Alpha2 = CAACoordinateTransformation.HoursToRadians(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 = CAACoordinateTransformation.RadiansToDegrees(@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 = CAACoordinateTransformation.DegreesToRadians(delta1);
Delta2 = CAACoordinateTransformation.DegreesToRadians(delta2);
Alpha1 = CAACoordinateTransformation.HoursToRadians(alpha1);
Alpha2 = CAACoordinateTransformation.HoursToRadians(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 = CAACoordinateTransformation.RadiansToDegrees(@value);
return(@value);
}
public static CAA2DCoordinate 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 = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta = CAACoordinateTransformation.DegreesToRadians(Delta);
double sigma = (2304.250 + 1.396 * T) * t + 0.302 * tsquared + 0.018 * tcubed;
sigma = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(0, 0, sigma));
double zeta = 0.791 * tsquared + 0.001 * tcubed;
zeta = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(0, 0, zeta));
zeta += sigma;
double phi = (2004.682 - 0.853 * T) * t - 0.426 * tsquared - 0.042 * tcubed;
phi = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(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);
CAA2DCoordinate @value = new CAA2DCoordinate();
@value.X = CAACoordinateTransformation.RadiansToHours(Math.Atan2(A, B) + zeta);
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CAACoordinateTransformation.RadiansToDegrees(Math.Asin(C));
return(@value);
}
//Static methods
public static CAA2DCoordinate 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 = CAACoordinateTransformation.HoursToRadians(Alpha);
Delta = CAACoordinateTransformation.DegreesToRadians(Delta);
double sigma = (2306.2181 + 1.39656 * T - 0.000139 * Tsquared) * t + (0.30188 - 0.0000344 * T) * tsquared + 0.017988 * tcubed;
sigma = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(0, 0, sigma));
double zeta = (2306.2181 + 1.39656 * T - 0.000138 * Tsquared) * t + (1.09468 + 0.000066 * T) * tsquared + 0.018203 * tcubed;
zeta = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(0, 0, zeta));
double phi = (2004.3109 - 0.8533 * T - 0.000217 * Tsquared) * t - (0.42665 + 0.000217 * T) * tsquared - 0.041833 * tcubed;
phi = CAACoordinateTransformation.DegreesToRadians(CAACoordinateTransformation.DMSToDegrees(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);
CAA2DCoordinate @value = new CAA2DCoordinate();
@value.X = CAACoordinateTransformation.RadiansToHours(Math.Atan2(A, B) + zeta);
if (@value.X < 0)
{
@value.X += 24;
}
@value.Y = CAACoordinateTransformation.RadiansToDegrees(Math.Asin(C));
return(@value);
}
protected static CAAPhysicalMoonDetails CalculateHelper(double JD, ref double Lambda, ref double Beta, ref double epsilon, ref CAA2DCoordinate Equatorial)
{
//What will be the return value
CAAPhysicalMoonDetails details = new CAAPhysicalMoonDetails();
//Calculate the initial quantities
Lambda = CAAMoon.EclipticLongitude(JD);
Beta = CAAMoon.EclipticLatitude(JD);
//Calculate the optical libration
double omega = 0;
double DeltaU = 0;
double sigma = 0;
double I = 0;
double rho = 0;
CalculateOpticalLibration(JD, Lambda, Beta, ref details.ldash, ref details.bdash, ref details.ldash2, ref details.bdash2, ref epsilon, ref omega, ref DeltaU, ref sigma, ref I, ref rho);
double epsilonrad = CAACoordinateTransformation.DegreesToRadians(epsilon);
//Calculate the total libration
details.l = details.ldash + details.ldash2;
details.b = details.bdash + details.bdash2;
double b = CAACoordinateTransformation.DegreesToRadians(details.b);
//Calculate the position angle
double V = omega + DeltaU + CAACoordinateTransformation.DegreesToRadians(sigma) / Math.Sin(I);
double I_rho = I + CAACoordinateTransformation.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 = CAACoordinateTransformation.Ecliptic2Equatorial(Lambda, Beta, epsilon);
double Alpha = CAACoordinateTransformation.HoursToRadians(Equatorial.X);
details.P = CAACoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sqrt(X * X + Y * Y) * Math.Cos(Alpha - w) / (Math.Cos(b))));
return(details);
}
