public static AASNodeObjectDetails PassageThroDescendingNode(ref AASEllipticalObjectElements elements)
{
double v = AASCoordinateTransformation.MapTo0To360Range(180 - elements.w);
v = AASCoordinateTransformation.DegreesToRadians(v);
double E = Math.Atan(Math.Sqrt((1 - elements.e) / (1 + elements.e)) * Math.Tan(v / 2)) * 2;
double M = E - elements.e * Math.Sin(E);
M = AASCoordinateTransformation.RadiansToDegrees(M);
double n = AASElliptical.MeanMotionFromSemiMajorAxis(elements.a);
AASNodeObjectDetails details = new AASNodeObjectDetails();
details.t = elements.T + M / n;
details.radius = elements.a * (1 - elements.e * Math.Cos(E));
return(details);
}
public static CAAPhysicalMarsDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
CAAPhysicalMarsDetails details = new CAAPhysicalMarsDetails();
//Step 1
double T = (JD - 2451545) / 36525;
double Lambda0 = 352.9065 + 1.17330 * T;
double Lambda0rad = AASCoordinateTransformation.DegreesToRadians(Lambda0);
double Beta0 = 63.2818 - 0.00394 * T;
double Beta0rad = AASCoordinateTransformation.DegreesToRadians(Beta0);
//Step 2
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
double PreviousLightTravelTime = 0;
double LightTravelTime = 0;
double x = 0;
double y = 0;
double z = 0;
bool bIterate = true;
double DELTA = 0;
double l = 0;
double lrad = 0;
double b = 0;
double r = 0;
while (bIterate)
{
double JD2 = JD - LightTravelTime;
//Step 3
l = AASMars.EclipticLongitude(JD2, bHighPrecision);
lrad = AASCoordinateTransformation.DegreesToRadians(l);
b = AASMars.EclipticLatitude(JD2, bHighPrecision);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASMars.RadiusVector(JD2, bHighPrecision);
//Step 4
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
LightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(LightTravelTime - PreviousLightTravelTime) > 2E-6); //2E-6 correponds to 0.17 of a second
if (bIterate)
{
PreviousLightTravelTime = LightTravelTime;
}
}
//Step 5
double lambdarad = Math.Atan2(y, x);
double lambda = AASCoordinateTransformation.RadiansToDegrees(lambdarad);
double betarad = Math.Atan2(z, Math.Sqrt(x * x + y * y));
double beta = AASCoordinateTransformation.RadiansToDegrees(betarad);
//Step 6
details.DE = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(betarad) - Math.Cos(Beta0rad) * Math.Cos(betarad) * Math.Cos(Lambda0rad - lambdarad)));
//Step 7
double N = 49.5581 + 0.7721 * T;
double Nrad = AASCoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.00697 / r;
double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000225 * (Math.Cos(lrad - Nrad) / r);
double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash);
//Step 8
details.DS = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(-Math.Sin(Beta0rad) * Math.Sin(bdashrad) - Math.Cos(Beta0rad) * Math.Cos(bdashrad) * Math.Cos(Lambda0rad - ldashrad)));
//Step 9
double W = AASCoordinateTransformation.MapTo0To360Range(11.504 + 350.89200025 * (JD - LightTravelTime - 2433282.5));
//Step 10
double e0 = AASNutation.MeanObliquityOfEcliptic(JD);
double e0rad = AASCoordinateTransformation.DegreesToRadians(e0);
AAS2DCoordinate PoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0rad = AASCoordinateTransformation.HoursToRadians(PoleEquatorial.X);
double delta0rad = AASCoordinateTransformation.DegreesToRadians(PoleEquatorial.Y);
//Step 11
double u = y * Math.Cos(e0rad) - z * Math.Sin(e0rad);
double v = y * Math.Sin(e0rad) + z * Math.Cos(e0rad);
double alpharad = Math.Atan2(u, x);
double alpha = AASCoordinateTransformation.RadiansToHours(alpharad);
double deltarad = Math.Atan2(v, Math.Sqrt(x * x + u * u));
double delta = AASCoordinateTransformation.RadiansToDegrees(deltarad);
double xi = Math.Atan2(Math.Sin(delta0rad) * Math.Cos(deltarad) * Math.Cos(alpha0rad - alpharad) - Math.Sin(deltarad) * Math.Cos(delta0rad), Math.Cos(deltarad) * Math.Sin(alpha0rad - alpharad));
//Step 12
details.w = AASCoordinateTransformation.MapTo0To360Range(W - AASCoordinateTransformation.RadiansToDegrees(xi));
//Step 13
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
double NutationInObliquity = AASNutation.NutationInObliquity(JD);
//Step 14
lambda += 0.005693 * Math.Cos(l0rad - lambdarad) / Math.Cos(betarad);
beta += 0.005693 * Math.Sin(l0rad - lambdarad) * Math.Sin(betarad);
//Step 15
Lambda0 += NutationInLongitude / 3600;
lambda += NutationInLongitude / 3600;
e0 += NutationInObliquity / 3600;
//Step 16
AAS2DCoordinate ApparentPoleEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(Lambda0, Beta0, e0);
double alpha0dash = AASCoordinateTransformation.HoursToRadians(ApparentPoleEquatorial.X);
double delta0dash = AASCoordinateTransformation.DegreesToRadians(ApparentPoleEquatorial.Y);
AAS2DCoordinate ApparentMars = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, e0);
double alphadash = AASCoordinateTransformation.HoursToRadians(ApparentMars.X);
double deltadash = AASCoordinateTransformation.DegreesToRadians(ApparentMars.Y);
//Step 17
details.P = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0dash) * Math.Sin(alpha0dash - alphadash), Math.Sin(delta0dash) * Math.Cos(deltadash) - Math.Cos(delta0dash) * Math.Sin(deltadash) * Math.Cos(alpha0dash - alphadash))));
//Step 18
