public static AAS2DCoordinate Equatorial2TopocentricDelta(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = AASGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = AASGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = AASSidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(g_AAParallax_C1 / Distance);
//Calculate the hour angle
double H = AASCoordinateTransformation.HoursToRadians(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
AAS2DCoordinate DeltaTopocentric = new AAS2DCoordinate {
X = AASCoordinateTransformation.RadiansToHours(-pi * RhoCosThetaPrime * sinH / cosDelta), Y = AASCoordinateTransformation.RadiansToDegrees(-pi * (RhoSinThetaPrime * cosDelta - RhoCosThetaPrime * cosH * Math.Sin(Delta)))
};
return(DeltaTopocentric);
}
public static AAS2DCoordinate Equatorial2Topocentric(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = AASGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = AASGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = AASSidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
//Calculate the hour angle
double H = AASCoordinateTransformation.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);
AAS2DCoordinate Topocentric = new AAS2DCoordinate {
X = AASCoordinateTransformation.MapTo0To24Range(Alpha + AASCoordinateTransformation.RadiansToHours(DeltaAlpha)), Y = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2((Math.Sin(Delta) - RhoSinThetaPrime * sinpi) * Math.Cos(DeltaAlpha), cosDelta - RhoCosThetaPrime * sinpi * cosH))
};
return(Topocentric);
}
public static AAS2DCoordinate 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 = AASCoordinateTransformation.HoursToRadians(Alpha);
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double sigma = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (2304.250 + 1.396 * T) * t + 0.302 * tsquared + 0.018 * tcubed));
double zeta = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, 0.791 * tsquared + 0.001 * tcubed)) + sigma;
double phi = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (2004.682 - 0.853 * T) * t - 0.426 * tsquared - 0.042 * tcubed));
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);
double DeltaAlpha = AASCoordinateTransformation.DMSToDegrees(0, 0, 0.0775 + 0.0850 * T);
AAS2DCoordinate value = new AAS2DCoordinate();
value.X = AASCoordinateTransformation.MapTo0To24Range(AASCoordinateTransformation.RadiansToHours(Math.Atan2(A, B) + zeta) + DeltaAlpha);
value.Y = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(C));
return(value);
}
public static AAS2DCoordinate 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 = AASCoordinateTransformation.HoursToRadians(Alpha);
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double sigma = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (2306.2181 + 1.39656 * T - 0.000139 * Tsquared) * t + (0.30188 - 0.000344 * T) * tsquared + 0.017998 * tcubed));
double zeta = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (2306.2181 + 1.39656 * T - 0.000139 * Tsquared) * t + (1.09468 + 0.000066 * T) * tsquared + 0.018203 * tcubed));
double phi = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (2004.3109 - 0.8533 * T - 0.000217 * Tsquared) * t - (0.42665 + 0.000217 * T) * tsquared - 0.041833 * tcubed));
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);
AAS2DCoordinate value = new AAS2DCoordinate();
value.X = AASCoordinateTransformation.MapTo0To24Range(AASCoordinateTransformation.RadiansToHours(Math.Atan2(A, B) + zeta));
value.Y = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(C));
return(value);
}
public static AAS2DCoordinate 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 = AASCoordinateTransformation.HoursToRadians(Alpha);
Delta = AASCoordinateTransformation.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;
AAS2DCoordinate value = new AAS2DCoordinate();
value.X = AASCoordinateTransformation.MapTo0To24Range(AASCoordinateTransformation.RadiansToHours(Math.Atan2(y, x)));
value.Y = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(z, Math.Sqrt(x * x + y * y)));
return(value);
}
public static AAS2DCoordinate EquatorialAberration(double Alpha, double Delta, double JD, bool bHighPrecision)
{
//Convert to radians
Alpha = AASCoordinateTransformation.DegreesToRadians(Alpha * 15);
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double cosAlpha = Math.Cos(Alpha);
double sinAlpha = Math.Sin(Alpha);
double cosDelta = Math.Cos(Delta);
double sinDelta = Math.Sin(Delta);
AAS3DCoordinate velocity = EarthVelocity(JD, bHighPrecision);
//What is the return value
AAS2DCoordinate aberration = new AAS2DCoordinate {
X = AASCoordinateTransformation.RadiansToHours((velocity.Y * cosAlpha - velocity.X * sinAlpha) / (17314463350.0 * cosDelta)), Y = AASCoordinateTransformation.RadiansToDegrees(-(((velocity.X * cosAlpha + velocity.Y * sinAlpha) * sinDelta - velocity.Z * cosDelta) / 17314463350.0))
};
return(aberration);
}
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);
}