/// <summary> /// Subtracts corrections to ecliptical coordinates /// </summary> public static CrdsEcliptical operator -(CrdsEcliptical lhs, CrdsEcliptical rhs) { CrdsEcliptical ecl = new CrdsEcliptical(); ecl.Lambda = Angle.To360(lhs.Lambda - rhs.Lambda); ecl.Beta = lhs.Beta - rhs.Beta; ecl.Distance = lhs.Distance; return(ecl); }
/// <summary> /// Calculates the aberration effect for a celestial body (star or planet) for given instant. /// </summary> /// <param name="ecl">Ecliptical coordinates of the body (not corrected).</param> /// <param name="ae">Aberration elements needed for calculation of aberration correction.</param> /// <returns>Returns aberration correction values for ecliptical coordinates.</returns> /// <remarks> /// AA(II), formula 23.2 /// </remarks> public static CrdsEcliptical AberrationEffect(CrdsEcliptical ecl, AberrationElements ae) { double thetaLambda = Angle.ToRadians(ae.lambda - ecl.Lambda); double piLambda = Angle.ToRadians(ae.pi - ecl.Lambda); double beta = Angle.ToRadians(ecl.Beta); double dLambda = (-k * Math.Cos(thetaLambda) + ae.e * k * Math.Cos(piLambda)) / Math.Cos(beta); double dBeta = -k *Math.Sin(beta) * (Math.Sin(thetaLambda) - ae.e * Math.Sin(piLambda)); return(new CrdsEcliptical(dLambda / 3600, dBeta / 3600)); }
/// <summary> /// Calculates appearance of Saturn rings /// </summary> /// <param name="jd">Julian date to calculate for</param> /// <param name="saturn">Heliocentric coordinates of Saturn.</param> /// <param name="earth">Heliocentric coordinates of Earth.</param> /// <param name="epsilon">True obliquity of ecliptic.</param> /// <returns> /// Appearance data for Saturn rings. /// </returns> /// <remarks> /// Method is taken from AA(II), chapter 45. /// </remarks> public static RingsAppearance SaturnRings(double jd, CrdsHeliocentrical saturn, CrdsHeliocentrical earth, double epsilon) { RingsAppearance rings = new RingsAppearance(); double T = (jd - 2451545.0) / 36525.0; double T2 = T * T; double i = 28.075216 - 0.012998 * T + 0.000004 * T2; double Omega = 169.508470 + 1.394681 * T + 0.000412 * T2; double lambda0 = Omega - 90; double beta0 = 90 - i; i = Angle.ToRadians(i); Omega = Angle.ToRadians(Omega); CrdsEcliptical ecl = saturn.ToRectangular(earth).ToEcliptical(); double beta = Angle.ToRadians(ecl.Beta); double lambda = Angle.ToRadians(ecl.Lambda); rings.B = Angle.ToDegrees(Math.Asin(Math.Sin(i) * Math.Cos(beta) * Math.Sin(lambda - Omega) - Math.Cos(i) * Math.Sin(beta))); rings.a = 375.35 / ecl.Distance; rings.b = rings.a * Math.Sin(Math.Abs(Angle.ToRadians(rings.B))); double N = 113.6655 + 0.8771 * T; double l_ = Angle.ToRadians(saturn.L - 0.01759 / saturn.R); double b_ = Angle.ToRadians(saturn.B - 0.000764 * Math.Cos(Angle.ToRadians(saturn.L - N)) / saturn.R); double U1 = Angle.ToDegrees(Math.Atan((Math.Sin(i) * Math.Sin(b_) + Math.Cos(i) * Math.Cos(b_) * Math.Sin(l_ - Omega)) / (Math.Cos(b_) * Math.Cos(l_ - Omega)))); double U2 = Angle.ToDegrees(Math.Atan((Math.Sin(i) * Math.Sin(beta) + Math.Cos(i) * Math.Cos(beta) * Math.Sin(lambda - Omega)) / (Math.Cos(beta) * Math.Cos(lambda - Omega)))); rings.DeltaU = Math.Abs(U1 - U2); CrdsEcliptical eclPole = new CrdsEcliptical(); eclPole.Set(lambda0, beta0); CrdsEquatorial eq = ecl.ToEquatorial(epsilon); CrdsEquatorial eqPole = eclPole.ToEquatorial(epsilon); double alpha = Angle.ToRadians(eq.Alpha); double delta = Angle.ToRadians(eq.Delta); double alpha0 = Angle.ToRadians(eqPole.Alpha); double delta0 = Angle.ToRadians(eqPole.Delta); double y = Math.Cos(delta0) * Math.Sin(alpha0 - alpha); double x = Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(alpha0 - alpha); rings.P = Angle.ToDegrees(Math.Atan2(y, x)); return(rings); }
/// <summary> /// Calculates angular separation between two points with ecliptical coordinates /// </summary> /// <param name="p1">Ecliptical coordinates of the first point</param> /// <param name="p2">Ecliptical coordinates of the second point</param> /// <returns>Angular separation in degrees</returns> public static double Separation(CrdsEcliptical p1, CrdsEcliptical p2) { double a1 = ToRadians(p1.Beta); double a2 = ToRadians(p2.Beta); double A1 = p1.Lambda; double A2 = p2.Lambda; double a = Math.Acos( Math.Sin(a1) * Math.Sin(a2) + Math.Cos(a1) * Math.Cos(a2) * Math.Cos(ToRadians(A1 - A2))); return(double.IsNaN(a) ? 0 : ToDegrees(a)); }
/// <summary> /// Gets correction for ecliptical coordinates obtained by VSOP87 theory, /// needed for conversion to standard FK5 system. /// This correction should be used only for high-precision version of VSOP87. /// </summary> /// <param name="jde">Julian Ephemeris Day</param> /// <param name="ecl">Non-corrected ecliptical coordinates of the body.</param> /// <returns>Corrections values for longutude and latitude, in degrees.</returns> /// <remarks> /// AA(II), formula 32.3. /// </remarks> public static CrdsEcliptical CorrectionForFK5(double jde, CrdsEcliptical ecl) { double T = (jde - 2451545) / 36525.0; double L_ = Angle.ToRadians(ecl.Lambda - 1.397 * T - 0.00031 * T * T); double sinL_ = Math.Sin(L_); double cosL_ = Math.Cos(L_); double deltaL = -0.09033 + 0.03916 * (cosL_ + sinL_) * Math.Tan(Angle.ToRadians(ecl.Beta)); double deltaB = 0.03916 * (cosL_ - sinL_); return(new CrdsEcliptical(deltaL / 3600, deltaB / 3600)); }
