/// <summary>
/// Performs reduction of equatorial coordinates from one epoch to another
/// with using of precessional elements.
/// </summary>
/// <param name="eq0">Equatorial coordinates for initial epoch.</param>
/// <param name="p">Precessional elements for reduction from initial epoch to target (final) epoch.</param>
/// <returns>Equatorial coordinates for target (final) epoch.</returns>
/// <remarks>
/// This method is taken from AA(I), formula 20.4.
/// </remarks>
public static CrdsEquatorial GetEquatorialCoordinates(CrdsEquatorial eq0, PrecessionalElements p)
{
CrdsEquatorial eq = new CrdsEquatorial();
double sinDelta0 = Math.Sin(Angle.ToRadians(eq0.Delta));
double cosDelta0 = Math.Cos(Angle.ToRadians(eq0.Delta));
double sinTheta = Math.Sin(Angle.ToRadians(p.theta));
double cosTheta = Math.Cos(Angle.ToRadians(p.theta));
double sinAlpha0Zeta = Math.Sin(Angle.ToRadians(eq0.Alpha + p.zeta));
double cosAlpha0Zeta = Math.Cos(Angle.ToRadians(eq0.Alpha + p.zeta));
double A = cosDelta0 * sinAlpha0Zeta;
double B = cosTheta * cosDelta0 * cosAlpha0Zeta - sinTheta * sinDelta0;
double C = sinTheta * cosDelta0 * cosAlpha0Zeta + cosTheta * sinDelta0;
eq.Alpha = Angle.ToDegrees(Math.Atan2(A, B)) + p.z;
eq.Alpha = Angle.To360(eq.Alpha);
if (Math.Abs(C) == 1)
{
eq.Delta = Angle.ToDegrees(Math.Acos(A * A + B * B));
}
else
{
eq.Delta = Angle.ToDegrees(Math.Asin(C));
}
return(eq);
}
/// <summary>
/// Gets geocentric elongation angle of the Moon from Sun
/// </summary>
/// <param name="sun">Ecliptical geocentrical coordinates of the Sun</param>
/// <param name="moon">Ecliptical geocentrical coordinates of the Moon</param>
/// <returns>Geocentric elongation angle, in degrees, from 0 to 180.</returns>
/// <remarks>
/// AA(II), formula 48.2
/// </remarks>
public static double Elongation(CrdsEcliptical sun, CrdsEcliptical moon)
{
double beta = Angle.ToRadians(moon.Beta);
double lambda = Angle.ToRadians(moon.Lambda);
double lambda0 = Angle.ToRadians(sun.Lambda);
return(Angle.ToDegrees(Math.Acos(Math.Cos(beta) * Math.Cos(lambda - lambda0))));
}
/// <summary>
/// Converts rectangular topocentric coordinates of a planet to topocentrical ecliptical coordinates
/// </summary>
/// <param name="rect">Rectangular topocentric coordinates of a planet</param>
/// <returns>Topocentrical ecliptical coordinates of a planet</returns>
public static CrdsEcliptical ToEcliptical(this CrdsRectangular rect)
{
double lambda = Angle.To360(Angle.ToDegrees(Math.Atan2(rect.Y, rect.X)));
double beta = Angle.ToDegrees(Math.Atan(rect.Z / Math.Sqrt(rect.X * rect.X + rect.Y * rect.Y)));
double distance = Math.Sqrt(rect.X * rect.X + rect.Y * rect.Y + rect.Z * rect.Z);
return(new CrdsEcliptical(lambda, beta, distance));
}
/// <summary>
/// Calculates phase angle of the Moon
/// </summary>
/// <param name="psi">Geocentric elongation of the Moon.</param>
/// <param name="R">Distance Earth-Sun, in kilometers</param>
/// <param name="Delta">Distance Earth-Moon, in kilometers</param>
/// <returns>Phase angle, in degrees, from 0 to 180</returns>
/// <remarks>
/// AA(II), formula 48.3.
/// </remarks>
public static double PhaseAngle(double psi, double R, double Delta)
{
psi = Angle.ToRadians(Math.Abs(psi));
double phaseAngle = Angle.ToDegrees(Math.Atan(R * Math.Sin(psi) / (Delta - R * Math.Cos(psi))));
if (phaseAngle < 0)
{
phaseAngle += 180;
}
return(phaseAngle);
}
/// <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 visible appearance of planet for given date.
/// </summary>
/// <param name="jd">Julian day</param>
/// <param name="planet">Planet number to calculate appearance, 1 = Mercury, 2 = Venus and etc.</param>
/// <param name="eq">Equatorial coordinates of the planet</param>
/// <param name="distance">Distance from the planet to the Earth</param>
/// <returns>Appearance parameters of the planet</returns>
/// <remarks>
/// This method is based on book "Practical Ephemeris Calculations", Montenbruck.
