Example #1
0
        private static AASGalileanMoonsDetails CalculateHelper(double JD, double sunlongrad, double betarad, double R, bool bHighPrecision)
        {
            //What will be the return value
            AASGalileanMoonsDetails details = new AASGalileanMoonsDetails();

            //Calculate the position of Jupiter decreased by the light travel time from Jupiter to the specified position
            double DELTA = 5;
            double PreviousLightTravelTime = 0;
            double LightTravelTime         = AASElliptical.DistanceToLightTime(DELTA);
            double x = 0;
            double y = 0;
            double z = 0;
            double l = 0;
            double lrad;
            double b = 0;
            double brad;
            double r;
            double JD1      = JD - LightTravelTime;
            bool   bIterate = true;

            while (bIterate)
            {
                //Calculate the position of Jupiter
                l    = AASJupiter.EclipticLongitude(JD1, bHighPrecision);
                lrad = AASCoordinateTransformation.DegreesToRadians(l);
                b    = AASJupiter.EclipticLatitude(JD1, bHighPrecision);
                brad = AASCoordinateTransformation.DegreesToRadians(b);
                r    = AASJupiter.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 Jupiter's Longitude and Latitude
            double lambda0 = Math.Atan2(y, x);
            double beta0   = Math.Atan(z / Math.Sqrt(x * x + y * y));

            double t = JD - 2443000.5 - LightTravelTime;

            //Calculate the mean longitudes
            double l1    = 106.07719 + 203.488955790 * t;
            double l1rad = AASCoordinateTransformation.DegreesToRadians(l1);
            double l2    = 175.73161 + 101.374724735 * t;
            double l2rad = AASCoordinateTransformation.DegreesToRadians(l2);
            double l3    = 120.55883 + 50.317609207 * t;
            double l3rad = AASCoordinateTransformation.DegreesToRadians(l3);
            double l4    = 84.44459 + 21.571071177 * t;
            double l4rad = AASCoordinateTransformation.DegreesToRadians(l4);

            //Calculate the perijoves
            double pi1 = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.MapTo0To360Range(97.0881 + 0.16138586 * t));
            double pi2 = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.MapTo0To360Range(154.8663 + 0.04726307 * t));
            double pi3 = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.MapTo0To360Range(188.1840 + 0.00712734 * t));
            double pi4 = AASCoordinateTransformation.DegreesToRadians(AASCoordinateTransformation.MapTo0To360Range(335.2868 + 0.00184000 * t));

            //Calculate the nodes on the equatorial plane of jupiter
            double w1    = 312.3346 - 0.13279386 * t;
            double w1rad = AASCoordinateTransformation.DegreesToRadians(w1);
            double w2    = 100.4411 - 0.03263064 * t;
            double w2rad = AASCoordinateTransformation.DegreesToRadians(w2);
            double w3    = 119.1942 - 0.00717703 * t;
            double w3rad = AASCoordinateTransformation.DegreesToRadians(w3);
            double w4    = 322.6186 - 0.00175934 * t;
            double w4rad = AASCoordinateTransformation.DegreesToRadians(w4);

            //Calculate the Principal inequality in the longitude of Jupiter
            double GAMMA = 0.33033 * Math.Sin(AASCoordinateTransformation.DegreesToRadians(163.679 + 0.0010512 * t)) +
                           0.03439 * Math.Sin(AASCoordinateTransformation.DegreesToRadians(34.486 - 0.0161731 * t));

            //Calculate the "phase of free libration"
            double philambda = AASCoordinateTransformation.DegreesToRadians(199.6766 + 0.17379190 * t);

            //Calculate the longitude of the node of the equator of Jupiter on the ecliptic
            double psi = AASCoordinateTransformation.DegreesToRadians(316.5182 - 0.00000208 * t);

            //Calculate the mean anomalies of Jupiter and Saturn
            double G     = AASCoordinateTransformation.DegreesToRadians(30.23756 + 0.0830925701 * t + GAMMA);
            double Gdash = AASCoordinateTransformation.DegreesToRadians(31.97853 + 0.0334597339 * t);

            //Calculate the longitude of the perihelion of Jupiter
            double PI = AASCoordinateTransformation.DegreesToRadians(13.469942);

            //Calculate the periodic terms in the longitudes of the satellites
            double Sigma1 = 0.47259 * Math.Sin(2 * (l1rad - l2rad)) +
                            -0.03478 * Math.Sin(pi3 - pi4) +
                            0.01081 * Math.Sin(l2rad - 2 * l3rad + pi3) +
                            0.00738 * Math.Sin(philambda) +
                            0.00713 * Math.Sin(l2rad - 2 * l3rad + pi2) +
                            -0.00674 * Math.Sin(pi1 + pi3 - 2 * PI - 2 * G) +
                            0.00666 * Math.Sin(l2rad - 2 * l3rad + pi4) +
                            0.00445 * Math.Sin(l1rad - pi3) +
                            -0.00354 * Math.Sin(l1rad - l2rad) +
                            -0.00317 * Math.Sin(2 * psi - 2 * PI) +
                            0.00265 * Math.Sin(l1rad - pi4) +
                            -0.00186 * Math.Sin(G) +
                            0.00162 * Math.Sin(pi2 - pi3) +
                            0.00158 * Math.Sin(4 * (l1rad - l2rad)) +
                            -0.00155 * Math.Sin(l1rad - l3rad) +
                            -0.00138 * Math.Sin(psi + w3rad - 2 * PI - 2 * G) +
                            -0.00115 * Math.Sin(2 * (l1rad - 2 * l2rad + w2rad)) +
                            0.00089 * Math.Sin(pi2 - pi4) +
                            0.00085 * Math.Sin(l1rad + pi3 - 2 * PI - 2 * G) +
                            0.00083 * Math.Sin(w2rad - w3rad) +
                            0.00053 * Math.Sin(psi - w2rad);
            double Sigma1rad = AASCoordinateTransformation.DegreesToRadians(Sigma1);

