/// <summary>
/// Gets longitude of ascending node of Lunar orbit for given instant.
/// </summary>
/// <param name="jd">Julian Day</param>
/// <param name="trueAscendingNode">True if position of true ascending node is needed, false for mean position</param>
/// <returns>Longitude of ascending node of Lunar orbit, in degrees.</returns>
private static double AscendingNode(double jd, bool trueAscendingNode)
{
double T = (jd - 2451545.0) / 36525.0;
double T2 = T * T;
double T3 = T2 * T;
double T4 = T3 * T;
double Omega = 125.0445479 - 1934.1362891 * T + 0.0020754 * T2 + T3 / 467441.0 - T4 / 60616000.0;
if (trueAscendingNode)
{
// 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;
Omega +=
-1.4979 * Math.Sin(Angle.ToRadians(2 * (D - F)))
- 0.1500 * Math.Sin(Angle.ToRadians(M))
- 0.1226 * Math.Sin(Angle.ToRadians(2 * D))
+ 0.1176 * Math.Sin(Angle.ToRadians(2 * F))
- 0.0801 * Math.Sin(Angle.ToRadians(2 * (M_ - F)));
}
return(Angle.To360(Omega));
}
public static CrdsHorizontal WithRefraction(this CrdsHorizontal h0)
{
//if (h0.Altitude < 0) return h0;
double R = 1.02 / Math.Tan(Angle.ToRadians(h0.Altitude + 10.3 / (h0.Altitude + 5.11)));
return(new CrdsHorizontal(h0.Azimuth, h0.Altitude + R / 60));
}
/// <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>
/// Calculates aberration elements for given instant.
/// </summary>
/// <param name="jde">Julian Ephemeris Day, corresponding to the given instant.</param>
/// <returns>Aberration elements for the given instant.</returns>
/// <remarks>
/// AA(II), pp. 151, 163, 164
/// </remarks>
public static AberrationElements AberrationElements(double jde)
{
double T = (jde - 2451545.0) / 36525.0;
double T2 = T * T;
double e = 0.016708634 - 0.000042037 * T - 0.0000001267 * T2;
double pi = 102.93735 + 1.71946 * T + 0.00046 * T2;
// geometric true longitude of the Sun
double L0 = 280.46646 + 36000.76983 * T + 0.0003032 * T2;
// mean anomaly of the Sun
double M = 357.52911 + 35999.05029 * T - 0.0001537 * T2;
M = Angle.ToRadians(M);
// Sun's equation of the center
double C = (1.914602 - 0.004817 * T - 0.000014 * T2) * Math.Sin(M)
+ (0.019993 - 0.000101 * T) * Math.Sin(2 * M)
+ 0.000289 * Math.Sin(3 * M);
return(new AberrationElements()
{
e = e,
pi = pi,
lambda = Angle.To360(L0 + C)
});
}
/// <summary>
/// Converts heliocentrical coordinates to rectangular topocentrical coordinates.
/// </summary>
/// <param name="planet">Heliocentrical coordinates of a planet</param>
/// <param name="earth">Heliocentrical coordinates of Earth</param>
/// <returns>Rectangular topocentrical coordinates of a planet.</returns>
public static CrdsRectangular ToRectangular(this CrdsHeliocentrical planet, CrdsHeliocentrical earth)
{
CrdsRectangular rect = new CrdsRectangular();
double B = Angle.ToRadians(planet.B);
double L = Angle.ToRadians(planet.L);
double R = planet.R;
double B0 = Angle.ToRadians(earth.B);
double L0 = Angle.ToRadians(earth.L);
double R0 = earth.R;
double cosL = Math.Cos(L);
double sinL = Math.Sin(L);
double cosB = Math.Cos(B);
double sinB = Math.Sin(B);
double cosL0 = Math.Cos(L0);
double sinL0 = Math.Sin(L0);
double cosB0 = Math.Cos(B0);
double sinB0 = Math.Sin(B0);
rect.X = R * cosB * cosL - R0 * cosB0 * cosL0;
rect.Y = R * cosB * sinL - R0 * cosB0 * sinL0;
rect.Z = R * sinB - R0 * sinB0;
return(rect);
}
/// <summary>
/// Gets magnitude of the Moon by its phase angle.