double SunLambda = AASSun.GeometricEclipticLongitude(JD, bHighPrecision);
double SunBeta = AASSun.GeometricEclipticLatitude(JD, bHighPrecision);
AAS2DCoordinate SunEquatorial = AASCoordinateTransformation.Ecliptic2Equatorial(SunLambda, SunBeta, e0);
details.X = AASMoonIlluminatedFraction.PositionAngle(SunEquatorial.X, SunEquatorial.Y, alpha, delta);
//Step 19
details.d = 9.36 / DELTA;
details.k = AASIlluminatedFraction.IlluminatedFraction(r, R, DELTA);
details.q = (1 - details.k) * details.d;
return(details);
}
public static AASNearParabolicObjectDetails Calculate(double JD, ref AASNearParabolicObjectElements elements, bool bHighPrecision)
{
double Epsilon = AASNutation.MeanObliquityOfEcliptic(elements.JDEquinox);
double JD0 = JD;
//What will be the return value
AASNearParabolicObjectDetails details = new AASNearParabolicObjectDetails();
Epsilon = AASCoordinateTransformation.DegreesToRadians(Epsilon);
double omega = AASCoordinateTransformation.DegreesToRadians(elements.omega);
double w = AASCoordinateTransformation.DegreesToRadians(elements.w);
double i = AASCoordinateTransformation.DegreesToRadians(elements.i);
double sinEpsilon = Math.Sin(Epsilon);
double cosEpsilon = Math.Cos(Epsilon);
double sinOmega = Math.Sin(omega);
double cosOmega = Math.Cos(omega);
double cosi = Math.Cos(i);
double sini = Math.Sin(i);
double F = cosOmega;
double G = sinOmega * cosEpsilon;
double H = sinOmega * sinEpsilon;
double P = -sinOmega * cosi;
double Q = cosOmega * cosi * cosEpsilon - sini * sinEpsilon;
double R = cosOmega * cosi * sinEpsilon + sini * cosEpsilon;
double a = Math.Sqrt(F * F + P * P);
double b = Math.Sqrt(G * G + Q * Q);
double c = Math.Sqrt(H * H + R * R);
double A = Math.Atan2(F, P);
double B = Math.Atan2(G, Q);
double C = Math.Atan2(H, R);
AAS3DCoordinate SunCoord = AASSun.EquatorialRectangularCoordinatesAnyEquinox(JD, elements.JDEquinox, bHighPrecision);
for (int j = 0; j < 2; j++)
{
double v = 0;
double r = 0;
CalulateTrueAnnomalyAndRadius(JD0, ref elements, ref v, ref r);
double x = r * a * Math.Sin(A + w + v);
double y = r * b * Math.Sin(B + w + v);
double z = r * c * Math.Sin(C + w + v);
if (j == 0)
{
details.HeliocentricRectangularEquatorial.X = x;
details.HeliocentricRectangularEquatorial.Y = y;
details.HeliocentricRectangularEquatorial.Z = z;
//Calculate the heliocentric ecliptic coordinates also
double u = w + v;
double cosu = Math.Cos(u);
double sinu = Math.Sin(u);
details.HeliocentricRectangularEcliptical.X = r * (cosOmega * cosu - sinOmega * sinu * cosi);
details.HeliocentricRectangularEcliptical.Y = r * (sinOmega * cosu + cosOmega * sinu * cosi);
details.HeliocentricRectangularEcliptical.Z = r * sini * sinu;
details.HeliocentricEclipticLongitude = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(details.HeliocentricRectangularEcliptical.Y, details.HeliocentricRectangularEcliptical.X)));
details.HeliocentricEclipticLatitude = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(details.HeliocentricRectangularEcliptical.Z / r));
}
double psi = SunCoord.X + x;
double nu = SunCoord.Y + y;
double sigma = SunCoord.Z + z;
double Alpha = Math.Atan2(nu, psi);
Alpha = AASCoordinateTransformation.RadiansToDegrees(Alpha);
double Delta = Math.Atan2(sigma, Math.Sqrt(psi * psi + nu * nu));
Delta = AASCoordinateTransformation.RadiansToDegrees(Delta);
double Distance = Math.Sqrt(psi * psi + nu * nu + sigma * sigma);
if (j == 0)
{
details.TrueGeocentricRA = AASCoordinateTransformation.MapTo0To24Range(Alpha / 15);
details.TrueGeocentricDeclination = Delta;
details.TrueGeocentricDistance = Distance;
details.TrueGeocentricLightTime = AASElliptical.DistanceToLightTime(Distance);
}
else
{
details.AstrometricGeocentricRA = AASCoordinateTransformation.MapTo0To24Range(Alpha / 15);
details.AstrometricGeocentricDeclination = Delta;
details.AstrometricGeocentricDistance = Distance;
details.AstrometricGeocentricLightTime = AASElliptical.DistanceToLightTime(Distance);
double RES = Math.Sqrt(SunCoord.X * SunCoord.X + SunCoord.Y * SunCoord.Y + SunCoord.Z * SunCoord.Z);
details.Elongation = AASCoordinateTransformation.RadiansToDegrees(Math.Acos((RES * RES + Distance * Distance - r * r) / (2 * RES * Distance)));
details.PhaseAngle = AASCoordinateTransformation.RadiansToDegrees(Math.Acos((r * r + Distance * Distance - RES * RES) / (2 * r * Distance)));
}
if (j == 0) //Prepare for the next loop around
{
JD0 = JD - details.TrueGeocentricLightTime;
}
}
return(details);
}
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 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);
}
private static AASSaturnMoonsDetails CalculateHelper(double JD, double sunlongrad, double betarad, double R, bool bHighPrecision)
{
//What will be the return value
AASSaturnMoonsDetails details = new AASSaturnMoonsDetails();
//Calculate the position of Saturn decreased by the light travel time from Saturn to the specified position
double DELTA = 9;
double PreviousLightTravelTime = 0;
double LightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
double x = 0;
double y = 0;
double z = 0;
double JD1 = JD - LightTravelTime;
bool bIterate = true;
while (bIterate)
{
//Calculate the position of Saturn
double l = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