/// <summary> /// Gets ecliptical coordinates of Neptunian moon /// </summary> /// <param name="jd">Julian day of calculation</param> /// <param name="neptune">Ecliptical coordinates of Neptune for the specified date</param> /// <param name="index">Moon index, 1 = Triton, 2 = Nereid</param> /// <returns></returns> public static CrdsEcliptical Position(double jd, CrdsEcliptical neptune, int index) { if (index == 1) { return(TritonPosition(jd, neptune)); } else if (index == 2) { return(NereidPosition(jd, neptune)); } else { throw new ArgumentException("Incorrect moon index", nameof(index)); } }
/// <summary> /// Converts ecliptical coordinates to equatorial. /// </summary> /// <param name="ecl">Pair of ecliptical cooordinates.</param> /// <param name="epsilon">Obliquity of the ecliptic, in degrees.</param> /// <returns>Pair of equatorial coordinates.</returns> public static CrdsEquatorial ToEquatorial(this CrdsEcliptical ecl, double epsilon) { CrdsEquatorial eq = new CrdsEquatorial(); epsilon = Angle.ToRadians(epsilon); double lambda = Angle.ToRadians(ecl.Lambda); double beta = Angle.ToRadians(ecl.Beta); double Y = Math.Sin(lambda) * Math.Cos(epsilon) - Math.Tan(beta) * Math.Sin(epsilon); double X = Math.Cos(lambda); eq.Alpha = Angle.To360(Angle.ToDegrees(Math.Atan2(Y, X))); eq.Delta = Angle.ToDegrees(Math.Asin(Math.Sin(beta) * Math.Cos(epsilon) + Math.Cos(beta) * Math.Sin(epsilon) * Math.Sin(lambda))); return(eq); }
/// <summary> /// Converts ecliptical coordinates to rectangular coordinates. /// </summary> /// <param name="ecl">Ecliptical coordinates</param> /// <param name="epsilon">Obliquity of the ecliptic, in degrees.</param> /// <returns>Rectangular coordinates.</returns> public static CrdsRectangular ToRectangular(this CrdsEcliptical ecl, double epsilon) { CrdsRectangular rect = new CrdsRectangular(); double beta = Angle.ToRadians(ecl.Beta); double lambda = Angle.ToRadians(ecl.Lambda); double R = ecl.Distance; epsilon = Angle.ToRadians(epsilon); double cosBeta = Math.Cos(beta); double sinBeta = Math.Sin(beta); double sinLambda = Math.Sin(lambda); double cosLambda = Math.Cos(lambda); double sinEpsilon = Math.Sin(epsilon); double cosEpsilon = Math.Cos(epsilon); rect.X = R * cosBeta * cosLambda; rect.Y = R * (cosBeta * sinLambda * cosEpsilon - sinBeta * sinEpsilon); rect.Z = R * (cosBeta * sinLambda * sinEpsilon + sinBeta * cosEpsilon); return(rect); }
/// <summary> /// Gets geocentric elongation angle of the celestial body /// </summary> /// <param name="sun">Ecliptical geocentrical coordinates of the Sun</param> /// <param name="body">Ecliptical geocentrical coordinates of the body</param> /// <returns>Geocentric elongation angle, in degrees, from -180 to 180. /// Negative sign means western elongation, positive eastern. /// </returns> /// <remarks> /// AA(II), formula 48.2 /// </remarks> // TODO: tests public static double Elongation(CrdsEcliptical sun, CrdsEcliptical body) { double beta = Angle.ToRadians(body.Beta); double lambda = Angle.ToRadians(body.Lambda); double lambda0 = Angle.ToRadians(sun.Lambda); double s = sun.Lambda; double b = body.Lambda; if (Math.Abs(s - b) > 180) { if (s < b) { s += 360; } else { b += 360; } } return(Math.Sign(b - s) * Angle.ToDegrees(Math.Acos(Math.Cos(beta) * Math.Cos(lambda - lambda0)))); }
/// <summary> /// Converts ecliptical coordinates for one equinox to another one /// </summary> /// <param name="jd0">Initial epoch (can be J2000 = 2451545.0)</param> /// <param name="jd">Target (final) epoch </param> /// <returns>Returns ecliptical coordinates for the target epoch</returns> /// <remarks>Method is taken from AA(II), p. 134</remarks> private static CrdsEcliptical ConvertCoordinatesToEquinox(double jd0, double jd, CrdsEcliptical e0) { double T = (jd0 - 2451545.0) / 36525.0; double t = (jd - jd0) / 36525.0; double eta = (47.0029 - 0.06603 * T + 0.000598 * T * T) * t + (-0.03302 + 0.000598 * T) * t * t + 0.000060 * t * t * t; eta /= 3600.0; double Pi = 3289.4789 * T + 0.60622 * T * T - (869.8089 + 0.50491 * T) * t + 0.03536 * t * t; Pi /= 3600.0; Pi += 174.876384; double p = (5029.0966 + 2.22226 * T - 0.000042 * T * T) * t + (1.11113 - 0.000042 * T) * t * t - 0.000006 * t * t * t; p /= 3600.0; double A_ = Cos(ToRadians(eta)) * Cos(ToRadians(e0.Beta)) * Sin(ToRadians(Pi - e0.Lambda)) - Sin(ToRadians(eta)) * Sin(ToRadians(e0.Beta)); double B_ = Cos(ToRadians(e0.Beta)) * Cos(ToRadians(Pi - e0.Lambda)); double C_ = Cos(ToRadians(eta)) * Sin(ToRadians(e0.Beta)) + Sin(ToRadians(eta)) * Cos(ToRadians(e0.Beta)) * Sin(ToRadians(Pi - e0.Lambda)); CrdsEcliptical e = new CrdsEcliptical(); e.Lambda = p + Pi - ToDegrees(Atan2(A_, B_)); e.Lambda = To360(e.Lambda); e.Beta = ToDegrees(Asin(C_)); e.Distance = e0.Distance; return(e); }
