/// <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>
/// Finds constellation name by point with specified equatorial coordinates for any epoch.
/// </summary>
/// <param name="eq">Equatorial coordinates of the point for any epoch.</param>
/// <param name="epoch">Epoch value, in Julian Days.</param>
/// <returns>International 3-letter code of a constellation.</returns>
/// <remarks>
/// Implementation is based on <see href="ftp://cdsarc.u-strasbg.fr/pub/cats/VI/42/"/>.
/// </remarks>
public static string FindConstellation(CrdsEquatorial eq, double epoch)
{
var pe = Precession.ElementsFK5(epoch, Date.EPOCH_B1875);
var eq1875 = Precession.GetEquatorialCoordinates(eq, pe);
return(FindConstellation(eq1875));
}
/// <summary>
/// Converts rectangular planetocentrical coordinates of satellite to equatorial coordinates as seen from Earth
/// </summary>
/// <param name="m">Rectangular planetocentrical coordinates of satellite</param>
/// <param name="planet">Equatorial coordinates of parent planet (as seen from Earth)</param>
/// <param name="P">Position angle of parent planet</param>
/// <param name="semidiameter">Visible semidiameter of parent planet, in seconds of arc.</param>
/// <returns>Equatorial coordinates of satellite as seen from Earth</returns>
/// <remarks>
/// The method is taken from geometrical drawing (own work)
/// </remarks>
public static CrdsEquatorial ToEquatorial(this CrdsRectangular m, CrdsEquatorial planet, double P, double semidiameter)
{
// convert rectangular planetocentrical coordinates to planetocentrical 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));
// delta of RA
double dAlpha = (1 / Math.Cos(Angle.ToRadians(planet.Delta))) * x * semidiameter / 3600;
// delta of Declination
// negative sign because positive delta means southward direction
double dDelta = -y * semidiameter / 3600;
return(new CrdsEquatorial(planet.Alpha - dAlpha, planet.Delta - dDelta));
}
/// <summary>
/// Adds corrections to equatorial coordinates
/// </summary>
public static CrdsEquatorial operator +(CrdsEquatorial lhs, CrdsEquatorial rhs)
{
CrdsEquatorial eq = new CrdsEquatorial();
eq.Alpha = Angle.To360(lhs.Alpha + rhs.Alpha);
eq.Delta = lhs.Delta + rhs.Delta;
return(eq);
}
// TODO: description
private static CrdsEquatorial InterpolateEq(double[] alpha, double[] delta, double n)
{
double[] x = new double[] { 0, 0.5, 1 };
CrdsEquatorial eq = new CrdsEquatorial();
eq.Alpha = Interpolation.Lagrange(x, alpha, n);
eq.Delta = Interpolation.Lagrange(x, delta, n);
return(eq);
}
/// <summary>
/// Finds constellation name by point with specified equatorial coordinates for epoch B1875.
/// </summary>
/// <param name="eq1875">Equatorial coordinates of the point for epoch B1875.</param>
/// <returns>International 3-letter code of a constellation.</returns>
/// <remarks>
/// Implementation is based on <see href="ftp://cdsarc.u-strasbg.fr/pub/cats/VI/42/"/>.
