//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 = CT.D2R(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = CT.D2R(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 = CT.D2R(l0);
b0 += CAAFK5.CorrectionInLatitude(l0, JD);
double b0rad = CT.D2R(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 = ELL.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 = CT.D2R(l);
double brad = CT.D2R(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 = ELL.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 = CT.R2D(details.B);
//Step 7. Calculate the longitude of the ascending node of Saturn's orbit
double N = 113.6655 + 0.8771 * T;
double Nrad = CT.D2R(N);
double ldash = l - 0.01759 / r;
double ldashrad = CT.D2R(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = CT.D2R(bdash);
//Step 8. Calculate Bdash
details.Bdash = CT.R2D(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 = CT.R2D(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 += CT.D2R(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += CT.D2R(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 = CT.R2D(lambda);
lambda += NutationInLongitude / 3600;
lambda = CT.M360(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = CT.M360(lambda0);
//Step 14. Convert to equatorial coordinates
beta = CT.R2D(beta);
COR GeocentricEclipticSaturn = CT.Ec2Eq(lambda, beta, Obliquity);
double alpha = CT.H2R(GeocentricEclipticSaturn.X);
double delta = CT.D2R(GeocentricEclipticSaturn.Y);
COR GeocentricEclipticNorthPole = CT.Ec2Eq(lambda0, beta0, Obliquity);
double alpha0 = CT.H2R(GeocentricEclipticNorthPole.X);
double delta0 = CT.D2R(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = CT.R2D(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 CAASaturnRingDetails Calculate(double JD)
{
//What will be the return value
var details = new CAASaturnRingDetails();
var T = (JD - 2451545) / 36525;
var 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
var i = 28.075216 - 0.012998 *T + 0.000004 *T2;
var irad = CAACoordinateTransformation.DegreesToRadians(i);
var omega = 169.508470 + 1.394681 *T + 0.000412 *T2;
var omegarad = CAACoordinateTransformation.DegreesToRadians(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
var l0 = CAAEarth.EclipticLongitude(JD);
var b0 = CAAEarth.EclipticLatitude(JD);
l0 += CAAFK5.CorrectionInLongitude(l0, b0, JD);
var l0rad = CAACoordinateTransformation.DegreesToRadians(l0);
b0 += CAAFK5.CorrectionInLatitude(l0, JD);
var b0rad = CAACoordinateTransformation.DegreesToRadians(b0);
var 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;
var EarthLightTravelTime = CAAElliptical.DistanceToLightTime(DELTA);
var JD1 = JD - EarthLightTravelTime;
var 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);
var lrad = CAACoordinateTransformation.DegreesToRadians(l);
var 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
var lambda = Math.Atan2(y, x);
var 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
var N = 113.6655 + 0.8771 *T;
var Nrad = CAACoordinateTransformation.DegreesToRadians(N);
var ldash = l - 0.01759/r;
var ldashrad = CAACoordinateTransformation.DegreesToRadians(ldash);
var bdash = b - 0.000764 *Math.Cos(ldashrad - Nrad)/r;
var 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
var 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));
var 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
var Obliquity = CAANutation.TrueObliquityOfEcliptic(JD);
var NutationInLongitude = CAANutation.NutationInLongitude(JD);
//Step 11. Calculate the Ecliptical longitude and latitude of the northern pole of the ring plane
var lambda0 = omega - 90;
var 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);
var GeocentricEclipticSaturn = CAACoordinateTransformation.Ecliptic2Equatorial(lambda, beta, Obliquity);
var alpha = CAACoordinateTransformation.HoursToRadians(GeocentricEclipticSaturn.X);
var delta = CAACoordinateTransformation.DegreesToRadians(GeocentricEclipticSaturn.Y);
var GeocentricEclipticNorthPole = CAACoordinateTransformation.Ecliptic2Equatorial(lambda0, beta0, Obliquity);
var alpha0 = CAACoordinateTransformation.HoursToRadians(GeocentricEclipticNorthPole.X);
var 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;
}