/// <summary> /// Calculates ecliptical coordinates of Triton, largest moon of Neptune. /// </summary> /// <param name="jd">Julian Day of calculation</param> /// <param name="neptune">Ecliptical coordinates of Neptune for the Julian Day specified.</param> /// <returns>Ecliptical coordinates of Triton for specified date.</returns> /// <remarks> /// /// The method is based on following works: /// /// 1. Harris, A.W. (1984), "Physical Properties of Neptune and Triton Inferred from the Orbit of Triton" NASA CP-2330, pages 357-373: /// http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1984NASCP2330..357H&defaultprint=YES&filetype=.pdf /// /// 2. Seidelmann, P. K.: Explanatory Supplement to The Astronomical Almanac, /// University Science Book, Mill Valley (California), 1992, /// Chapter 6 "Orbital Ephemerides and Rings of Satellites", page 373, 6.61-1 Triton /// https://archive.org/download/131123ExplanatorySupplementAstronomicalAlmanac/131123-explanatory-supplement-astronomical-almanac.pdf /// /// </remarks> private static CrdsEcliptical TritonPosition(double jd, CrdsEcliptical neptune) { NutationElements ne = Nutation.NutationElements(jd); double epsilon = Date.TrueObliquity(jd, ne.deltaEpsilon); // convert current coordinates to J1950 epoch, as algorithm requires CrdsEquatorial eq = neptune.ToEquatorial(epsilon); PrecessionalElements pe1950 = Precession.ElementsFK5(jd, Date.EPOCH_J1950); CrdsEquatorial eqNeptune1950 = Precession.GetEquatorialCoordinates(eq, pe1950); const double t0 = 2433282.5; // 1.0 Jan 1950 const double a = 0.0023683; // semimajor axis of Triton, in a.u. const double n = 61.2588532; // nodal mean motion, degrees per day const double lambda0 = 200.913; // longitude from ascending node through the invariable plane at epoch const double i = 158.996; // inclination of orbit to the invariable plane const double Omega0 = 151.401; // angle from the intersection of invariable plane with the earth's // equatorial plane of 1950.0 to the ascending node // of the orbit through the invariable plane const double OmegaDot = 0.57806; // nodal precision rate, degrees per year // Calculate J2000.0 RA and Declination of the pole of the invariable plane // These formulae are taken from the book: // Seidelmann, P. K.: Explanatory Supplement to The Astronomical Almanac, // University Science Book, Mill Valley (California), 1992, // Chapter 6 "Orbital Ephemerides and Rings of Satellites", page 373, 6.61-1 Triton double T = (jd - 2451545.0) / 36525.0; double N = ToRadians(359.28 + 54.308 * T); double ap = 298.72 + 2.58 * Sin(N) - 0.04 * Sin(2 * N); double dp = 42.63 - 1.90 * Cos(N) + 0.01 * Cos(2 * N); // Convert pole coordinates to J1950 CrdsEquatorial eqPole1950 = Precession.GetEquatorialCoordinates(new CrdsEquatorial(ap, dp), pe1950); ap = eqPole1950.Alpha; dp = eqPole1950.Delta; // take light-time effect into account double tau = PlanetPositions.LightTimeEffect(neptune.Distance); double lambda = To360(lambda0 + n * (jd - t0 - tau)); double omega = Omega0 + OmegaDot * (jd - t0 - tau) / 365.25; // cartesian state vector of Triton var r = Matrix.R3(ToRadians(-ap - 90)) * Matrix.R1(ToRadians(dp - 90)) * Matrix.R3(ToRadians(-omega)) * Matrix.R1(ToRadians(-i)) * new Matrix(new[, ] { { a *Cos(ToRadians(lambda)) }, { a *Sin(ToRadians(lambda)) }, { 0 } }); // normalize by distance to Neptune r.Values[0, 0] /= neptune.Distance; r.Values[1, 0] /= neptune.Distance; r.Values[2, 0] /= neptune.Distance; // offsets vector var d = Matrix.R2(ToRadians(-eqNeptune1950.Delta)) * Matrix.R3(ToRadians(eqNeptune1950.Alpha)) * r; // radial component, positive away from observer // converted to degrees double x = ToDegrees(d.Values[0, 0]); // semimajor axis, expressed in degrees, as visible from Earth double theta = ToDegrees(Atan(a / neptune.Distance)); // offsets values in degrees double dAlphaCosDelta = ToDegrees(d.Values[1, 0]); double dDelta = ToDegrees(d.Values[2, 0]); double delta = eqNeptune1950.Delta + dDelta; double dAlpha = dAlphaCosDelta / Cos(ToRadians(eqNeptune1950.Delta)); double alpha = eqNeptune1950.Alpha + dAlpha; CrdsEquatorial eqTriton1950 = new CrdsEquatorial(alpha, delta); // convert J1950 equatorial coordinates to current epoch // and to ecliptical PrecessionalElements pe = Precession.ElementsFK5(Date.EPOCH_J1950, jd); CrdsEquatorial eqTriton = Precession.GetEquatorialCoordinates(eqTriton1950, pe); CrdsEcliptical eclTriton = eqTriton.ToEcliptical(epsilon); // calculate distance to Earth eclTriton.Distance = neptune.Distance + x / theta * a; return(eclTriton); }