/// </remarks>
public static string FindConstellation(CrdsEquatorial eq1875)
{
// Load borders data if needed
if (Borders == null)
{
using (var stream = Assembly.GetExecutingAssembly().GetManifestResourceStream($"Astrarium.Algorithms.Data.Constells.dat"))
using (var reader = new StreamReader(stream))
{
Borders = new List <Border>();
string line;
while ((line = reader.ReadLine()) != null)
{
float ra1 = float.Parse(line.Substring(0, 8), CultureInfo.InvariantCulture);
float ra2 = float.Parse(line.Substring(9, 7), CultureInfo.InvariantCulture);
float dec = float.Parse(line.Substring(17, 8), CultureInfo.InvariantCulture);
string constName = line.Substring(26, 3);
Borders.Add(new Border(ra1, ra2, dec, constName));
}
}
}
double alpha = eq1875.Alpha / 15.0;
double delta = eq1875.Delta;
for (int i = 0; i < Borders.Count; i++)
{
if (Borders[i].Dec > delta)
{
continue;
}
if (Borders[i].RA1 <= alpha)
{
continue;
}
if (Borders[i].RA2 > alpha)
{
continue;
}
if (alpha >= Borders[i].RA2 &&
alpha < Borders[i].RA1 &&
Borders[i].Dec <= delta)
{
return(Borders[i].ConstName);
}
else if (Borders[i].RA1 < alpha)
{
continue;
}
}
return("");
}
/// <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 angular separation between two points with equatorial coordinates
/// </summary>
/// <param name="p1">Equatorial coordinates of the first point</param>
/// <param name="p2">Equatorial coordinates of the second point</param>
/// <returns>Angular separation in degrees</returns>
public static double Separation(CrdsEquatorial p1, CrdsEquatorial p2)
{
double a1 = ToRadians(p1.Delta);
double a2 = ToRadians(p2.Delta);
double A1 = p1.Alpha;
double A2 = p2.Alpha;
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>
/// Creates new instance
/// </summary>
public LunarEclipseLocalCircumstancesContactPoint(InstantLunarEclipseElements e, CrdsGeographical g)
{
CrdsEquatorial eq = new CrdsEquatorial(e.Alpha, e.Delta);
// Nutation elements
var nutation = Nutation.NutationElements(e.JulianDay);
// True obliquity
var epsilon = Date.TrueObliquity(e.JulianDay, nutation.deltaEpsilon);
// Greenwich apparent sidereal time
double siderealTime = Date.ApparentSiderealTime(e.JulianDay, nutation.deltaPsi, epsilon);
// Geocenric distance to the Moon, in km
double dist = 358473400.0 / (e.F3 * 3600);
// Horizontal parallax of the Moon
double parallax = LunarEphem.Parallax(dist);
// Topocentrical equatorial coordinates
var eqTopo = eq.ToTopocentric(g, siderealTime, parallax);
// Horizontal coordinates
var h = eqTopo.ToHorizontal(g, siderealTime);
// Hour angle
double H = Coordinates.HourAngle(siderealTime, g.Longitude, eqTopo.Alpha);
// Position angles
// Parallactic angle - AA(II), p.98, formula 14.1
double qAngle = ToDegrees(Atan2(Sin(ToRadians(H)), Tan(ToRadians(g.Latitude)) * Cos(ToRadians(eqTopo.Delta)) - Sin(ToRadians(eqTopo.Delta)) * Cos(ToRadians(H))));
// Position angle, measured from North to East (CCW)
double pAngle = To360(ToDegrees(Atan2(e.X, e.Y)));
// Position angle, measured from Zenith CCW
double zAngle = To360(pAngle - qAngle);
JulianDay = e.JulianDay;
LunarAltitude = h.Altitude;
QAngle = qAngle;
PAngle = pAngle;
ZAngle = zAngle;
X = e.X;
Y = e.Y;
F1 = e.F1;
F2 = e.F2;
F3 = e.F3;
}
/// <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 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>
/// Finds horizon circle point for a given geographical longitude
/// for an instant of lunar eclipse, where Moon has zero altitude.
/// </summary>
/// <param name="e">Besselian elements of the Moon for the given instant.</param>
/// <param name="L">Geographical longitude, positive west, negative east, from -180 to +180 degrees.</param>
/// <returns>
/// Geographical coordinates for the point.