            double Sigma2 = 1.06476 * Math.Sin(2 * (l2rad - l3rad)) +
                            0.04256 * Math.Sin(l1rad - 2 * l2rad + pi3) +
                            0.03581 * Math.Sin(l2rad - pi3) +
                            0.02395 * Math.Sin(l1rad - 2 * l2rad + pi4) +
                            0.01984 * Math.Sin(l2rad - pi4) +
                            -0.01778 * Math.Sin(philambda) +
                            0.01654 * Math.Sin(l2rad - pi2) +
                            0.01334 * Math.Sin(l2rad - 2 * l3rad + pi2) +
                            0.01294 * Math.Sin(pi3 - pi4) +
                            -0.01142 * Math.Sin(l2rad - l3rad) +
                            -0.01057 * Math.Sin(G) +
                            -0.00775 * Math.Sin(2 * (psi - PI)) +
                            0.00524 * Math.Sin(2 * (l1rad - l2rad)) +
                            -0.00460 * Math.Sin(l1rad - l3rad) +
                            0.00316 * Math.Sin(psi - 2 * G + w3rad - 2 * PI) +
                            -0.00203 * Math.Sin(pi1 + pi3 - 2 * PI - 2 * G) +
                            0.00146 * Math.Sin(psi - w3rad) +
                            -0.00145 * Math.Sin(2 * G) +
                            0.00125 * Math.Sin(psi - w4rad) +
                            -0.00115 * Math.Sin(l1rad - 2 * l3rad + pi3) +
                            -0.00094 * Math.Sin(2 * (l2rad - w2rad)) +
                            0.00086 * Math.Sin(2 * (l1rad - 2 * l2rad + w2rad)) +
                            -0.00086 * Math.Sin(5 * Gdash - 2 * G + AASCoordinateTransformation.DegreesToRadians(52.225)) +
                            -0.00078 * Math.Sin(l2rad - l4rad) +
                            -0.00064 * Math.Sin(3 * l3rad - 7 * l4rad + 4 * pi4) +
                            0.00064 * Math.Sin(pi1 - pi4) +
                            -0.00063 * Math.Sin(l1rad - 2 * l3rad + pi4) +
                            0.00058 * Math.Sin(w3rad - w4rad) +
                            0.00056 * Math.Sin(2 * (psi - PI - G)) +
                            0.00056 * Math.Sin(2 * (l2rad - l4rad)) +
                            0.00055 * Math.Sin(2 * (l1rad - l3rad)) +
                            0.00052 * Math.Sin(3 * l3rad - 7 * l4rad + pi3 + 3 * pi4) +
                            -0.00043 * Math.Sin(l1rad - pi3) +
                            0.00041 * Math.Sin(5 * (l2rad - l3rad)) +
                            0.00041 * Math.Sin(pi4 - PI) +
                            0.00032 * Math.Sin(w2rad - w3rad) +
                            0.00032 * Math.Sin(2 * (l3rad - G - PI));
            double Sigma2rad = AASCoordinateTransformation.DegreesToRadians(Sigma2);

