/// <summary>
/// Calculates lunar eclipse map
/// </summary>
/// <param name="eclipse">Eclipse general details</param>
/// <param name="elements">Besselian elements for the eclipse</param>
/// <returns>Eclipse map</returns>
public static LunarEclipseMap EclipseMap(LunarEclipse eclipse, PolynomialLunarEclipseElements elements)
{
return(new LunarEclipseMap()
{
PenumbralBegin = !double.IsNaN(eclipse.JulianDayFirstContactPenumbra) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayFirstContactPenumbra)) : null,
PartialBegin = !double.IsNaN(eclipse.JulianDayFirstContactUmbra) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayFirstContactUmbra)) : null,
TotalBegin = !double.IsNaN(eclipse.JulianDayTotalBegin) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayTotalBegin)) : null,
TotalEnd = !double.IsNaN(eclipse.JulianDayTotalEnd) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayTotalEnd)) : null,
PartialEnd = !double.IsNaN(eclipse.JulianDayLastContactUmbra) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayLastContactUmbra)) : null,
PenumbralEnd = !double.IsNaN(eclipse.JulianDayLastContactPenumbra) ? FindCurvePoints(elements.GetInstantBesselianElements(eclipse.JulianDayLastContactPenumbra)) : null,
});
}
public static LunarEclipseLocalCircumstances LocalCircumstances(LunarEclipse eclipse, PolynomialLunarEclipseElements e, CrdsGeographical g)
{
return(new LunarEclipseLocalCircumstances()
{
Location = g,
PenumbralBegin = GetLocalCircumstancesContactPoint(eclipse.JulianDayFirstContactPenumbra, eclipse, e, g),
PartialBegin = GetLocalCircumstancesContactPoint(eclipse.JulianDayFirstContactUmbra, eclipse, e, g),
TotalBegin = GetLocalCircumstancesContactPoint(eclipse.JulianDayTotalBegin, eclipse, e, g),
Maximum = GetLocalCircumstancesContactPoint(eclipse.JulianDayMaximum, eclipse, e, g),
TotalEnd = GetLocalCircumstancesContactPoint(eclipse.JulianDayTotalEnd, eclipse, e, g),
PartialEnd = GetLocalCircumstancesContactPoint(eclipse.JulianDayLastContactUmbra, eclipse, e, g),
PenumbralEnd = GetLocalCircumstancesContactPoint(eclipse.JulianDayLastContactPenumbra, eclipse, e, g),
});
}
/// <summary>
/// Calculates nearest lunar eclipse (next or previous) for the provided lunation number.
/// </summary>
/// <param name="lunationNumber">Meeus lunation number of interest.</param>
/// <param name="next">Flag indicating searching direction. True means searching next eclipse, false means previous.</param>
public static LunarEclipse NearestEclipse(int lunationNumber, bool next)
{
double k = lunationNumber + 0.5;
bool eclipseFound;
double T = k / 1236.85;
double T2 = T * T;
double T3 = T2 * T;
double T4 = T3 * T;
LunarEclipse eclipse = new LunarEclipse();
do
{
// Moon's argument of latitude (mean dinstance of the Moon from its ascending node)
double F = 160.7108 + 390.67050284 * k
- 0.0016118 * T2
- 0.00000227 * T3
+ 0.000000011 * T4;
F = To360(F);
eclipseFound = Abs(Sin(ToRadians(F))) <= 0.36;
if (eclipseFound)
{
double jdMeanPhase = 2451550.09766 + 29.530588861 * k
+ 0.00015437 * T2
- 0.000000150 * T3
+ 0.00000000073 * T4;
// Sun's mean anomaly
double M = 2.5534 + 29.10535670 * k
- 0.0000014 * T2
- 0.00000011 * T3;
M = To360(M);
M = ToRadians(M);
// Moon's mean anomaly