double lrad = AASCoordinateTransformation.DegreesToRadians(l);
double b = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
double r = AASSaturn.RadiusVector(JD1, bHighPrecision);
x = r * Math.Cos(brad) * Math.Cos(lrad) + R * Math.Cos(sunlongrad);
y = r * Math.Cos(brad) * Math.Sin(lrad) + R * Math.Sin(sunlongrad);
z = r * Math.Sin(brad) + R * Math.Sin(betarad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
LightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(LightTravelTime - PreviousLightTravelTime) > 2e-6); //2e-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - LightTravelTime;
PreviousLightTravelTime = LightTravelTime;
}
}
//Calculate Saturn's Longitude and Latitude
double lambda0 = Math.Atan2(y, x);
lambda0 = AASCoordinateTransformation.RadiansToDegrees(lambda0);
double beta0 = Math.Atan(z / Math.Sqrt(x * x + y * y));
beta0 = AASCoordinateTransformation.RadiansToDegrees(beta0);
//Precess the longtitude and Latitutude to B1950.0
AAS2DCoordinate Saturn1950 = AASPrecession.PrecessEcliptic(lambda0, beta0, JD, 2433282.4235);
lambda0 = Saturn1950.X;
double lambda0rad = AASCoordinateTransformation.DegreesToRadians(lambda0);
beta0 = Saturn1950.Y;
double beta0rad = AASCoordinateTransformation.DegreesToRadians(beta0);
double JDE = JD - LightTravelTime;
double t1 = JDE - 2411093.0;
double t2 = t1 / 365.25;
double t3 = ((JDE - 2433282.423) / 365.25) + 1950.0;
double t4 = JDE - 2411368.0;
double t5 = t4 / 365.25;
double t6 = JDE - 2415020.0;
double t7 = t6 / 36525.0;
double t8 = t6 / 365.25;
double t9 = (JDE - 2442000.5) / 365.25;
double t10 = JDE - 2409786.0;
double t11 = t10 / 36525.0;
double t112 = t11 * t11;
double t113 = t112 * t11;
double W0 = AASCoordinateTransformation.MapTo0To360Range(5.095 * (t3 - 1866.39));
double W0rad = AASCoordinateTransformation.DegreesToRadians(W0);
double W1 = AASCoordinateTransformation.MapTo0To360Range(74.4 + 32.39 * t2);
double W1rad = AASCoordinateTransformation.DegreesToRadians(W1);
double W2 = AASCoordinateTransformation.MapTo0To360Range(134.3 + 92.62 * t2);
double W2rad = AASCoordinateTransformation.DegreesToRadians(W2);
double W3 = AASCoordinateTransformation.MapTo0To360Range(42.0 - 0.5118 * t5);
double W3rad = AASCoordinateTransformation.DegreesToRadians(W3);
double W4 = AASCoordinateTransformation.MapTo0To360Range(276.59 + 0.5118 * t5);
double W4rad = AASCoordinateTransformation.DegreesToRadians(W4);
double W5 = AASCoordinateTransformation.MapTo0To360Range(267.2635 + 1222.1136 * t7);
double W5rad = AASCoordinateTransformation.DegreesToRadians(W5);
double W6 = AASCoordinateTransformation.MapTo0To360Range(175.4762 + 1221.5515 * t7);
double W6rad = AASCoordinateTransformation.DegreesToRadians(W6);
double W7 = AASCoordinateTransformation.MapTo0To360Range(2.4891 + 0.002435 * t7);
double W7rad = AASCoordinateTransformation.DegreesToRadians(W7);
double W8 = AASCoordinateTransformation.MapTo0To360Range(113.35 - 0.2597 * t7);
double W8rad = AASCoordinateTransformation.DegreesToRadians(W8);
double s1 = Math.Sin(AASCoordinateTransformation.DegreesToRadians(28.0817));
double s2 = Math.Sin(AASCoordinateTransformation.DegreesToRadians(168.8112));
double c1 = Math.Cos(AASCoordinateTransformation.DegreesToRadians(28.0817));
double c2 = Math.Cos(AASCoordinateTransformation.DegreesToRadians(168.8112));
double e1 = 0.05589 - 0.000346 * t7;
//Satellite 1
double L = AASCoordinateTransformation.MapTo0To360Range(127.64 + 381.994497 * t1 - 43.57 * Math.Sin(W0rad) - 0.720 * Math.Sin(3 * W0rad) - 0.02144 * Math.Sin(5 * W0rad));
double p = 106.1 + 365.549 * t2;
double M = L - p;
double Mrad = AASCoordinateTransformation.DegreesToRadians(M);
double C = 2.18287 * Math.Sin(Mrad) + 0.025988 * Math.Sin(2 * Mrad) + 0.00043 * Math.Sin(3 * Mrad);
double Crad = AASCoordinateTransformation.DegreesToRadians(C);
double lambda1 = AASCoordinateTransformation.MapTo0To360Range(L + C);
double r1 = 3.06879 / (1 + 0.01905 * Math.Cos(Mrad + Crad));
double gamma1 = 1.563;
double omega1 = AASCoordinateTransformation.MapTo0To360Range(54.5 - 365.072 * t2);
//Satellite 2
L = AASCoordinateTransformation.MapTo0To360Range(200.317 + 262.7319002 * t1 + 0.25667 * Math.Sin(W1rad) + 0.20883 * Math.Sin(W2rad));
p = 309.107 + 123.44121 * t2;
M = L - p;
Mrad = AASCoordinateTransformation.DegreesToRadians(M);
C = 0.55577 * Math.Sin(Mrad) + 0.00168 * Math.Sin(2 * Mrad);
Crad = AASCoordinateTransformation.DegreesToRadians(C);
double lambda2 = AASCoordinateTransformation.MapTo0To360Range(L + C);
double r2 = 3.94118 / (1 + 0.00485 * Math.Cos(Mrad + Crad));
double gamma2 = 0.0262;
double omega2 = AASCoordinateTransformation.MapTo0To360Range(348 - 151.95 * t2);
//Satellite 3
double lambda3 = AASCoordinateTransformation.MapTo0To360Range(285.306 + 190.69791226 * t1 + 2.063 * Math.Sin(W0rad) + 0.03409 * Math.Sin(3 * W0rad) + 0.001015 * Math.Sin(5 * W0rad));
double r3 = 4.880998;
double gamma3 = 1.0976;
double omega3 = AASCoordinateTransformation.MapTo0To360Range(111.33 - 72.2441 * t2);
//Satellite 4
L = AASCoordinateTransformation.MapTo0To360Range(254.712 + 131.53493193 * t1 - 0.0215 * Math.Sin(W1rad) - 0.01733 * Math.Sin(W2rad));
p = 174.8 + 30.820 * t2;
M = L - p;
Mrad = AASCoordinateTransformation.DegreesToRadians(M);