            double Sigma3 = 0.16490 * Math.Sin(l3rad - pi3) +
                            0.09081 * Math.Sin(l3rad - pi4) +
                            -0.06907 * Math.Sin(l2rad - l3rad) +
                            0.03784 * Math.Sin(pi3 - pi4) +
                            0.01846 * Math.Sin(2 * (l3rad - l4rad)) +
                            -0.01340 * Math.Sin(G) +
                            -0.01014 * Math.Sin(2 * (psi - PI)) +
                            0.00704 * Math.Sin(l2rad - 2 * l3rad + pi3) +
                            -0.00620 * Math.Sin(l2rad - 2 * l3rad + pi2) +
                            -0.00541 * Math.Sin(l3rad - l4rad) +
                            0.00381 * Math.Sin(l2rad - 2 * l3rad + pi4) +
                            0.00235 * Math.Sin(psi - w3rad) +
                            0.00198 * Math.Sin(psi - w4rad) +
                            0.00176 * Math.Sin(philambda) +
                            0.00130 * Math.Sin(3 * (l3rad - l4rad)) +
                            0.00125 * Math.Sin(l1rad - l3rad) +
                            -0.00119 * Math.Sin(5 * Gdash - 2 * G + AASCoordinateTransformation.DegreesToRadians(52.225)) +
                            0.00109 * Math.Sin(l1rad - l2rad) +
                            -0.00100 * Math.Sin(3 * l3rad - 7 * l4rad + 4 * pi4) +
                            0.00091 * Math.Sin(w3rad - w4rad) +
                            0.00080 * Math.Sin(3 * l3rad - 7 * l4rad + pi3 + 3 * pi4) +
                            -0.00075 * Math.Sin(2 * l2rad - 3 * l3rad + pi3) +
                            0.00072 * Math.Sin(pi1 + pi3 - 2 * PI - 2 * G) +
                            0.00069 * Math.Sin(pi4 - PI) +
                            -0.00058 * Math.Sin(2 * l3rad - 3 * l4rad + pi4) +
                            -0.00057 * Math.Sin(l3rad - 2 * l4rad + pi4) +
                            0.00056 * Math.Sin(l3rad + pi3 - 2 * PI - 2 * G) +
                            -0.00052 * Math.Sin(l2rad - 2 * l3rad + pi1) +
                            -0.00050 * Math.Sin(pi2 - pi3) +
                            0.00048 * Math.Sin(l3rad - 2 * l4rad + pi3) +
                            -0.00045 * Math.Sin(2 * l2rad - 3 * l3rad + pi4) +
                            -0.00041 * Math.Sin(pi2 - pi4) +
                            -0.00038 * Math.Sin(2 * G) +
                            -0.00037 * Math.Sin(pi3 - pi4 + w3rad - w4rad) +
                            -0.00032 * Math.Sin(3 * l3rad - 7 * l4rad + 2 * pi3 + 2 * pi4) +
                            0.00030 * Math.Sin(4 * (l3rad - l4rad)) +
                            0.00029 * Math.Sin(l3rad + pi4 - 2 * PI - 2 * G) +
                            -0.00028 * Math.Sin(w3rad + psi - 2 * PI - 2 * G) +
                            0.00026 * Math.Sin(l3rad - PI - G) +
                            0.00024 * Math.Sin(l2rad - 3 * l3rad + 2 * l4rad) +
                            0.00021 * Math.Sin(l3rad - PI - G) +
                            -0.00021 * Math.Sin(l3rad - pi2) +
                            0.00017 * Math.Sin(2 * (l3rad - pi3));
            double Sigma3rad = AASCoordinateTransformation.DegreesToRadians(Sigma3);

            double Sigma4 = 0.84287 * Math.Sin(l4rad - pi4) +
                            0.03431 * Math.Sin(pi4 - pi3) +
                            -0.03305 * Math.Sin(2 * (psi - PI)) +
                            -0.03211 * Math.Sin(G) +
                            -0.01862 * Math.Sin(l4rad - pi3) +
                            0.01186 * Math.Sin(psi - w4rad) +
                            0.00623 * Math.Sin(l4rad + pi4 - 2 * G - 2 * PI) +
                            0.00387 * Math.Sin(2 * (l4rad - pi4)) +
                            -0.00284 * Math.Sin(5 * Gdash - 2 * G + AASCoordinateTransformation.DegreesToRadians(52.225)) +
                            -0.00234 * Math.Sin(2 * (psi - pi4)) +
                            -0.00223 * Math.Sin(l3rad - l4rad) +
                            -0.00208 * Math.Sin(l4rad - PI) +
                            0.00178 * Math.Sin(psi + w4rad - 2 * pi4) +
                            0.00134 * Math.Sin(pi4 - PI) +
                            0.00125 * Math.Sin(2 * (l4rad - G - PI)) +
                            -0.00117 * Math.Sin(2 * G) +
                            -0.00112 * Math.Sin(2 * (l3rad - l4rad)) +
                            0.00107 * Math.Sin(3 * l3rad - 7 * l4rad + 4 * pi4) +
                            0.00102 * Math.Sin(l4rad - G - PI) +
                            0.00096 * Math.Sin(2 * l4rad - psi - w4rad) +
                            0.00087 * Math.Sin(2 * (psi - w4rad)) +
                            -0.00085 * Math.Sin(3 * l3rad - 7 * l4rad + pi3 + 3 * pi4) +
                            0.00085 * Math.Sin(l3rad - 2 * l4rad + pi4) +
                            -0.00081 * Math.Sin(2 * (l4rad - psi)) +
                            0.00071 * Math.Sin(l4rad + pi4 - 2 * PI - 3 * G) +
                            0.00061 * Math.Sin(l1rad - l4rad) +
                            -0.00056 * Math.Sin(psi - w3rad) +
                            -0.00054 * Math.Sin(l3rad - 2 * l4rad + pi3) +
                            0.00051 * Math.Sin(l2rad - l4rad) +
                            0.00042 * Math.Sin(2 * (psi - G - PI)) +
                            0.00039 * Math.Sin(2 * (pi4 - w4rad)) +
                            0.00036 * Math.Sin(psi + PI - pi4 - w4rad) +
                            0.00035 * Math.Sin(2 * Gdash - G + AASCoordinateTransformation.DegreesToRadians(188.37)) +
                            -0.00035 * Math.Sin(l4rad - pi4 + 2 * PI - 2 * psi) +
                            -0.00032 * Math.Sin(l4rad + pi4 - 2 * PI - G) +
                            0.00030 * Math.Sin(2 * Gdash - 2 * G + AASCoordinateTransformation.DegreesToRadians(149.15)) +
                            0.00029 * Math.Sin(3 * l3rad - 7 * l4rad + 2 * pi3 + 2 * pi4) +
                            0.00028 * Math.Sin(l4rad - pi4 + 2 * psi - 2 * PI) +
                            -0.00028 * Math.Sin(2 * (l4rad - w4rad)) +
                            -0.00027 * Math.Sin(pi3 - pi4 + w3rad - w4rad) +
                            -0.00026 * Math.Sin(5 * Gdash - 3 * G + AASCoordinateTransformation.DegreesToRadians(188.37)) +
                            0.00025 * Math.Sin(w4rad - w3rad) +
                            -0.00025 * Math.Sin(l2rad - 3 * l3rad + 2 * l4rad) +
                            -0.00023 * Math.Sin(3 * (l3rad - l4rad)) +
                            0.00021 * Math.Sin(2 * l4rad - 2 * PI - 3 * G) +
                            -0.00021 * Math.Sin(2 * l3rad - 3 * l4rad + pi4) +
                            0.00019 * Math.Sin(l4rad - pi4 - G) +
                            -0.00019 * Math.Sin(2 * l4rad - pi3 - pi4) +
                            -0.00018 * Math.Sin(l4rad - pi4 + G) +
                            -0.00016 * Math.Sin(l4rad + pi3 - 2 * PI - 2 * G);

