public static AASSaturnMoonsDetails Calculate(double JD, bool bHighPrecision)
        {
            //Calculate the position of the Sun
            double sunlong    = AASSun.GeometricEclipticLongitude(JD, bHighPrecision);
            double sunlongrad = AASCoordinateTransformation.DegreesToRadians(sunlong);
            double beta       = AASSun.GeometricEclipticLatitude(JD, bHighPrecision);
            double betarad    = AASCoordinateTransformation.DegreesToRadians(beta);
            double R          = AASEarth.RadiusVector(JD, bHighPrecision);

            //Calculate the the light travel time from Saturn to the Earth
            double DELTA = 9;
            double PreviousEarthLightTravelTime = 0;
            double EarthLightTravelTime         = AASElliptical.DistanceToLightTime(DELTA);
            double JD1      = JD - EarthLightTravelTime;
            bool   bIterate = true;
            double x;
            double y;
            double z;

            while (bIterate)
            {
                //Calculate the position of Jupiter
                double l    = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
                double lrad = AASCoordinateTransformation.DegreesToRadians(l);
                double b    = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
                double brad = AASCoordinateTransformation.DegreesToRadians(b);
                double r    = AASSaturn.RadiusVector(JD1, bHighPrecision);

                x     = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
                y     = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
                z     = r * Math.Sin(brad) + R * Math.Sin(betarad);
                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;
                }
            }

            //Calculate the details as seen from the earth
            AASSaturnMoonsDetails details1 = CalculateHelper(JD, sunlongrad, betarad, R, bHighPrecision);
            var details1Satellite1         = details1.Satellite1;
            var details1Satellite2         = details1.Satellite2;
            var details1Satellite3         = details1.Satellite3;
            var details1Satellite4         = details1.Satellite4;
            var details1Satellite5         = details1.Satellite5;
            var details1Satellite6         = details1.Satellite6;
            var details1Satellite7         = details1.Satellite7;
            var details1Satellite8         = details1.Satellite8;

            FillInPhenomenaDetails(ref details1Satellite1);
            FillInPhenomenaDetails(ref details1Satellite2);
            FillInPhenomenaDetails(ref details1Satellite3);
            FillInPhenomenaDetails(ref details1Satellite4);
            FillInPhenomenaDetails(ref details1Satellite5);
            FillInPhenomenaDetails(ref details1Satellite6);
            FillInPhenomenaDetails(ref details1Satellite7);
            FillInPhenomenaDetails(ref details1Satellite8);


            //Calculate the the light travel time from Saturn to the Sun
            JD1 = JD - EarthLightTravelTime;
            {
                double l    = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
                double lrad = AASCoordinateTransformation.DegreesToRadians(l);
                double b    = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
                double brad = AASCoordinateTransformation.DegreesToRadians(b);
                double r    = AASSaturn.RadiusVector(JD1, bHighPrecision);
                x = r * Math.Cos(brad) * Math.Cos(lrad);
                y = r * Math.Cos(brad) * Math.Sin(lrad);
                z = r * Math.Sin(brad);
            }

            DELTA = Math.Sqrt(x * x + y * y + z * z);
            double SunLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);

            //Calculate the details as seen from the Sun
            AASSaturnMoonsDetails details2 = CalculateHelper(JD + SunLightTravelTime - EarthLightTravelTime, sunlongrad, betarad, 0, bHighPrecision);
            var details2Satellite1         = details2.Satellite1;
            var details2Satellite2         = details2.Satellite2;
            var details2Satellite3         = details2.Satellite3;
            var details2Satellite4         = details2.Satellite4;
            var details2Satellite5         = details2.Satellite5;
            var details2Satellite6         = details2.Satellite6;
            var details2Satellite7         = details2.Satellite7;
            var details2Satellite8         = details2.Satellite8;

            FillInPhenomenaDetails(ref details2Satellite1);
            FillInPhenomenaDetails(ref details2Satellite2);
            FillInPhenomenaDetails(ref details2Satellite3);
            FillInPhenomenaDetails(ref details2Satellite4);
            FillInPhenomenaDetails(ref details2Satellite5);
            FillInPhenomenaDetails(ref details2Satellite6);
            FillInPhenomenaDetails(ref details2Satellite7);
            FillInPhenomenaDetails(ref details2Satellite8);

