/// <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);
}