            //There is no need to calculate a Sigma4rad as it is not used in any subsequent trignometric functions

            details.Satellite1.MeanLongitude = AASCoordinateTransformation.MapTo0To360Range(l1);
            details.Satellite1.TrueLongitude = AASCoordinateTransformation.MapTo0To360Range(l1 + Sigma1);
            double L1 = AASCoordinateTransformation.DegreesToRadians(details.Satellite1.TrueLongitude);

            details.Satellite2.MeanLongitude = AASCoordinateTransformation.MapTo0To360Range(l2);
            details.Satellite2.TrueLongitude = AASCoordinateTransformation.MapTo0To360Range(l2 + Sigma2);
            double L2 = AASCoordinateTransformation.DegreesToRadians(details.Satellite2.TrueLongitude);

            details.Satellite3.MeanLongitude = AASCoordinateTransformation.MapTo0To360Range(l3);
            details.Satellite3.TrueLongitude = AASCoordinateTransformation.MapTo0To360Range(l3 + Sigma3);
            double L3 = AASCoordinateTransformation.DegreesToRadians(details.Satellite3.TrueLongitude);

            details.Satellite4.MeanLongitude = AASCoordinateTransformation.MapTo0To360Range(l4);
            details.Satellite4.TrueLongitude = AASCoordinateTransformation.MapTo0To360Range(l4 + Sigma4);
            double L4 = AASCoordinateTransformation.DegreesToRadians(details.Satellite4.TrueLongitude);

            //Calculate the periodic terms in the latitudes of the satellites
            double B1 = Math.Atan(0.0006393 * Math.Sin(L1 - w1rad) +
                                  0.0001825 * Math.Sin(L1 - w2rad) +
                                  0.0000329 * Math.Sin(L1 - w3rad) +
                                  -0.0000311 * Math.Sin(L1 - psi) +
                                  0.0000093 * Math.Sin(L1 - w4rad) +
                                  0.0000075 * Math.Sin(3 * L1 - 4 * l2rad - 1.9927 * Sigma1rad + w2rad) +
                                  0.0000046 * Math.Sin(L1 + psi - 2 * PI - 2 * G));

            details.Satellite1.EquatorialLatitude = AASCoordinateTransformation.RadiansToDegrees(B1);

            double B2 = Math.Atan(0.0081004 * Math.Sin(L2 - w2rad) +
                                  0.0004512 * Math.Sin(L2 - w3rad) +
                                  -0.0003284 * Math.Sin(L2 - psi) +
                                  0.0001160 * Math.Sin(L2 - w4rad) +
                                  0.0000272 * Math.Sin(l1rad - 2 * l3rad + 1.0146 * Sigma2rad + w2rad) +
                                  -0.0000144 * Math.Sin(L2 - w1rad) +
                                  0.0000143 * Math.Sin(L2 + psi - 2 * PI - 2 * G) +
                                  0.0000035 * Math.Sin(L2 - psi + G) +
                                  -0.0000028 * Math.Sin(l1rad - 2 * l3rad + 1.0146 * Sigma2rad + w3rad));

            details.Satellite2.EquatorialLatitude = AASCoordinateTransformation.RadiansToDegrees(B2);

            double B3 = Math.Atan(0.0032402 * Math.Sin(L3 - w3rad) +
                                  -0.0016911 * Math.Sin(L3 - psi) +
                                  0.0006847 * Math.Sin(L3 - w4rad) +
                                  -0.0002797 * Math.Sin(L3 - w2rad) +
                                  0.0000321 * Math.Sin(L3 + psi - 2 * PI - 2 * G) +
                                  0.0000051 * Math.Sin(L3 - psi + G) +
                                  -0.0000045 * Math.Sin(L3 - psi - G) +
                                  -0.0000045 * Math.Sin(L3 + psi - 2 * PI) +
                                  0.0000037 * Math.Sin(L3 + psi - 2 * PI - 3 * G) +
                                  0.0000030 * Math.Sin(2 * l2rad - 3 * L3 + 4.03 * Sigma3rad + w2rad) +
                                  -0.0000021 * Math.Sin(2 * l2rad - 3 * L3 + 4.03 * Sigma3rad + w3rad));