/// </summary>
/// <param name="phaseAngle">Phase angle value, in degrees, from 0 to 180.</param>
/// <returns>Moon magnitude</returns>
/// <remarks>
/// Formula is taken from <see href="https://astronomy.stackexchange.com/questions/10246/is-there-a-simple-analytical-formula-for-the-lunar-phase-brightness-curve"/>
/// </remarks>
public static double Magnitude(double phaseAngle)
{
double psi = Angle.ToRadians(phaseAngle);
double psi4 = Math.Pow(psi, 4);
return(-12.73 + 1.49 * Math.Abs(psi) + 0.043 * psi4);
}
/// <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>
/// 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 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>
/// Returns nutation corrections for equatorial coordiantes.
/// </summary>
/// <param name="eq">Initial (not corrected) equatorial coordiantes.</param>
/// <param name="ne">Nutation elements for given instant.</param>
/// <param name="epsilon">True obliquity of the ecliptic (ε), in degrees.</param>
/// <returns>Nutation corrections for equatorial coordiantes.</returns>
/// <remarks>AA(II), formula 23.1</remarks>
public static CrdsEquatorial NutationEffect(CrdsEquatorial eq, NutationElements ne, double epsilon)
{
CrdsEquatorial correction = new CrdsEquatorial();
epsilon = Angle.ToRadians(epsilon);
double alpha = Angle.ToRadians(eq.Alpha);
double delta = Angle.ToRadians(eq.Delta);
correction.Alpha = (Math.Cos(epsilon) + Math.Sin(epsilon) * Math.Sin(alpha) * Math.Tan(delta)) * ne.deltaPsi - (Math.Cos(alpha) * Math.Tan(delta)) * ne.deltaEpsilon;
correction.Delta = Math.Sin(epsilon) * Math.Cos(alpha) * ne.deltaPsi + Math.Sin(alpha) * ne.deltaEpsilon;
return(correction);
}
/// <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>
/// Calculates longitude of Central Meridian of Jupiter in System II.
/// </summary>
/// <param name="jd">Julian Day</param>
/// <returns>Longitude of Central Meridian of Jupiter in System II, in degrees.</returns>
/// <remarks>
/// This method is based on formula described here: <see href="https://www.projectpluto.com/grs_form.htm"/>
/// </remarks>
private static double JupiterCM2(double jd)
{
double jup_mean = (jd - 2455636.938) * 360.0 / 4332.89709;
double eqn_center = 5.55 * Math.Sin(Angle.ToRadians(jup_mean));
double angle = (jd - 2451870.628) * 360.0 / 398.884 - eqn_center;
double correction = 11 * Math.Sin(Angle.ToRadians(angle))
+ 5 * Math.Cos(Angle.ToRadians(angle))
- 1.25 * Math.Cos(Angle.ToRadians(jup_mean)) - eqn_center;
double cm = 181.62 + 870.1869147 * jd + correction;
return(Angle.To360(cm));
}
/// <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>
/// 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 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 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 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_));
}
/// <summary>
/// Calculates the aberration effect for a celestial body (star or planet) for given instant.