            //Finally transfer the required values from details2 to details1
            details1.Satellite1.bInEclipse       = details2.Satellite1.bInOccultation;
            details1.Satellite2.bInEclipse       = details2.Satellite2.bInOccultation;
            details1.Satellite3.bInEclipse       = details2.Satellite3.bInOccultation;
            details1.Satellite4.bInEclipse       = details2.Satellite4.bInOccultation;
            details1.Satellite5.bInEclipse       = details2.Satellite5.bInOccultation;
            details1.Satellite6.bInEclipse       = details2.Satellite6.bInOccultation;
            details1.Satellite7.bInEclipse       = details2.Satellite7.bInOccultation;
            details1.Satellite8.bInEclipse       = details2.Satellite8.bInOccultation;
            details1.Satellite1.bInShadowTransit = details2.Satellite1.bInTransit;
            details1.Satellite2.bInShadowTransit = details2.Satellite2.bInTransit;
            details1.Satellite3.bInShadowTransit = details2.Satellite3.bInTransit;
            details1.Satellite4.bInShadowTransit = details2.Satellite4.bInTransit;
            details1.Satellite5.bInShadowTransit = details2.Satellite5.bInTransit;
            details1.Satellite6.bInShadowTransit = details2.Satellite6.bInTransit;
            details1.Satellite7.bInShadowTransit = details2.Satellite7.bInTransit;
            details1.Satellite8.bInShadowTransit = details2.Satellite8.bInTransit;

            return(details1);
        }
        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);
        }
        private static AASSaturnMoonsDetails CalculateHelper(double JD, double sunlongrad, double betarad, double R, bool bHighPrecision)
        {
            //What will be the return value
            AASSaturnMoonsDetails details = new AASSaturnMoonsDetails();

            //Calculate the position of Saturn decreased by the light travel time from Saturn to the specified position
            double DELTA = 9;
            double PreviousLightTravelTime = 0;
            double LightTravelTime         = AASElliptical.DistanceToLightTime(DELTA);
            double x        = 0;
            double y        = 0;
            double z        = 0;
            double JD1      = JD - LightTravelTime;
            bool   bIterate = true;

            while (bIterate)
            {
                //Calculate the position of Saturn
                double l    = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
                double lrad = AASCoordinateTransformation.DegreesToRadians(l);
                double b    = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
                double brad = AASCoordinateTransformation.DegreesToRadians(b);
                double r    = AASSaturn.RadiusVector(JD1, bHighPrecision);

                x               = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
                y               = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
                z               = r * Math.Sin(brad) + R * Math.Sin(betarad);
                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 corresponds to 0.17 of a second
                if (bIterate)
                {
                    JD1 = JD - LightTravelTime;
                    PreviousLightTravelTime = LightTravelTime;
                }
            }

            //Calculate Saturn's Longitude and Latitude
            double lambda0 = Math.Atan2(y, x);

            lambda0 = AASCoordinateTransformation.RadiansToDegrees(lambda0);
            double beta0 = Math.Atan(z / Math.Sqrt(x * x + y * y));

            beta0 = AASCoordinateTransformation.RadiansToDegrees(beta0);

            //Precess the longtitude and Latitutude to B1950.0
            AAS2DCoordinate Saturn1950 = AASPrecession.PrecessEcliptic(lambda0, beta0, JD, 2433282.4235);

            lambda0 = Saturn1950.X;
            double lambda0rad = AASCoordinateTransformation.DegreesToRadians(lambda0);

            beta0 = Saturn1950.Y;
            double beta0rad = AASCoordinateTransformation.DegreesToRadians(beta0);

            double JDE = JD - LightTravelTime;

            double t1   = JDE - 2411093.0;
            double t2   = t1 / 365.25;
            double t3   = ((JDE - 2433282.423) / 365.25) + 1950.0;
            double t4   = JDE - 2411368.0;
            double t5   = t4 / 365.25;
            double t6   = JDE - 2415020.0;
            double t7   = t6 / 36525.0;
            double t8   = t6 / 365.25;
            double t9   = (JDE - 2442000.5) / 365.25;
            double t10  = JDE - 2409786.0;
            double t11  = t10 / 36525.0;
            double t112 = t11 * t11;
            double t113 = t112 * t11;