/// <summary> /// Calculates ecliptical coordinates of Nereid, the third-largest moon of Neptune. /// </summary> /// <param name="jd">Julian Day of calculation</param> /// <param name="neptune">Ecliptical coordinates of Neptune for the Julian Day specified.</param> /// <returns>Ecliptical coordinates of Nereid for specified date.</returns> /// <remarks> /// /// The method is based on work of F. Mignard (1981), "The Mean Elements of Nereid", /// The Astronomical Journal, Vol 86, Number 11, pages 1728-1729 /// The work can be found by link: http://adsabs.harvard.edu/full/1981AJ.....86.1728M /// /// There are some changes from the original algorithm were made, /// to be compliant with ephemeris provided by Nasa JPL Horizons system (https://ssd.jpl.nasa.gov/?ephemerides): /// /// 1. Other value of mean motion (n) is used: /// - original work : n = 0.999552 /// - implementation: n = 360.0 / 360.1362 (where 360.1362 is an orbital period) /// /// 2. Rotation around Z axis by angle OmegaN should by taken with NEGATIVE sign, /// insted of POSITIVE sign in original work (possible typo?), /// note the NEGATIVE sign for "Ne" angle (same meaning as "OmegaN" in original work) in the book: /// Seidelmann, P. K.: Explanatory Supplement to The Astronomical Almanac, /// University Science Book, Mill Valley (California), 1992, /// Chapter 6 "Orbital Ephemerides and Rings of Satellites", page 376, formula 6.62-3 /// /// </remarks> private static CrdsEcliptical NereidPosition(double jd, CrdsEcliptical neptune) { NutationElements ne = Nutation.NutationElements(jd); double epsilon = Date.TrueObliquity(jd, ne.deltaEpsilon); // convert current coordinates to J1950 epoch, as algorithm requires CrdsEquatorial eq = neptune.ToEquatorial(epsilon); PrecessionalElements pe1950 = Precession.ElementsFK5(jd, Date.EPOCH_J1950); CrdsEquatorial eqNeptune1950 = Precession.GetEquatorialCoordinates(eq, pe1950); const double jd0 = 2433680.5; // Initial Epoch: 3.0 Feb 1951 const double a = 0.036868; // Semi-major axis, in a.u. const double e0 = 0.74515; // Orbit eccentricity for jd0 epoch const double i0 = 10.041; // Inclination of the orbit for jd0 epoch, in degrees const double Omega0 = 329.3; // Longitude of the node of the orbit for jd0 epoch, in degrees const double M0 = 358.91; // Mean anomaly for jd0 epoch, in degrees const double n = 360.0 / 360.1362; // Mean motion, in degrees per day const double OmegaN = 3.552; // Longitude of ascending node of the orbit of Neptune, for J1950.0 epoch, in degrees const double gamma = 22.313; // Inclination of the orbit of Neptune, for J1950.0 epoch, in degrees // take light-time effect into account double tau = PlanetPositions.LightTimeEffect(neptune.Distance); double t = jd - tau - jd0; // in days double T = t / 36525.0; // in Julian centuries double psi = ToRadians(To360(282.9 + 2.68 * T)); double twoTheta = ToRadians(To360(107.4 + 0.01196 * t)); // Equation to found omega, argument of pericenter Func <double, double> omegaEquation = (om) => To360(282.9 + 2.68 * T - 19.25 * Sin(2 * psi) + 3.23 * Sin(4 * psi) - 0.725 * Sin(6 * psi) - 0.351 * Sin(twoTheta) - 0.7 * Sin(ToRadians(2 * om) - twoTheta)) - om; // Solve equation (find root: omega value) double omega = ToRadians(FindRoots(omegaEquation, 0, 360, 1e-8)); // Find longitude of the node double Omega = Omega0 - 2.4 * T + 19.7 * Sin(2 * psi) - 3.3 * Sin(4 * psi) + 0.7 * Sin(6 * psi) + 0.357 * Sin(twoTheta) + 0.276 * Sin(2 * omega - twoTheta); // Find orbit eccentricity double e = e0 - 0.006 * Cos(2 * psi) + 0.0056 * Cos(2 * omega - twoTheta); // Find mean anomaly double M = To360(M0 + n * t - 0.38 * Sin(2 * psi) + 1.0 * Sin(2 * omega - twoTheta)); // Find inclination double cosi = Cos(ToRadians(i0)) - 9.4e-3 * Cos(2 * psi); double i = Acos(cosi); // Find eccentric anomaly by solving Kepler equation double E = SolveKepler(M, e); double X = a * (Cos(E) - e); double Y = a * Sqrt(1 - e * e) * Sin(E); Matrix d = Matrix.R2(ToRadians(-eqNeptune1950.Delta)) * Matrix.R3(ToRadians(eqNeptune1950.Alpha)) * Matrix.R3(ToRadians(-OmegaN)) * Matrix.R1(ToRadians(-gamma)) * Matrix.R3(ToRadians(-Omega)) * Matrix.R1(-i) * Matrix.R3(-omega) * new Matrix(new double[, ] { { X / neptune.Distance }, { Y / neptune.Distance }, { 0 } }); // radial component, positive away from observer // converted to degrees double x = ToDegrees(d.Values[0, 0]); // offsets values in degrees double dAlphaCosDelta = ToDegrees(d.Values[1, 0]); double dDelta = ToDegrees(d.Values[2, 0]); double delta = eqNeptune1950.Delta + dDelta; double dAlpha = dAlphaCosDelta / Cos(ToRadians(eqNeptune1950.Delta)); double alpha = eqNeptune1950.Alpha + dAlpha; CrdsEquatorial eqNereid1950 = new CrdsEquatorial(alpha, delta); // convert J1950 equatorial coordinates to current epoch // and to ecliptical PrecessionalElements pe = Precession.ElementsFK5(Date.EPOCH_J1950, jd); CrdsEquatorial eqNereid = Precession.GetEquatorialCoordinates(eqNereid1950, pe); CrdsEcliptical eclNereid = eqNereid.ToEcliptical(epsilon); // semimajor axis, expressed in degrees, as visible from Earth double theta = ToDegrees(Atan(a / neptune.Distance)); // calculate distance to Earth eclNereid.Distance = neptune.Distance + x / theta * a; return(eclNereid); }