C = 0.24717 * Math.Sin(Mrad) + 0.00033 * Math.Sin(2 * Mrad);
Crad = AASCoordinateTransformation.DegreesToRadians(C);
double lambda4 = AASCoordinateTransformation.MapTo0To360Range(L + C);
double r4 = 6.24871 / (1 + 0.002157 * Math.Cos(Mrad + Crad));
double gamma4 = 0.0139;
double omega4 = AASCoordinateTransformation.MapTo0To360Range(232 - 30.27 * t2);
//Satellite 5
double pdash = 342.7 + 10.057 * t2;
double pdashrad = AASCoordinateTransformation.DegreesToRadians(pdash);
double a1 = 0.000265 * Math.Sin(pdashrad) + 0.001 * Math.Sin(W4rad); //Note the book uses the incorrect constant 0.01*Math.Sin(W4rad);
double a2 = 0.000265 * Math.Cos(pdashrad) + 0.001 * Math.Cos(W4rad); //Note the book uses the incorrect constant 0.01*cos(W4rad);
double e = Math.Sqrt(a1 * a1 + a2 * a2);
p = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(a1, a2));
double N = 345 - 10.057 * t2;
double Nrad = AASCoordinateTransformation.DegreesToRadians(N);
double lambdadash = AASCoordinateTransformation.MapTo0To360Range(359.244 + 79.69004720 * t1 + 0.086754 * Math.Sin(Nrad));
double i = 28.0362 + 0.346898 * Math.Cos(Nrad) + 0.01930 * Math.Cos(W3rad);
double omega = 168.8034 + 0.736936 * Math.Sin(Nrad) + 0.041 * Math.Sin(W3rad);
double a = 8.725924;
double lambda5 = 0;
double gamma5 = 0;
double omega5 = 0;
double r5 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r5, ref lambda5, ref gamma5, ref omega5);
//Satellite 6
L = 261.1582 + 22.57697855 * t4 + 0.074025 * Math.Sin(W3rad);
double idash = 27.45141 + 0.295999 * Math.Cos(W3rad);
double idashrad = AASCoordinateTransformation.DegreesToRadians(idash);
double omegadash = 168.66925 + 0.628808 * Math.Sin(W3rad);
double omegadashrad = AASCoordinateTransformation.DegreesToRadians(omegadash);
a1 = Math.Sin(W7rad) * Math.Sin(omegadashrad - W8rad);
a2 = Math.Cos(W7rad) * Math.Sin(idashrad) - Math.Sin(W7rad) * Math.Cos(idashrad) * Math.Cos(omegadashrad - W8rad);
double g0 = AASCoordinateTransformation.DegreesToRadians(102.8623);
double psi = Math.Atan2(a1, a2);
if (a2 < 0)
{
psi += AASCoordinateTransformation.PI();
}
double psideg = AASCoordinateTransformation.RadiansToDegrees(psi);
double s = Math.Sqrt(a1 * a1 + a2 * a2);
double g = W4 - omegadash - psideg;
double w_ = 0;
for (int j = 0; j < 3; j++)
{
w_ = W4 + 0.37515 * (Math.Sin(2 * AASCoordinateTransformation.DegreesToRadians(g)) - Math.Sin(2 * g0));
g = w_ - omegadash - psideg;
}
double grad = AASCoordinateTransformation.DegreesToRadians(g);
double edash = 0.029092 + 0.00019048 * (Math.Cos(2 * grad) - Math.Cos(2 * g0));
double q = AASCoordinateTransformation.DegreesToRadians(2 * (W5 - w_));
double b1 = Math.Sin(idashrad) * Math.Sin(omegadashrad - W8rad);
double b2 = Math.Cos(W7rad) * Math.Sin(idashrad) * Math.Cos(omegadashrad - W8rad) - Math.Sin(W7rad) * Math.Cos(idashrad);
double atanb1b2 = Math.Atan2(b1, b2);
double theta = atanb1b2 + W8rad;
e = edash + 0.002778797 * edash * Math.Cos(q);
p = w_ + 0.159215 * Math.Sin(q);
double u = 2 * W5rad - 2 * theta + psi;
double h = 0.9375 * edash * edash * Math.Sin(q) + 0.1875 * s * s * Math.Sin(2 * (W5rad - theta));
lambdadash = AASCoordinateTransformation.MapTo0To360Range(L - 0.254744 * (e1 * Math.Sin(W6rad) + 0.75 * e1 * e1 * Math.Sin(2 * W6rad) + h));
i = idash + 0.031843 * s * Math.Cos(u);
omega = omegadash + (0.031843 * s * Math.Sin(u)) / Math.Sin(idashrad);
a = 20.216193;
double lambda6 = 0;
double gamma6 = 0;
double omega6 = 0;
double r6 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r6, ref lambda6, ref gamma6, ref omega6);
//Satellite 7
double eta = 92.39 + 0.5621071 * t6;
double etarad = AASCoordinateTransformation.DegreesToRadians(eta);
double zeta = 148.19 - 19.18 * t8;
double zetarad = AASCoordinateTransformation.DegreesToRadians(zeta);
theta = AASCoordinateTransformation.DegreesToRadians(184.8 - 35.41 * t9);
double thetadash = theta - AASCoordinateTransformation.DegreesToRadians(7.5);
double aS = AASCoordinateTransformation.DegreesToRadians(176 + 12.22 * t8);
double bs = AASCoordinateTransformation.DegreesToRadians(8 + 24.44 * t8);
double cs = bs + AASCoordinateTransformation.DegreesToRadians(5);
w_ = 69.898 - 18.67088 * t8;
double phi = 2 * (w_ - W5);
double phirad = AASCoordinateTransformation.DegreesToRadians(phi);
double chi = 94.9 - 2.292 * t8;
double chirad = AASCoordinateTransformation.DegreesToRadians(chi);
a = 24.50601 - 0.08686 * Math.Cos(etarad) - 0.00166 * Math.Cos(zetarad + etarad) + 0.00175 * Math.Cos(zetarad - etarad);
e = 0.103458 - 0.004099 * Math.Cos(etarad) - 0.000167 * Math.Cos(zetarad + etarad) + 0.000235 * Math.Cos(zetarad - etarad) +
0.02303 * Math.Cos(zetarad) - 0.00212 * Math.Cos(2 * zetarad) + 0.000151 * Math.Cos(3 * zetarad) + 0.00013 * Math.Cos(phirad);
p = w_ + 0.15648 * Math.Sin(chirad) - 0.4457 * Math.Sin(etarad) - 0.2657 * Math.Sin(zetarad + etarad) +
-0.3573 * Math.Sin(zetarad - etarad) - 12.872 * Math.Sin(zetarad) + 1.668 * Math.Sin(2 * zetarad) +
-0.2419 * Math.Sin(3 * zetarad) - 0.07 * Math.Sin(phirad);
lambdadash = AASCoordinateTransformation.MapTo0To360Range(177.047 + 16.91993829 * t6 + 0.15648 * Math.Sin(chirad) + 9.142 * Math.Sin(etarad) +
0.007 * Math.Sin(2 * etarad) - 0.014 * Math.Sin(3 * etarad) + 0.2275 * Math.Sin(zetarad + etarad) +