/// See topic 6.4, pp. 88-92.
/// </remarks>
public static PlanetAppearance PlanetAppearance(double jd, int planet, CrdsEquatorial eq, double distance)
{
PlanetAppearance a = new PlanetAppearance();
double d = jd - 2451545.0;
double T = d / 36525.0;
// coordinates of the point to which the north pole of the planet is pointing.
CrdsEquatorial eq0 = new CrdsEquatorial();
eq0.Alpha = Angle.To360(cAlpha0[planet - 1][0] + cAlpha0[planet - 1][1] * T + cAlpha0[planet - 1][2] * T);
eq0.Delta = cDelta0[planet - 1][0] + cDelta0[planet - 1][1] * T + cDelta0[planet - 1][2] * T;
// take light time effect into account
d -= PlanetPositions.LightTimeEffect(distance);
T = d / 36525.0;
// position of null meridian
double W = Angle.To360(cW[planet - 1][0] + cW[planet - 1][1] * d + cW[planet - 1][2] * T);
double delta = Angle.ToRadians(eq.Delta);
double alpha = Angle.ToRadians(eq.Alpha);
double delta0 = Angle.ToRadians(eq0.Delta);
double dAlpha0 = Angle.ToRadians(eq0.Alpha - eq.Alpha);
double sinD = -Math.Sin(delta0) * Math.Sin(delta) - Math.Cos(delta0) * Math.Cos(delta) * Math.Cos(dAlpha0);
// planetographic latitude of the Earth
a.D = Angle.ToDegrees(Math.Asin(sinD));
double cosD = Math.Cos(Angle.ToRadians(a.D));
double sinP = Math.Cos(delta0) * Math.Sin(dAlpha0) / cosD;
double cosP = (Math.Sin(delta0) * Math.Cos(delta) - Math.Cos(delta0) * Math.Sin(delta) * Math.Cos(dAlpha0)) / cosD;
// position angle of the axis
a.P = Angle.To360(Angle.ToDegrees(Math.Atan2(sinP, cosP)));
double sinK = (-Math.Cos(delta0) * Math.Sin(delta) + Math.Sin(delta0) * Math.Cos(delta) * Math.Cos(dAlpha0)) / cosD;
double cosK = Math.Cos(delta) * Math.Sin(dAlpha0) / cosD;
double K = Angle.ToDegrees(Math.Atan2(sinK, cosK));
// planetographic longitude of the central meridian
a.CM = planet == 5 ?
JupiterCM2(jd) :
Angle.To360(Math.Sign(W) * (W - K));
return(a);
}
/// <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 galactical coodinates to equatorial, for equinox B1950.0.
/// </summary>
/// <param name="gal">Galactical coodinates.</param>
/// <returns>Equatorial coodinates, for equinox B1950.0.</returns>
public static CrdsEquatorial ToEquatorial(this CrdsGalactical gal)
{
CrdsEquatorial eq = new CrdsEquatorial();
double l_l0 = Angle.ToRadians(gal.l - 123.0);
double delta0 = Angle.ToRadians(27.4);
double b = Angle.ToRadians(gal.b);
double Y = Math.Sin(l_l0);
double X = Math.Cos(l_l0) * Math.Sin(delta0) - Math.Tan(b) * Math.Cos(delta0);
double sinDelta = Math.Sin(b) * Math.Sin(delta0) + Math.Cos(b) * Math.Cos(delta0) * Math.Cos(l_l0);
eq.Alpha = Angle.To360(Angle.ToDegrees(Math.Atan2(Y, X)) + 12.25);
eq.Delta = Angle.ToDegrees(Math.Asin(sinDelta));
return(eq);
}
/// <summary>
/// Converts equatorial coordinates (for equinox B1950.0) to galactical coordinates.
/// </summary>
/// <param name="eq">Equatorial coordinates for equinox B1950.0</param>
/// <returns>Galactical coordinates.</returns>
public static CrdsGalactical ToGalactical(this CrdsEquatorial eq)
{
CrdsGalactical gal = new CrdsGalactical();
double alpha0_alpha = Angle.ToRadians(192.25 - eq.Alpha);
double delta = Angle.ToRadians(eq.Delta);
double delta0 = Angle.ToRadians(27.4);
double Y = Math.Sin(alpha0_alpha);
double X = Math.Cos(alpha0_alpha) * Math.Sin(delta0) - Math.Tan(delta) * Math.Cos(delta0);
double sinb = Math.Sin(delta) * Math.Sin(delta0) + Math.Cos(delta) * Math.Cos(delta0) * Math.Cos(alpha0_alpha);
gal.l = Angle.To360(303 - Angle.ToDegrees(Math.Atan2(Y, X)));
gal.b = Angle.ToDegrees(Math.Asin(sinb));
return(gal);
}
/// <summary>
/// Converts equatorial coordinates to ecliptical coordinates.
