/// <summary>
///
/// </summary>
/// <param name="startDate">Start Date</param>
/// <param name="phase">0, 1/3, 1/2 or 3/4</param>
/// <returns></returns>
public static DateTime TruePhase(DateTime startDate, MPhase phase)
{
//What will be the return value
double JD = DateTimeUtil.DateTimeToJulian(MeanPhase(startDate, phase));
double ph = 0.0;
if (phase == MPhase.FirstQuater)
{
ph = 0.25;
}
else if (phase == MPhase.Full)
{
ph = 0.50;
}
else if (phase == MPhase.LastQuater)
{
ph = 0.75;
}
TimeSpan tp = startDate - NEW_MOON_TIME;
double k = tp.TotalDays / MOON_PERIOD;
double kint = Math.Floor(k);
double kfra = k - kint;
if (kfra > ph)
{
k = kint + 1 + ph; //we already pass that phase, look for the next one
}
else
{
k = kint + ph;
}
//convert from K to T
double T = k / 1236.85;
double T2 = T * T;
double T3 = T2 * T;
double T4 = T3 * T;
double E = 1 - 0.002516 * T - 0.0000074 * T2;
double E2 = E * E;
double M = CoordinateTransformation.MapTo0To360Range(2.5534 + 29.10535670 * k - 0.0000014 * T2 - 0.00000011 * T3);
M = CoordinateTransformation.DegreesToRadians(M);
double Mdash = CoordinateTransformation.MapTo0To360Range(201.5643 + 385.81693528 * k + 0.0107582 * T2 + 0.00001238 * T3 - 0.000000058 * T4);
Mdash = CoordinateTransformation.DegreesToRadians(Mdash);
double F = CoordinateTransformation.MapTo0To360Range(160.7108 + 390.67050284 * k - 0.0016118 * T2 - 0.00000227 * T3 + 0.00000001 * T4);
F = CoordinateTransformation.DegreesToRadians(F);
double omega = CoordinateTransformation.MapTo0To360Range(124.7746 - 1.56375588 * k + 0.0020672 * T2 + 0.00000215 * T3);
omega = CoordinateTransformation.DegreesToRadians(omega);
double A1 = CoordinateTransformation.MapTo0To360Range(299.77 + 0.107408 * k - 0.009173 * T2);
A1 = CoordinateTransformation.DegreesToRadians(A1);
double A2 = CoordinateTransformation.MapTo0To360Range(251.88 + 0.016321 * k);
A2 = CoordinateTransformation.DegreesToRadians(A2);
double A3 = CoordinateTransformation.MapTo0To360Range(251.83 + 26.651886 * k);
A3 = CoordinateTransformation.DegreesToRadians(A3);
double A4 = CoordinateTransformation.MapTo0To360Range(349.42 + 36.412478 * k);
A4 = CoordinateTransformation.DegreesToRadians(A4);
double A5 = CoordinateTransformation.MapTo0To360Range(84.66 + 18.206239 * k);
A5 = CoordinateTransformation.DegreesToRadians(A5);
double A6 = CoordinateTransformation.MapTo0To360Range(141.74 + 53.303771 * k);
A6 = CoordinateTransformation.DegreesToRadians(A6);
double A7 = CoordinateTransformation.MapTo0To360Range(207.14 + 2.453732 * k);
A7 = CoordinateTransformation.DegreesToRadians(A7);
double A8 = CoordinateTransformation.MapTo0To360Range(154.84 + 7.306860 * k);
A8 = CoordinateTransformation.DegreesToRadians(A8);
double A9 = CoordinateTransformation.MapTo0To360Range(34.52 + 27.261239 * k);
A9 = CoordinateTransformation.DegreesToRadians(A9);
double A10 = CoordinateTransformation.MapTo0To360Range(207.19 + 0.121824 * k);
A10 = CoordinateTransformation.DegreesToRadians(A10);
double A11 = CoordinateTransformation.MapTo0To360Range(291.34 + 1.844379 * k);
A11 = CoordinateTransformation.DegreesToRadians(A11);