            double W0    = AASCoordinateTransformation.MapTo0To360Range(5.095 * (t3 - 1866.39));
            double W0rad = AASCoordinateTransformation.DegreesToRadians(W0);
            double W1    = AASCoordinateTransformation.MapTo0To360Range(74.4 + 32.39 * t2);
            double W1rad = AASCoordinateTransformation.DegreesToRadians(W1);
            double W2    = AASCoordinateTransformation.MapTo0To360Range(134.3 + 92.62 * t2);
            double W2rad = AASCoordinateTransformation.DegreesToRadians(W2);
            double W3    = AASCoordinateTransformation.MapTo0To360Range(42.0 - 0.5118 * t5);
            double W3rad = AASCoordinateTransformation.DegreesToRadians(W3);
            double W4    = AASCoordinateTransformation.MapTo0To360Range(276.59 + 0.5118 * t5);
            double W4rad = AASCoordinateTransformation.DegreesToRadians(W4);
            double W5    = AASCoordinateTransformation.MapTo0To360Range(267.2635 + 1222.1136 * t7);
            double W5rad = AASCoordinateTransformation.DegreesToRadians(W5);
            double W6    = AASCoordinateTransformation.MapTo0To360Range(175.4762 + 1221.5515 * t7);
            double W6rad = AASCoordinateTransformation.DegreesToRadians(W6);
            double W7    = AASCoordinateTransformation.MapTo0To360Range(2.4891 + 0.002435 * t7);
            double W7rad = AASCoordinateTransformation.DegreesToRadians(W7);
            double W8    = AASCoordinateTransformation.MapTo0To360Range(113.35 - 0.2597 * t7);
            double W8rad = AASCoordinateTransformation.DegreesToRadians(W8);

            double s1 = Math.Sin(AASCoordinateTransformation.DegreesToRadians(28.0817));
            double s2 = Math.Sin(AASCoordinateTransformation.DegreesToRadians(168.8112));
            double c1 = Math.Cos(AASCoordinateTransformation.DegreesToRadians(28.0817));
            double c2 = Math.Cos(AASCoordinateTransformation.DegreesToRadians(168.8112));
            double e1 = 0.05589 - 0.000346 * t7;


            //Satellite 1
            double L       = AASCoordinateTransformation.MapTo0To360Range(127.64 + 381.994497 * t1 - 43.57 * Math.Sin(W0rad) - 0.720 * Math.Sin(3 * W0rad) - 0.02144 * Math.Sin(5 * W0rad));
            double p       = 106.1 + 365.549 * t2;
            double M       = L - p;
            double Mrad    = AASCoordinateTransformation.DegreesToRadians(M);
            double C       = 2.18287 * Math.Sin(Mrad) + 0.025988 * Math.Sin(2 * Mrad) + 0.00043 * Math.Sin(3 * Mrad);
            double Crad    = AASCoordinateTransformation.DegreesToRadians(C);
            double lambda1 = AASCoordinateTransformation.MapTo0To360Range(L + C);
            double r1      = 3.06879 / (1 + 0.01905 * Math.Cos(Mrad + Crad));
            double gamma1  = 1.563;
            double omega1  = AASCoordinateTransformation.MapTo0To360Range(54.5 - 365.072 * t2);

            //Satellite 2
            L    = AASCoordinateTransformation.MapTo0To360Range(200.317 + 262.7319002 * t1 + 0.25667 * Math.Sin(W1rad) + 0.20883 * Math.Sin(W2rad));
            p    = 309.107 + 123.44121 * t2;
            M    = L - p;
            Mrad = AASCoordinateTransformation.DegreesToRadians(M);
            C    = 0.55577 * Math.Sin(Mrad) + 0.00168 * Math.Sin(2 * Mrad);
            Crad = AASCoordinateTransformation.DegreesToRadians(C);
            double lambda2 = AASCoordinateTransformation.MapTo0To360Range(L + C);
            double r2      = 3.94118 / (1 + 0.00485 * Math.Cos(Mrad + Crad));
            double gamma2  = 0.0262;
            double omega2  = AASCoordinateTransformation.MapTo0To360Range(348 - 151.95 * t2);

            //Satellite 3
            double lambda3 = AASCoordinateTransformation.MapTo0To360Range(285.306 + 190.69791226 * t1 + 2.063 * Math.Sin(W0rad) + 0.03409 * Math.Sin(3 * W0rad) + 0.001015 * Math.Sin(5 * W0rad));
            double r3      = 4.880998;
            double gamma3  = 1.0976;
            double omega3  = AASCoordinateTransformation.MapTo0To360Range(111.33 - 72.2441 * t2);

            //Satellite 4
            L    = AASCoordinateTransformation.MapTo0To360Range(254.712 + 131.53493193 * t1 - 0.0215 * Math.Sin(W1rad) - 0.01733 * Math.Sin(W2rad));
            p    = 174.8 + 30.820 * t2;
            M    = L - p;
            Mrad = AASCoordinateTransformation.DegreesToRadians(M);
            C    = 0.24717 * Math.Sin(Mrad) + 0.00033 * Math.Sin(2 * Mrad);
            Crad = AASCoordinateTransformation.DegreesToRadians(C);
            double lambda4 = AASCoordinateTransformation.MapTo0To360Range(L + C);
            double r4      = 6.24871 / (1 + 0.002157 * Math.Cos(Mrad + Crad));
            double gamma4  = 0.0139;
            double omega4  = AASCoordinateTransformation.MapTo0To360Range(232 - 30.27 * t2);