public static CrdsRectangular[] Positions(double jd, CrdsHeliocentrical earth, CrdsHeliocentrical mars) { CrdsRectangular[] moons = new CrdsRectangular[MOONS_COUNT]; // Rectangular topocentrical coordinates of Mars CrdsRectangular rectMars = mars.ToRectangular(earth); // Ecliptical coordinates of Mars CrdsEcliptical eclMars = rectMars.ToEcliptical(); // Distance from Earth to Mars, in AU double distanceMars = eclMars.Distance; // light-time effect double tau = PlanetPositions.LightTimeEffect(distanceMars); // ESAPHODEI model double t = jd - 2451545.0 + 6491.5 - tau; GenerateMarsSatToVSOP87(t, ref mars_sat_to_vsop87); // Get rectangular (Mars-reffered) coordinates of moons CrdsRectangular[] esaphodeiRect = new CrdsRectangular[MOONS_COUNT]; for (int body = 0; body < MOONS_COUNT; body++) { MarsSatBody bp = mars_sat_bodies[body]; double[] elem = new double[6]; for (int n = 0; n < 6; n++) { elem[n] = bp.constants[n]; } for (int j = 0; j < 2; j++) { for (int i = bp.lists[j].size - 1; i >= 0; i--) { double d = bp.lists[j].terms[i].phase + t * bp.lists[j].terms[i].frequency; elem[j] += bp.lists[j].terms[i].amplitude * Cos(d); } } for (int j = 2; j < 4; j++) { for (int i = bp.lists[j].size - 1; i >= 0; i--) { double d = bp.lists[j].terms[i].phase + t * bp.lists[j].terms[i].frequency; elem[2 * j - 2] += bp.lists[j].terms[i].amplitude * Cos(d); elem[2 * j - 1] += bp.lists[j].terms[i].amplitude * Sin(d); } } elem[1] += (bp.l + bp.acc * t) * t; double[] x = new double[3]; EllipticToRectangularA(mars_sat_bodies[body].mu, elem, ref x); esaphodeiRect[body] = new CrdsRectangular(); esaphodeiRect[body].X = mars_sat_to_vsop87[0] * x[0] + mars_sat_to_vsop87[1] * x[1] + mars_sat_to_vsop87[2] * x[2]; esaphodeiRect[body].Y = mars_sat_to_vsop87[3] * x[0] + mars_sat_to_vsop87[4] * x[1] + mars_sat_to_vsop87[5] * x[2]; esaphodeiRect[body].Z = mars_sat_to_vsop87[6] * x[0] + mars_sat_to_vsop87[7] * x[1] + mars_sat_to_vsop87[8] * x[2]; moons[body] = new CrdsRectangular( rectMars.X + esaphodeiRect[body].X, rectMars.Y + esaphodeiRect[body].Y, rectMars.Z + esaphodeiRect[body].Z ); } return(moons); }
public static CrdsEcliptical Position(double jd, GenericSatelliteOrbit orbit, CrdsEcliptical planet) { NutationElements ne = Nutation.NutationElements(jd); double epsilon = Date.TrueObliquity(jd, ne.deltaEpsilon); // convert current coordinates to epoch, as algorithm requires CrdsEquatorial eq = planet.ToEquatorial(epsilon); PrecessionalElements peEpoch = Precession.ElementsFK5(jd, Date.EPOCH_J2000); CrdsEquatorial eqPlanetEpoch = Precession.GetEquatorialCoordinates(eq, peEpoch); // ecliptical pole CrdsEquatorial pole = new CrdsEcliptical(0, 90).ToEquatorial(epsilon); double distance0; double distance = planet.Distance; CrdsEcliptical eclSatellite; do { distance0 = distance; // take light-time effect into account double tau = PlanetPositions.LightTimeEffect(distance); double t = jd - tau - orbit.jd; double M = To360(orbit.M + orbit.n * t); double omega = To360(orbit.w + t * 360.0 / (orbit.Pw * 365.25)); double node = To360(orbit.Om + t * 360.0 / (orbit.POm * 365.25)); // Find eccentric anomaly by solving Kepler equation double E = SolveKepler(M, orbit.e); double X = orbit.a * (Cos(E) - orbit.e); double Y = orbit.a * Sqrt(1 - orbit.e * orbit.e) * Sin(E); // cartesian state vector of satellite var d = Matrix.R2(ToRadians(-eqPlanetEpoch.Delta)) * Matrix.R3(ToRadians(eqPlanetEpoch.Alpha)) * Matrix.R3(ToRadians(-pole.Alpha - 90)) * Matrix.R1(ToRadians(pole.Delta - 90)) * Matrix.R3(ToRadians(-node)) * Matrix.R1(ToRadians(-orbit.i)) * Matrix.R3(ToRadians(-omega)) * new Matrix(new double[, ] { { X / distance }, { Y / distance }, { 0 } }); // radial component, positive away from observer // converted to degrees double x = ToDegrees(d.Values[0, 0]); // semimajor axis, expressed in degrees, as visible from Earth double theta = ToDegrees(Atan(orbit.a / distance)); // offsets values in degrees double dAlphaCosDelta = ToDegrees(d.Values[1, 0]); double dDelta = ToDegrees(d.Values[2, 0]); double delta = eqPlanetEpoch.Delta + dDelta; double dAlpha = dAlphaCosDelta / Cos(ToRadians(delta)); double alpha = eqPlanetEpoch.Alpha + dAlpha; CrdsEquatorial eqSatelliteEpoch = new CrdsEquatorial(alpha, delta); // convert jd0 equatorial coordinates to current epoch // and to ecliptical PrecessionalElements pe = Precession.ElementsFK5(Date.EPOCH_J2000, jd); CrdsEquatorial eqSatellite = Precession.GetEquatorialCoordinates(eqSatelliteEpoch, pe); eclSatellite = eqSatellite.ToEcliptical(epsilon); // calculate distance to Earth distance = planet.Distance + x / theta * orbit.a; }while (Abs(distance - distance0) > 1e-6); eclSatellite.Distance = distance; return(eclSatellite); }
