/// <summary>
/// Calculates visible appearance of planet for given date.
/// </summary>
/// <param name="jd">Julian day</param>
/// <param name="planet">Planet number to calculate appearance, 1 = Mercury, 2 = Venus and etc.</param>
/// <param name="eq">Equatorial coordinates of the planet</param>
/// <param name="distance">Distance from the planet to the Earth</param>
/// <returns>Appearance parameters of the planet</returns>
/// <remarks>
/// This method is based on book "Practical Ephemeris Calculations", Montenbruck.
/// See topic 6.4, pp. 88-92.
/// </remarks>
public static PlanetAppearance PlanetAppearance(double jd, int planet, CrdsEquatorial eq, double distance)
{
PlanetAppearance a = new PlanetAppearance();
double d = jd - 2451545.0;
double T = d / 36525.0;
// coordinates of the point to which the north pole of the planet is pointing.
CrdsEquatorial eq0 = new CrdsEquatorial();
eq0.Alpha = Angle.To360(cAlpha0[planet - 1][0] + cAlpha0[planet - 1][1] * T + cAlpha0[planet - 1][2] * T);
eq0.Delta = cDelta0[planet - 1][0] + cDelta0[planet - 1][1] * T + cDelta0[planet - 1][2] * T;
// take light time effect into account
d -= PlanetPositions.LightTimeEffect(distance);
T = d / 36525.0;
// position of null meridian
double W = Angle.To360(cW[planet - 1][0] + cW[planet - 1][1] * d + cW[planet - 1][2] * T);
double delta = Angle.ToRadians(eq.Delta);
double alpha = Angle.ToRadians(eq.Alpha);
double delta0 = Angle.ToRadians(eq0.Delta);
double dAlpha0 = Angle.ToRadians(eq0.Alpha - eq.Alpha);
double sinD = -Math.Sin(delta0) * Math.Sin(delta) - Math.Cos(delta0) * Math.Cos(delta) * Math.Cos(dAlpha0);
// planetographic latitude of the Earth
a.D = Angle.ToDegrees(Math.Asin(sinD));
double cosD = Math.Cos(Angle.ToRadians(a.D));
double sinP = Math.Cos(delta0) * Math.Sin(dAlpha0) / cosD;
double cosP = (Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(dAlpha0)) / cosD;
// position angle of the axis
a.P = Angle.To360(Angle.ToDegrees(Math.Atan2(sinP, cosP)));
double sinK = (-Math.Cos(delta0) * Math.Sin(delta) + Math.Sin(delta0) * Math.Cos(delta) * Math.Cos(dAlpha0)) / cosD;
double cosK = Math.Cos(delta) * Math.Sin(dAlpha0) / cosD;
double K = Angle.ToDegrees(Math.Atan2(sinK, cosK));
// planetographic longitude of the central meridian
a.CM = planet == 5 ?
