/// <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>
/// 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);
}
public static PolynomialLunarEclipseElements BesselianElements(double jdMaximum, SunMoonPosition[] positions)
{
if (positions.Length != 5)
{
throw new ArgumentException("Five positions are required", nameof(positions));
}
double step = positions[1].JulianDay - positions[0].JulianDay;
if (!positions.Zip(positions.Skip(1),
(a, b) => new { a, b })
.All(p => Abs(p.b.JulianDay - p.a.JulianDay - step) <= 1e-6))
{
throw new ArgumentException("Positions should be sorted ascending by JulianDay value, and have same JulianDay step.", nameof(positions));
}
// 5 time instants required
InstantLunarEclipseElements[] elements = new InstantLunarEclipseElements[5];
PointF[] points = new PointF[5];
for (int i = 0; i < 5; i++)
{
elements[i] = BesselianElements(positions[i]);
points[i].X = i - 2;
}
// Alpha expressed in degrees and can cross zero point (360 -> 0).
// Values must be aligned in order to avoid crossing.
double[] Alpha = Align(elements.Select(e => e.Alpha).ToArray());
return(new PolynomialLunarEclipseElements()
{
JulianDay0 = positions[2].JulianDay,
JulianDayMaximum = jdMaximum,
DeltaT = Date.DeltaT(positions[2].JulianDay),
Step = step,
X = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].X)), 3),
Y = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].Y)), 3),
F1 = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].F1)), 3),
F2 = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].F2)), 3),
F3 = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].F3)), 3),
Alpha = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)Alpha[i])), 3),
Delta = LeastSquares.FindCoeffs(points.Select((p, i) => new PointF(p.X, (float)elements[i].Delta)), 3),
});
}
private static IList <CrdsGeographical> FindCurvePoints(InstantLunarEclipseElements e)
{
var curve = new List <CrdsGeographical>();
var p0 = Project(e, -180);
curve.Add(new CrdsGeographical(p0.Longitude, -88 * Sign(e.Delta)));
for (int i = -180; i <= 180; i++)
{
var p = Project(e, i);
curve.Add(p);
}
var p1 = Project(e, 180);
curve.Add(new CrdsGeographical(p1.Longitude, -88 * Sign(e.Delta)));
return(curve);
}