0.2112 * Math.Sin(zetarad - etarad) - 0.26 * Math.Sin(zetarad) - 0.0098 * Math.Sin(2 * zetarad) +
-0.013 * Math.Sin(aS) + 0.017 * Math.Sin(bs) - 0.0303 * Math.Sin(phirad));
i = 27.3347 + 0.643486 * Math.Cos(chirad) + 0.315 * Math.Cos(W3rad) + 0.018 * Math.Cos(theta) - 0.018 * Math.Cos(cs);
omega = 168.6812 + 1.40136 * Math.Cos(chirad) + 0.68599 * Math.Sin(W3rad) - 0.0392 * Math.Sin(cs) + 0.0366 * Math.Sin(thetadash);
double lambda7 = 0;
double gamma7 = 0;
double omega7 = 0;
double r7 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r7, ref lambda7, ref gamma7, ref omega7);
//Satellite 8
L = AASCoordinateTransformation.MapTo0To360Range(261.1582 + 22.57697855 * t4);
double w_dash = 91.796 + 0.562 * t7;
psi = 4.367 - 0.195 * t7;
double psirad = AASCoordinateTransformation.DegreesToRadians(psi);
theta = 146.819 - 3.198 * t7;
phi = 60.470 + 1.521 * t7;
phirad = AASCoordinateTransformation.DegreesToRadians(phi);
double PHI = 205.055 - 2.091 * t7;
edash = 0.028298 + 0.001156 * t11;
double w_0 = 352.91 + 11.71 * t11;
double mu = AASCoordinateTransformation.MapTo0To360Range(76.3852 + 4.53795125 * t10);
idash = 18.4602 - 0.9518 * t11 - 0.072 * t112 + 0.0054 * t113;
idashrad = AASCoordinateTransformation.DegreesToRadians(idash);
omegadash = 143.198 - 3.919 * t11 + 0.116 * t112 + 0.008 * t113;
double _l = AASCoordinateTransformation.DegreesToRadians(mu - w_0);
g = AASCoordinateTransformation.DegreesToRadians(w_0 - omegadash - psi);
double g1 = AASCoordinateTransformation.DegreesToRadians(w_0 - omegadash - phi);
double ls = AASCoordinateTransformation.DegreesToRadians(W5 - w_dash);
double gs = AASCoordinateTransformation.DegreesToRadians(w_dash - theta);
double lt = AASCoordinateTransformation.DegreesToRadians(L - W4);
double gt = AASCoordinateTransformation.DegreesToRadians(W4 - PHI);
double u1 = 2 * (_l + g - ls - gs);
double u2 = _l + g1 - lt - gt;
double u3 = _l + 2 * (g - ls - gs);
double u4 = lt + gt - g1;
double u5 = 2 * (ls + gs);
a = 58.935028 + 0.004638 * Math.Cos(u1) + 0.058222 * Math.Cos(u2);
e = edash - 0.0014097 * Math.Cos(g1 - gt) + 0.0003733 * Math.Cos(u5 - 2 * g) +
0.0001180 * Math.Cos(u3) + 0.0002408 * Math.Cos(_l) +
0.0002849 * Math.Cos(_l + u2) + 0.0006190 * Math.Cos(u4);
double w = 0.08077 * Math.Sin(g1 - gt) + 0.02139 * Math.Sin(u5 - 2 * g) - 0.00676 * Math.Sin(u3) +
0.01380 * Math.Sin(_l) + 0.01632 * Math.Sin(_l + u2) + 0.03547 * Math.Sin(u4);
p = w_0 + w / edash;
lambdadash = mu - 0.04299 * Math.Sin(u2) - 0.00789 * Math.Sin(u1) - 0.06312 * Math.Sin(ls) +
-0.00295 * Math.Sin(2 * ls) - 0.02231 * Math.Sin(u5) + 0.00650 * Math.Sin(u5 + psirad);
i = idash + 0.04204 * Math.Cos(u5 + psirad) + 0.00235 * Math.Cos(_l + g1 + lt + gt + phirad) +
0.00360 * Math.Cos(u2 + phirad);
double wdash = 0.04204 * Math.Sin(u5 + psirad) + 0.00235 * Math.Sin(_l + g1 + lt + gt + phirad) +
0.00358 * Math.Sin(u2 + phirad);
omega = omegadash + wdash / Math.Sin(idashrad);
double lambda8 = 0;
double gamma8 = 0;
double omega8 = 0;
double r8 = 0;
HelperSubroutine(e, lambdadash, p, a, omega, i, c1, s1, ref r8, ref lambda8, ref gamma8, ref omega8);
u = AASCoordinateTransformation.DegreesToRadians(lambda1 - omega1);
w = AASCoordinateTransformation.DegreesToRadians(omega1 - 168.8112);
double gamma1rad = AASCoordinateTransformation.DegreesToRadians(gamma1);
double X1 = r1 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma1rad) * Math.Sin(w));
double Y1 = r1 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma1rad) + Math.Cos(u) * Math.Sin(w));
double Z1 = r1 * Math.Sin(u) * Math.Sin(gamma1rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda2 - omega2);
w = AASCoordinateTransformation.DegreesToRadians(omega2 - 168.8112);
double gamma2rad = AASCoordinateTransformation.DegreesToRadians(gamma2);
double X2 = r2 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma2rad) * Math.Sin(w));
double Y2 = r2 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma2rad) + Math.Cos(u) * Math.Sin(w));
double Z2 = r2 * Math.Sin(u) * Math.Sin(gamma2rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda3 - omega3);
w = AASCoordinateTransformation.DegreesToRadians(omega3 - 168.8112);
double gamma3rad = AASCoordinateTransformation.DegreesToRadians(gamma3);
double X3 = r3 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma3rad) * Math.Sin(w));
double Y3 = r3 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma3rad) + Math.Cos(u) * Math.Sin(w));
double Z3 = r3 * Math.Sin(u) * Math.Sin(gamma3rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda4 - omega4);
w = AASCoordinateTransformation.DegreesToRadians(omega4 - 168.8112);
double gamma4rad = AASCoordinateTransformation.DegreesToRadians(gamma4);
double X4 = r4 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma4rad) * Math.Sin(w));
double Y4 = r4 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma4rad) + Math.Cos(u) * Math.Sin(w));
double Z4 = r4 * Math.Sin(u) * Math.Sin(gamma4rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda5 - omega5);
w = AASCoordinateTransformation.DegreesToRadians(omega5 - 168.8112);
double gamma5rad = AASCoordinateTransformation.DegreesToRadians(gamma5);
double X5 = r5 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma5rad) * Math.Sin(w));