JupiterCM2(jd) :
Angle.To360(Math.Sign(W) * (W - K));
return(a);
}
public static CrdsRectangular[,] Positions(double jd, CrdsHeliocentrical earth, CrdsHeliocentrical jupiter)
{
CrdsRectangular[,] positions = new CrdsRectangular[4, 2];
// distance from Earth to Jupiter
double distance = jupiter.ToRectangular(earth).ToEcliptical().Distance;
// light-time effect
double tau = PlanetPositions.LightTimeEffect(distance);
// time, in days, since calculation epoch, with respect of light-time effect
double t = jd - 2443000.5 - tau;
double[] l_deg = new double[5];
l_deg[1] = 106.07719 + 203.488955790 * t;
l_deg[2] = 175.73161 + 101.374724735 * t;
l_deg[3] = 120.55883 + 50.317609207 * t;
l_deg[4] = 84.44459 + 21.571071177 * t;
double[] l = new double[5];
for (int i = 0; i < 5; i++)
{
l[i] = ToRadians(l_deg[i]);
}
double[] pi = new double[5];
pi[1] = ToRadians(To360(97.0881 + 0.16138586 * t));
pi[2] = ToRadians(To360(154.8663 + 0.04726307 * t));
pi[3] = ToRadians(To360(188.1840 + 0.00712734 * t));
pi[4] = ToRadians(To360(335.2868 + 0.00184000 * t));
double[] w = new double[5];
w[1] = ToRadians(312.3346 - 0.13279386 * t);
w[2] = ToRadians(100.4411 - 0.03263064 * t);
w[3] = ToRadians(119.1942 - 0.00717703 * t);
w[4] = ToRadians(322.6186 - 0.00175934 * t);
// Principal inequality in the longitude of Jupiter:
double GAMMA = 0.33033 * Sin(ToRadians(163.679 + 0.0010512 * t)) +
0.03439 * Sin(ToRadians(34.486 - 0.0161731 * t));
// Phase of small libraton:
double PHI_lambda = ToRadians(199.6766 + 0.17379190 * t);
// Longitude of the node of the equator of Jupiter on the ecliptic:
double psi = ToRadians(316.5182 - 0.00000208 * t);
// Mean anomalies of Jupiter and Saturn:
double G = ToRadians(30.23756 + 0.0830925701 * t + GAMMA);
double G_ = ToRadians(31.97853 + 0.0334597339 * t);
// Longitude of the perihelion of Jupiter:
double Pi = ToRadians(13.469942);
double[] SIGMA = new double[5];
SIGMA[1] =
0.47259 * Sin(2 * (l[1] - l[2])) +
-0.03478 * Sin(pi[3] - pi[4]) +
0.01081 * Sin(l[2] - 2 * l[3] + pi[3]) +
0.00738 * Sin(PHI_lambda) +
0.00713 * Sin(l[2] - 2 * l[3] + pi[2]) +
-0.00674 * Sin(pi[1] + pi[3] - 2 * Pi - 2 * G) +
0.00666 * Sin(l[2] - 2 * l[3] + pi[4]) +
0.00445 * Sin(l[1] - pi[3]) +
-0.00354 * Sin(l[1] - l[2]) +
-0.00317 * Sin(2 * psi - 2 * Pi) +
0.00265 * Sin(l[1] - pi[4]) +
-0.00186 * Sin(G) +
0.00162 * Sin(pi[2] - pi[3]) +
0.00158 * Sin(4 * (l[1] - l[2])) +
