/// <summary>
/// Calculates Besselian elements for lunar eclipse,
/// valid only for specified instant.
/// </summary>
/// <param name="position">Sun and Moon position data</param>
/// <returns>
/// Besselian elements for lunar eclipse
/// </returns>
/// <remarks>
/// The method is based on formulae given here:
/// https://de.wikipedia.org/wiki/Besselsche_Elemente
/// </remarks>
internal static InstantLunarEclipseElements BesselianElements(SunMoonPosition position)
{
// Geocentric RA of the center of Earth shadow
double a = ToRadians(position.Sun.Alpha + 180);
// Geocentric Dec of the center of Earth shadow
double d = ToRadians(-position.Sun.Delta);
// Geocentric RA of the Moon, in radians
double am = ToRadians(position.Moon.Alpha);
// Geocentric Dec of the Moon, in radians
double dm = ToRadians(position.Moon.Delta);
double x = Cos(dm) * Sin(am - a);
double y = Sin(dm) * Cos(d) - Cos(dm) * Sin(d) * Cos(am - a);
// Astronomical unit, in km
const double AU = 149597870;
// Earth radius, in km
const double EARTH_RADIUS = 6371;
// Seconds in degree
const double SEC_IN_DEGREE = 3600;
// Geocentric solar radius, in degrees
double rs = SolarEphem.Semidiameter(position.DistanceSun * EARTH_RADIUS / AU) / SEC_IN_DEGREE;
// Geocentric lunar radius, in degrees
double rm = LunarEphem.Semidiameter(position.DistanceMoon * EARTH_RADIUS) / SEC_IN_DEGREE;
// Geocentric parallax of the Sun, in degrees
double pi_s = LunarEphem.Parallax(position.DistanceSun * EARTH_RADIUS);
// Geocentric parallax of the Moon, in degrees
double pi_m = LunarEphem.Parallax(position.DistanceMoon * EARTH_RADIUS);
// Danjon rule of shadow enlargement is used
const double ENLARGEMENT = 1.01;
// Earth penumbra radius, in degrees
double f1 = ENLARGEMENT * pi_m + pi_s + rs;
// Earth umbra radius, in degrees
double f2 = ENLARGEMENT * pi_m + pi_s - rs;
// Lunar radius (semidiameter), in degrees
double f3 = rm;
return(new InstantLunarEclipseElements()
{
JulianDay = position.JulianDay,
// Convert to degrees:
// http://www.eclipsewise.com/lunar/LEprime/2001-2100/LE2021May26Tprime.html
X = ToDegrees(x),
Y = ToDegrees(y),
F1 = f1,
F2 = f2,
F3 = f3,
Alpha = position.Moon.Alpha,
Delta = position.Moon.Delta
});
}
/// <summary>
/// Gets visible semidiameter of the Moon, in seconds of arc
/// </summary>
public double Semidiameter(SkyContext c)
{
return(LunarEphem.Semidiameter(c.Get(Ecliptical0).Distance));
}