            details.Satellite3.EquatorialLatitude = AASCoordinateTransformation.RadiansToDegrees(B3);

            double B4 = Math.Atan(-0.0076579 * Math.Sin(L4 - psi) +
                                  0.0044134 * Math.Sin(L4 - w4rad) +
                                  -0.0005112 * Math.Sin(L4 - w3rad) +
                                  0.0000773 * Math.Sin(L4 + psi - 2 * PI - 2 * G) +
                                  0.0000104 * Math.Sin(L4 - psi + G) +
                                  -0.0000102 * Math.Sin(L4 - psi - G) +
                                  0.0000088 * Math.Sin(L4 + psi - 2 * PI - 3 * G) +
                                  -0.0000038 * Math.Sin(L4 + psi - 2 * PI - G));

            details.Satellite4.EquatorialLatitude = AASCoordinateTransformation.RadiansToDegrees(B4);

            //Calculate the periodic terms for the radius vector
            details.Satellite1.r = 5.90569 * (1 + (-0.0041339 * Math.Cos(2 * (l1rad - l2rad)) +
                                                   -0.0000387 * Math.Cos(l1rad - pi3) +
                                                   -0.0000214 * Math.Cos(l1rad - pi4) +
                                                   0.0000170 * Math.Cos(l1rad - l2rad) +
                                                   -0.0000131 * Math.Cos(4 * (l1rad - l2rad)) +
                                                   0.0000106 * Math.Cos(l1rad - l3rad) +
                                                   -0.0000066 * Math.Cos(l1rad + pi3 - 2 * PI - 2 * G)));

            details.Satellite2.r = 9.39657 * (1 + (0.0093848 * Math.Cos(l1rad - l2rad) +
                                                   -0.0003116 * Math.Cos(l2rad - pi3) +
                                                   -0.0001744 * Math.Cos(l2rad - pi4) +
                                                   -0.0001442 * Math.Cos(l2rad - pi2) +
                                                   0.0000553 * Math.Cos(l2rad - l3rad) +
                                                   0.0000523 * Math.Cos(l1rad - l3rad) +
                                                   -0.0000290 * Math.Cos(2 * (l1rad - l2rad)) +
                                                   0.0000164 * Math.Cos(2 * (l2rad - w2rad)) +
                                                   0.0000107 * Math.Cos(l1rad - 2 * l3rad + pi3) +
                                                   -0.0000102 * Math.Cos(l2rad - pi1) +
                                                   -0.0000091 * Math.Cos(2 * (l1rad - l3rad))));

            details.Satellite3.r = 14.98832 * (1 + (-0.0014388 * Math.Cos(l3rad - pi3) +
                                                    -0.0007919 * Math.Cos(l3rad - pi4) +
                                                    0.0006342 * Math.Cos(l2rad - l3rad) +
                                                    -0.0001761 * Math.Cos(2 * (l3rad - l4rad)) +
                                                    0.0000294 * Math.Cos(l3rad - l4rad) +
                                                    -0.0000156 * Math.Cos(3 * (l3rad - l4rad)) +
                                                    0.0000156 * Math.Cos(l1rad - l3rad) +
                                                    -0.0000153 * Math.Cos(l1rad - l2rad) +
                                                    0.0000070 * Math.Cos(2 * l2rad - 3 * l3rad + pi3) +
                                                    -0.0000051 * Math.Cos(l3rad + pi3 - 2 * PI - 2 * G)));

            details.Satellite4.r = 26.36273 * (1 + (-0.0073546 * Math.Cos(l4rad - pi4) +
                                                    0.0001621 * Math.Cos(l4rad - pi3) +
                                                    0.0000974 * Math.Cos(l3rad - l4rad) +
                                                    -0.0000543 * Math.Cos(l4rad + pi4 - 2 * PI - 2 * G) +
                                                    -0.0000271 * Math.Cos(2 * (l4rad - pi4)) +
                                                    0.0000182 * Math.Cos(l4rad - PI) +
                                                    0.0000177 * Math.Cos(2 * (l3rad - l4rad)) +
                                                    -0.0000167 * Math.Cos(2 * l4rad - psi - w4rad) +
                                                    0.0000167 * Math.Cos(psi - w4rad) +
                                                    -0.0000155 * Math.Cos(2 * (l4rad - PI - G)) +
                                                    0.0000142 * Math.Cos(2 * (l4rad - psi)) +
                                                    0.0000105 * Math.Cos(l1rad - l4rad) +
                                                    0.0000092 * Math.Cos(l2rad - l4rad) +
                                                    -0.0000089 * Math.Cos(l4rad - PI - G) +
                                                    -0.0000062 * Math.Cos(l4rad + pi4 - 2 * PI - 3 * G) +
                                                    0.0000048 * Math.Cos(2 * (l4rad - w4rad))));

            //Calculate T0
            double T0 = (JD - 2433282.423) / 36525;

            //Calculate the precession in longitude from Epoch B1950 to the date
            double P = AASCoordinateTransformation.DegreesToRadians(1.3966626 * T0 + 0.0003088 * T0 * T0);