-0.00155 * Sin(l[1] - l[3]) +
-0.00138 * Sin(psi + w[3] - 2 * Pi - 2 * G) +
-0.00115 * Sin(2 * (l[1] - 2 * l[2] + w[2])) +
0.00089 * Sin(pi[2] - pi[4]) +
0.00085 * Sin(l[1] + pi[3] - 2 * Pi - 2 * G) +
0.00083 * Sin(w[2] - w[3]) +
0.00053 * Sin(psi - w[2]);
SIGMA[2] =
1.06476 * Sin(2 * (l[2] - l[3])) +
0.04256 * Sin(l[1] - 2 * l[2] + pi[3]) +
0.03581 * Sin(l[2] - pi[3]) +
0.02395 * Sin(l[1] - 2 * l[2] + pi[4]) +
0.01984 * Sin(l[2] - pi[4]) +
-0.01778 * Sin(PHI_lambda) +
0.01654 * Sin(l[2] - pi[2]) +
0.01334 * Sin(l[2] - 2 * l[3] + pi[2]) +
0.01294 * Sin(pi[3] - pi[4]) +
-0.01142 * Sin(l[2] - l[3]) +
-0.01057 * Sin(G) +
-0.00775 * Sin(2 * (psi - Pi)) +
0.00524 * Sin(2 * (l[1] - l[2])) +
-0.00460 * Sin(l[1] - l[3]) +
0.00316 * Sin(psi - 2 * G + w[3] - 2 * Pi) +
-0.00203 * Sin(pi[1] + pi[3] - 2 * Pi - 2 * G) +
0.00146 * Sin(psi - w[3]) +
-0.00145 * Sin(2 * G) +
0.00125 * Sin(psi - w[4]) +
-0.00115 * Sin(l[1] - 2 * l[3] + pi[3]) +
-0.00094 * Sin(2 * (l[2] - w[2])) +
0.00086 * Sin(2 * (l[1] - 2 * l[2] + w[2])) +
-0.00086 * Sin(5 * G_ - 2 * G + ToRadians(52.225)) +
-0.00078 * Sin(l[2] - l[4]) +
-0.00064 * Sin(3 * l[3] - 7 * l[4] + 4 * pi[4]) +
0.00064 * Sin(pi[1] - pi[4]) +
-0.00063 * Sin(l[1] - 2 * l[3] + pi[4]) +
0.00058 * Sin(w[3] - w[4]) +
0.00056 * Sin(2 * (psi - Pi - G)) +
0.00056 * Sin(2 * (l[2] - l[4])) +
0.00055 * Sin(2 * (l[1] - l[3])) +
0.00052 * Sin(3 * l[3] - 7 * l[4] + pi[3] + 3 * pi[4]) +
-0.00043 * Sin(l[1] - pi[3]) +
0.00041 * Sin(5 * (l[2] - l[3])) +
0.00041 * Sin(pi[4] - Pi) +
0.00032 * Sin(w[2] - w[3]) +
0.00032 * Sin(2 * (l[3] - G - Pi));
SIGMA[3] =
0.16490 * Sin(l[3] - pi[3]) +
0.09081 * Sin(l[3] - pi[4]) +
-0.06907 * Sin(l[2] - l[3]) +
0.03784 * Sin(pi[3] - pi[4]) +
0.01846 * Sin(2 * (l[3] - l[4])) +
-0.01340 * Sin(G) +
-0.01014 * Sin(2 * (psi - Pi)) +
0.00704 * Sin(l[2] - 2 * l[3] + pi[3]) +
-0.00620 * Sin(l[2] - 2 * l[3] + pi[2]) +
-0.00541 * Sin(l[3] - l[4]) +
0.00381 * Sin(l[2] - 2 * l[3] + pi[4]) +
0.00235 * Sin(psi - w[3]) +
0.00198 * Sin(psi - w[4]) +
0.00176 * Sin(PHI_lambda) +
0.00130 * Sin(3 * (l[3] - l[4])) +
0.00125 * Sin(l[1] - l[3]) +
-0.00119 * Sin(5 * G_ - 2 * G + ToRadians(52.225)) +
0.00109 * Sin(l[1] - l[2]) +
-0.00100 * Sin(3 * l[3] - 7 * l[4] + 4 * pi[4]) +
0.00091 * Sin(w[3] - w[4]) +
0.00080 * Sin(3 * l[3] - 7 * l[4] + pi[3] + 3 * pi[4]) +
-0.00075 * Sin(2 * l[2] - 3 * l[3] + pi[3]) +