/// </summary>
/// <param name="eq">Pair of equatorial coordinates.</param>
/// <param name="epsilon">Obliquity of the ecliptic, in degrees.</param>
/// <returns></returns>
public static CrdsEcliptical ToEcliptical(this CrdsEquatorial eq, double epsilon)
{
CrdsEcliptical ecl = new CrdsEcliptical();
epsilon = Angle.ToRadians(epsilon);
double alpha = Angle.ToRadians(eq.Alpha);
double delta = Angle.ToRadians(eq.Delta);
double Y = Math.Sin(alpha) * Math.Cos(epsilon) + Math.Tan(delta) * Math.Sin(epsilon);
double X = Math.Cos(alpha);
ecl.Lambda = Angle.ToDegrees(Math.Atan2(Y, X));
ecl.Beta = Angle.ToDegrees(Math.Asin(Math.Sin(delta) * Math.Cos(epsilon) - Math.Cos(delta) * Math.Sin(epsilon) * Math.Sin(alpha)));
return(ecl);
}
/// <summary>
/// Converts local horizontal coordinates to equatorial coordinates.
/// </summary>
/// <param name="hor">Pair of local horizontal coordinates.</param>
/// <param name="geo">Geographical of the observer</param>
/// <param name="theta0">Local sidereal time.</param>
/// <returns>Pair of equatorial coordinates</returns>
public static CrdsEquatorial ToEquatorial(this CrdsHorizontal hor, CrdsGeographical geo, double theta0)
{
CrdsEquatorial eq = new CrdsEquatorial();
double A = Angle.ToRadians(hor.Azimuth);
double h = Angle.ToRadians(hor.Altitude);
double phi = Angle.ToRadians(geo.Latitude);
double Y = Math.Sin(A);
double X = Math.Cos(A) * Math.Sin(phi) + Math.Tan(h) * Math.Cos(phi);
double H = Angle.ToDegrees(Math.Atan2(Y, X));
eq.Alpha = Angle.To360(theta0 - geo.Longitude - H);
eq.Delta = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(h) - Math.Cos(phi) * Math.Cos(h) * Math.Cos(A)));
return(eq);
}
/// <summary>
/// Converts equatorial coodinates to local horizontal
/// </summary>
/// <param name="eq">Pair of equatorial coodinates</param>
/// <param name="geo">Geographical coordinates of the observer</param>
/// <param name="theta0">Local sidereal time</param>
/// <remarks>
/// Implementation is taken from AA(I), formulae 12.5, 12.6.
/// </remarks>
public static CrdsHorizontal ToHorizontal(this CrdsEquatorial eq, CrdsGeographical geo, double theta0)
{
double H = Angle.ToRadians(HourAngle(theta0, geo.Longitude, eq.Alpha));
double phi = Angle.ToRadians(geo.Latitude);
double delta = Angle.ToRadians(eq.Delta);
CrdsHorizontal hor = new CrdsHorizontal();
double Y = Math.Sin(H);
double X = Math.Cos(H) * Math.Sin(phi) - Math.Tan(delta) * Math.Cos(phi);
hor.Altitude = Angle.ToDegrees(Math.Asin(Math.Sin(phi) * Math.Sin(delta) + Math.Cos(phi) * Math.Cos(delta) * Math.Cos(H)));
hor.Azimuth = Angle.ToDegrees(Math.Atan2(Y, X));
hor.Azimuth = Angle.To360(hor.Azimuth);
return(hor);
}
/// <summary>
/// Calculates topocentric equatorial coordinates of celestial body
/// with taking into account correction for parallax.
/// </summary>
/// <param name="eq">Geocentric equatorial coordinates of the body</param>
/// <param name="geo">Geographical coordinates of the body</param>
/// <param name="theta0">Apparent sidereal time at Greenwich</param>
/// <param name="pi">Parallax of a body</param>
/// <returns>Topocentric equatorial coordinates of the celestial body</returns>
/// <remarks>
/// Method is taken from AA(II), formulae 40.6-40.7.