            //Satellite 5
            double pdash    = 342.7 + 10.057 * t2;
            double pdashrad = AASCoordinateTransformation.DegreesToRadians(pdash);
            double a1       = 0.000265 * Math.Sin(pdashrad) + 0.001 * Math.Sin(W4rad); //Note the book uses the incorrect constant 0.01*Math.Sin(W4rad);
            double a2       = 0.000265 * Math.Cos(pdashrad) + 0.001 * Math.Cos(W4rad); //Note the book uses the incorrect constant 0.01*cos(W4rad);
            double e        = Math.Sqrt(a1 * a1 + a2 * a2);

            p = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(a1, a2));
            double N          = 345 - 10.057 * t2;
            double Nrad       = AASCoordinateTransformation.DegreesToRadians(N);
            double lambdadash = AASCoordinateTransformation.MapTo0To360Range(359.244 + 79.69004720 * t1 + 0.086754 * Math.Sin(Nrad));
            double i          = 28.0362 + 0.346898 * Math.Cos(Nrad) + 0.01930 * Math.Cos(W3rad);
            double omega      = 168.8034 + 0.736936 * Math.Sin(Nrad) + 0.041 * Math.Sin(W3rad);
            double a          = 8.725924;
            double lambda5    = 0;
            double gamma5     = 0;
            double omega5     = 0;
            double r5         = 0;

            HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r5, ref lambda5, ref gamma5, ref omega5);

            //Satellite 6
            L = 261.1582 + 22.57697855 * t4 + 0.074025 * Math.Sin(W3rad);
            double idash        = 27.45141 + 0.295999 * Math.Cos(W3rad);
            double idashrad     = AASCoordinateTransformation.DegreesToRadians(idash);
            double omegadash    = 168.66925 + 0.628808 * Math.Sin(W3rad);
            double omegadashrad = AASCoordinateTransformation.DegreesToRadians(omegadash);

            a1 = Math.Sin(W7rad) * Math.Sin(omegadashrad - W8rad);
            a2 = Math.Cos(W7rad) * Math.Sin(idashrad) - Math.Sin(W7rad) * Math.Cos(idashrad) * Math.Cos(omegadashrad - W8rad);
            double g0  = AASCoordinateTransformation.DegreesToRadians(102.8623);
            double psi = Math.Atan2(a1, a2);

            if (a2 < 0)
            {
                psi += AASCoordinateTransformation.PI();
            }
            double psideg = AASCoordinateTransformation.RadiansToDegrees(psi);
            double s      = Math.Sqrt(a1 * a1 + a2 * a2);
            double g      = W4 - omegadash - psideg;
            double w_     = 0;

            for (int j = 0; j < 3; j++)
            {
                w_ = W4 + 0.37515 * (Math.Sin(2 * AASCoordinateTransformation.DegreesToRadians(g)) - Math.Sin(2 * g0));
                g  = w_ - omegadash - psideg;
            }
            double grad     = AASCoordinateTransformation.DegreesToRadians(g);
            double edash    = 0.029092 + 0.00019048 * (Math.Cos(2 * grad) - Math.Cos(2 * g0));
            double q        = AASCoordinateTransformation.DegreesToRadians(2 * (W5 - w_));
            double b1       = Math.Sin(idashrad) * Math.Sin(omegadashrad - W8rad);
            double b2       = Math.Cos(W7rad) * Math.Sin(idashrad) * Math.Cos(omegadashrad - W8rad) - Math.Sin(W7rad) * Math.Cos(idashrad);
            double atanb1b2 = Math.Atan2(b1, b2);
            double theta    = atanb1b2 + W8rad;

            e = edash + 0.002778797 * edash * Math.Cos(q);
            p = w_ + 0.159215 * Math.Sin(q);
            double u = 2 * W5rad - 2 * theta + psi;
            double h = 0.9375 * edash * edash * Math.Sin(q) + 0.1875 * s * s * Math.Sin(2 * (W5rad - theta));

            lambdadash = AASCoordinateTransformation.MapTo0To360Range(L - 0.254744 * (e1 * Math.Sin(W6rad) + 0.75 * e1 * e1 * Math.Sin(2 * W6rad) + h));
            i          = idash + 0.031843 * s * Math.Cos(u);
            omega      = omegadash + (0.031843 * s * Math.Sin(u)) / Math.Sin(idashrad);
            a          = 20.216193;
            double lambda6 = 0;
            double gamma6  = 0;
            double omega6  = 0;
            double r6      = 0;

            HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r6, ref lambda6, ref gamma6, ref omega6);