/// </summary>
/// <param name="eq">Equatorial 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 equatorial coordinates.</returns>
/// <remarks>AA(II), formula 23.3</remarks>
public static CrdsEquatorial AberrationEffect(CrdsEquatorial eq, AberrationElements ae, double epsilon)
{
double a = Angle.ToRadians(eq.Alpha);
double d = Angle.ToRadians(eq.Delta);
double theta = Angle.ToRadians(ae.lambda);
double pi = Angle.ToRadians(ae.pi);
epsilon = Angle.ToRadians(epsilon);
double da = -k * (Math.Cos(a) * Math.Cos(theta) * Math.Cos(epsilon) + Math.Sin(a) * Math.Sin(theta)) / Math.Cos(d)
+ epsilon * k * (Math.Cos(a) * Math.Cos(pi) * Math.Cos(epsilon) + Math.Sin(a) * Math.Sin(pi)) / Math.Cos(d);
double m = Math.Tan(epsilon) * Math.Cos(d) - Math.Sin(a) * Math.Sin(d);
double dd = -k * (Math.Cos(theta) * Math.Cos(epsilon) * m
+ Math.Cos(a) * Math.Sin(d) * Math.Sin(theta))
+ epsilon * k * (Math.Cos(pi) * Math.Cos(epsilon) * m + Math.Cos(a) * Math.Sin(d) * Math.Sin(pi));
return(new CrdsEquatorial(da / 3600, dd / 3600));
}
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>
/// 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>
/// Calculates nutation elements for given instant.
/// </summary>
/// <param name="jd">Julian Day, corresponding to the given instant.</param>
/// <returns>Aberration elements for the given instant.</returns>
/// <remarks>
/// The method is taken from AA(II), page 144.
/// Accuracy of the method is 0.1" for Δε and 0.5" for Δψ.
/// </remarks>
public static NutationElements NutationElements(double jd)
{
double T = (jd - 2451545) / 36525.0;
// Longitude of the ascending node of Moon's mean orbit on the ecliptic,
// measured from the mean equinox of the date:
double Omega = 125.04452 - 1934.136261 * T;
// Mean longutude of Sun
double L = 280.4665 + 36000.7698 * T;
// Mean longitude of Moon
double L_ = 218.3165 + 481267.8813 * T;
double deltaEpsilon = 9.20 * Math.Cos(Angle.ToRadians(Omega)) + 0.57 * Math.Cos(Angle.ToRadians(2 * L)) + 0.10 * Math.Cos(Angle.ToRadians(2 * L_)) - 0.09 * Math.Cos(Angle.ToRadians(2 * Omega));
double deltaPsi = -17.20 * Math.Sin(Angle.ToRadians(Omega)) - 1.32 * Math.Sin(Angle.ToRadians(2 * L)) - 0.23 * Math.Sin(Angle.ToRadians(2 * L_)) + 0.21 * Math.Sin(Angle.ToRadians(2 * Omega));
return(new NutationElements()
{
deltaEpsilon = deltaEpsilon / 3600,
deltaPsi = deltaPsi / 3600
});
}
/// <summary>
/// Gets magnitude component of Saturn rings, that should be added to Saturn disk magnitude (see <see cref="PlanetEphem.Magnitude(int, double, double, double)"/>).
/// </summary>
/// <returns></returns>
public float GetRingsMagnitude()
{
double sinB = Math.Sin(Angle.ToRadians(B));
return((float)(0.044 * Math.Abs(DeltaU) - 2.6 * Math.Sin(Angle.ToRadians(Math.Abs(B))) + 1.25 * sinB * sinB));
}
/// <summary>
/// Calculates apparent sidereal time at Greenwich for given instant.
/// </summary>
/// <param name="jd">Julian Day</param>
/// <returns>Apparent sidereal time at Greenwich, expressed in degrees.</returns>
/// <remarks>
/// AA(II), formula 12.4, with corrections for nutation (chapter 22).
/// </remarks>
public static double ApparentSiderealTime(double jd, double deltaPsi, double epsilon)
{
double cosEpsilon = Math.Cos(Angle.ToRadians(epsilon));
return(MeanSiderealTime(jd) + deltaPsi * cosEpsilon);
}
/// <summary>
/// Calculates instants of rising, transit and setting for non-stationary celestial body for the desired date.