double Y5 = r5 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma5rad) + Math.Cos(u) * Math.Sin(w));
double Z5 = r5 * Math.Sin(u) * Math.Sin(gamma5rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda6 - omega6);
w = AASCoordinateTransformation.DegreesToRadians(omega6 - 168.8112);
double gamma6rad = AASCoordinateTransformation.DegreesToRadians(gamma6);
double X6 = r6 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma6rad) * Math.Sin(w));
double Y6 = r6 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma6rad) + Math.Cos(u) * Math.Sin(w));
double Z6 = r6 * Math.Sin(u) * Math.Sin(gamma6rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda7 - omega7);
w = AASCoordinateTransformation.DegreesToRadians(omega7 - 168.8112);
double gamma7rad = AASCoordinateTransformation.DegreesToRadians(gamma7);
double X7 = r7 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma7rad) * Math.Sin(w));
double Y7 = r7 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma7rad) + Math.Cos(u) * Math.Sin(w));
double Z7 = r7 * Math.Sin(u) * Math.Sin(gamma7rad);
u = AASCoordinateTransformation.DegreesToRadians(lambda8 - omega8);
w = AASCoordinateTransformation.DegreesToRadians(omega8 - 168.8112);
double gamma8rad = AASCoordinateTransformation.DegreesToRadians(gamma8);
double X8 = r8 * (Math.Cos(u) * Math.Cos(w) - Math.Sin(u) * Math.Cos(gamma8rad) * Math.Sin(w));
double Y8 = r8 * (Math.Sin(u) * Math.Cos(w) * Math.Cos(gamma8rad) + Math.Cos(u) * Math.Sin(w));
double Z8 = r8 * Math.Sin(u) * Math.Sin(gamma8rad);
double X9 = 0;
double Y9 = 0;
double Z9 = 1;
//Now do the rotations, first for the ficticious 9th satellite, so that we can calculate D
double A4 = 0;
double B4 = 0;
double C4 = 0;
Rotations(X9, Y9, Z9, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
double D = Math.Atan2(A4, C4);
//Now calculate the values for satellite 1
Rotations(X1, Y1, Z1, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite1.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite1.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite1.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 2
Rotations(X2, Y2, Z2, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite2.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite2.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite2.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 3
Rotations(X3, Y3, Z3, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite3.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite3.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite3.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 4
Rotations(X4, Y4, Z4, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite4.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite4.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite4.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 5
Rotations(X5, Y5, Z5, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite5.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite5.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite5.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 6
Rotations(X6, Y6, Z6, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite6.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite6.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite6.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 7
Rotations(X7, Y7, Z7, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite7.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite7.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite7.TrueRectangularCoordinates.Z = B4;
//Now calculate the values for satellite 8
Rotations(X8, Y8, Z8, c1, s1, c2, s2, lambda0rad, beta0rad, ref A4, ref B4, ref C4);
details.Satellite8.TrueRectangularCoordinates.X = A4 * Math.Cos(D) - C4 * Math.Sin(D);
details.Satellite8.TrueRectangularCoordinates.Y = A4 * Math.Sin(D) + C4 * Math.Cos(D);
details.Satellite8.TrueRectangularCoordinates.Z = B4;
//apply the differential light-time correction
details.Satellite1.ApparentRectangularCoordinates.X = details.Satellite1.TrueRectangularCoordinates.X + Math.Abs(details.Satellite1.TrueRectangularCoordinates.Z) / 20947 * Math.Sqrt(1 - (details.Satellite1.TrueRectangularCoordinates.X / r1) * (details.Satellite1.TrueRectangularCoordinates.X / r1));
details.Satellite1.ApparentRectangularCoordinates.Y = details.Satellite1.TrueRectangularCoordinates.Y;
details.Satellite1.ApparentRectangularCoordinates.Z = details.Satellite1.TrueRectangularCoordinates.Z;
details.Satellite2.ApparentRectangularCoordinates.X = details.Satellite2.TrueRectangularCoordinates.X + Math.Abs(details.Satellite2.TrueRectangularCoordinates.Z) / 23715 * Math.Sqrt(1 - (details.Satellite2.TrueRectangularCoordinates.X / r2) * (details.Satellite2.TrueRectangularCoordinates.X / r2));
details.Satellite2.ApparentRectangularCoordinates.Y = details.Satellite2.TrueRectangularCoordinates.Y;
details.Satellite2.ApparentRectangularCoordinates.Z = details.Satellite2.TrueRectangularCoordinates.Z;
details.Satellite3.ApparentRectangularCoordinates.X = details.Satellite3.TrueRectangularCoordinates.X + Math.Abs(details.Satellite3.TrueRectangularCoordinates.Z) / 26382 * Math.Sqrt(1 - (details.Satellite3.TrueRectangularCoordinates.X / r3) * (details.Satellite3.TrueRectangularCoordinates.X / r3));