            //Satellite 7
            double eta     = 92.39 + 0.5621071 * t6;
            double etarad  = AASCoordinateTransformation.DegreesToRadians(eta);
            double zeta    = 148.19 - 19.18 * t8;
            double zetarad = AASCoordinateTransformation.DegreesToRadians(zeta);

            theta = AASCoordinateTransformation.DegreesToRadians(184.8 - 35.41 * t9);
            double thetadash = theta - AASCoordinateTransformation.DegreesToRadians(7.5);
            double aS        = AASCoordinateTransformation.DegreesToRadians(176 + 12.22 * t8);
            double bs        = AASCoordinateTransformation.DegreesToRadians(8 + 24.44 * t8);
            double cs        = bs + AASCoordinateTransformation.DegreesToRadians(5);

            w_ = 69.898 - 18.67088 * t8;
            double phi    = 2 * (w_ - W5);
            double phirad = AASCoordinateTransformation.DegreesToRadians(phi);
            double chi    = 94.9 - 2.292 * t8;
            double chirad = AASCoordinateTransformation.DegreesToRadians(chi);

            a = 24.50601 - 0.08686 * Math.Cos(etarad) - 0.00166 * Math.Cos(zetarad + etarad) + 0.00175 * Math.Cos(zetarad - etarad);
            e = 0.103458 - 0.004099 * Math.Cos(etarad) - 0.000167 * Math.Cos(zetarad + etarad) + 0.000235 * Math.Cos(zetarad - etarad) +
                0.02303 * Math.Cos(zetarad) - 0.00212 * Math.Cos(2 * zetarad) + 0.000151 * Math.Cos(3 * zetarad) + 0.00013 * Math.Cos(phirad);
            p = w_ + 0.15648 * Math.Sin(chirad) - 0.4457 * Math.Sin(etarad) - 0.2657 * Math.Sin(zetarad + etarad) +
                -0.3573 * Math.Sin(zetarad - etarad) - 12.872 * Math.Sin(zetarad) + 1.668 * Math.Sin(2 * zetarad) +
                -0.2419 * Math.Sin(3 * zetarad) - 0.07 * Math.Sin(phirad);
            lambdadash = AASCoordinateTransformation.MapTo0To360Range(177.047 + 16.91993829 * t6 + 0.15648 * Math.Sin(chirad) + 9.142 * Math.Sin(etarad) +
                                                                      0.007 * Math.Sin(2 * etarad) - 0.014 * Math.Sin(3 * etarad) + 0.2275 * Math.Sin(zetarad + etarad) +
                                                                      0.2112 * Math.Sin(zetarad - etarad) - 0.26 * Math.Sin(zetarad) - 0.0098 * Math.Sin(2 * zetarad) +
                                                                      -0.013 * Math.Sin(aS) + 0.017 * Math.Sin(bs) - 0.0303 * Math.Sin(phirad));
            i     = 27.3347 + 0.643486 * Math.Cos(chirad) + 0.315 * Math.Cos(W3rad) + 0.018 * Math.Cos(theta) - 0.018 * Math.Cos(cs);
            omega = 168.6812 + 1.40136 * Math.Cos(chirad) + 0.68599 * Math.Sin(W3rad) - 0.0392 * Math.Sin(cs) + 0.0366 * Math.Sin(thetadash);
            double lambda7 = 0;
            double gamma7  = 0;
            double omega7  = 0;
            double r7      = 0;

            HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r7, ref lambda7, ref gamma7, ref omega7);

            //Satellite 8
            L = AASCoordinateTransformation.MapTo0To360Range(261.1582 + 22.57697855 * t4);
            double w_dash = 91.796 + 0.562 * t7;

            psi = 4.367 - 0.195 * t7;
            double psirad = AASCoordinateTransformation.DegreesToRadians(psi);

            theta  = 146.819 - 3.198 * t7;
            phi    = 60.470 + 1.521 * t7;
            phirad = AASCoordinateTransformation.DegreesToRadians(phi);
            double PHI = 205.055 - 2.091 * t7;

            edash = 0.028298 + 0.001156 * t11;
            double w_0 = 352.91 + 11.71 * t11;
            double mu  = AASCoordinateTransformation.MapTo0To360Range(76.3852 + 4.53795125 * t10);

            idash     = 18.4602 - 0.9518 * t11 - 0.072 * t112 + 0.0054 * t113;
            idashrad  = AASCoordinateTransformation.DegreesToRadians(idash);
            omegadash = 143.198 - 3.919 * t11 + 0.116 * t112 + 0.008 * t113;
            double _l = AASCoordinateTransformation.DegreesToRadians(mu - w_0);