            //Add it to L1 - L4 and psi
            L1 += P;
            details.Satellite1.TropicalLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(L1));
            L2 += P;
            details.Satellite2.TropicalLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(L2));
            L3 += P;
            details.Satellite3.TropicalLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(L3));
            L4 += P;
            details.Satellite4.TropicalLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(L4));
            psi += P;

            //Calculate the inclination of Jupiter's axis of rotation on the orbital plane
            double T    = (JD - 2415020.5) / 36525;
            double I    = 3.120262 + 0.0006 * T;
            double Irad = AASCoordinateTransformation.DegreesToRadians(I);

            double X1 = details.Satellite1.r * Math.Cos(L1 - psi) * Math.Cos(B1);
            double X2 = details.Satellite2.r * Math.Cos(L2 - psi) * Math.Cos(B2);
            double X3 = details.Satellite3.r * Math.Cos(L3 - psi) * Math.Cos(B3);
            double X4 = details.Satellite4.r * Math.Cos(L4 - psi) * Math.Cos(B4);
            double X5 = 0;

            double Y1 = details.Satellite1.r * Math.Sin(L1 - psi) * Math.Cos(B1);
            double Y2 = details.Satellite2.r * Math.Sin(L2 - psi) * Math.Cos(B2);
            double Y3 = details.Satellite3.r * Math.Sin(L3 - psi) * Math.Cos(B3);
            double Y4 = details.Satellite4.r * Math.Sin(L4 - psi) * Math.Cos(B4);
            double Y5 = 0;

            double Z1 = details.Satellite1.r * Math.Sin(B1);
            double Z2 = details.Satellite2.r * Math.Sin(B2);
            double Z3 = details.Satellite3.r * Math.Sin(B3);
            double Z4 = details.Satellite4.r * Math.Sin(B4);
            double Z5 = 1;

            //Now do the rotations, first for the ficticious 5th satellite, so that we can calculate D
            double omega = AASCoordinateTransformation.DegreesToRadians(AASElementsPlanetaryOrbit.JupiterLongitudeAscendingNode(JD));
            double i     = AASCoordinateTransformation.DegreesToRadians(AASElementsPlanetaryOrbit.JupiterInclination(JD));
            double A6    = 0;
            double B6    = 0;
            double C6    = 0;

            Rotations(X5, Y5, Z5, Irad, psi, i, omega, lambda0, beta0, ref A6, ref B6, ref C6);
            double D = Math.Atan2(A6, C6);

            //Now calculate the values for satellite 1
            Rotations(X1, Y1, Z1, Irad, psi, i, omega, lambda0, beta0, ref A6, ref B6, ref C6);
            details.Satellite1.TrueRectangularCoordinates.X = A6 * Math.Cos(D) - C6 * Math.Sin(D);
            details.Satellite1.TrueRectangularCoordinates.Y = A6 * Math.Sin(D) + C6 * Math.Cos(D);
            details.Satellite1.TrueRectangularCoordinates.Z = B6;

            //Now calculate the values for satellite 2
            Rotations(X2, Y2, Z2, Irad, psi, i, omega, lambda0, beta0, ref A6, ref B6, ref C6);
            details.Satellite2.TrueRectangularCoordinates.X = A6 * Math.Cos(D) - C6 * Math.Sin(D);
            details.Satellite2.TrueRectangularCoordinates.Y = A6 * Math.Sin(D) + C6 * Math.Cos(D);
            details.Satellite2.TrueRectangularCoordinates.Z = B6;

            //Now calculate the values for satellite 3
            Rotations(X3, Y3, Z3, Irad, psi, i, omega, lambda0, beta0, ref A6, ref B6, ref C6);
            details.Satellite3.TrueRectangularCoordinates.X = A6 * Math.Cos(D) - C6 * Math.Sin(D);
            details.Satellite3.TrueRectangularCoordinates.Y = A6 * Math.Sin(D) + C6 * Math.Cos(D);
            details.Satellite3.TrueRectangularCoordinates.Z = B6;

            //And finally for satellite 4
            Rotations(X4, Y4, Z4, Irad, psi, i, omega, lambda0, beta0, ref A6, ref B6, ref C6);
            details.Satellite4.TrueRectangularCoordinates.X = A6 * Math.Cos(D) - C6 * Math.Sin(D);
            details.Satellite4.TrueRectangularCoordinates.Y = A6 * Math.Sin(D) + C6 * Math.Cos(D);
            details.Satellite4.TrueRectangularCoordinates.Z = B6;

            //apply the differential light-time correction
            details.Satellite1.ApparentRectangularCoordinates.X = details.Satellite1.TrueRectangularCoordinates.X + Math.Abs(details.Satellite1.TrueRectangularCoordinates.Z) / 17295 * Math.Sqrt(1 - (details.Satellite1.TrueRectangularCoordinates.X / details.Satellite1.r) * (details.Satellite1.TrueRectangularCoordinates.X / details.Satellite1.r));
            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) / 21819 * Math.Sqrt(1 - (details.Satellite2.TrueRectangularCoordinates.X / details.Satellite2.r) * (details.Satellite2.TrueRectangularCoordinates.X / details.Satellite2.r));
            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) / 27558 * Math.Sqrt(1 - (details.Satellite3.TrueRectangularCoordinates.X / details.Satellite3.r) * (details.Satellite3.TrueRectangularCoordinates.X / details.Satellite3.r));
            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) / 36548 * Math.Sqrt(1 - (details.Satellite4.TrueRectangularCoordinates.X / details.Satellite4.r) * (details.Satellite4.TrueRectangularCoordinates.X / details.Satellite4.r));
            details.Satellite4.ApparentRectangularCoordinates.Y = details.Satellite4.TrueRectangularCoordinates.Y;
            details.Satellite4.ApparentRectangularCoordinates.Z = details.Satellite4.TrueRectangularCoordinates.Z;

