public static double MeanObliquityOfEcliptic(double JD)
{
double U = (JD - 2451545) / 3652500;
double Usquared = U * U;
double Ucubed = Usquared * U;
double U4 = Ucubed * U;
double U5 = U4 * U;
double U6 = U5 * U;
double U7 = U6 * U;
double U8 = U7 * U;
double U9 = U8 * U;
double U10 = U9 * U;
return(AASCoordinateTransformation.DMSToDegrees(23, 26, 21.448) - AASCoordinateTransformation.DMSToDegrees(0, 0, 4680.93) * U
- AASCoordinateTransformation.DMSToDegrees(0, 0, 1.55) * Usquared
+ AASCoordinateTransformation.DMSToDegrees(0, 0, 1999.25) * Ucubed
- AASCoordinateTransformation.DMSToDegrees(0, 0, 51.38) * U4
- AASCoordinateTransformation.DMSToDegrees(0, 0, 249.67) * U5
- AASCoordinateTransformation.DMSToDegrees(0, 0, 39.05) * U6
+ AASCoordinateTransformation.DMSToDegrees(0, 0, 7.12) * U7
+ AASCoordinateTransformation.DMSToDegrees(0, 0, 27.87) * U8
+ AASCoordinateTransformation.DMSToDegrees(0, 0, 5.79) * U9
+ AASCoordinateTransformation.DMSToDegrees(0, 0, 2.45) * U10);
}
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 AASPhysicalSunDetails Calculate(double JD)
{
double theta = AASCoordinateTransformation.MapTo0To360Range((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 = AASEarth.EclipticLongitude(JD);
double R = AASEarth.RadiusVector(JD);
double SunLong = L + 180 - AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
double epsilon = AASNutation.TrueObliquityOfEcliptic(JD);
//Convert to radians
epsilon = AASCoordinateTransformation.DegreesToRadians(epsilon);
SunLong = AASCoordinateTransformation.DegreesToRadians(SunLong);
K = AASCoordinateTransformation.DegreesToRadians(K);
I = AASCoordinateTransformation.DegreesToRadians(I);
theta = AASCoordinateTransformation.DegreesToRadians(theta);
double x = Math.Atan(-Math.Cos(SunLong) * Math.Tan(epsilon));
double y = Math.Atan(-Math.Cos(SunLong - K) * Math.Tan(I));
AASPhysicalSunDetails details = new AASPhysicalSunDetails();
details.P = AASCoordinateTransformation.RadiansToDegrees(x + y);
details.B0 = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(SunLong - K) * Math.Sin(I)));
double eta = Math.Atan(Math.Tan(SunLong - K) * Math.Cos(I));
details.L0 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(eta - theta));
return(details);
}
public static AAS2DCoordinate 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 = AASCoordinateTransformation.DegreesToRadians(Lambda);
Beta = AASCoordinateTransformation.DegreesToRadians(Beta);
double eta = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (47.0029 - 0.06603 * T + 0.000598 * Tsquared) * t + (-0.03302 + 0.000598 * T) * tsquared + 0.00006 * tcubed));
double pi = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, 174.876384 * 3600 + 3289.4789 * T + 0.60622 * Tsquared - (869.8089 + 0.50491 * T) * t + 0.03536 * tsquared));
double p = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, (5029.0966 + 2.22226 * T - 0.000042 * Tsquared) * t + (1.11113 - 0.000042 * T) * tsquared - 0.000006 * tcubed));
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);
AAS2DCoordinate value = new AAS2DCoordinate();
value.X = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(p + pi - Math.Atan2(A, B)));
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 double Calculate(double JD)
{
double rho = (JD - 2451545) / 365250;
double rhosquared = rho * rho;
double rhocubed = rhosquared * rho;
double rho4 = rhocubed * rho;
double rho5 = rho4 * rho;
//Calculate the Suns mean longitude
double L0 = AASCoordinateTransformation.MapTo0To360Range(280.4664567 + 360007.6982779 * rho + 0.03032028 * rhosquared +