0.00072 * Sin(pi[1] + pi[3] - 2 * Pi - 2 * G) +
0.00069 * Sin(pi[4] - Pi) +
-0.00058 * Sin(2 * l[3] - 3 * l[4] + pi[4]) +
-0.00057 * Sin(l[3] - 2 * l[4] + pi[4]) +
0.00056 * Sin(l[3] + pi[3] - 2 * Pi - 2 * G) +
-0.00052 * Sin(l[2] - 2 * l[3] + pi[1]) +
-0.00050 * Sin(pi[2] - pi[3]) +
0.00048 * Sin(l[3] - 2 * l[4] + pi[3]) +
-0.00045 * Sin(2 * l[2] - 3 * l[3] + pi[4]) +
-0.00041 * Sin(pi[2] - pi[4]) +
-0.00038 * Sin(2 * G) +
-0.00037 * Sin(pi[3] - pi[4] + w[3] - w[4]) +
-0.00032 * Sin(3 * l[3] - 7 * l[4] + 2 * pi[3] + 2 * pi[4]) +
0.00030 * Sin(4 * (l[3] - l[4])) +
0.00029 * Sin(l[3] + pi[4] - 2 * Pi - 2 * G) +
-0.00028 * Sin(w[3] + psi - 2 * Pi - 2 * G) +
0.00026 * Sin(l[3] - Pi - G) +
0.00024 * Sin(l[2] - 3 * l[3] + 2 * l[4]) +
0.00021 * Sin(l[3] - Pi - G) +
-0.00021 * Sin(l[3] - pi[2]) +
0.00017 * Sin(2 * (l[3] - pi[3]));
SIGMA[4] =
0.84287 * Sin(l[4] - pi[4]) +
0.03431 * Sin(pi[4] - pi[3]) +
-0.03305 * Sin(2 * (psi - Pi)) +
-0.03211 * Sin(G) +
-0.01862 * Sin(l[4] - pi[3]) +
0.01186 * Sin(psi - w[4]) +
0.00623 * Sin(l[4] + pi[4] - 2 * G - 2 * Pi) +
0.00387 * Sin(2 * (l[4] - pi[4])) +
-0.00284 * Sin(5 * G_ - 2 * G + ToRadians(52.225)) +
-0.00234 * Sin(2 * (psi - pi[4])) +
-0.00223 * Sin(l[3] - l[4]) +
-0.00208 * Sin(l[4] - Pi) +
0.00178 * Sin(psi + w[4] - 2 * pi[4]) +
0.00134 * Sin(pi[4] - Pi) +
0.00125 * Sin(2 * (l[4] - G - Pi)) +
-0.00117 * Sin(2 * G) +
-0.00112 * Sin(2 * (l[3] - l[4])) +
0.00107 * Sin(3 * l[3] - 7 * l[4] + 4 * pi[4]) +
0.00102 * Sin(l[4] - G - Pi) +
0.00096 * Sin(2 * l[4] - psi - w[4]) +
0.00087 * Sin(2 * (psi - w[4])) +
-0.00085 * Sin(3 * l[3] - 7 * l[4] + pi[3] + 3 * pi[4]) +
0.00085 * Sin(l[3] - 2 * l[4] + pi[4]) +
-0.00081 * Sin(2 * (l[4] - psi)) +
0.00071 * Sin(l[4] + pi[4] - 2 * Pi - 3 * G) +
0.00061 * Sin(l[1] - l[4]) +
-0.00056 * Sin(psi - w[3]) +
-0.00054 * Sin(l[3] - 2 * l[4] + pi[3]) +
0.00051 * Sin(l[2] - l[4]) +
0.00042 * Sin(2 * (psi - G - Pi)) +
0.00039 * Sin(2 * (pi[4] - w[4])) +
0.00036 * Sin(psi + Pi - pi[4] - w[4]) +
0.00035 * Sin(2 * G_ - G + ToRadians(188.37)) +
-0.00035 * Sin(l[4] - pi[4] + 2 * Pi - 2 * psi) +
-0.00032 * Sin(l[4] + pi[4] - 2 * Pi - G) +
0.00030 * Sin(2 * G_ - 2 * G + ToRadians(149.15)) +
0.00029 * Sin(3 * l[3] - 7 * l[4] + 2 * pi[3] + 2 * pi[4]) +
0.00028 * Sin(l[4] - pi[4] + 2 * psi - 2 * Pi) +
-0.00028 * Sin(2 * (l[4] - w[4])) +
-0.00027 * Sin(pi[3] - pi[4] + w[3] - w[4]) +