            g = AASCoordinateTransformation.DegreesToRadians(w_0 - omegadash - psi);
            double g1 = AASCoordinateTransformation.DegreesToRadians(w_0 - omegadash - phi);
            double ls = AASCoordinateTransformation.DegreesToRadians(W5 - w_dash);
            double gs = AASCoordinateTransformation.DegreesToRadians(w_dash - theta);
            double lt = AASCoordinateTransformation.DegreesToRadians(L - W4);
            double gt = AASCoordinateTransformation.DegreesToRadians(W4 - PHI);
            double u1 = 2 * (_l + g - ls - gs);
            double u2 = _l + g1 - lt - gt;
            double u3 = _l + 2 * (g - ls - gs);
            double u4 = lt + gt - g1;
            double u5 = 2 * (ls + gs);

            a = 58.935028 + 0.004638 * Math.Cos(u1) + 0.058222 * Math.Cos(u2);
            e = edash - 0.0014097 * Math.Cos(g1 - gt) + 0.0003733 * Math.Cos(u5 - 2 * g) +
                0.0001180 * Math.Cos(u3) + 0.0002408 * Math.Cos(_l) +
                0.0002849 * Math.Cos(_l + u2) + 0.0006190 * Math.Cos(u4);
            double w = 0.08077 * Math.Sin(g1 - gt) + 0.02139 * Math.Sin(u5 - 2 * g) - 0.00676 * Math.Sin(u3) +
                       0.01380 * Math.Sin(_l) + 0.01632 * Math.Sin(_l + u2) + 0.03547 * Math.Sin(u4);

            p          = w_0 + w / edash;
            lambdadash = mu - 0.04299 * Math.Sin(u2) - 0.00789 * Math.Sin(u1) - 0.06312 * Math.Sin(ls) +
                         -0.00295 * Math.Sin(2 * ls) - 0.02231 * Math.Sin(u5) + 0.00650 * Math.Sin(u5 + psirad);
            i = idash + 0.04204 * Math.Cos(u5 + psirad) + 0.00235 * Math.Cos(_l + g1 + lt + gt + phirad) +
                0.00360 * Math.Cos(u2 + phirad);
            double wdash = 0.04204 * Math.Sin(u5 + psirad) + 0.00235 * Math.Sin(_l + g1 + lt + gt + phirad) +
                           0.00358 * Math.Sin(u2 + phirad);

            omega = omegadash + wdash / Math.Sin(idashrad);
            double lambda8 = 0;
            double gamma8  = 0;
            double omega8  = 0;
            double r8      = 0;

            HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r8, ref lambda8, ref gamma8, ref omega8);


            u = AASCoordinateTransformation.DegreesToRadians(lambda1 - omega1);
            w = AASCoordinateTransformation.DegreesToRadians(omega1 - 168.8112);
            double gamma1rad = AASCoordinateTransformation.DegreesToRadians(gamma1);
            double X1        = r1 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma1rad) * Math.Sin(w));
            double Y1        = r1 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma1rad) + Math.Cos(u) * Math.Sin(w));
            double Z1        = r1 * Math.Sin(u) * Math.Sin(gamma1rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda2 - omega2);
            w = AASCoordinateTransformation.DegreesToRadians(omega2 - 168.8112);
            double gamma2rad = AASCoordinateTransformation.DegreesToRadians(gamma2);
            double X2        = r2 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma2rad) * Math.Sin(w));
            double Y2        = r2 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma2rad) + Math.Cos(u) * Math.Sin(w));
            double Z2        = r2 * Math.Sin(u) * Math.Sin(gamma2rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda3 - omega3);
            w = AASCoordinateTransformation.DegreesToRadians(omega3 - 168.8112);
            double gamma3rad = AASCoordinateTransformation.DegreesToRadians(gamma3);
            double X3        = r3 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma3rad) * Math.Sin(w));
            double Y3        = r3 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma3rad) + Math.Cos(u) * Math.Sin(w));
            double Z3        = r3 * Math.Sin(u) * Math.Sin(gamma3rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda4 - omega4);
            w = AASCoordinateTransformation.DegreesToRadians(omega4 - 168.8112);
            double gamma4rad = AASCoordinateTransformation.DegreesToRadians(gamma4);
            double X4        = r4 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma4rad) * Math.Sin(w));
            double Y4        = r4 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma4rad) + Math.Cos(u) * Math.Sin(w));
            double Z4        = r4 * Math.Sin(u) * Math.Sin(gamma4rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda5 - omega5);
            w = AASCoordinateTransformation.DegreesToRadians(omega5 - 168.8112);
            double gamma5rad = AASCoordinateTransformation.DegreesToRadians(gamma5);
            double X5        = r5 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma5rad) * Math.Sin(w));
            double Y5        = r5 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma5rad) + Math.Cos(u) * Math.Sin(w));
            double Z5        = r5 * Math.Sin(u) * Math.Sin(gamma5rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda6 - omega6);
            w = AASCoordinateTransformation.DegreesToRadians(omega6 - 168.8112);
            double gamma6rad = AASCoordinateTransformation.DegreesToRadians(gamma6);
            double X6        = r6 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma6rad) * Math.Sin(w));
            double Y6        = r6 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma6rad) + Math.Cos(u) * Math.Sin(w));
            double Z6        = r6 * Math.Sin(u) * Math.Sin(gamma6rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda7 - omega7);
            w = AASCoordinateTransformation.DegreesToRadians(omega7 - 168.8112);
            double gamma7rad = AASCoordinateTransformation.DegreesToRadians(gamma7);
            double X7        = r7 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma7rad) * Math.Sin(w));
            double Y7        = r7 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma7rad) + Math.Cos(u) * Math.Sin(w));
            double Z7        = r7 * Math.Sin(u) * Math.Sin(gamma7rad);