details.Satellite3.ApparentRectangularCoordinates.Y = details.Satellite3.TrueRectangularCoordinates.Y;
details.Satellite3.ApparentRectangularCoordinates.Z = details.Satellite3.TrueRectangularCoordinates.Z;
details.Satellite4.ApparentRectangularCoordinates.X = details.Satellite4.TrueRectangularCoordinates.X + Math.Abs(details.Satellite4.TrueRectangularCoordinates.Z) / 29876 * Math.Sqrt(1 - (details.Satellite4.TrueRectangularCoordinates.X / r4) * (details.Satellite4.TrueRectangularCoordinates.X / r4));
details.Satellite4.ApparentRectangularCoordinates.Y = details.Satellite4.TrueRectangularCoordinates.Y;
details.Satellite4.ApparentRectangularCoordinates.Z = details.Satellite4.TrueRectangularCoordinates.Z;
details.Satellite5.ApparentRectangularCoordinates.X = details.Satellite5.TrueRectangularCoordinates.X + Math.Abs(details.Satellite5.TrueRectangularCoordinates.Z) / 35313 * Math.Sqrt(1 - (details.Satellite5.TrueRectangularCoordinates.X / r5) * (details.Satellite5.TrueRectangularCoordinates.X / r5));
details.Satellite5.ApparentRectangularCoordinates.Y = details.Satellite5.TrueRectangularCoordinates.Y;
details.Satellite5.ApparentRectangularCoordinates.Z = details.Satellite5.TrueRectangularCoordinates.Z;
details.Satellite6.ApparentRectangularCoordinates.X = details.Satellite6.TrueRectangularCoordinates.X + Math.Abs(details.Satellite6.TrueRectangularCoordinates.Z) / 53800 * Math.Sqrt(1 - (details.Satellite6.TrueRectangularCoordinates.X / r6) * (details.Satellite6.TrueRectangularCoordinates.X / r6));
details.Satellite6.ApparentRectangularCoordinates.Y = details.Satellite6.TrueRectangularCoordinates.Y;
details.Satellite6.ApparentRectangularCoordinates.Z = details.Satellite6.TrueRectangularCoordinates.Z;
details.Satellite7.ApparentRectangularCoordinates.X = details.Satellite7.TrueRectangularCoordinates.X + Math.Abs(details.Satellite7.TrueRectangularCoordinates.Z) / 59222 * Math.Sqrt(1 - (details.Satellite7.TrueRectangularCoordinates.X / r7) * (details.Satellite7.TrueRectangularCoordinates.X / r7));
details.Satellite7.ApparentRectangularCoordinates.Y = details.Satellite7.TrueRectangularCoordinates.Y;
details.Satellite7.ApparentRectangularCoordinates.Z = details.Satellite7.TrueRectangularCoordinates.Z;
details.Satellite8.ApparentRectangularCoordinates.X = details.Satellite8.TrueRectangularCoordinates.X + Math.Abs(details.Satellite8.TrueRectangularCoordinates.Z) / 91820 * Math.Sqrt(1 - (details.Satellite8.TrueRectangularCoordinates.X / r8) * (details.Satellite8.TrueRectangularCoordinates.X / r8));
details.Satellite8.ApparentRectangularCoordinates.Y = details.Satellite8.TrueRectangularCoordinates.Y;
details.Satellite8.ApparentRectangularCoordinates.Z = details.Satellite8.TrueRectangularCoordinates.Z;
//apply the perspective effect correction
double W = DELTA / (DELTA + details.Satellite1.TrueRectangularCoordinates.Z / 2475);
details.Satellite1.ApparentRectangularCoordinates.X *= W;
details.Satellite1.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite2.TrueRectangularCoordinates.Z / 2475);
details.Satellite2.ApparentRectangularCoordinates.X *= W;
details.Satellite2.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite3.TrueRectangularCoordinates.Z / 2475);
details.Satellite3.ApparentRectangularCoordinates.X *= W;
details.Satellite3.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite4.TrueRectangularCoordinates.Z / 2475);
details.Satellite4.ApparentRectangularCoordinates.X *= W;
details.Satellite4.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite5.TrueRectangularCoordinates.Z / 2475);
details.Satellite5.ApparentRectangularCoordinates.X *= W;
details.Satellite5.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite6.TrueRectangularCoordinates.Z / 2475);
details.Satellite6.ApparentRectangularCoordinates.X *= W;
details.Satellite6.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite7.TrueRectangularCoordinates.Z / 2475);
details.Satellite7.ApparentRectangularCoordinates.X *= W;
details.Satellite7.ApparentRectangularCoordinates.Y *= W;
W = DELTA / (DELTA + details.Satellite8.TrueRectangularCoordinates.Z / 2475);
details.Satellite8.ApparentRectangularCoordinates.X *= W;
details.Satellite8.ApparentRectangularCoordinates.Y *= W;
return(details);
}
public static AASSaturnRingDetails Calculate(double JD, bool bHighPrecision)
{
//What will be the return value
AASSaturnRingDetails details = new AASSaturnRingDetails();
double T = (JD - 2451545) / 36525;
double T2 = T * T;
//Step 1. Calculate the inclination of the plane of the ring and the longitude of the ascending node referred to the ecliptic and mean equinox of the date
double i = 28.075216 - 0.012998 * T + 0.000004 * T2;
double irad = AASCoordinateTransformation.DegreesToRadians(i);
double omega = 169.508470 + 1.394681 * T + 0.000412 * T2;
double omegarad = AASCoordinateTransformation.DegreesToRadians(omega);
//Step 2. Calculate the heliocentric longitude, latitude and radius vector of the Earth in the FK5 system
double l0 = AASEarth.EclipticLongitude(JD, bHighPrecision);
double b0 = AASEarth.EclipticLatitude(JD, bHighPrecision);