/// Non-stationary in this particular case means that body has fastly changing celestial coordinates during the day.
/// </summary>
/// <param name="eq">Array of three equatorial coordinates of the celestial body correspoding to local midnight, local noon, and local midnight of the following day after the desired date respectively.</param>
/// <param name="location">Geographical location of the observation point.</param>
/// <param name="theta0">Apparent sidereal time at Greenwich for local midnight of the desired date.</param>
/// <param name="pi">Horizontal equatorial parallax of the body.</param>
/// <param name="sd">Visible semidiameter of the body, expressed in degrees.</param>
/// <returns>Instants of rising, transit and setting for the celestial body for the desired date.</returns>
public static RTS RiseTransitSet(CrdsEquatorial[] eq, CrdsGeographical location, double theta0, double pi = 0, double sd = 0)
{
if (eq.Length != 3)
{
throw new ArgumentException("Number of equatorial coordinates in the array should be equal to 3.");
}
double[] alpha = new double[3];
double[] delta = new double[3];
for (int i = 0; i < 3; i++)
{
alpha[i] = eq[i].Alpha;
delta[i] = eq[i].Delta;
}
Angle.Align(alpha);
Angle.Align(delta);
List <CrdsHorizontal> hor = new List <CrdsHorizontal>();
for (int i = 0; i <= 24; i++)
{
double n = i / 24.0;
CrdsEquatorial eq0 = InterpolateEq(alpha, delta, n);
var sidTime = InterpolateSiderialTime(theta0, n);
hor.Add(eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime));
}
var result = new RTS();
for (int i = 0; i < 24; i++)
{
double n = (i + 0.5) / 24.0;
CrdsEquatorial eq0 = InterpolateEq(alpha, delta, n);
var sidTime = InterpolateSiderialTime(theta0, n);
var hor0 = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime);
if (double.IsNaN(result.Transit) && hor0.Altitude > 0)
{
double r = SolveParabola(Math.Sin(Angle.ToRadians(hor[i].Azimuth)), Math.Sin(Angle.ToRadians(hor0.Azimuth)), Math.Sin(Angle.ToRadians(hor[i + 1].Azimuth)));
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
eq0 = InterpolateEq(alpha, delta, t);
sidTime = InterpolateSiderialTime(theta0, t);
result.Transit = t;
result.TransitAltitude = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Altitude;
}
}
if (double.IsNaN(result.Rise) || double.IsNaN(result.Set))
{
double r = SolveParabola(hor[i].Altitude + sd, hor0.Altitude + sd, hor[i + 1].Altitude + sd);
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
eq0 = InterpolateEq(alpha, delta, t);
sidTime = InterpolateSiderialTime(theta0, t);
if (double.IsNaN(result.Rise) && hor[i].Altitude + sd < 0 && hor[i + 1].Altitude + sd > 0)
{
result.Rise = t;
result.RiseAzimuth = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Azimuth;
}
if (double.IsNaN(result.Set) && hor[i].Altitude + sd > 0 && hor[i + 1].Altitude + sd < 0)
{
result.Set = t;
result.SetAzimuth = eq0.ToTopocentric(location, sidTime, pi).ToHorizontal(location, sidTime).Azimuth;
}
if (!double.IsNaN(result.Transit) && !double.IsNaN(result.Rise) && !double.IsNaN(result.Set))
{
break;
}
}
}
}
return(result);
}
/// <summary>
/// Gets phase value (illuminated fraction of the Moon disk).
/// </summary>
/// <param name="phaseAngle">Phase angle of the Moon, in degrees.</param>
/// <returns>Illuminated fraction of the Moon disk, from 0 to 1.</returns>
/// <remarks>
/// AA(II), formula 48.1
/// </remarks>
public static double Phase(double phaseAngle)
{
return((1 + Math.Cos(Angle.ToRadians(phaseAngle))) / 2);
}
