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); }