            u = AASCoordinateTransformation.DegreesToRadians(lambda8 - omega8);
            w = AASCoordinateTransformation.DegreesToRadians(omega8 - 168.8112);
            double gamma8rad = AASCoordinateTransformation.DegreesToRadians(gamma8);
            double X8        = r8 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma8rad) * Math.Sin(w));
            double Y8        = r8 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma8rad) + Math.Cos(u) * Math.Sin(w));
            double Z8        = r8 * Math.Sin(u) * Math.Sin(gamma8rad);

            double X9 = 0;
            double Y9 = 0;
            double Z9 = 1;

            //Now do the rotations, first for the ficticious 9th satellite, so that we can calculate D
            double A4 = 0;
            double B4 = 0;
            double C4 = 0;

            Rotations(X9, Y9, Z9, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            double D = Math.Atan2(A4, C4);

            //Now calculate the values for satellite 1
            Rotations(X1, Y1, Z1, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite1.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite1.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite1.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 2
            Rotations(X2, Y2, Z2, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite2.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite2.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite2.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 3
            Rotations(X3, Y3, Z3, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite3.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite3.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite3.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 4
            Rotations(X4, Y4, Z4, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite4.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite4.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite4.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 5
            Rotations(X5, Y5, Z5, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite5.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite5.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite5.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 6
            Rotations(X6, Y6, Z6, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite6.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite6.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite6.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 7
            Rotations(X7, Y7, Z7, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite7.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite7.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite7.TrueRectangularCoordinates.Z = B4;

            //Now calculate the values for satellite 8
            Rotations(X8, Y8, Z8, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
            details.Satellite8.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
            details.Satellite8.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
            details.Satellite8.TrueRectangularCoordinates.Z = B4;


            //apply the differential light-time correction
            details.Satellite1.ApparentRectangularCoordinates.X = details.Satellite1.TrueRectangularCoordinates.X + Math.Abs(details.Satellite1.TrueRectangularCoordinates.Z) / 20947 * Math.Sqrt(1 - (details.Satellite1.TrueRectangularCoordinates.X / r1) * (details.Satellite1.TrueRectangularCoordinates.X / r1));
            details.Satellite1.ApparentRectangularCoordinates.Y = details.Satellite1.TrueRectangularCoordinates.Y;
            details.Satellite1.ApparentRectangularCoordinates.Z = details.Satellite1.TrueRectangularCoordinates.Z;

            details.Satellite2.ApparentRectangularCoordinates.X = details.Satellite2.TrueRectangularCoordinates.X + Math.Abs(details.Satellite2.TrueRectangularCoordinates.Z) / 23715 * Math.Sqrt(1 - (details.Satellite2.TrueRectangularCoordinates.X / r2) * (details.Satellite2.TrueRectangularCoordinates.X / r2));
            details.Satellite2.ApparentRectangularCoordinates.Y = details.Satellite2.TrueRectangularCoordinates.Y;
            details.Satellite2.ApparentRectangularCoordinates.Z = details.Satellite2.TrueRectangularCoordinates.Z;

            details.Satellite3.ApparentRectangularCoordinates.X = details.Satellite3.TrueRectangularCoordinates.X + Math.Abs(details.Satellite3.TrueRectangularCoordinates.Z) / 26382 * Math.Sqrt(1 - (details.Satellite3.TrueRectangularCoordinates.X / r3) * (details.Satellite3.TrueRectangularCoordinates.X / r3));
            details.Satellite3.ApparentRectangularCoordinates.Y = details.Satellite3.TrueRectangularCoordinates.Y;
            details.Satellite3.ApparentRectangularCoordinates.Z = details.Satellite3.TrueRectangularCoordinates.Z;

