public static double DistanceFromGreatArc(double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3) { Delta1 = AASCoordinateTransformation.DegreesToRadians(Delta1); Delta2 = AASCoordinateTransformation.DegreesToRadians(Delta2); Delta3 = AASCoordinateTransformation.DegreesToRadians(Delta3); Alpha1 = AASCoordinateTransformation.HoursToRadians(Alpha1); Alpha2 = AASCoordinateTransformation.HoursToRadians(Alpha2); Alpha3 = AASCoordinateTransformation.HoursToRadians(Alpha3); double X1 = Math.Cos(Delta1) * Math.Cos(Alpha1); double X2 = Math.Cos(Delta2) * Math.Cos(Alpha2); double Y1 = Math.Cos(Delta1) * Math.Sin(Alpha1); double Y2 = Math.Cos(Delta2) * Math.Sin(Alpha2); double Z1 = Math.Sin(Delta1); double Z2 = Math.Sin(Delta2); double A = Y1 * Z2 - Z1 * Y2; double B = Z1 * X2 - X1 * Z2; double C = X1 * Y2 - Y1 * X2; double m = Math.Tan(Alpha3); double n = Math.Tan(Delta3) / Math.Cos(Alpha3); double value = Math.Asin((A + B * m + C * n) / (Math.Sqrt(A * A + B * B + C * C) * Math.Sqrt(1 + m * m + n * n))); value = AASCoordinateTransformation.RadiansToDegrees(value); if (value < 0) { value = Math.Abs(value); } return(value); }
public static CAAPhysicalMarsDetails Calculate(double JD, bool bHighPrecision) { //What will be the return value CAAPhysicalMarsDetails details = new CAAPhysicalMarsDetails(); //Step 1 double T = (JD - 2451545) / 36525; double Lambda0 = 352.9065 + 1.17330 * T; double Lambda0rad = AASCoordinateTransformation.DegreesToRadians(Lambda0); double Beta0 = 63.2818 - 0.00394 * T; double Beta0rad = AASCoordinateTransformation.DegreesToRadians(Beta0); //Step 2 double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision); double l0rad = AASCoordinateTransformation.DegreesToRadians(l0); double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision); double b0rad = AASCoordinateTransformation.DegreesToRadians(b0); double R = AASEarth.RadiusVector(JD, bHighPrecision); double PreviousLightTravelTime = 0; double LightTravelTime = 0; double x = 0; double y = 0; double z = 0; bool bIterate = true; double DELTA = 0; double l = 0; double lrad = 0; double b = 0; double r = 0; while (bIterate) { double JD2 = JD - LightTravelTime; //Step 3 l = AASMars.EclipticLongitude(JD2, bHighPrecision); lrad = AASCoordinateTransformation.DegreesToRadians(l); b = AASMars.EclipticLatitude(JD2, bHighPrecision); double brad = AASCoordinateTransformation.DegreesToRadians(b); r = AASMars.RadiusVector(JD2, 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); LightTravelTime = AASElliptical.DistanceToLightTime(DELTA); //Prepare for the next loop around bIterate = (Math.Abs(LightTravelTime - PreviousLightTravelTime) > 2E-6); //2E-6 correponds to 0.17 of a second if (bIterate) { PreviousLightTravelTime = LightTravelTime; } } //Step 5 double lambdarad = Math.Atan2(y, x); double lambda = AASCoordinateTransformation.RadiansToDegrees(lambdarad); double betarad = Math.Atan2(z, Math.Sqrt(x * x + y * y)); double beta = AASCoordinateTransformation.RadiansToDegrees(betarad); //Step 6 details.DE = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(betarad) - Math.Cos(Beta0rad) * Math.Cos(betarad) * Math.Cos(Lambda0rad - lambdarad))); //Step 7 double N = 49.5581 + 0.7721 * T; double Nrad = AASCoordinateTransformation.DegreesToRadians(N); double ldash = l - 0.00697 / r; double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash); double bdash = b - 0.000225 * (Math.Cos(lrad - Nrad) / r); double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash); //Step 8 details.DS = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(bdashrad) - Math.Cos(Beta0rad) * Math.Cos(bdashrad) * Math.Cos(Lambda0rad - ldashrad))); //Step 9 double W = AASCoordinateTransformation.MapTo0To360Range(11.504 + 350.89200025 * (JD - LightTravelTime - 2433282.5)); //Step 10 double e0 = AASNutation.MeanObliquityOfEcliptic(JD); double e0rad = AASCoordinateTransformation.DegreesToRadians(e0); AAS2DCoordinate PoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0); double alpha0rad = AASCoordinateTransformation.HoursToRadians(PoleEquatorial.X); double delta0rad = AASCoordinateTransformation.DegreesToRadians(PoleEquatorial.Y); //Step 11 double u = y * Math.Cos(e0rad) - z * Math.Sin(e0rad); double v = y * Math.Sin(e0rad) + z * Math.Cos(e0rad); double alpharad = Math.Atan2(u, x); double alpha = AASCoordinateTransformation.RadiansToHours(alpharad); double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u)); double delta = AASCoordinateTransformation.RadiansToDegrees(deltarad); double xi = Math.Atan2(Math.Sin(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad) - Math.Sin(deltarad) * Math.Cos(delta0rad), Math.Cos(deltarad) * Math.Sin(alpha0rad - alpharad)); //Step 12 details.w = AASCoordinateTransformation.MapTo0To360Range(W - AASCoordinateTransformation.RadiansToDegrees(xi)); //Step 13 double NutationInLongitude = AASNutation.NutationInLongitude(JD); double NutationInObliquity = AASNutation.NutationInObliquity(JD); //Step 14 lambda += 0.005693 * Math.Cos(l0rad - lambdarad) / Math.Cos(betarad); beta += 0.005693 * Math.Sin(l0rad - lambdarad) * Math.Sin(betarad); //Step 15 Lambda0 += NutationInLongitude / 3600; lambda += NutationInLongitude / 3600; e0 += NutationInObliquity / 3600; //Step 16 AAS2DCoordinate ApparentPoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0); double alpha0dash = AASCoordinateTransformation.HoursToRadians(ApparentPoleEquatorial.X); double delta0dash = AASCoordinateTransformation.DegreesToRadians(ApparentPoleEquatorial.Y); AAS2DCoordinate ApparentMars = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, e0); double alphadash = AASCoordinateTransformation.HoursToRadians(ApparentMars.X); double deltadash = AASCoordinateTransformation.DegreesToRadians(ApparentMars.Y); //Step 17 details.P = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0dash) * Math.Sin(alpha0dash - alphadash), Math.Sin(delta0dash) * Math.Cos(deltadash) - Math.Cos(delta0dash) * Math.Sin(deltadash) * Math.Cos(alpha0dash - alphadash)))); //Step 18 double SunLambda = AASSun.GeometricEclipticLongitude(JD, bHighPrecision); double SunBeta = AASSun.GeometricEclipticLatitude(JD, bHighPrecision); AAS2DCoordinate SunEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(SunLambda, SunBeta, e0); details.X = AASMoonIlluminatedFraction.PositionAngle(SunEquatorial.X, SunEquatorial.Y, alpha, delta); //Step 19 details.d = 9.36 / DELTA; details.k = AASIlluminatedFraction.IlluminatedFraction(r, R, DELTA); details.q = (1 - details.k) * details.d; return(details); }
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); }