rhocubed / 49931 - rho4 / 15300 - rho5 / 2000000);
//Calculate the Suns apparent right ascension
double SunLong = AASSun.ApparentEclipticLongitude(JD);
double SunLat = AASSun.ApparentEclipticLatitude(JD);
double epsilon = AASNutation.TrueObliquityOfEcliptic(JD);
AAS2DCoordinate Equatorial = AASCoordinateTransformation.Ecliptic2Equatorial(SunLong, SunLat, epsilon);
epsilon = AASCoordinateTransformation.DegreesToRadians(epsilon);
double E = L0 - 0.0057183 - Equatorial.X * 15 + AASCoordinateTransformation.DMSToDegrees(0, 0, AASNutation.NutationInLongitude(JD)) * Math.Cos(epsilon);
if (E > 180)
{
E = -(360 - E);
}
E *= 4; //Convert to minutes of time
return(E);
}
public static AASEclipticalElementDetails 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 = AASCoordinateTransformation.DegreesToRadians(i0);
double omega0rad = AASCoordinateTransformation.DegreesToRadians(omega0);
double eta = (47.0029 - 0.06603 * T + 0.000598 * Tsquared) * t + (-0.03302 + 0.000598 * T) * tsquared + 0.00006 * tcubed;
eta = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, eta));
double pi = 174.876384 * 3600 + 3289.4789 * T + 0.60622 * Tsquared - (869.8089 + 0.50491 * T) * t + 0.03536 * tsquared;
pi = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, pi));
double p = (5029.0966 + 2.22226 * T - 0.000042 * Tsquared) * t + (1.11113 - 0.000042 * T) * tsquared - 0.000006 * tcubed;
p = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(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));
AASEclipticalElementDetails details = new AASEclipticalElementDetails();
details.i = AASCoordinateTransformation.RadiansToDegrees(irad);
double cosi = cosi0rad * coseta + sini0rad * sineta * cosomega0rad_pi;
if (cosi < 0)
{
details.i = 180 - details.i;
}
double phi = pi + p;
details.omega = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(A, B) + phi));
A = -sineta * sinomega0rad_pi;
B = sini0rad * coseta - cosi0rad * sineta * cosomega0rad_pi;
double deltaw = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(A, B));
details.w = AASCoordinateTransformation.MapTo0To360Range(w0 + deltaw);
return(details);
}
public static double CorrectionInLatitude(double Longitude, double JD)
{
double T = (JD - 2451545) / 36525;
double Ldash = Longitude - 1.397 * T - 0.00031 * T * T;
//Convert to radians
Ldash = AASCoordinateTransformation.DegreesToRadians(Ldash);
double value = 0.03916 * (Math.Cos(Ldash) - Math.Sin(Ldash));
return(AASCoordinateTransformation.DMSToDegrees(0, 0, value));
}
public static double ApparentEclipticLongitude(double JD)
{
double Longitude = GeometricFK5EclipticLongitude(JD);
//Apply the correction in longitude due to nutation
Longitude += AASCoordinateTransformation.DMSToDegrees(0, 0, AASNutation.NutationInLongitude(JD));
//Apply the correction in longitude due to aberration
double R = AASEarth.RadiusVector(JD);
Longitude -= AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
return(Longitude);
}
public static AAS3DCoordinate ConvertVSOPToFK5AnyEquinox(AAS3DCoordinate value, double JDEquinox)
{
double t = (JDEquinox - 2451545.0) / 36525;
double tsquared = t * t;
double tcubed = tsquared * t;
double sigma = 2306.2181 * t + 0.30188 * tsquared + 0.017988 * tcubed;
sigma = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, sigma));
double zeta = 2306.2181 * t + 1.09468 * tsquared + 0.018203 * tcubed;
zeta = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, zeta));
double phi = 2004.3109 * t - 0.42665 * tsquared - 0.041833 * tcubed;
phi = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.DMSToDegrees(0, 0, phi));