-0.00026 * Sin(5 * G_ - 3 * G + ToRadians(188.37)) +
0.00025 * Sin(w[4] - w[3]) +
-0.00025 * Sin(l[2] - 3 * l[3] + 2 * l[4]) +
-0.00023 * Sin(3 * (l[3] - l[4])) +
0.00021 * Sin(2 * l[4] - 2 * Pi - 3 * G) +
-0.00021 * Sin(2 * l[3] - 3 * l[4] + pi[4]) +
0.00019 * Sin(l[4] - pi[4] - G) +
-0.00019 * Sin(2 * l[4] - pi[3] - pi[4]) +
-0.00018 * Sin(l[4] - pi[4] + G) +
-0.00016 * Sin(l[4] + pi[3] - 2 * Pi - 2 * G);
// True longitudes of the sattelites:
double[] L = new double[5];
for (int i = 0; i < 5; i++)
{
L[i] = ToRadians(To360(l_deg[i] + SIGMA[i]));
SIGMA[i] = ToRadians(SIGMA[i]);
}
double[] BB = new double[5];
BB[1] = Atan(
0.0006393 * Sin(L[1] - w[1]) +
0.0001825 * Sin(L[1] - w[2]) +
0.0000329 * Sin(L[1] - w[3]) +
-0.0000311 * Sin(L[1] - psi) +
0.0000093 * Sin(L[1] - w[4]) +
0.0000075 * Sin(3 * L[1] - 4 * l[2] - 1.9927 * SIGMA[1] + w[2]) +
0.0000046 * Sin(L[1] + psi - 2 * Pi - 2 * G));
BB[2] = Atan(
0.0081004 * Sin(L[2] - w[2]) +
0.0004512 * Sin(L[2] - w[3]) +
-0.0003284 * Sin(L[2] - psi) +
0.0001160 * Sin(L[2] - w[4]) +
0.0000272 * Sin(l[1] - 2 * l[3] + 1.0146 * SIGMA[2] + w[2]) +
-0.0000144 * Sin(L[2] - w[1]) +
0.0000143 * Sin(L[2] + psi - 2 * Pi - 2 * G) +
0.0000035 * Sin(L[2] - psi + G) +
-0.0000028 * Sin(l[1] - 2 * l[3] + 1.0146 * SIGMA[2] + w[3]));
BB[3] = Atan(
0.0032402 * Sin(L[3] - w[3]) +
-0.0016911 * Sin(L[3] - psi) +
0.0006847 * Sin(L[3] - w[4]) +
-0.0002797 * Sin(L[3] - w[2]) +
0.0000321 * Sin(L[3] + psi - 2 * Pi - 2 * G) +
0.0000051 * Sin(L[3] - psi + G) +
-0.0000045 * Sin(L[3] - psi - G) +
-0.0000045 * Sin(L[3] + psi - 2 * Pi) +
0.0000037 * Sin(L[3] + psi - 2 * Pi - 3 * G) +
0.0000030 * Sin(2 * l[2] - 3 * L[3] + 4.03 * SIGMA[3] + w[2]) +
-0.0000021 * Sin(2 * l[2] - 3 * L[3] + 4.03 * SIGMA[3] + w[3]));
BB[4] = Atan(
-0.0076579 * Sin(L[4] - psi) +
0.0044134 * Sin(L[4] - w[4]) +
-0.0005112 * Sin(L[4] - w[3]) +
0.0000773 * Sin(L[4] + psi - 2 * Pi - 2 * G) +
0.0000104 * Sin(L[4] - psi + G) +
-0.0000102 * Sin(L[4] - psi - G) +
0.0000088 * Sin(L[4] + psi - 2 * Pi - 3 * G) +
-0.0000038 * Sin(L[4] + psi - 2 * Pi - G));
double[] R = new double[5];
R[1] =
5.90569 * (1 + (-0.0041339 * Cos(2 * (l[1] - l[2])) +
-0.0000387 * Cos(l[1] - pi[3]) +
-0.0000214 * Cos(l[1] - pi[4]) +
0.0000170 * Cos(l[1] - l[2]) +
-0.0000131 * Cos(4 * (l[1] - l[2])) +
0.0000106 * Cos(l[1] - l[3]) +
-0.0000066 * Cos(l[1] + pi[3] - 2 * Pi - 2 * G)));
R[2] =
9.39657 * (1 + (0.0093848 * Cos(l[1] - l[2]) +