double M_ = 201.5643 + 385.81693528 * k
+ 0.0107582 * T2
+ 0.00001238 * T3
- 0.000000058 * T4;
M_ = To360(M_);
M_ = ToRadians(M_);
// Mean longitude of ascending node
double Omega = 124.7746 - 1.56375588 * k
+ 0.0020672 * T2
+ 0.00000215 * T3;
Omega = To360(Omega);
Omega = ToRadians(Omega);
// Multiplier related to the eccentricity of the Earth orbit
double E = 1 - 0.002516 * T - 0.0000074 * T2;
double F1 = ToRadians(F - 0.02665 * Sin(Omega));
double A1 = ToRadians(To360(299.77 + 0.107408 * k - 0.009173 * T2));
double jdMax =
jdMeanPhase
- 0.4065 * Sin(M_)
+ 0.1727 * E * Sin(M)
+ 0.0161 * Sin(2 * M_)
- 0.0097 * Sin(2 * F1)
+ 0.0073 * E * Sin(M_ - M)
- 0.0050 * E * Sin(M_ + M)
- 0.0023 * Sin(M_ - 2 * F1)
+ 0.0021 * E * Sin(2 * M)
+ 0.0012 * Sin(M_ + 2 * F1)
+ 0.0006 * E * Sin(2 * M_ + M)
- 0.0004 * Sin(3 * M_)
- 0.0003 * E * Sin(M + 2 * F1)
+ 0.0003 * Sin(A1)
- 0.0002 * E * Sin(M - 2 * F1)
- 0.0002 * E * Sin(2 * M_ - M)
- 0.0002 * Sin(Omega);
double P =
0.2070 * E * Sin(M)
+ 0.0024 * E * Sin(2 * M)
- 0.0392 * Sin(M_)
+ 0.0116 * Sin(2 * M_)
- 0.0073 * E * Sin(M_ + M)
+ 0.0067 * E * Sin(M_ - M)
+ 0.0118 * Sin(2 * F1);
double Q =
5.2207 - 0.0048 * E * Cos(M)
+ 0.0020 * E * Cos(2 * M)
- 0.3299 * Cos(M_)
- 0.0060 * E * Cos(M_ + M)
+ 0.0041 * E * Cos(M_ - M);
double W = Abs(Cos(F1));
double gamma = (P * Cos(F1) + Q * Sin(F1)) * (1 - 0.0048 * W);
double u = 0.0059
+ 0.0046 * E * Cos(M)
- 0.0182 * Cos(M_)
+ 0.0004 * Cos(2 * M_)
- 0.0005 * E * Cos(M + M_);
double rho = 1.2848 + u;
double sigma = 0.7403 - u;
double mag = (1.0128 - u - Abs(gamma)) / 0.5450;
if (mag >= 1)
{
eclipse.EclipseType = LunarEclipseType.Total;
}
if (mag > 0 && mag < 1)
{
eclipse.EclipseType = LunarEclipseType.Partial;
}
// Check if elipse is penumbral only
if (mag < 0)
{
eclipse.EclipseType = LunarEclipseType.Penumbral;
mag = (1.5573 + u - Abs(gamma)) / 0.5450;
}
// No eclipse, if both phases is less than 0.
// Examine other lunation
if (mag < 0)
{
eclipseFound = false;
}
// Eclipse found
else
{
eclipse.JulianDayMaximum = jdMax;
eclipse.Magnitude = mag;
eclipse.Rho = rho;
eclipse.Gamma = gamma;
eclipse.Sigma = sigma;
double p = 1.0128 - u;
double t = 0.4678 - u;
double n = 1.0 / (24 * (0.5458 + 0.04 * Cos(M_)));
double h = 1.5573 + u;
double sdPartial = n * Sqrt(p * p - gamma * gamma);
double sdTotal = n * Sqrt(t * t - gamma * gamma);
double sdPenumbra = n * Sqrt(h * h - gamma * gamma);
eclipse.JulianDayFirstContactPenumbra = jdMax - sdPenumbra;
eclipse.JulianDayFirstContactUmbra = jdMax - sdPartial;
eclipse.JulianDayTotalBegin = jdMax - sdTotal;
eclipse.JulianDayTotalEnd = jdMax + sdTotal;
eclipse.JulianDayLastContactUmbra = jdMax + sdPartial;
eclipse.JulianDayLastContactPenumbra = jdMax + sdPenumbra;
eclipse.Saros = Saros(jdMax);
eclipse.MeeusLunationNumber = (int)Round(k - 0.5);
}
}
if (!eclipseFound)
{
if (next)
{
k++;
}
else
{
k--;
}
}
}while (!eclipseFound);
return(eclipse);
}
private static LunarEclipseLocalCircumstancesContactPoint GetLocalCircumstancesContactPoint(double jd, LunarEclipse eclipse, PolynomialLunarEclipseElements e, CrdsGeographical g)
{
if (!double.IsNaN(jd))
{
return(new LunarEclipseLocalCircumstancesContactPoint(e.GetInstantBesselianElements(jd), g));
}
else
{
return(null);
}
}