public static double DistanceFromGreatArc(double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3)
{
Delta1 = CAACoordinateTransformation.DegreesToRadians(Delta1);
Delta2 = CAACoordinateTransformation.DegreesToRadians(Delta2);
Delta3 = CAACoordinateTransformation.DegreesToRadians(Delta3);
Alpha1 = CAACoordinateTransformation.HoursToRadians(Alpha1);
Alpha2 = CAACoordinateTransformation.HoursToRadians(Alpha2);
Alpha3 = CAACoordinateTransformation.HoursToRadians(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 = CAACoordinateTransformation.RadiansToDegrees(@value);
if (@value < 0)
{
@value = Math.Abs(@value);
}
return(@value);
}
public static CAAPhysicalMoonDetails CalculateTopocentric(double JD, double Longitude, double Latitude)
{
//First convert to radians
Longitude = CAACoordinateTransformation.DegreesToRadians(Longitude);
Latitude = CAACoordinateTransformation.DegreesToRadians(Latitude);
double Lambda = 0;
double Beta = 0;
double epsilon = 0;
CAA2DCoordinate Equatorial = new CAA2DCoordinate();
CAAPhysicalMoonDetails details = CalculateHelper(JD, ref Lambda, ref Beta, ref epsilon, ref Equatorial);
double R = CAAMoon.RadiusVector(JD);
double pi = CAAMoon.RadiusVectorToHorizontalParallax(R);
double Alpha = CAACoordinateTransformation.HoursToRadians(Equatorial.X);
double Delta = CAACoordinateTransformation.DegreesToRadians(Equatorial.Y);
double AST = CAASidereal.ApparentGreenwichSiderealTime(JD);
double H = CAACoordinateTransformation.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 = CAACoordinateTransformation.DegreesToRadians(details.P);
double DeltaL = -pidash *Math.Sin(Q - Prad) / Math.Cos(CAACoordinateTransformation.DegreesToRadians(details.b));
details.l += DeltaL;
double DeltaB = pidash * Math.Cos(Q - Prad);
details.b += DeltaB;
details.P += DeltaL * Math.Sin(CAACoordinateTransformation.DegreesToRadians(details.b)) - pidash * Math.Sin(Q) * Math.Tan(Delta);
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 = CAACoordinateTransformation.DegreesToRadians(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = CAACoordinateTransformation.DegreesToRadians(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 = CAACoordinateTransformation.DegreesToRadians(l0);
b0 += CAAFK5.CorrectionInLatitude(l0, JD);
double b0rad = CAACoordinateTransformation.DegreesToRadians(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 = CAAElliptical.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 = CAACoordinateTransformation.DegreesToRadians(l);
double brad = CAACoordinateTransformation.DegreesToRadians(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 = CAAElliptical.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 = CAACoordinateTransformation.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 = CAACoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.01759 / r;
double ldashrad = CAACoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = CAACoordinateTransformation.DegreesToRadians(bdash);
//Step 8. Calculate Bdash
details.Bdash = CAACoordinateTransformation.RadiansToDegrees(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 = CAACoordinateTransformation.RadiansToDegrees(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 += CAACoordinateTransformation.DegreesToRadians(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += CAACoordinateTransformation.DegreesToRadians(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 = CAACoordinateTransformation.RadiansToDegrees(lambda);
lambda += NutationInLongitude / 3600;
lambda = CAACoordinateTransformation.MapTo0To360Range(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = CAACoordinateTransformation.MapTo0To360Range(lambda0);
//Step 14. Convert to equatorial coordinates
beta = CAACoordinateTransformation.RadiansToDegrees(beta);
CAA2DCoordinate GeocentricEclipticSaturn = CAACoordinateTransformation.Ecliptic2Equatorial(lambda, beta, Obliquity);
double alpha = CAACoordinateTransformation.HoursToRadians(GeocentricEclipticSaturn.X);
double delta = CAACoordinateTransformation.DegreesToRadians(GeocentricEclipticSaturn.Y);