            //apply the perspective effect correction
            double W = DELTA / (DELTA + details.Satellite1.TrueRectangularCoordinates.Z / 2095);

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

            W = DELTA / (DELTA + details.Satellite2.TrueRectangularCoordinates.Z / 2095);
            details.Satellite2.ApparentRectangularCoordinates.X *= W;
            details.Satellite2.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite3.TrueRectangularCoordinates.Z / 2095);
            details.Satellite3.ApparentRectangularCoordinates.X *= W;
            details.Satellite3.ApparentRectangularCoordinates.Y *= W;

            W = DELTA / (DELTA + details.Satellite4.TrueRectangularCoordinates.Z / 2095);
            details.Satellite4.ApparentRectangularCoordinates.X *= W;
            details.Satellite4.ApparentRectangularCoordinates.Y *= W;

            return(details);
        }
Example #2
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);
        }
Example #3
0
        public static AASGalileanMoonsDetails 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 Jupiter to the Earth
            double DELTA = 5;
            double PreviousEarthLightTravelTime = 0;
            double EarthLightTravelTime         = AASElliptical.DistanceToLightTime(DELTA);
            double JD1      = JD - EarthLightTravelTime;
            bool   bIterate = true;
            double x;
            double y;
            double z;
            double l;
            double lrad;
            double b;
            double brad;
            double r;

            while (bIterate)
            {
                //Calculate the position of Jupiter
                l    = AASJupiter.EclipticLongitude(JD1, bHighPrecision);
                lrad = AASCoordinateTransformation.DegreesToRadians(l);
                b    = AASJupiter.EclipticLatitude(JD1, bHighPrecision);
                brad = AASCoordinateTransformation.DegreesToRadians(b);
                r    = AASJupiter.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
            AASGalileanMoonsDetails details1           = CalculateHelper(JD, sunlongrad, betarad, R, bHighPrecision);
            AASGalileanMoonDetail   details1Satellite1 = details1.Satellite1;
            AASGalileanMoonDetail   details1Satellite2 = details1.Satellite2;
            AASGalileanMoonDetail   details1Satellite3 = details1.Satellite3;
            AASGalileanMoonDetail   details1Satellite4 = details1.Satellite4;

            FillInPhenomenaDetails(ref details1Satellite1);
            FillInPhenomenaDetails(ref details1Satellite2);
            FillInPhenomenaDetails(ref details1Satellite3);
            FillInPhenomenaDetails(ref details1Satellite4);

            //Calculate the the light travel time from Jupiter to the Sun
            JD1   = JD - EarthLightTravelTime;
            l     = AASJupiter.EclipticLongitude(JD1, bHighPrecision);
            lrad  = AASCoordinateTransformation.DegreesToRadians(l);
            b     = AASJupiter.EclipticLatitude(JD1, bHighPrecision);
            brad  = AASCoordinateTransformation.DegreesToRadians(b);
            r     = AASJupiter.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
            AASGalileanMoonsDetails details2           = CalculateHelper(JD + SunLightTravelTime - EarthLightTravelTime, sunlongrad, betarad, 0, bHighPrecision);
            AASGalileanMoonDetail   details2Satellite1 = details2.Satellite1;
            AASGalileanMoonDetail   details2Satellite2 = details2.Satellite2;
            AASGalileanMoonDetail   details2Satellite3 = details2.Satellite3;
            AASGalileanMoonDetail   details2Satellite4 = details2.Satellite4;

            FillInPhenomenaDetails(ref details2Satellite1);
            FillInPhenomenaDetails(ref details2Satellite2);
            FillInPhenomenaDetails(ref details2Satellite3);
            FillInPhenomenaDetails(ref details2Satellite4);

            //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.Satellite1.bInShadowTransit = details2.Satellite1.bInTransit;
            details1.Satellite2.bInShadowTransit = details2.Satellite2.bInTransit;
            details1.Satellite3.bInShadowTransit = details2.Satellite3.bInTransit;
            details1.Satellite4.bInShadowTransit = details2.Satellite4.bInTransit;

            return(details1);
        }
        public static CAAPhysicalJupiterDetails Calculate(double JD, bool bHighPrecision)
        {
            //What will be the return value
            CAAPhysicalJupiterDetails details = new CAAPhysicalJupiterDetails();

            //Step 1
            double d         = JD - 2433282.5;
            double T1        = d / 36525;
            double alpha0    = 268.00 + 0.1061 * T1;
            double alpha0rad = AASCoordinateTransformation.DegreesToRadians(alpha0);
            double delta0    = 64.50 - 0.0164 * T1;
            double delta0rad = AASCoordinateTransformation.DegreesToRadians(delta0);

            //Step 2
            double W1 = AASCoordinateTransformation.MapTo0To360Range(17.710 + 877.90003539 * d);
            double W2 = AASCoordinateTransformation.MapTo0To360Range(16.838 + 870.27003539 * d);