/// </remarks>
public static CrdsEquatorial ToTopocentric(this CrdsEquatorial eq, CrdsGeographical geo, double theta0, double pi)
{
double H = Angle.ToRadians(HourAngle(theta0, geo.Longitude, eq.Alpha));
double delta = Angle.ToRadians(eq.Delta);
double sinPi = Math.Sin(Angle.ToRadians(pi));
double A = Math.Cos(delta) * Math.Sin(H);
double B = Math.Cos(delta) * Math.Cos(H) - geo.RhoCosPhi * sinPi;
double C = Math.Sin(delta) - geo.RhoSinPhi * sinPi;
double q = Math.Sqrt(A * A + B * B + C * C);
double H_ = Angle.ToDegrees(Math.Atan2(A, B));
double alpha_ = Angle.To360(theta0 - geo.Longitude - H_);
double delta_ = Angle.ToDegrees(Math.Asin(C / q));
return(new CrdsEquatorial(alpha_, delta_));
}
public static CrdsEquatorial ToEquatorial(this CrdsRectangular m, CrdsEquatorial planet, double P, double semidiameter)
{
// convert to polar coordinates
// radius-vector of moon, in planet's equatorial radii
double r = Math.Sqrt(m.X * m.X + m.Y * m.Y);
// rotation angle
double theta = Angle.ToDegrees(Math.Atan2(m.Y, m.X));
// rotate with position angle of the planet
theta += P;
// convert back to rectangular coordinates, but rotated with P angle:
double x = r * Math.Cos(Angle.ToRadians(theta));
double y = r * Math.Sin(Angle.ToRadians(theta));
double dAlpha = (1 / Math.Cos(Angle.ToRadians(planet.Delta))) * x * semidiameter / 3600;
double dDelta = y * semidiameter / 3600;
return(new CrdsEquatorial(planet.Alpha - dAlpha, planet.Delta + dDelta));
}
/// <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>
/// Calculates heliocentrical coordinates of the planet using VSOP87 motion theory.
/// </summary>
/// <param name="planet">Planet serial number - from 1 (Mercury) to 8 (Neptune) to calculate heliocentrical coordinates.</param>
/// <param name="jde">Julian Ephemeris Day</param>
/// <returns>Returns heliocentric coordinates of the planet for given date.</returns>
public static CrdsHeliocentrical GetPlanetCoordinates(int planet, double jde, bool highPrecision = true, bool epochOfDate = true)
{
Initialize();
const int L = 0;
const int B = 1;
const int R = 2;
int p = planet - 1;
int e = epochOfDate ? 1 : 0;
double t = (jde - 2451545.0) / 365250.0;
double t2 = t * t;
double t3 = t * t2;
double t4 = t * t3;
double t5 = t * t4;
double[] l = new double[6];
double[] b = new double[6];
double[] r = new double[6];
for (int j = 0; j < 6; j++)
{
l[j] = 0;
for (int i = 0; i < Terms[e, p, L, j]?.Count; i++)
{
if (!highPrecision && i > LPTermsCount[e, p, L, j])
{
break;
}
l[j] += Terms[e, p, L, j][i].A * Math.Cos(Terms[e, p, L, j][i].B + Terms[e, p, L, j][i].C * t);
}
b[j] = 0;
for (int i = 0; i < Terms[e, p, B, j]?.Count; i++)
{
if (!highPrecision && i > LPTermsCount[e, p, B, j])
{
break;
}
b[j] += Terms[e, p, B, j][i].A * Math.Cos(Terms[e, p, B, j][i].B + Terms[e, p, B, j][i].C * t);
}
r[j] = 0;
for (int i = 0; i < Terms[e, p, R, j]?.Count; i++)
{
if (!highPrecision && i > LPTermsCount[e, p, R, j])
{
break;
}
r[j] += Terms[e, p, R, j][i].A * Math.Cos(Terms[e, p, R, j][i].B + Terms[e, p, R, j][i].C * t);
}
}
CrdsHeliocentrical result = new CrdsHeliocentrical();
result.L = l[0] + l[1] * t + l[2] * t2 + l[3] * t3 + l[4] * t4 + l[5] * t5;
result.L = Angle.ToDegrees(result.L);
result.L = Angle.To360(result.L);
result.B = b[0] + b[1] * t + b[2] * t2 + b[3] * t3 + b[4] * t4 + b[5] * t5;
result.B = Angle.ToDegrees(result.B);
result.R = r[0] + r[1] * t + r[2] * t2 + r[3] * t3 + r[4] * t4 + r[5] * t5;
return(result);
}
/// <summary>
/// Loads VSOP terms from file if not loaded yet
/// </summary>
private static void Initialize()
{
// high precision
if (Terms == null)