double A12 = CoordinateTransformation.MapTo0To360Range(161.72 + 24.198154 * k);
A12 = CoordinateTransformation.DegreesToRadians(A12);
double A13 = CoordinateTransformation.MapTo0To360Range(239.56 + 25.513099 * k);
A13 = CoordinateTransformation.DegreesToRadians(A13);
double A14 = CoordinateTransformation.MapTo0To360Range(331.55 + 3.592518 * k);
A14 = CoordinateTransformation.DegreesToRadians(A14);
//convert to radians
if (phase == MPhase.New) //New Moon
{
double DeltaJD = -0.40720 * Math.Sin(Mdash) +
0.17241 * E * Math.Sin(M) +
0.01608 * Math.Sin(2 * Mdash) +
0.01039 * Math.Sin(2 * F) +
0.00739 * E * Math.Sin(Mdash - M) +
-0.00514 * E * Math.Sin(Mdash + M) +
0.00208 * E2 * Math.Sin(2 * M) +
-0.00111 * Math.Sin(Mdash - 2 * F) +
-0.00057 * Math.Sin(Mdash + 2 * F) +
0.00056 * E * Math.Sin(2 * Mdash + M) +
-0.00042 * Math.Sin(3 * Mdash) +
0.00042 * E * Math.Sin(M + 2 * F) +
0.00038 * E * Math.Sin(M - 2 * F) +
-0.00024 * E * Math.Sin(2 * Mdash - M) +
-0.00017 * Math.Sin(omega) +
-0.00007 * Math.Sin(Mdash + 2 * M) +
0.00004 * Math.Sin(2 * Mdash - 2 * F) +
0.00004 * Math.Sin(3 * M) +
0.00003 * Math.Sin(Mdash + M - 2 * F) +
0.00003 * Math.Sin(2 * Mdash + 2 * F) +
-0.00003 * Math.Sin(Mdash + M + 2 * F) +
0.00003 * Math.Sin(Mdash - M + 2 * F) +
-0.00002 * Math.Sin(Mdash - M - 2 * F) +
-0.00002 * Math.Sin(3 * Mdash + M) +
0.00002 * Math.Sin(4 * Mdash);
JD += DeltaJD;
}
else if ((phase == MPhase.FirstQuater) || (phase == MPhase.LastQuater)) //First Quarter or Last Quarter
{
double DeltaJD = -0.62801 * Math.Sin(Mdash) +
0.17172 * E * Math.Sin(M) +
-0.01183 * E * Math.Sin(Mdash + M) +
0.00862 * Math.Sin(2 * Mdash) +
0.00804 * Math.Sin(2 * F) +
0.00454 * E * Math.Sin(Mdash - M) +
0.00204 * E2 * Math.Sin(2 * M) +
-0.00180 * Math.Sin(Mdash - 2 * F) +
-0.00070 * Math.Sin(Mdash + 2 * F) +
-0.00040 * Math.Sin(3 * Mdash) +
-0.00034 * E * Math.Sin(2 * Mdash - M) +
0.00032 * E * Math.Sin(M + 2 * F) +
0.00032 * E * Math.Sin(M - 2 * F) +
-0.00028 * E2 * Math.Sin(Mdash + 2 * M) +
0.00027 * E * Math.Sin(2 * Mdash + M) +
-0.00017 * Math.Sin(omega) +
-0.00005 * Math.Sin(Mdash - M - 2 * F) +
0.00004 * Math.Sin(2 * Mdash + 2 * F) +
-0.00004 * Math.Sin(Mdash + M + 2 * F) +
0.00004 * Math.Sin(Mdash - 2 * M) +
0.00003 * Math.Sin(Mdash + M - 2 * F) +
0.00003 * Math.Sin(3 * M) +
0.00002 * Math.Sin(2 * Mdash - 2 * F) +
0.00002 * Math.Sin(Mdash - M + 2 * F) +
-0.00002 * Math.Sin(3 * Mdash + M);
JD += DeltaJD;
double W = 0.00306 - 0.00038 * E * Math.Cos(M) + 0.00026 * Math.Cos(Mdash) - 0.00002 * Math.Cos(Mdash - M) + 0.00002 * Math.Cos(Mdash + M) + 0.00002 * Math.Cos(2 * F);
if (phase == MPhase.FirstQuater) //First quarter
{
JD += W;
}
else
{
JD -= W;
}
}
else if (phase == MPhase.Full) //Full Moon
{
double DeltaJD = -0.40614 * Math.Sin(Mdash) +
0.17302 * E * Math.Sin(M) +
0.01614 * Math.Sin(2 * Mdash) +
0.01043 * Math.Sin(2 * F) +
0.00734 * E * Math.Sin(Mdash - M) +
-0.00514 * E * Math.Sin(Mdash + M) +
0.00209 * E2 * Math.Sin(2 * M) +
-0.00111 * Math.Sin(Mdash - 2 * F) +
-0.00057 * Math.Sin(Mdash + 2 * F) +
0.00056 * E * Math.Sin(2 * Mdash + M) +
-0.00042 * Math.Sin(3 * Mdash) +