CAA2DCoordinate GeocentricEclipticNorthPole = CAACoordinateTransformation.Ecliptic2Equatorial(lambda0, beta0, Obliquity);
double alpha0 = CAACoordinateTransformation.HoursToRadians(GeocentricEclipticNorthPole.X);
double delta0 = CAACoordinateTransformation.DegreesToRadians(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = CAACoordinateTransformation.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);
}
//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 = CAACoordinateTransformation.DegreesToRadians(Lambda0);
double Beta0 = 63.2818 - 0.00394 * T;
double Beta0rad = CAACoordinateTransformation.DegreesToRadians(Beta0);
//Step 2
double l0 = CAAEarth.EclipticLongitude(JD);
double l0rad = CAACoordinateTransformation.DegreesToRadians(l0);
double b0 = CAAEarth.EclipticLatitude(JD);
double b0rad = CAACoordinateTransformation.DegreesToRadians(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 = CAACoordinateTransformation.DegreesToRadians(l);
b = CAAMars.EclipticLatitude(JD2);
brad = CAACoordinateTransformation.DegreesToRadians(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 = CAAElliptical.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 = CAACoordinateTransformation.RadiansToDegrees(lambdarad);
double betarad = Math.Atan2(z, Math.Sqrt(x * x + y * y));
double beta = CAACoordinateTransformation.RadiansToDegrees(betarad);
//Step 6
details.DE = CAACoordinateTransformation.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 = CAACoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.00697 / r;
double ldashrad = CAACoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000225 * (Math.Cos(lrad - Nrad) / r);
double bdashrad = CAACoordinateTransformation.DegreesToRadians(bdash);
//Step 8
details.DS = CAACoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(bdashrad) - Math.Cos(Beta0rad) * Math.Cos(bdashrad) * Math.Cos(Lambda0rad - ldashrad)));
//Step 9
double W = CAACoordinateTransformation.MapTo0To360Range(11.504 + 350.89200025 * (JD - LightTravelTime - 2433282.5));
//Step 10
double e0 = CAANutation.MeanObliquityOfEcliptic(JD);
double e0rad = CAACoordinateTransformation.DegreesToRadians(e0);
CAA2DCoordinate PoleEquatorial = CAACoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0rad = CAACoordinateTransformation.HoursToRadians(PoleEquatorial.X);
double delta0rad = CAACoordinateTransformation.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 = CAACoordinateTransformation.RadiansToHours(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = CAACoordinateTransformation.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 = CAACoordinateTransformation.MapTo0To360Range(W - CAACoordinateTransformation.RadiansToDegrees(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 = CAACoordinateTransformation.DegreesToRadians(Lambda0);
lambda += NutationInLongitude / 3600;
lambdarad = CAACoordinateTransformation.DegreesToRadians(lambda);
e0 += NutationInObliquity / 3600;
e0rad = CAACoordinateTransformation.DegreesToRadians(e0rad);
//Step 16
CAA2DCoordinate ApparentPoleEquatorial = CAACoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0dash = CAACoordinateTransformation.HoursToRadians(ApparentPoleEquatorial.X);
double delta0dash = CAACoordinateTransformation.DegreesToRadians(ApparentPoleEquatorial.Y);
CAA2DCoordinate ApparentMars = CAACoordinateTransformation.Ecliptic2Equatorial(lambda, beta, e0);
double alphadash = CAACoordinateTransformation.HoursToRadians(ApparentMars.X);
double deltadash = CAACoordinateTransformation.DegreesToRadians(ApparentMars.Y);
//Step 17
details.P = CAACoordinateTransformation.MapTo0To360Range(CAACoordinateTransformation.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 = CAASun.GeometricEclipticLongitude(JD);
double SunBeta = CAASun.GeometricEclipticLatitude(JD);
CAA2DCoordinate SunEquatorial = CAACoordinateTransformation.Ecliptic2Equatorial(SunLambda, SunBeta, e0);
details.X = CAAMoonIlluminatedFraction.PositionAngle(SunEquatorial.X, SunEquatorial.Y, alpha, delta);
//Step 19
details.d = 9.36 / DELTA;
details.k = CAAIlluminatedFraction.IlluminatedFraction(r, R, DELTA);
details.q = (1 - details.k) * details.d;
return(details);
}