l0 += AASFK5.CorrectionInLongitude(l0, b0, JD);
double l0rad = AASCoordinateTransformation.DegreesToRadians(l0);
b0 += AASFK5.CorrectionInLatitude(l0, JD);
double b0rad = AASCoordinateTransformation.DegreesToRadians(b0);
double R = AASEarth.RadiusVector(JD, bHighPrecision);
//Step 3. Calculate the corresponding coordinates l,b,r for Saturn but for the instance t-lightraveltime
double DELTA = 9;
double PreviousEarthLightTravelTime = 0;
double EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
double JD1 = JD - EarthLightTravelTime;
bool bIterate = true;
double x = 0;
double y = 0;
double z = 0;
double l = 0;
double b = 0;
double r = 0;
while (bIterate)
{
//Calculate the position of Saturn
l = AASSaturn.EclipticLongitude(JD1, bHighPrecision);
b = AASSaturn.EclipticLatitude(JD1, bHighPrecision);
l += AASFK5.CorrectionInLongitude(l, b, JD1);
b += AASFK5.CorrectionInLatitude(l, JD1);
double lrad = AASCoordinateTransformation.DegreesToRadians(l);
double brad = AASCoordinateTransformation.DegreesToRadians(b);
r = AASSaturn.RadiusVector(JD1, bHighPrecision);
//Step 4
x = r * Math.Cos(brad) * Math.Cos(lrad) - R * Math.Cos(l0rad);
y = r * Math.Cos(brad) * Math.Sin(lrad) - R * Math.Sin(l0rad);
z = r * Math.Sin(brad) - R * Math.Sin(b0rad);
DELTA = Math.Sqrt(x * x + y * y + z * z);
EarthLightTravelTime = AASElliptical.DistanceToLightTime(DELTA);
//Prepare for the next loop around
bIterate = (Math.Abs(EarthLightTravelTime - PreviousEarthLightTravelTime) > 2e-6); //2e-6 corresponds to 0.17 of a second
if (bIterate)
{
JD1 = JD - EarthLightTravelTime;
PreviousEarthLightTravelTime = EarthLightTravelTime;
}
}
//Step 5. Calculate Saturn's geocentric Longitude and Latitude
double lambda = Math.Atan2(y, x);
double beta = Math.Atan2(z, Math.Sqrt(x * x + y * y));
//Step 6. Calculate B, a and b
details.B = Math.Asin(Math.Sin(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad) - Math.Cos(irad) * Math.Sin(beta));
details.a = 375.35 / DELTA;
details.b = details.a * Math.Sin(Math.Abs(details.B));
details.B = AASCoordinateTransformation.RadiansToDegrees(details.B);
//Step 7. Calculate the longitude of the ascending node of Saturn's orbit
double N = 113.6655 + 0.8771 * T;
double Nrad = AASCoordinateTransformation.DegreesToRadians(N);
double ldash = l - 0.01759 / r;
double ldashrad = AASCoordinateTransformation.DegreesToRadians(ldash);
double bdash = b - 0.000764 * Math.Cos(ldashrad - Nrad) / r;
double bdashrad = AASCoordinateTransformation.DegreesToRadians(bdash);
//Step 8. Calculate Bdash
details.Bdash = AASCoordinateTransformation.RadiansToDegrees(Math.Asin(Math.Sin(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad) - Math.Cos(irad) * Math.Sin(bdashrad)));
//Step 9. Calculate DeltaU
details.U1 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Sin(irad) * Math.Sin(bdashrad) + Math.Cos(irad) * Math.Cos(bdashrad) * Math.Sin(ldashrad - omegarad), Math.Cos(bdashrad) * Math.Cos(ldashrad - omegarad))));
details.U2 = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Sin(irad) * Math.Sin(beta) + Math.Cos(irad) * Math.Cos(beta) * Math.Sin(lambda - omegarad), Math.Cos(beta) * Math.Cos(lambda - omegarad))));
details.DeltaU = Math.Abs(details.U1 - details.U2);
if (details.DeltaU > 180)
{
details.DeltaU = 360 - details.DeltaU;
}
//Step 10. Calculate the Nutations
double Obliquity = AASNutation.TrueObliquityOfEcliptic(JD);
double NutationInLongitude = AASNutation.NutationInLongitude(JD);
//Step 11. Calculate the Ecliptical longitude and latitude of the northern pole of the ring plane
double lambda0 = omega - 90;
double beta0 = 90 - i;
//Step 12. Correct lambda and beta for the aberration of Saturn
lambda += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Cos(l0rad - lambda) / Math.Cos(beta));
beta += AASCoordinateTransformation.DegreesToRadians(0.005693 * Math.Sin(l0rad - lambda) * Math.Sin(beta));
//Step 13. Add nutation in longitude to lambda0 and lambda
lambda = AASCoordinateTransformation.RadiansToDegrees(lambda);
lambda += NutationInLongitude / 3600;
lambda = AASCoordinateTransformation.MapTo0To360Range(lambda);
lambda0 += NutationInLongitude / 3600;
lambda0 = AASCoordinateTransformation.MapTo0To360Range(lambda0);
//Step 14. Convert to equatorial coordinates
beta = AASCoordinateTransformation.RadiansToDegrees(beta);
AAS2DCoordinate GeocentricEclipticSaturn = AASCoordinateTransformation.Ecliptic2Equatorial(lambda, beta, Obliquity);
double alpha = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticSaturn.X);
double delta = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticSaturn.Y);
AAS2DCoordinate GeocentricEclipticNorthPole = AASCoordinateTransformation.Ecliptic2Equatorial(lambda0, beta0, Obliquity);
double alpha0 = AASCoordinateTransformation.HoursToRadians(GeocentricEclipticNorthPole.X);
double delta0 = AASCoordinateTransformation.DegreesToRadians(GeocentricEclipticNorthPole.Y);
//Step 15. Calculate the Position angle
details.P = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2(Math.Cos(delta0) * Math.Sin(alpha0 - alpha), Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(alpha0 - alpha)));
return(details);
}
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);
}