0.00042 * E * Math.Sin(M + 2 * F) +
0.00038 * E * Math.Sin(M - 2 * F) +
-0.00024 * E * Math.Sin(2 * Mdash - M) +
-0.00017 * Math.Sin(omega) +
-0.00007 * Math.Sin(Mdash + 2 * M) +
0.00004 * Math.Sin(2 * Mdash - 2 * F) +
0.00004 * Math.Sin(3 * M) +
0.00003 * Math.Sin(Mdash + M - 2 * F) +
0.00003 * Math.Sin(2 * Mdash + 2 * F) +
-0.00003 * Math.Sin(Mdash + M + 2 * F) +
0.00003 * Math.Sin(Mdash - M + 2 * F) +
-0.00002 * Math.Sin(Mdash - M - 2 * F) +
-0.00002 * Math.Sin(3 * Mdash + M) +
0.00002 * Math.Sin(4 * Mdash);
JD += DeltaJD;
}
//Additional corrections for all phases
double DeltaJD2 = 0.000325 * Math.Sin(A1) +
0.000165 * Math.Sin(A2) +
0.000164 * Math.Sin(A3) +
0.000126 * Math.Sin(A4) +
0.000110 * Math.Sin(A5) +
0.000062 * Math.Sin(A6) +
0.000060 * Math.Sin(A7) +
0.000056 * Math.Sin(A8) +
0.000047 * Math.Sin(A9) +
0.000042 * Math.Sin(A10) +
0.000040 * Math.Sin(A11) +
0.000037 * Math.Sin(A12) +
0.000035 * Math.Sin(A13) +
0.000023 * Math.Sin(A14);
JD += DeltaJD2;
return(DateTimeUtil.JulianToDateTime(JD));
}
/// <summary>
/// get earth ecliptic longitude with a specific Julian date
/// </summary>
/// <param name="JD"></param>
/// <returns></returns>
public static double EclipticLongitude(double JD)
{
double rho = (JD - 2451545) / 365250;
double rhosquared = rho * rho;
double rhocubed = rhosquared * rho;
double rho4 = rhocubed * rho;
double rho5 = rho4 * rho;
//Calculate L0
int nL0Coefficients = g_L0EarthCoefficients.Length / 3;
double L0 = 0;
int i;
for (i = 0; i < nL0Coefficients; i++)
{
L0 += g_L0EarthCoefficients[i, 0] * Math.Cos(g_L0EarthCoefficients[i, 1] + g_L0EarthCoefficients[i, 2] * rho);
}
//Calculate L1
int nL1Coefficients = g_L1EarthCoefficients.Length / 3;
double L1 = 0;
for (i = 0; i < nL1Coefficients; i++)
{
L1 += g_L1EarthCoefficients[i, 0] * Math.Cos(g_L1EarthCoefficients[i, 1] + g_L1EarthCoefficients[i, 2] * rho);
}
//Calculate L2
int nL2Coefficients = g_L2EarthCoefficients.Length / 3;
double L2 = 0;
for (i = 0; i < nL2Coefficients; i++)
{
L2 += g_L2EarthCoefficients[i, 0] * Math.Cos(g_L2EarthCoefficients[i, 1] + g_L2EarthCoefficients[i, 2] * rho);
}
//Calculate L3
int nL3Coefficients = g_L3EarthCoefficients.Length / 3;
double L3 = 0;
for (i = 0; i < nL3Coefficients; i++)
{
L3 += g_L3EarthCoefficients[i, 0] * Math.Cos(g_L3EarthCoefficients[i, 1] + g_L3EarthCoefficients[i, 2] * rho);
}
//Calculate L4
int nL4Coefficients = g_L4EarthCoefficients.Length / 3;
double L4 = 0;
for (i = 0; i < nL4Coefficients; i++)
{
L4 += g_L4EarthCoefficients[i, 0] * Math.Cos(g_L4EarthCoefficients[i, 1] + g_L4EarthCoefficients[i, 2] * rho);
}
//Calculate L5
int nL5Coefficients = g_L5EarthCoefficients.Length / 3;
double L5 = 0;
for (i = 0; i < nL5Coefficients; i++)
{
L5 += g_L5EarthCoefficients[i, 0] * Math.Cos(g_L5EarthCoefficients[i, 1] + g_L5EarthCoefficients[i, 2] * rho);
}
double value = (L0 + L1 * rho + L2 * rhosquared + L3 * rhocubed + L4 * rho4 + L5 * rho5) / 100000000;
//convert results back to degrees
value = CoordinateTransformation.MapTo0To360Range(CoordinateTransformation.RadiansToDegrees(value));
return(value);
}