-0.0003116 * Cos(l[2] - pi[3]) +
-0.0001744 * Cos(l[2] - pi[4]) +
-0.0001442 * Cos(l[2] - pi[2]) +
0.0000553 * Cos(l[2] - l[3]) +
0.0000523 * Cos(l[1] - l[3]) +
-0.0000290 * Cos(2 * (l[1] - l[2])) +
0.0000164 * Cos(2 * (l[2] - w[2])) +
0.0000107 * Cos(l[1] - 2 * l[3] + pi[3]) +
-0.0000102 * Cos(l[2] - pi[1]) +
-0.0000091 * Cos(2 * (l[1] - l[3]))));
R[3] =
14.98832 * (1 + (-0.0014388 * Cos(l[3] - pi[3]) +
-0.0007919 * Cos(l[3] - pi[4]) +
0.0006342 * Cos(l[2] - l[3]) +
-0.0001761 * Cos(2 * (l[3] - l[4])) +
0.0000294 * Cos(l[3] - l[4]) +
-0.0000156 * Cos(3 * (l[3] - l[4])) +
0.0000156 * Cos(l[1] - l[3]) +
-0.0000153 * Cos(l[1] - l[2]) +
0.0000070 * Cos(2 * l[2] - 3 * l[3] + pi[3]) +
-0.0000051 * Cos(l[3] + pi[3] - 2 * Pi - 2 * G)));
R[4] =
26.36273 * (1 + (-0.0073546 * Cos(l[4] - pi[4]) +
0.0001621 * Cos(l[4] - pi[3]) +
0.0000974 * Cos(l[3] - l[4]) +
-0.0000543 * Cos(l[4] + pi[4] - 2 * Pi - 2 * G) +
-0.0000271 * Cos(2 * (l[4] - pi[4])) +
0.0000182 * Cos(l[4] - Pi) +
0.0000177 * Cos(2 * (l[3] - l[4])) +
-0.0000167 * Cos(2 * l[4] - psi - w[4]) +
0.0000167 * Cos(psi - w[4]) +
-0.0000155 * Cos(2 * (l[4] - Pi - G)) +
0.0000142 * Cos(2 * (l[4] - psi)) +
0.0000105 * Cos(l[1] - l[4]) +
0.0000092 * Cos(l[2] - l[4]) +
-0.0000089 * Cos(l[4] - Pi - G) +
-0.0000062 * Cos(l[4] + pi[4] - 2 * Pi - 3 * G) +
0.0000048 * Cos(2 * (l[4] - w[4]))));
double T0 = (jd - 2433282.423) / 36525.0;
double P = ToRadians(1.3966626 * T0 + 0.0003088 * T0 * T0);
for (int i = 0; i < 5; i++)
{
L[i] += P;
}
psi += P;
double T = (jd - 2415020.5) / 36525;
double I = ToRadians(3.120262 + 0.0006 * T);
double[] X = new double[6];
double[] Y = new double[6];
double[] Z = new double[6];
for (int i = 1; i < 5; i++)
{
X[i] = R[i] * Cos(L[i] - psi) * Cos(BB[i]);
Y[i] = R[i] * Sin(L[i] - psi) * Cos(BB[i]);
Z[i] = R[i] * Sin(BB[i]);
}
X[5] = 0; Y[5] = 0; Z[5] = 1;
double[] A1 = new double[6];
double[] B1 = new double[6];
double[] C1 = new double[6];
for (int i = 1; i < 6; i++)
{
A1[i] = X[i];
B1[i] = Y[i] * Cos(I) - Z[i] * Sin(I);
C1[i] = Y[i] * Sin(I) + Z[i] * Cos(I);
}
double[] A2 = new double[6];
double[] B2 = new double[6];
double[] C2 = new double[6];
double T1 = (jd - 2451545.0) / 36525;
double T2 = T1 * T1;
double T3 = T2 * T1;
double OMEGA = 100.464407 + 1.0209774 * T1 + 0.00040315 * T2 + 0.000000404 * T3;
OMEGA = ToRadians(OMEGA);
double Inc = 1.303267 - 0.0054965 * T1 + 0.00000466 * T2 + 0.000000002 * T3;