/// <summary> /// Gets ecliptical coordinates of the Moon for given instant. /// </summary> /// <param name="jd">Julian Day.</param> /// <returns>Geocentric ecliptical coordinates of the Moon, referred to mean equinox of the date.</returns> /// <remarks> /// This method is taken from AA(II), chapter 47, /// and based on the Charpont ELP-2000/82 lunar theory. /// Accuracy of the method is 10" in longitude and 4" in latitude. /// </remarks> // TODO: use full ELP2000/82 theory: // http://totaleclipse.eu/Astronomy/ELP2000.html // http://cdsarc.u-strasbg.fr/viz-bin/cat/VI/79 public static CrdsEcliptical GetCoordinates(double jd) { Initialize(); double T = (jd - 2451545.0) / 36525.0; double T2 = T * T; double T3 = T2 * T; double T4 = T3 * T; // Moon's mean longitude double L_ = 218.3164477 + 481267.88123421 * T - 0.0015786 * T2 + T3 / 538841.0 - T4 / 65194000.0; // Preserve the L_ value in degrees double Lm = L_; // Mean elongation of the Moon double D = 297.8501921 + 445267.1114034 * T - 0.0018819 * T2 + T3 / 545868.0 - T4 / 113065000.0; // Sun's mean anomaly double M = 357.5291092 + 35999.0502909 * T - 0.0001536 * T2 + T3 / 24490000.0; // Moon's mean anomaly double M_ = 134.9633964 + 477198.8675055 * T + 0.0087414 * T2 + T3 / 69699.0 - T4 / 14712000.0; // Moon's argument of latitude (mean dinstance of the Moon from its ascending node) double F = 93.2720950 + 483202.0175233 * T - 0.0036539 * T2 - T3 / 3526000.0 + T4 / 863310000.0; // Correction arguments double A1 = 119.75 + 131.849 * T; double A2 = 53.09 + 479264.290 * T; double A3 = 313.45 + 481266.484 * T; // Multiplier related to the eccentricity of the Earth orbit double E = 1 - 0.002516 * T - 0.0000074 * T2; L_ = Angle.ToRadians(L_); D = Angle.ToRadians(D); M = Angle.ToRadians(M); M_ = Angle.ToRadians(M_); F = Angle.ToRadians(F); A1 = Angle.ToRadians(A1); A2 = Angle.ToRadians(A2); A3 = Angle.ToRadians(A3); double Sum_l = 0; double Sum_b = 0; double Sum_r = 0; double[] DMMF = new double[] { D, M, M_, F }; double[] powE = new double[3] { 1, E, E *E }; double lrArg, bArg; for (int i = 0; i < 60; i++) { lrArg = 0; bArg = 0; for (int j = 0; j < 4; j++) { lrArg += DMMF[j] * ArgsLR[i, j]; bArg += DMMF[j] * ArgsB[i, j]; } Sum_l += SinCoeffLR[i] * Math.Sin(lrArg) * powE[Math.Abs(ArgsLR[i, 1])]; Sum_r += CosCoeffLR[i] * Math.Cos(lrArg) * powE[Math.Abs(ArgsLR[i, 1])]; Sum_b += CoeffB[i] * Math.Sin(bArg) * powE[Math.Abs(ArgsB[i, 1])]; } Sum_l += 3958 * Math.Sin(A1) + 1962 * Math.Sin(L_ - F) + 318 * Math.Sin(A2); Sum_b += -2235 * Math.Sin(L_) + 382 * Math.Sin(A3) + 175 * Math.Sin(A1 - F) + 175 * Math.Sin(A1 + F) + 127 * Math.Sin(L_ - M_) - 115 * Math.Sin(L_ + M_); CrdsEcliptical ecl = new CrdsEcliptical(); ecl.Lambda = Lm + Sum_l / 1e6; ecl.Lambda = Angle.To360(ecl.Lambda); ecl.Beta = Sum_b / 1e6; ecl.Distance = 385000.56 + Sum_r / 1e3; return(ecl); }
public static CrdsRectangular[] Positions(double jd, CrdsHeliocentrical earth, CrdsHeliocentrical uranus) { CrdsRectangular[] moons = new CrdsRectangular[MOONS_COUNT]; // Rectangular topocentrical coordinates of Uranus CrdsRectangular rectUranus = uranus.ToRectangular(earth); // Ecliptical coordinates of Uranus CrdsEcliptical eclUranus = rectUranus.ToEcliptical(); // Distance from Earth to Uranus, in AU double distanceUranus = eclUranus.Distance; // light-time effect double tau = PlanetPositions.LightTimeEffect(distanceUranus); double t = jd - 2444239.5 - tau; double[] elem = new double[6 * MOONS_COUNT]; double[] an = new double[MOONS_COUNT]; double[] ae = new double[MOONS_COUNT]; double[] ai = new double[MOONS_COUNT]; // Calculate GUST86 elements: for (int i = 0; i < 5; i++) { an[i] = IEEERemainder(fqn[i] * t + phn[i], 2 * PI); ae[i] = IEEERemainder(fqe[i] * t + phe[i], 2 * PI); ai[i] = IEEERemainder(fqi[i] * t + phi[i], 2 * PI); } elem[0 * 6 + 0] = 4.44352267 - Cos(an[0] - an[1] * 3.0 + an[2] * 2.0) * 3.492e-5 + Cos(an[0] * 2.0 - an[1] * 6.0 + an[2] * 4.0) * 8.47e-6 + Cos(an[0] * 3.0 - an[1] * 9.0 + an[2] * 6.0) * 1.31e-6 - Cos(an[0] - an[1]) * 5.228e-5 - Cos(an[0] * 2.0 - an[1] * 2.0) * 1.3665e-4; elem[0 * 6 + 1] = Sin(an[0] - an[1] * 3.0 + an[2] * 2.0) * .02547217 - Sin(an[0] * 2.0 - an[1] * 6.0 + an[2] * 4.0) * .00308831 - Sin(an[0] * 3.0 - an[1] * 9.0 + an[2] * 6.0) * 3.181e-4 - Sin(an[0] * 4.0 - an[1] * 12 + an[2] * 8.0) * 3.749e-5 - Sin(an[0] - an[1]) * 5.785e-5 - Sin(an[0] * 2.0 - an[1] * 2.0) * 6.232e-5 - Sin(an[0] * 3.0 - an[1] * 3.0) * 2.795e-5 + t * 4.44519055 - .23805158; elem[0 * 6 + 2] = Cos(ae[0]) * .00131238 + Cos(ae[1]) * 7.181e-5 + Cos(ae[2]) * 6.977e-5 + Cos(ae[3]) * 6.75e-6 + Cos(ae[4]) * 6.27e-6 + Cos(an[0]) * 1.941e-4 - Cos(-an[0] + an[1] * 2.0) * 1.2331e-4 + Cos(an[0] * -2.0 + an[1] * 3.0) * 3.952e-5; elem[0 * 6 + 3] = Sin(ae[0]) * .00131238 + Sin(ae[1]) * 7.181e-5 + Sin(ae[2]) * 6.977e-5 + Sin(ae[3]) * 6.75e-6 + Sin(ae[4]) * 6.27e-6 + Sin(an[0]) * 1.941e-4 - Sin(-an[0] + an[1] * 2.0) * 1.2331e-4 + Sin(an[0] * -2.0 + an[1] * 3.0) * 3.952e-5; elem[0 * 6 + 4] = Cos(ai[0]) * .03787171 + Cos(ai[1]) * 2.701e-5 + Cos(ai[2]) * 3.076e-5 + Cos(ai[3]) * 1.218e-5 + Cos(ai[4]) * 5.37e-6; elem[0 * 6 + 4] = Sin(ai[0]) * .03787171 + Sin(ai[1]) * 2.701e-5 + Sin(ai[2]) * 3.076e-5 + Sin(ai[3]) * 1.218e-5 + Sin(ai[4]) * 5.37e-6; elem[1 * 6 + 0] = 2.49254257 + Cos(an[0] - an[1] * 3.0 + an[2] * 2.0) * 2.55e-6 - Cos(an[1] - an[2]) * 4.216e-5 - Cos(an[1] * 2.0 - an[2] * 2.0) * 1.0256e-4; elem[1 * 6 + 1] = -Sin(an[0] - an[1] * 3.0 + an[2] * 2.0) * .0018605 + Sin(an[0] * 2.0 - an[1] * 6.0 + an[2] * 4.0) * 2.1999e-4 + Sin(an[0] * 3.0 - an[1] * 9.0 + an[2] * 6.0) * 2.31e-5 + Sin(an[0] * 4.0 - an[1] * 12 + an[2] * 8.0) * 4.3e-6 - Sin(an[1] - an[2]) * 9.011e-5 - Sin(an[1] * 2.0 - an[2] * 2.0) * 9.107e-5 - Sin(an[1] * 3.0 - an[2] * 3.0) * 4.275e-5 - Sin(an[1] * 2.0 - an[3] * 2.0) * 1.649e-5 + t * 2.49295252 + 3.09804641; elem[1 * 6 + 2] = Cos(ae[0]) * -3.35e-6 + Cos(ae[1]) * .00118763 + Cos(ae[2]) * 8.6159e-4 + Cos(ae[3]) * 7.15e-5 + Cos(ae[4]) * 5.559e-5 - Cos(-an[1] + an[2] * 2.0) * 8.46e-5 + Cos(an[1] * -2.0 + an[2] * 3.0) * 9.181e-5 + Cos(-an[1] + an[3] * 2.0) * 2.003e-5 + Cos(an[1]) * 8.977e-5; elem[1 * 6 + 3] = Sin(ae[0]) * -3.35e-6 + Sin(ae[1]) * .00118763 + Sin(ae[2]) * 8.6159e-4 + Sin(ae[3]) * 7.15e-5 + Sin(ae[4]) * 5.559e-5 - Sin(-an[1] + an[2] * 2.0) * 8.46e-5 + Sin(an[1] * -2.0 + an[2] * 3.0) * 9.181e-5 + Sin(-an[1] + an[3] * 2.0) * 2.003e-5 + Sin(an[1]) * 8.977e-5; elem[1 * 6 + 4] = Cos(ai[0]) * -1.2175e-4 + Cos(ai[1]) * 3.5825e-4 + Cos(ai[2]) * 2.9008e-4 + Cos(ai[3]) * 9.778e-5 + Cos(ai[4]) * 3.397e-5; elem[1 * 6 + 5] = Sin(ai[0]) * -1.2175e-4 + Sin(ai[1]) * 3.5825e-4 + Sin(ai[2]) * 2.9008e-4 + Sin(ai[3]) * 9.778e-5 + Sin(ai[4]) * 3.397e-5; elem[2 * 6 + 0] = 1.5159549 + Cos(an[2] - an[3] * 2.0 + ae[2]) * 9.74e-6 - Cos(an[1] - an[2]) * 1.06e-4 + Cos(an[1] * 2.0 - an[2] * 2.0) * 5.416e-5 - Cos(an[2] - an[3]) * 2.359e-5 - Cos(an[2] * 2.0 - an[3] * 2.0) * 7.07e-5 - Cos(an[2] * 3.0 - an[3] * 3.0) * 3.628e-5; elem[2 * 6 + 1] = Sin(an[0] - an[1] * 3.0 + an[2] * 2.0) * 6.6057e-4 - Sin(an[0] * 2.0 - an[1] * 6.0 + an[2] * 4.0) * 7.651e-5 - Sin(an[0] * 3.0 - an[1] * 9.0 + an[2] * 6.0) * 8.96e-6 - Sin(an[0] * 4.0 - an[1] * 12.0 + an[2] * 8.0) * 2.53e-6 - Sin(an[2] - an[3] * 4.0 + an[4] * 3.0) * 5.291e-5 - Sin(an[2] - an[3] * 2.0 + ae[4]) * 7.34e-6 - Sin(an[2] - an[3] * 2.0 + ae[3]) * 1.83e-6 + Sin(an[2] - an[3] * 2.0 + ae[2]) * 1.4791e-4 + Sin(an[2] - an[3] * 2.0 + ae[1]) * -7.77e-6 + Sin(an[1] - an[2]) * 9.776e-5 + Sin(an[1] * 2.0 - an[2] * 2.0) * 7.313e-5 + Sin(an[1] * 3.0 - an[2] * 3.0) * 3.471e-5 + Sin(an[1] * 4.0 - an[2] * 4.0) * 1.889e-5 - Sin(an[2] - an[3]) * 6.789e-5 - Sin(an[2] * 2.0 - an[3] * 2.0) * 8.286e-5 + Sin(an[2] * 3.0 - an[3] * 3.0) * -3.381e-5 - Sin(an[2] * 4.0 - an[3] * 4.0) * 1.579e-5 - Sin(an[2] - an[4]) * 1.021e-5 - Sin(an[2] * 2.0 - an[4] * 2.0) * 1.708e-5 + t * 1.51614811 + 2.28540169; elem[2 * 6 + 2] = Cos(ae[0]) * -2.1e-7 - Cos(ae[1]) * 2.2795e-4 + Cos(ae[2]) * .00390469 + Cos(ae[3]) * 3.0917e-4 + Cos(ae[4]) * 2.2192e-4 + Cos(an[1]) * 2.934e-5 + Cos(an[2]) * 2.62e-5 + Cos(-an[1] + an[2] * 2.0) * 5.119e-5 - Cos(an[1] * -2.0 + an[2] * 3.0) * 1.0386e-4 - Cos(an[1] * -3.0 + an[2] * 4.0) * 2.716e-5 + Cos(an[3]) * -1.622e-5 + Cos(-an[2] + an[3] * 2.0) * 5.4923e-4 + Cos(an[2] * -2.0 + an[3] * 3.0) * 3.47e-5 + Cos(an[2] * -3.0 + an[3] * 4.0) * 1.281e-5 + Cos(-an[2] + an[4] * 2.0) * 2.181e-5 + Cos(an[2]) * 4.625e-5; elem[2 * 6 + 3] = Sin(ae[0]) * -2.1e-7 - Sin(ae[1]) * 2.2795e-4 + Sin(ae[2]) * .00390469 + Sin(ae[3]) * 3.0917e-4 + Sin(ae[4]) * 2.2192e-4 + Sin(an[1]) * 2.934e-5 + Sin(an[2]) * 2.62e-5 + Sin(-an[1] + an[2] * 2.0) * 5.119e-5 - Sin(an[1] * -2.0 + an[2] * 3.0) * 1.0386e-4 - Sin(an[1] * -3.0 + an[2] * 4.0) * 2.716e-5 + Sin(an[3]) * -1.622e-5 + Sin(-an[2] + an[3] * 2.0) * 5.4923e-4 + Sin(an[2] * -2.0 + an[3] * 3.0) * 3.47e-5 + Sin(an[2] * -3.0 + an[3] * 4.0) * 1.281e-5 + Sin(-an[2] + an[4] * 2.0) * 2.181e-5 + Sin(an[2]) * 4.625e-5; elem[2 * 6 + 4] = Cos(ai[0]) * -1.086e-5 - Cos(ai[1]) * 8.151e-5 + Cos(ai[2]) * .00111336 + Cos(ai[3]) * 3.5014e-4 + Cos(ai[4]) * 1.065e-4; elem[2 * 6 + 5] = Sin(ai[0]) * -1.086e-5 - Sin(ai[1]) * 8.151e-5 + Sin(ai[2]) * .00111336 + Sin(ai[3]) * 3.5014e-4 + Sin(ai[4]) * 1.065e-4; elem[3 * 6 + 0] = .72166316 - Cos(an[2] - an[3] * 2.0 + ae[2]) * 2.64e-6 - Cos(an[3] * 2.0 - an[4] * 3.0 + ae[4]) * 2.16e-6 + Cos(an[3] * 2.0 - an[4] * 3.0 + ae[3]) * 6.45e-6 - Cos(an[3] * 2.0 - an[4] * 3.0 + ae[2]) * 1.11e-6 + Cos(an[1] - an[3]) * -6.223e-5 - Cos(an[2] - an[3]) * 5.613e-5 - Cos(an[3] - an[4]) * 3.994e-5 - Cos(an[3] * 2.0 - an[4] * 2.0) * 9.185e-5 - Cos(an[3] * 3.0 - an[4] * 3.0) * 5.831e-5 - Cos(an[3] * 4.0 - an[4] * 4.0) * 3.86e-5 - Cos(an[3] * 5.0 - an[4] * 5.0) * 2.618e-5 - Cos(an[3] * 6.0 - an[4] * 6.0) * 1.806e-5; elem[3 * 6 + 1] = Sin(an[2] - an[3] * 4.0 + an[4] * 3.0) * 2.061e-5 - Sin(an[2] - an[3] * 2.0 + ae[4]) * 2.07e-6 - Sin(an[2] - an[3] * 2.0 + ae[3]) * 2.88e-6 - Sin(an[2] - an[3] * 2.0 + ae[2]) * 4.079e-5 + Sin(an[2] - an[3] * 2.0 + ae[1]) * 2.11e-6 - Sin(an[3] * 2.0 - an[4] * 3.0 + ae[4]) * 5.183e-5 + Sin(an[3] * 2.0 - an[4] * 3.0 + ae[3]) * 1.5987e-4 + Sin(an[3] * 2.0 - an[4] * 3.0 + ae[2]) * -3.505e-5 - Sin(an[3] * 3.0 - an[4] * 4.0 + ae[4]) * 1.56e-6 + Sin(an[1] - an[3]) * 4.054e-5 + Sin(an[2] - an[3]) * 4.617e-5 - Sin(an[3] - an[4]) * 3.1776e-4 - Sin(an[3] * 2.0 - an[4] * 2.0) * 3.0559e-4 - Sin(an[3] * 3.0 - an[4] * 3.0) * 1.4836e-4 - Sin(an[3] * 4.0 - an[4] * 4.0) * 8.292e-5 + Sin(an[3] * 5.0 - an[4] * 5.0) * -4.998e-5 - Sin(an[3] * 6.0 - an[4] * 6.0) * 