public static void CalulateTrueAnnomalyAndRadius(double JD, ref AASNearParabolicObjectElements elements, ref double v, ref double r)
{
double k = 0.01720209895;
double a = 0.75 * (JD - elements.T) * k * Math.Sqrt((1 + elements.e) / (elements.q * elements.q * elements.q));
double b = Math.Sqrt(1 + a * a);
double W = Cbrt(b + a) - Cbrt(b - a);
double W2 = W * W;
double W4 = W2 * W2;
double f = (1 - elements.e) / (1 + elements.e);
double a1 = (2.0 / 3) + (0.4) * W2;
double a2 = (7.0 / 5) + (33.0 / 35) * W2 + (37.0 / 175) * W4;
double a3 = W2 * ((432.0 / 175) + (956.0 / 1125) * W2 + (84.0 / 1575) * W4);
double C = W2 / (1 + W2);
double g = f * C * C;
double w = W * (1 + f * C * (a1 + a2 * g + a3 * g * g));
double w2 = w * w;
v = 2 * Math.Atan(w);
r = elements.q * (1 + w2) / (1 + w2 * f);
}
public static AASNearParabolicObjectDetails Calculate(double JD, ref AASNearParabolicObjectElements elements, bool bHighPrecision)
{
double Epsilon = AASNutation.MeanObliquityOfEcliptic(elements.JDEquinox);
double JD0 = JD;
//What will be the return value
AASNearParabolicObjectDetails details = new AASNearParabolicObjectDetails();
Epsilon = AASCoordinateTransformation.DegreesToRadians(Epsilon);
double omega = AASCoordinateTransformation.DegreesToRadians(elements.omega);
double w = AASCoordinateTransformation.DegreesToRadians(elements.w);
double i = AASCoordinateTransformation.DegreesToRadians(elements.i);
double sinEpsilon = Math.Sin(Epsilon);
double cosEpsilon = Math.Cos(Epsilon);
double sinOmega = Math.Sin(omega);
double cosOmega = Math.Cos(omega);
double cosi = Math.Cos(i);
double sini = Math.Sin(i);
double F = cosOmega;
double G = sinOmega * cosEpsilon;
double H = sinOmega * sinEpsilon;
double P = -sinOmega * cosi;
double Q = cosOmega * cosi * cosEpsilon - sini * sinEpsilon;
double R = cosOmega * cosi * sinEpsilon + sini * cosEpsilon;
double a = Math.Sqrt(F * F + P * P);
double b = Math.Sqrt(G * G + Q * Q);
double c = Math.Sqrt(H * H + R * R);
double A = Math.Atan2(F, P);
double B = Math.Atan2(G, Q);
double C = Math.Atan2(H, R);
AAS3DCoordinate SunCoord = AASSun.EquatorialRectangularCoordinatesAnyEquinox(JD, elements.JDEquinox, bHighPrecision);
for (int j = 0; j < 2; j++)
{
double v = 0;
double r = 0;
CalulateTrueAnnomalyAndRadius(JD0, ref elements, ref v, ref r);
double x = r * a * Math.Sin(A + w + v);
double y = r * b * Math.Sin(B + w + v);
double z = r * c * Math.Sin(C + w + v);
if (j == 0)
{
details.HeliocentricRectangularEquatorial.X = x;
details.HeliocentricRectangularEquatorial.Y = y;
details.HeliocentricRectangularEquatorial.Z = z;
//Calculate the heliocentric ecliptic coordinates also
double u = w + v;
double cosu = Math.Cos(u);
double sinu = Math.Sin(u);
details.HeliocentricRectangularEcliptical.X = r * (cosOmega * cosu - sinOmega * sinu * cosi);
details.HeliocentricRectangularEcliptical.Y = r * (sinOmega * cosu + cosOmega * sinu * cosi);
details.HeliocentricRectangularEcliptical.Z = r * sini * sinu;
details.HeliocentricEclipticLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(details.HeliocentricRectangularEcliptical.Y, details.HeliocentricRectangularEcliptical.X)));
details.HeliocentricEclipticLatitude = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(details.HeliocentricRectangularEcliptical.Z / r));
}
double psi = SunCoord.X + x;
double nu = SunCoord.Y + y;
double sigma = SunCoord.Z + z;
double Alpha = Math.Atan2(nu, psi);
Alpha = AASCoordinateTransformation.RadiansToDegrees(Alpha);
double Delta = Math.Atan2(sigma, Math.Sqrt(psi * psi + nu * nu));
Delta = AASCoordinateTransformation.RadiansToDegrees(Delta);
double Distance = Math.Sqrt(psi * psi + nu * nu + sigma * sigma);
if (j == 0)
{
details.TrueGeocentricRA = AASCoordinateTransformation.MapTo0To24Range(Alpha / 15);
details.TrueGeocentricDeclination = Delta;
details.TrueGeocentricDistance = Distance;
details.TrueGeocentricLightTime = AASElliptical.DistanceToLightTime(Distance);
}
else
{
details.AstrometricGeocentricRA = AASCoordinateTransformation.MapTo0To24Range(Alpha / 15);
details.AstrometricGeocentricDeclination = Delta;
details.AstrometricGeocentricDistance = Distance;
details.AstrometricGeocentricLightTime = AASElliptical.DistanceToLightTime(Distance);
double RES = Math.Sqrt(SunCoord.X * SunCoord.X + SunCoord.Y * SunCoord.Y + SunCoord.Z * SunCoord.Z);
details.Elongation = AASCoordinateTransformation.RadiansToDegrees(Math.Acos((RES * RES + Distance * Distance - r * r) / (2 * RES * Distance)));
details.PhaseAngle = AASCoordinateTransformation.RadiansToDegrees(Math.Acos((r * r + Distance * Distance - RES * RES) / (2 * r * Distance)));
}
if (j == 0) //Prepare for the next loop around
{
JD0 = JD - details.TrueGeocentricLightTime;
}
}
return(details);
}