/// </returns>
/// <remarks>
/// The method core is based on formulae from the book:
/// Seidelmann, P. K.: Explanatory Supplement to The Astronomical Almanac,
/// University Science Book, Mill Valley (California), 1992,
/// Chapter 8 "Eclipses of the Sun and Moon"
/// https://archive.org/download/131123ExplanatorySupplementAstronomicalAlmanac/131123-explanatory-supplement-astronomical-almanac.pdf
/// </remarks>
private static CrdsGeographical Project(InstantLunarEclipseElements e, double L)
{
CrdsGeographical g = null;
// Nutation elements
var nutation = Nutation.NutationElements(e.JulianDay);
// True obliquity
var epsilon = Date.TrueObliquity(e.JulianDay, nutation.deltaEpsilon);
// Greenwich apparent sidereal time
double siderealTime = Date.ApparentSiderealTime(e.JulianDay, nutation.deltaPsi, epsilon);
// Geocenric distance to the Moon, in km
double dist = 358473400.0 / (e.F3 * 3600);
// Horizontal parallax of the Moon
double parallax = LunarEphem.Parallax(dist);
// Equatorial coordinates of the Moon, initial value is geocentric
CrdsEquatorial eq = new CrdsEquatorial(e.Alpha, e.Delta);
// two iterations:
// 1st: find geo location needed to perform topocentric correction
// 2nd: correct sublunar point with topocentric position and find true geoposition
for (int i = 0; i < 2; i++)
{
// sublunar point latitude, preserve sign!
double phi0 = Sign(e.Delta) * Abs(eq.Delta);
// sublunar point longitude (formula 8.426-1)
double lambda0 = siderealTime - eq.Alpha;
// sublunar point latitude (formula 8.426-2)
double tanPhi = -1.0 / Tan(ToRadians(phi0)) * Cos(ToRadians(lambda0 - L));
double phi = ToDegrees(Atan(tanPhi));
g = new CrdsGeographical(L, phi);
if (i == 0)
{
// correct to topocentric
eq = eq.ToTopocentric(g, siderealTime, parallax);
}
}
return(g);
}
/// <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 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 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));
}
/// <summary>
/// Copying construtor
/// </summary>
/// <param name="eq">Equatorial coordinates to be copied</param>
public CrdsEquatorial(CrdsEquatorial eq)
{
Alpha = eq.Alpha;
Delta = eq.Delta;
}
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>
/// 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);
}
/// <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 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>
/// Calculates visibity details for the celestial body,
/// </summary>
/// <param name="eqBody">Mean equatorial coordinates of the body for the desired day.</param>
/// <param name="eqSun">Mean equatorial coordinates of the Sun for the desired day.</param>
/// <param name="minAltitude">Minimal altitude of the body, in degrees, to be considered as approproate for observations. By default it's 5 degrees for planet.</param>
/// <returns><see cref="VisibilityDetails"/> instance describing details of visibility.</returns>
// TODO: tests
public static VisibilityDetails Details(CrdsEquatorial eqBody, CrdsEquatorial eqSun, CrdsGeographical location, double theta0, double minAltitude = 5)
{
var details = new VisibilityDetails();
// period when the planet is above the horizon and its altitude is larger than "minAltitude"
RTS body = RiseTransitSet(eqBody, location, theta0, minAltitude);
// period when the Sun is above the horizon
RTS sun = RiseTransitSet(eqSun, location, theta0);
// body reaches minimal altitude but Sun does not rise at all (polar night)
if (body.TransitAltitude > minAltitude && sun.TransitAltitude <= 0)
{
details.Period = VisibilityPeriod.WholeNight;
details.Duration = body.Duration * 24;
}
// body does not reach the minimal altitude during the day
else if (body.TransitAltitude <= minAltitude)
{
details.Period = VisibilityPeriod.Invisible;
details.Duration = 0;
}
// there is a day/night change during the day and body reaches minimal altitude
else if (body.TransitAltitude > minAltitude)
{
// "Sun is below horizon" time range, expressed in degrees (0 is midnight, 180 is noon)
var r1 = new AngleRange(sun.Set * 360, (1 - sun.Duration) * 360);
// "body is above horizon" time range, expressed in degrees (0 is midnight, 180 is noon)
var r2 = new AngleRange(body.Rise * 360, body.Duration * 360);
// find the intersections of two ranges
var ranges = r1.Overlaps(r2);
// no intersections of time ranges
if (!ranges.Any())
{
details.Period = VisibilityPeriod.Invisible;
details.Duration = 0;
details.Begin = double.NaN;
details.End = double.NaN;
}
// the body is observable during the day
else
{
// duration of visibility
details.Duration = ranges.Sum(i => i.Range / 360 * 24);
// beginning of visibility
details.Begin = ranges.First().Start / 360;
// end of visibility
details.End = (details.Begin + details.Duration / 24) % 1;
// Evening time range, expressed in degrees
// Start is a sunset time, range is a timespan from sunset to midnight.