3.156e-5 - Sin(an[3] * 7.0 - an[4] * 7.0) * 2.056e-5 - Sin(an[3] * 8.0 - an[4] * 8.0) * 1.369e-5 + t * .72171851 + .85635879; elem[3 * 6 + 2] = Cos(ae[0]) * -2e-8 - Cos(ae[1]) * 1.29e-6 - Cos(ae[2]) * 3.2451e-4 + Cos(ae[3]) * 9.3281e-4 + Cos(ae[4]) * .00112089 + Cos(an[1]) * 3.386e-5 + Cos(an[3]) * 1.746e-5 + Cos(-an[1] + an[3] * 2.0) * 1.658e-5 + Cos(an[2]) * 2.889e-5 - Cos(-an[2] + an[3] * 2.0) * 3.586e-5 + Cos(an[3]) * -1.786e-5 - Cos(an[4]) * 3.21e-5 - Cos(-an[3] + an[4] * 2.0) * 1.7783e-4 + Cos(an[3] * -2.0 + an[4] * 3.0) * 7.9343e-4 + Cos(an[3] * -3.0 + an[4] * 4.0) * 9.948e-5 + Cos(an[3] * -4.0 + an[4] * 5.0) * 4.483e-5 + Cos(an[3] * -5.0 + an[4] * 6.0) * 2.513e-5 + Cos(an[3] * -6.0 + an[4] * 7.0) * 1.543e-5; elem[3 * 6 + 3] = Sin(ae[0]) * -2e-8 - Sin(ae[1]) * 1.29e-6 - Sin(ae[2]) * 3.2451e-4 + Sin(ae[3]) * 9.3281e-4 + Sin(ae[4]) * .00112089 + Sin(an[1]) * 3.386e-5 + Sin(an[3]) * 1.746e-5 + Sin(-an[1] + an[3] * 2.0) * 1.658e-5 + Sin(an[2]) * 2.889e-5 - Sin(-an[2] + an[3] * 2.0) * 3.586e-5 + Sin(an[3]) * -1.786e-5 - Sin(an[4]) * 3.21e-5 - Sin(-an[3] + an[4] * 2.0) * 1.7783e-4 + Sin(an[3] * -2.0 + an[4] * 3.0) * 7.9343e-4 + Sin(an[3] * -3.0 + an[4] * 4.0) * 9.948e-5 + Sin(an[3] * -4.0 + an[4] * 5.0) * 4.483e-5 + Sin(an[3] * -5.0 + an[4] * 6.0) * 2.513e-5 + Sin(an[3] * -6.0 + an[4] * 7.0) * 1.543e-5; elem[3 * 6 + 4] = Cos(ai[0]) * -1.43e-6 - Cos(ai[1]) * 1.06e-6 - Cos(ai[2]) * 1.4013e-4 + Cos(ai[3]) * 6.8572e-4 + Cos(ai[4]) * 3.7832e-4; elem[3 * 6 + 5] = Sin(ai[0]) * -1.43e-6 - Sin(ai[1]) * 1.06e-6 - Sin(ai[2]) * 1.4013e-4 + Sin(ai[3]) * 6.8572e-4 + Sin(ai[4]) * 3.7832e-4; elem[4 * 6 + 0] = .46658054 + Cos(an[3] * 2.0 - an[4] * 3.0 + ae[4]) * 2.08e-6 - Cos(an[3] * 2.0 - an[4] * 3.0 + ae[3]) * 6.22e-6 + Cos(an[3] * 2.0 - an[4] * 3.0 + ae[2]) * 1.07e-6 - Cos(an[1] - an[4]) * 4.31e-5 + Cos(an[2] - an[4]) * -3.894e-5 - Cos(an[3] - an[4]) * 8.011e-5 + Cos(an[3] * 2.0 - an[4] * 2.0) * 5.906e-5 + Cos(an[3] * 3.0 - an[4] * 3.0) * 3.749e-5 + Cos(an[3] * 4.0 - an[4] * 4.0) * 2.482e-5 + Cos(an[3] * 5.0 - an[4] * 5.0) * 1.684e-5; elem[4 * 6 + 1] = -Sin(an[2] - an[3] * 4.0 + an[4] * 3.0) * 7.82e-6 + Sin(an[3] * 2.0 - an[4] * 3.0 + ae[4]) * 5.129e-5 - Sin(an[3] * 2.0 - an[4] * 3.0 + ae[3]) * 1.5824e-4 + Sin(an[3] * 2.0 - an[4] * 3.0 + ae[2]) * 3.451e-5 + Sin(an[1] - an[4]) * 4.751e-5 + Sin(an[2] - an[4]) * 3.896e-5 + Sin(an[3] - an[4]) * 3.5973e-4 + Sin(an[3] * 2.0 - an[4] * 2.0) * 2.8278e-4 + Sin(an[3] * 3.0 - an[4] * 3.0) * 1.386e-4 + Sin(an[3] * 4.0 - an[4] * 4.0) * 7.803e-5 + Sin(an[3] * 5.0 - an[4] * 5.0) * 4.729e-5 + Sin(an[3] * 6.0 - an[4] * 6.0) * 3e-5 + Sin(an[3] * 7.0 - an[4] * 7.0) * 1.962e-5 + Sin(an[3] * 8.0 - an[4] * 8.0) * 1.311e-5 + t * .46669212 - .9155918; elem[4 * 6 + 2] = Cos(ae[1]) * -3.5e-7 + Cos(ae[2]) * 7.453e-5 - Cos(ae[3]) * 7.5868e-4 + Cos(ae[4]) * .00139734 + Cos(an[1]) * 3.9e-5 + Cos(-an[1] + an[4] * 2.0) * 1.766e-5 + Cos(an[2]) * 3.242e-5 + Cos(an[3]) * 7.975e-5 + Cos(an[4]) * 7.566e-5 + Cos(-an[3] + an[4] * 2.0) * 1.3404e-4 - Cos(an[3] * -2.0 + an[4] * 3.0) * 9.8726e-4 - Cos(an[3] * -3.0 + an[4] * 4.0) * 1.2609e-4 - Cos(an[3] * -4.0 + an[4] * 5.0) * 5.742e-5 - Cos(an[3] * -5.0 + an[4] * 6.0) * 3.241e-5 - Cos(an[3] * -6.0 + an[4] * 7.0) * 1.999e-5 - Cos(an[3] * -7.0 + an[4] * 8.0) * 1.294e-5; elem[4 * 6 + 3] = Sin(ae[1]) * -3.5e-7 + Sin(ae[2]) * 7.453e-5 - Sin(ae[3]) * 7.5868e-4 + Sin(ae[4]) * .00139734 + Sin(an[1]) * 3.9e-5 + Sin(-an[1] + an[4] * 2.0) * 1.766e-5 + Sin(an[2]) * 3.242e-5 + Sin(an[3]) * 7.975e-5 + Sin(an[4]) * 7.566e-5 + Sin(-an[3] + an[4] * 2.0) * 1.3404e-4 - Sin(an[3] * -2.0 + an[4] * 3.0) * 9.8726e-4 - Sin(an[3] * -3.0 + an[4] * 4.0) * 1.2609e-4 - Sin(an[3] * -4.0 + an[4] * 5.0) * 5.742e-5 - Sin(an[3] * -5.0 + an[4] * 6.0) * 3.241e-5 - Sin(an[3] * -6.0 + an[4] * 7.0) * 1.999e-5 - Sin(an[3] * -7.0 + an[4] * 8.0) * 1.294e-5; elem[4 * 6 + 4] = Cos(ai[0]) * -4.4e-7 - Cos(ai[1]) * 3.1e-7 + Cos(ai[2]) * 3.689e-5 - Cos(ai[3]) * 5.9633e-4 + Cos(ai[4]) * 4.5169e-4; elem[4 * 6 + 5] = Sin(ai[0]) * -4.4e-7 - Sin(ai[1]) * 3.1e-7 + Sin(ai[2]) * 3.689e-5 - Sin(ai[3]) * 5.9633e-4 + Sin(ai[4]) * 4.5169e-4; // Get rectangular (Uranus-reffered) coordinates of moons CrdsRectangular[] gust86Rect = new CrdsRectangular[MOONS_COUNT]; for (int body = 0; body < MOONS_COUNT; body++) { double[] elem_body = new double[6]; for (int i = 0; i < 6; i++) { elem_body[i] = elem[body * 6 + i]; } double[] x = new double[3]; EllipticToRectangularN(gust86_rmu[body], elem_body, ref x); gust86Rect[body] = new CrdsRectangular(); gust86Rect[body].X = GUST86toVsop87[0] * x[0] + GUST86toVsop87[1] * x[1] + GUST86toVsop87[2] * x[2]; gust86Rect[body].Y = GUST86toVsop87[3] * x[0] + GUST86toVsop87[4] * x[1] + GUST86toVsop87[5] * x[2]; gust86Rect[body].Z = GUST86toVsop87[6] * x[0] + GUST86toVsop87[7] * x[1] + GUST86toVsop87[8] * x[2]; } for (int i = 0; i < MOONS_COUNT; i++) { moons[i] = new CrdsRectangular( rectUranus.X + gust86Rect[i].X, rectUranus.Y + gust86Rect[i].Y, rectUranus.Z + gust86Rect[i].Z ); } return(moons); }