public static double GeometricFK5EclipticLatitude(double JD, bool bHighPrecision)
{
//Convert to the FK5 stystem
double Longitude = GeometricEclipticLongitude(JD, bHighPrecision);
double Latitude = GeometricEclipticLatitude(JD, bHighPrecision);
double SunLatCorrection = AASFK5.CorrectionInLatitude(Longitude, JD);
Latitude += SunLatCorrection;
return(Latitude);
}
public static AASSaturnRingDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
AASSaturnRingDetails details = new AASSaturnRingDetails();
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 = AASCoordinateTransformation.DegreesToRadians(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = AASCoordinateTransformation.DegreesToRadians(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
l0 += AASFK5.CorrectionInLongitude(l0, b0, JD);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
b0 += AASFK5.CorrectionInLatitude(l0, JD);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
//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 = AASElliptical.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 = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
b = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
l += AASFK5.CorrectionInLongitude(l, b, JD1);
b += AASFK5.CorrectionInLatitude(l, JD1);
double lrad = AASCoordinateTransformation.DegreesToRadians(l);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASSaturn.RadiusVector(JD1, 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);
EarthLightTravelTime = AASElliptical.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 = AASCoordinateTransformation.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 = AASCoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.01759 / r;
double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash);
//Step 8. Calculate Bdash
details.Bdash = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad) - Math.Cos(irad) * Math.Sin(bdashrad)));
//Step 9. Calculate DeltaU
details.U1 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(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))));
details.U2 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(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 = Math.Abs(details.U1 - details.U2);
if (details.DeltaU > 180)
{
details.DeltaU = 360 - details.DeltaU;
}
//Step 10. Calculate the Nutations
double Obliquity = AASNutation.TrueObliquityOfEcliptic(JD);
double NutationInLongitude = AASNutation.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 += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Sin(l0rad - lambda) * Math.Sin(beta));
//Step 13. Add nutation in longitude to lambda0 and lambda
lambda = AASCoordinateTransformation.RadiansToDegrees(lambda);
lambda += NutationInLongitude / 3600;
lambda = AASCoordinateTransformation.MapTo0To360Range(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = AASCoordinateTransformation.MapTo0To360Range(lambda0);
//Step 14. Convert to equatorial coordinates
beta = AASCoordinateTransformation.RadiansToDegrees(beta);
AAS2DCoordinate GeocentricEclipticSaturn = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, Obliquity);
double alpha = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticSaturn.X);
double delta = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticSaturn.Y);
AAS2DCoordinate GeocentricEclipticNorthPole = AASCoordinateTransformation.Ecliptic2Equatorial(lambda0, beta0, Obliquity);
double alpha0 = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticNorthPole.X);
double delta0 = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = AASCoordinateTransformation.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);
}
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);
}