double cossigma = Math.Cos(sigma);
double coszeta = Math.Cos(zeta);
double cosphi = Math.Cos(phi);
double sinsigma = Math.Sin(sigma);
double sinzeta = Math.Sin(zeta);
double sinphi = Math.Sin(phi);
double xx = cossigma * coszeta * cosphi - sinsigma * sinzeta;
double xy = sinsigma * coszeta + cossigma * sinzeta * cosphi;
double xz = cossigma * sinphi;
double yx = -cossigma * sinzeta - sinsigma * coszeta * cosphi;
double yy = cossigma * coszeta - sinsigma * sinzeta * cosphi;
double yz = -sinsigma * sinphi;
double zx = -coszeta * sinphi;
double zy = -sinzeta * sinphi;
double zz = cosphi;
AAS3DCoordinate result = new AAS3DCoordinate()
{
X = xx * value.X + yx * value.Y + zx * value.Z,
Y = xy * value.X + yy * value.Y + zy * value.Z,
Z = xz * value.X + yz * value.Y + zz * value.Z
};
return(result);
}
public static double ApparentEclipticLongitude(double JD, bool bHighPrecision)
{
double Longitude = GeometricFK5EclipticLongitude(JD, bHighPrecision);
//Apply the correction in longitude due to nutation
Longitude += AASCoordinateTransformation.DMSToDegrees(0, 0, AASNutation.NutationInLongitude(JD));
//Apply the correction in longitude due to aberration
double R = AASEarth.RadiusVector(JD, bHighPrecision);
if (bHighPrecision)
{
Longitude -= (0.005775518 * R * AASCoordinateTransformation.DMSToDegrees(0, 0, VariationGeometricEclipticLongitude(JD)));
}
else
{
Longitude -= AASCoordinateTransformation.DMSToDegrees(0, 0, 20.4898 / R);
}
return(Longitude);
}
public static double TrueObliquityOfEcliptic(double JD)
{
return(MeanObliquityOfEcliptic(JD) + AASCoordinateTransformation.DMSToDegrees(0, 0, NutationInObliquity(JD)));
}
public static AASEllipticalPlanetaryDetails Calculate(double JD, AASEllipticalObject ellipticalObject, bool bHighPrecision)
{
//What will the the return value
AASEllipticalPlanetaryDetails details = new AASEllipticalPlanetaryDetails();
//Calculate the position of the earth first
double JD0 = JD;
double L0 = AASEarth.EclipticLongitude(JD0, bHighPrecision);
double B0 = AASEarth.EclipticLatitude(JD0, bHighPrecision);
double R0 = AASEarth.RadiusVector(JD0, bHighPrecision);
L0 = AASCoordinateTransformation.DegreesToRadians(L0);
B0 = AASCoordinateTransformation.DegreesToRadians(B0);
double cosB0 = Math.Cos(B0);
//Iterate to find the positions adjusting for light-time correction if required
double L = 0;
double B = 0;
double R = 0;
if (ellipticalObject != AASEllipticalObject.SUN)
{
bool bRecalc = true;
bool bFirstRecalc = true;
double LPrevious = 0;
double BPrevious = 0;
double RPrevious = 0;
while (bRecalc)
{
switch (ellipticalObject)
{
case AASEllipticalObject.SUN:
L = AASSun.GeometricEclipticLongitude(JD0, bHighPrecision);
B = AASSun.GeometricEclipticLatitude(JD0, bHighPrecision);
R = AASEarth.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.MERCURY:
L = AASMercury.EclipticLongitude(JD0, bHighPrecision);
B = AASMercury.EclipticLatitude(JD0, bHighPrecision);
R = AASMercury.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.VENUS:
L = AASVenus.EclipticLongitude(JD0, bHighPrecision);
B = AASVenus.EclipticLatitude(JD0, bHighPrecision);
R = AASVenus.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.MARS:
L = AASMars.EclipticLongitude(JD0, bHighPrecision);
B = AASMars.EclipticLatitude(JD0, bHighPrecision);
R = AASMars.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.JUPITER:
L = AASJupiter.EclipticLongitude(JD0, bHighPrecision);
B = AASJupiter.EclipticLatitude(JD0, bHighPrecision);
R = AASJupiter.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.SATURN:
L = AASSaturn.EclipticLongitude(JD0, bHighPrecision);
B = AASSaturn.EclipticLatitude(JD0, bHighPrecision);
R = AASSaturn.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.URANUS:
L = AASUranus.EclipticLongitude(JD0, bHighPrecision);
B = AASUranus.EclipticLatitude(JD0, bHighPrecision);
R = AASUranus.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.NEPTUNE:
L = AASNeptune.EclipticLongitude(JD0, bHighPrecision);
B = AASNeptune.EclipticLatitude(JD0, bHighPrecision);
R = AASNeptune.RadiusVector(JD0, bHighPrecision);
break;
case AASEllipticalObject.PLUTO:
L = AASPluto.EclipticLongitude(JD0);
B = AASPluto.EclipticLatitude(JD0);
R = AASPluto.RadiusVector(JD0);
break;
default:
break;
}
if (!bFirstRecalc)
{
bRecalc = ((Math.Abs(L - LPrevious) > 0.00001) || (Math.Abs(B - BPrevious) > 0.00001) || (Math.Abs(R - RPrevious) > 0.000001));
LPrevious = L;
BPrevious = B;
RPrevious = R;
}
else
{
bFirstRecalc = false;
}
//Calculate the new value
if (bRecalc)
{
double Lrad = AASCoordinateTransformation.DegreesToRadians(L);
double Brad = AASCoordinateTransformation.DegreesToRadians(B);
double cosB = Math.Cos(Brad);
double cosL = Math.Cos(Lrad);
double x1 = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
double y1 = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
double z1 = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
double distance = Math.Sqrt(x1 * x1 + y1 * y1 + z1 * z1);
//Prepare for the next loop around
JD0 = JD - AASElliptical.DistanceToLightTime(distance);
}
}
}
double x = 0;
double y = 0;
double z = 0;
if (ellipticalObject != AASEllipticalObject.SUN)
{
double Lrad = AASCoordinateTransformation.DegreesToRadians(L);
double Brad = AASCoordinateTransformation.DegreesToRadians(B);
double cosB = Math.Cos(Brad);
double cosL = Math.Cos(Lrad);
x = R * cosB * cosL - R0 * cosB0 * Math.Cos(L0);
y = R * cosB * Math.Sin(Lrad) - R0 * cosB0 * Math.Sin(L0);
z = R * Math.Sin(Brad) - R0 * Math.Sin(B0);
}
else
{
x = -R0 *cosB0 *Math.Cos(L0);
y = -R0 *cosB0 *Math.Sin(L0);
z = -R0 *Math.Sin(B0);
}
double x2 = x * x;
double y2 = y * y;
details.ApparentGeocentricLatitude = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(z, Math.Sqrt(x2 + y2)));
details.ApparentGeocentricDistance = Math.Sqrt(x2 + y2 + z * z);
details.ApparentGeocentricLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(y, x)));
details.ApparentLightTime = AASElliptical.DistanceToLightTime(details.ApparentGeocentricDistance);
//Adjust for Aberration
AAS2DCoordinate Aberration = AASAberration.EclipticAberration(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD, bHighPrecision);
details.ApparentGeocentricLongitude += Aberration.X;
details.ApparentGeocentricLatitude += Aberration.Y;
//convert to the FK5 system
double DeltaLong = AASFK5.CorrectionInLongitude(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD);
details.ApparentGeocentricLatitude += AASFK5.CorrectionInLatitude(details.ApparentGeocentricLongitude, JD);
details.ApparentGeocentricLongitude += DeltaLong;
//Correct for nutation
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
double Epsilon = AASNutation.TrueObliquityOfEcliptic(JD);
details.ApparentGeocentricLongitude += AASCoordinateTransformation.DMSToDegrees(0, 0, NutationInLongitude);
//Convert to RA and Dec
AAS2DCoordinate ApparentEqu = AASCoordinateTransformation.Ecliptic2Equatorial(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, Epsilon);
details.ApparentGeocentricRA = ApparentEqu.X;
details.ApparentGeocentricDeclination = ApparentEqu.Y;
return(details);
}