            //Step 3
            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);

            //Step 4
            double l    = AASJupiter.EclipticLongitude(JD, bHighPrecision);
            double lrad = AASCoordinateTransformation.DegreesToRadians(l);
            double b    = AASJupiter.EclipticLatitude(JD, bHighPrecision);
            double brad = AASCoordinateTransformation.DegreesToRadians(b);
            double r    = AASJupiter.RadiusVector(JD, bHighPrecision);

            //Step 5
            double x     = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
            double y     = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
            double z     = r * Math.Sin(brad) - R * Math.Sin(b0rad);
            double DELTA = Math.Sqrt(x * x + y * y + z * z);

            //Step 6
            l   -= 0.012990 * DELTA / (r * r);
            lrad = AASCoordinateTransformation.DegreesToRadians(l);

            //Step 7
            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);

            //Step 8
            double e0    = AASNutation.MeanObliquityOfEcliptic(JD);
            double e0rad = AASCoordinateTransformation.DegreesToRadians(e0);

            //Step 9
            double alphas = Math.Atan2(Math.Cos(e0rad) * Math.Sin(lrad) - Math.Sin(e0rad) * Math.Tan(brad), Math.Cos(lrad));
            double deltas = Math.Asin(Math.Cos(e0rad) * Math.Sin(brad) + Math.Sin(e0rad) * Math.Cos(brad) * Math.Sin(lrad));

            //Step 10
            details.DS = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(delta0rad) * Math.Sin(deltas) - Math.Cos(delta0rad) * Math.Cos(deltas) * Math.Cos(alpha0rad - alphas)));

            //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.RadiansToDegrees(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.DE = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(delta0rad) * Math.Sin(deltarad) - Math.Cos(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad)));

            //Step 13
            details.Geometricw1 = AASCoordinateTransformation.MapTo0To360Range(W1 - AASCoordinateTransformation.RadiansToDegrees(xi) - 5.07033 * DELTA);
            details.Geometricw2 = AASCoordinateTransformation.MapTo0To360Range(W2 - AASCoordinateTransformation.RadiansToDegrees(xi) - 5.02626 * DELTA);

            //Step 14
            double C = 57.2958 * (2 * r * DELTA + R * R - r * r - DELTA * DELTA) / (4 * r * DELTA);

            if (Math.Sin(lrad - l0rad) > 0)
            {
                details.Apparentw1 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw1 + C);
                details.Apparentw2 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw2 + C);
            }
            else
            {
                details.Apparentw1 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw1 - C);
                details.Apparentw2 = AASCoordinateTransformation.MapTo0To360Range(details.Geometricw2 - C);
            }

            //Step 15
            double NutationInLongitude = AASNutation.NutationInLongitude(JD);
            double NutationInObliquity = AASNutation.NutationInObliquity(JD);

            e0   += NutationInObliquity / 3600;
            e0rad = AASCoordinateTransformation.DegreesToRadians(e0);

            //Step 16
            alpha   += 0.005693 * (Math.Cos(alpharad) * Math.Cos(l0rad) * Math.Cos(e0rad) + Math.Sin(alpharad) * Math.Sin(l0rad)) / Math.Cos(deltarad);
            alpha    = AASCoordinateTransformation.MapTo0To360Range(alpha);
            alpharad = AASCoordinateTransformation.DegreesToRadians(alpha);
            delta   += 0.005693 * (Math.Cos(l0rad) * Math.Cos(e0rad) * (Math.Tan(e0rad) * Math.Cos(deltarad) - Math.Sin(alpharad) * Math.Sin(deltarad)) + Math.Cos(alpharad) * Math.Sin(deltarad) * Math.Sin(l0rad));

            //Step 17
            double NutationRA   = AASNutation.NutationInRightAscension(alpha / 15, delta, e0, NutationInLongitude, NutationInObliquity);
            double alphadash    = alpha + NutationRA / 3600;
            double alphadashrad = AASCoordinateTransformation.DegreesToRadians(alphadash);
            double NutationDec  = AASNutation.NutationInDeclination(alpha / 15, e0, NutationInLongitude, NutationInObliquity);
            double deltadash    = delta + NutationDec / 3600;
            double deltadashrad = AASCoordinateTransformation.DegreesToRadians(deltadash);

            NutationRA = AASNutation.NutationInRightAscension(alpha0 / 15, delta0, e0, NutationInLongitude, NutationInObliquity);
            double alpha0dash    = alpha0 + NutationRA / 3600;
            double alpha0dashrad = AASCoordinateTransformation.DegreesToRadians(alpha0dash);

            NutationDec = AASNutation.NutationInDeclination(alpha0 / 15, e0, NutationInLongitude, NutationInObliquity);
            double delta0dash    = delta0 + NutationDec / 3600;
            double delta0dashrad = AASCoordinateTransformation.DegreesToRadians(delta0dash);

            //Step 18
            details.P = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0dashrad) * Math.Sin(alpha0dashrad - alphadashrad), Math.Sin(delta0dashrad) * Math.Cos(deltadashrad) - Math.Cos(delta0dashrad) * Math.Sin(deltadashrad) * Math.Cos(alpha0dashrad - alphadashrad))));

            return(details);
        }