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);
}
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);
}
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);
}