public static CAA3DCoordinate EquatorialRectangularCoordinatesAnyEquinox(double JD, double JDEquinox) { CAA3DCoordinate @value = EquatorialRectangularCoordinatesJ2000(JD); @value = CAAFK5.ConvertVSOPToFK5AnyEquinox(@value, JDEquinox); return(@value); }
public static CAA3DCoordinate EquatorialRectangularCoordinatesB1950(double JD) { CAA3DCoordinate @value = EclipticRectangularCoordinatesJ2000(JD); @value = CAAFK5.ConvertVSOPToFK5B1950(@value); return(@value); }
public static double GeometricFK5EclipticLongitude(double JD) { //Convert to the FK5 stystem double Longitude = GeometricEclipticLongitude(JD); double Latitude = GeometricEclipticLatitude(JD); Longitude += CAAFK5.CorrectionInLongitude(Longitude, Latitude, JD); return(Longitude); }
//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); }
public static EPD Calculate(double JD, EO @object) { //What will the the return value EPD details = new EPD(); double JD0 = JD; double L0 = 0; double B0 = 0; double R0 = 0; double cosB0 = 0; if (@object != EO.SUN) { L0 = CAAEarth.EclipticLongitude(JD0); B0 = CAAEarth.EclipticLatitude(JD0); R0 = CAAEarth.RadiusVector(JD0); L0 = CT.D2R(L0); B0 = CT.D2R(B0); cosB0 = Math.Cos(B0); } //Calculate the initial values double L = 0; double B = 0; double R = 0; double Lrad; double Brad; double cosB; double cosL; double x; double y; double z; bool bRecalc = true; bool bFirstRecalc = true; double LPrevious = 0; double BPrevious = 0; double RPrevious = 0; while (bRecalc) { switch (@object) { case EO.SUN: { L = CAASun.GeometricEclipticLongitude(JD0); B = CAASun.GeometricEclipticLatitude(JD0); R = CAAEarth.RadiusVector(JD0); break; } case EO.MERCURY: { L = CAAMercury.EclipticLongitude(JD0); B = CAAMercury.EclipticLatitude(JD0); R = CAAMercury.RadiusVector(JD0); break; } case EO.VENUS: { L = CAAVenus.EclipticLongitude(JD0); B = CAAVenus.EclipticLatitude(JD0); R = CAAVenus.RadiusVector(JD0); break; } case EO.MARS: { L = CAAMars.EclipticLongitude(JD0); B = CAAMars.EclipticLatitude(JD0); R = CAAMars.RadiusVector(JD0); break; } case EO.JUPITER: { L = CAAJupiter.EclipticLongitude(JD0); B = CAAJupiter.EclipticLatitude(JD0); R = CAAJupiter.RadiusVector(JD0); break; } case EO.SATURN: { L = CAASaturn.EclipticLongitude(JD0); B = CAASaturn.EclipticLatitude(JD0); R = CAASaturn.RadiusVector(JD0); break; } case EO.URANUS: { L = CAAUranus.EclipticLongitude(JD0); B = CAAUranus.EclipticLatitude(JD0); R = CAAUranus.RadiusVector(JD0); break; } case EO.NEPTUNE: { L = CAANeptune.EclipticLongitude(JD0); B = CAANeptune.EclipticLatitude(JD0); R = CAANeptune.RadiusVector(JD0); break; } case EO.PLUTO: { L = CAAPluto.EclipticLongitude(JD0); B = CAAPluto.EclipticLatitude(JD0); R = CAAPluto.RadiusVector(JD0); break; } default: { Debug.Assert(false); 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 distance = 0; if (@object != EO.SUN) { Lrad = CT.D2R(L); Brad = CT.D2R(B); cosB = Math.Cos(Brad); 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); distance = Math.Sqrt(x * x + y * y + z * z); } else { distance = R; //Distance to the sun from the earth is in fact the radius vector } //Prepare for the next loop around JD0 = JD - ELL.DistanceToLightTime(distance); } } Lrad = CT.D2R(L); Brad = CT.D2R(B); cosB = Math.Cos(Brad); 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); double x2 = x * x; double y2 = y * y; details.ApparentGeocentricLatitude = CT.R2D(Math.Atan2(z, Math.Sqrt(x2 + y2))); details.ApparentGeocentricDistance = Math.Sqrt(x2 + y2 + z * z); details.ApparentGeocentricLongitude = CT.M360(CT.R2D(Math.Atan2(y, x))); details.ApparentLightTime = ELL.DistanceToLightTime(details.ApparentGeocentricDistance); //Adjust for Aberration COR Aberration = ABR.EclipticAberration(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD); details.ApparentGeocentricLongitude += Aberration.X; details.ApparentGeocentricLatitude += Aberration.Y; //convert to the FK5 system double DeltaLong = CAAFK5.CorrectionInLongitude(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, JD); details.ApparentGeocentricLatitude += CAAFK5.CorrectionInLatitude(details.ApparentGeocentricLongitude, JD); details.ApparentGeocentricLongitude += DeltaLong; //Correct for nutation double NutationInLongitude = CAANutation.NutationInLongitude(JD); double Epsilon = CAANutation.TrueObliquityOfEcliptic(JD); details.ApparentGeocentricLongitude += CT.DMS2D(0, 0, NutationInLongitude); //Convert to RA and Dec COR ApparentEqu = CT.Ec2Eq(details.ApparentGeocentricLongitude, details.ApparentGeocentricLatitude, Epsilon); details.ApparentGeocentricRA = ApparentEqu.X; details.ApparentGeocentricDeclination = ApparentEqu.Y; return(details); }