var rE = new AngleRange(sun.Set * 360, (1 - sun.Set) * 360);
// Night time range, expressed in degrees
// Start is a midnight time, range is a half of timespan from midnight to sunrise
var rN = new AngleRange(0, sun.Rise / 2 * 360);
// Morning time range, expressed in degrees
// Start is a half of time from midnight to sunrise, range is a time to sunrise
var rM = new AngleRange(sun.Rise / 2 * 360, sun.Rise / 2 * 360);
foreach (var r in ranges)
{
var isEvening = r.Overlaps(rE);
if (isEvening.Any())
{
details.Period |= VisibilityPeriod.Evening;
}
var isNight = r.Overlaps(rN);
if (isNight.Any())
{
details.Period |= VisibilityPeriod.Night;
}
var isMorning = r.Overlaps(rM);
if (isMorning.Any())
{
details.Period |= VisibilityPeriod.Morning;
}
}
}
}
return(details);
}
/// <summary>
/// Calculates instants of rising, transit and setting for stationary celestial body for the desired date.
/// Stationary in this particular case means that body has unchanged (or slightly changing) celestial coordinates during the day.
/// </summary>
/// <param name="eq">Equatorial coordinates of the celestial body.</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="minAltitude">Minimal altitude of the body above the horizon, in degrees, to detect rise/set. Used only for calculating visibility conditions.</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 minAltitude = 0)
{
List <CrdsHorizontal> hor = new List <CrdsHorizontal>();
for (int i = 0; i <= 24; i++)
{
double n = i / 24.0;
var sidTime = InterpolateSiderialTime(theta0, n);
hor.Add(eq.ToHorizontal(location, sidTime));
}
var result = new RTS();
for (int i = 0; i < 24; i++)
{
double n = (i + 0.5) / 24.0;
var sidTime = InterpolateSiderialTime(theta0, n);
var hor0 = eq.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;
sidTime = InterpolateSiderialTime(theta0, t);
result.Transit = t;
result.TransitAltitude = eq.ToHorizontal(location, sidTime).Altitude;
}
}
if (double.IsNaN(result.Rise) || double.IsNaN(result.Set))
{
double r = SolveParabola(hor[i].Altitude - minAltitude, hor0.Altitude - minAltitude, hor[i + 1].Altitude - minAltitude);
if (!double.IsNaN(r))
{
double t = (i + r) / 24.0;
sidTime = InterpolateSiderialTime(theta0, t);
if (double.IsNaN(result.Rise) && hor[i].Altitude - minAltitude < 0 && hor[i + 1].Altitude - minAltitude > 0)
{
result.Rise = t;
result.RiseAzimuth = eq.ToHorizontal(location, sidTime).Azimuth;
}
if (double.IsNaN(result.Set) && hor[i].Altitude - minAltitude > 0 && hor[i + 1].Altitude - minAltitude < 0)
{
result.Set = t;
result.SetAzimuth = eq.ToHorizontal(location, sidTime).Azimuth;
}
if (!double.IsNaN(result.Transit) && !double.IsNaN(result.Rise) && !double.IsNaN(result.Set))
{
break;
}
}
}
}
return(result);
}