            details.Satellite4.ApparentRectangularCoordinates.X = details.Satellite4.TrueRectangularCoordinates.X + Math.Abs(details.Satellite4.TrueRectangularCoordinates.Z) / 29876 * Math.Sqrt(1 - (details.Satellite4.TrueRectangularCoordinates.X / r4) * (details.Satellite4.TrueRectangularCoordinates.X / r4));
            details.Satellite4.ApparentRectangularCoordinates.Y = details.Satellite4.TrueRectangularCoordinates.Y;
            details.Satellite4.ApparentRectangularCoordinates.Z = details.Satellite4.TrueRectangularCoordinates.Z;

            details.Satellite5.ApparentRectangularCoordinates.X = details.Satellite5.TrueRectangularCoordinates.X + Math.Abs(details.Satellite5.TrueRectangularCoordinates.Z) / 35313 * Math.Sqrt(1 - (details.Satellite5.TrueRectangularCoordinates.X / r5) * (details.Satellite5.TrueRectangularCoordinates.X / r5));
            details.Satellite5.ApparentRectangularCoordinates.Y = details.Satellite5.TrueRectangularCoordinates.Y;
            details.Satellite5.ApparentRectangularCoordinates.Z = details.Satellite5.TrueRectangularCoordinates.Z;

            details.Satellite6.ApparentRectangularCoordinates.X = details.Satellite6.TrueRectangularCoordinates.X + Math.Abs(details.Satellite6.TrueRectangularCoordinates.Z) / 53800 * Math.Sqrt(1 - (details.Satellite6.TrueRectangularCoordinates.X / r6) * (details.Satellite6.TrueRectangularCoordinates.X / r6));
            details.Satellite6.ApparentRectangularCoordinates.Y = details.Satellite6.TrueRectangularCoordinates.Y;
            details.Satellite6.ApparentRectangularCoordinates.Z = details.Satellite6.TrueRectangularCoordinates.Z;

            details.Satellite7.ApparentRectangularCoordinates.X = details.Satellite7.TrueRectangularCoordinates.X + Math.Abs(details.Satellite7.TrueRectangularCoordinates.Z) / 59222 * Math.Sqrt(1 - (details.Satellite7.TrueRectangularCoordinates.X / r7) * (details.Satellite7.TrueRectangularCoordinates.X / r7));
            details.Satellite7.ApparentRectangularCoordinates.Y = details.Satellite7.TrueRectangularCoordinates.Y;
            details.Satellite7.ApparentRectangularCoordinates.Z = details.Satellite7.TrueRectangularCoordinates.Z;

            details.Satellite8.ApparentRectangularCoordinates.X = details.Satellite8.TrueRectangularCoordinates.X + Math.Abs(details.Satellite8.TrueRectangularCoordinates.Z) / 91820 * Math.Sqrt(1 - (details.Satellite8.TrueRectangularCoordinates.X / r8) * (details.Satellite8.TrueRectangularCoordinates.X / r8));
            details.Satellite8.ApparentRectangularCoordinates.Y = details.Satellite8.TrueRectangularCoordinates.Y;
            details.Satellite8.ApparentRectangularCoordinates.Z = details.Satellite8.TrueRectangularCoordinates.Z;


            //apply the perspective effect correction
            double W = DELTA / (DELTA + details.Satellite1.TrueRectangularCoordinates.Z / 2475);

            details.Satellite1.ApparentRectangularCoordinates.X *= W;
            details.Satellite1.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite2.TrueRectangularCoordinates.Z / 2475);
            details.Satellite2.ApparentRectangularCoordinates.X *= W;
            details.Satellite2.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite3.TrueRectangularCoordinates.Z / 2475);
            details.Satellite3.ApparentRectangularCoordinates.X *= W;
            details.Satellite3.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite4.TrueRectangularCoordinates.Z / 2475);
            details.Satellite4.ApparentRectangularCoordinates.X *= W;
            details.Satellite4.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite5.TrueRectangularCoordinates.Z / 2475);
            details.Satellite5.ApparentRectangularCoordinates.X *= W;
            details.Satellite5.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite6.TrueRectangularCoordinates.Z / 2475);
            details.Satellite6.ApparentRectangularCoordinates.X *= W;
            details.Satellite6.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite7.TrueRectangularCoordinates.Z / 2475);
            details.Satellite7.ApparentRectangularCoordinates.X *= W;
            details.Satellite7.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite8.TrueRectangularCoordinates.Z / 2475);
            details.Satellite8.ApparentRectangularCoordinates.X *= W;
            details.Satellite8.ApparentRectangularCoordinates.Y *= W;

            return(details);
        }
예제 #4
0
        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);
        }