{
Terms = new List <Term> [EPOCHS_COUNT, PLANETS_COUNT, SERIES_COUNT, POWERS_COUNT];
LPTermsCount = new int[EPOCHS_COUNT, PLANETS_COUNT, SERIES_COUNT, POWERS_COUNT];
}
// already initialized
else
{
return;
}
for (int e = 0; e < 2; e++)
{
using (var stream = Assembly.GetExecutingAssembly().GetManifestResourceStream($"ADK.Data.VSOP87{(e == 0 ? "B" : "D")}.bin"))
using (var reader = new BinaryReader(stream))
{
while (reader.BaseStream.Position != reader.BaseStream.Length)
{
int p = reader.ReadInt32();
int t = reader.ReadInt32();
int power = reader.ReadInt32();
int count = reader.ReadInt32();
double A, B, C;
Terms[e, p, t, power] = new List <Term>();
for (int i = 0; i < count; i++)
{
A = reader.ReadDouble();
B = reader.ReadDouble();
C = reader.ReadDouble();
Terms[e, p, t, power].Add(new Term(A, B, C));
}
// sort terms by A coefficient descending
Terms[e, p, t, power].Sort((x, y) => Math.Sign(y.A - x.A));
LPTermsCount[e, p, t, power] = count;
for (int i = 0; i < count; i++)
{
// L, B
if (t < 2)
{
// maximal error in seconds of arc
// calculated by rule descibed in AA(II), p. 220 (Accuracy of the results)
double err = Angle.ToDegrees(2 * Math.Sqrt(i + 1) * Terms[e, p, t, power][i].A) * 3600;
if (err < 1)
{
LPTermsCount[e, p, t, power] = i;
break;
}
}
// R
else
{
// maximal error in AU
// calculated by rule descibed in AA(II), p. 220 (Accuracy of the results)
double err = 2 * Math.Sqrt(i + 1) * Terms[e, p, t, power][i].A;
if (err < 1e-8)
{
LPTermsCount[e, p, t, power] = i;
break;
}
}
}
}
}
}
}
/// <summary>
/// Calculates heliocentrical coordinates of the planet using VSOP87 motion theory.
/// </summary>
/// <param name="planet"><see cref="Planet"/> to calculate heliocentrical coordinates.</param>
/// <param name="jde">Julian Ephemeris Day</param>
/// <returns>Returns heliocentric coordinates of the planet for given date.</returns>
public static CrdsHeliocentrical GetPlanetCoordinates(Planet planet, double jde, bool highPrecision = true)
{
Initialize(highPrecision);
const int L = 0;
const int B = 1;
const int R = 2;
int p = (int)planet - 1;
double t = (jde - 2451545.0) / 365250.0;
double t2 = t * t;
double t3 = t * t2;
double t4 = t * t3;
double t5 = t * t4;
double[] l = new double[6];
double[] b = new double[6];
double[] r = new double[6];
List <Term>[,,] terms = highPrecision ? TermsHP : TermsLP;
for (int j = 0; j < 6; j++)
{
l[j] = 0;
for (int i = 0; i < terms[p, L, j]?.Count; i++)
{
l[j] += terms[p, L, j][i].A * Math.Cos(terms[p, L, j][i].B + terms[p, L, j][i].C * t);
}
b[j] = 0;
for (int i = 0; i < terms[p, B, j]?.Count; i++)
{
b[j] += terms[p, B, j][i].A * Math.Cos(terms[p, B, j][i].B + terms[p, B, j][i].C * t);
}
r[j] = 0;
for (int i = 0; i < terms[p, R, j]?.Count; i++)
{
r[j] += terms[p, R, j][i].A * Math.Cos(terms[p, R, j][i].B + terms[p, R, j][i].C * t);
}
}
// Dimension coefficient.
// Should be applied for the shortened VSOP87 formulae listed in AA book
// because "A" coefficient expressed in 1e-8 radian for longitude and latitude and in 1e-8 AU for radius vector
// Original (high-precision) version of VSOP has "A" expressed in radians and AU respectively.
double d = highPrecision ? 1 : 1e-8;
CrdsHeliocentrical result = new CrdsHeliocentrical();
result.L = (l[0] + l[1] * t + l[2] * t2 + l[3] * t3 + l[4] * t4 + l[5] * t5) * d;
result.L = Angle.ToDegrees(result.L);
result.L = Angle.To360(result.L);
result.B = (b[0] + b[1] * t + b[2] * t2 + b[3] * t3 + b[4] * t4 + b[5] * t5) * d;
result.B = Angle.ToDegrees(result.B);
result.R = (r[0] + r[1] * t + r[2] * t2 + r[3] * t3 + r[4] * t4 + r[5] * t5) * d;
return(result);
}