Inc = ToRadians(Inc);
double PHI = psi - OMEGA;
for (int i = 5; i >= 1; i--)
{
A2[i] = A1[i] * Cos(PHI) - B1[i] * Sin(PHI);
B2[i] = A1[i] * Sin(PHI) + B1[i] * Cos(PHI);
C2[i] = C1[i];
}
double[] A3 = new double[6];
double[] B3 = new double[6];
double[] C3 = new double[6];
for (int i = 5; i >= 1; i--)
{
A3[i] = A2[i];
B3[i] = B2[i] * Cos(Inc) - C2[i] * Sin(Inc);
C3[i] = B2[i] * Sin(Inc) + C2[i] * Cos(Inc);
}
double[] A4 = new double[6];
double[] B4 = new double[6];
double[] C4 = new double[6];
for (int i = 5; i >= 1; i--)
{
A4[i] = A3[i] * Cos(OMEGA) - B3[i] * Sin(OMEGA);
B4[i] = A3[i] * Sin(OMEGA) + B3[i] * Cos(OMEGA);
C4[i] = C3[i];
}
double[] A5 = new double[6];
double[] B5 = new double[6];
double[] C5 = new double[6];
for (int m = 0; m < 2; m++)
{
// "0" for shadows
double Radius = m == 0 ? earth.R : 0;
// Rectangular geocentric ecliptic coordinates of Jupiter:
double x = jupiter.R * Cos(ToRadians(jupiter.B)) * Cos(ToRadians(jupiter.L)) + Radius * Cos(ToRadians(earth.L + 180));
double y = jupiter.R * Cos(ToRadians(jupiter.B)) * Sin(ToRadians(jupiter.L)) + Radius * Sin(ToRadians(earth.L + 180));
double z = jupiter.R * Sin(ToRadians(jupiter.B)) + Radius * Sin(ToRadians(-earth.B));
double Delta = Sqrt(x * x + y * y + z * z);
double LAMBDA = Atan2(y, x);
double alpha = Atan(z / Sqrt(x * x + y * y));
for (int i = 5; i >= 1; i--)
{
A5[i] = A4[i] * Sin(LAMBDA) - B4[i] * Cos(LAMBDA);
B5[i] = A4[i] * Cos(LAMBDA) + B4[i] * Sin(LAMBDA);
C5[i] = C4[i];
}
double[] A6 = new double[6];
double[] B6 = new double[6];
double[] C6 = new double[6];
for (int i = 5; i >= 1; i--)
{
A6[i] = A5[i];
B6[i] = C5[i] * Sin(alpha) + B5[i] * Cos(alpha);
C6[i] = C5[i] * Cos(alpha) - B5[i] * Sin(alpha);
}
double D = Atan2(A6[5], C6[5]);
CrdsRectangular[] rectangular = new CrdsRectangular[4];
for (int i = 0; i < 4; i++)
{
rectangular[i] = new CrdsRectangular(
A6[i + 1] * Cos(D) - C6[i + 1] * Sin(D),
A6[i + 1] * Sin(D) + C6[i + 1] * Cos(D),
B6[i + 1]
);
}
double[] K = { 17295, 21819, 27558, 36548 };
for (int i = 0; i < 4; i++)
{
rectangular[i].X += Abs(rectangular[i].Z) / K[i] * Sqrt(1 - Pow(rectangular[i].X / R[i + 1], 2));
}
for (int i = 0; i < 4; i++)
{
double W = Delta / (Delta + rectangular[i].Z / 2095.0);
rectangular[i].X *= W;
rectangular[i].Y *= W;
}
for (int i = 0; i < 4; i++)
{
positions[i, m] = rectangular[i];
}
}
return(positions);
}