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PositionalAstronomy.cs
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PositionalAstronomy.cs
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using System;
namespace KCalendar
{
public abstract class PositionalAstronomy
{
public virtual double Mod(double a, double b)
{
return a - (b * Math.Floor(a / b));
}
public virtual double J2000 => 2451545.0;
// Days in Julian century
public virtual double JulianCentury => 36525.0;
// Days in Julian millennium
public virtual double JulianMillennium => (JulianCentury * 10);
// Astronomical unit in kilometres
public virtual double AstronomicalUnit => 149597870.0;
// Mean solar tropical year
public virtual double TropicalYear => 365.24219878;
protected double[] EquinoxpTerms => _equinoxpTerms;
protected double[,] Jde0Tab1000 => _jde0Tab1000;
protected double[,] Jde0Tab2000 => _jde0Tab2000;
protected double[] Oterms => _oterms;
protected double[] NutArgMult
{
get { return _nutArgMult; }
set { _nutArgMult = value; }
}
protected double[] NutArgCoeff => _nutArgCoeff;
protected double[] DeltaTtab => _deltaTtab;
/* ASTOR -- Arc-seconds to radians. */
protected virtual double Astor(double a)
{
return a * (Math.PI / (180.0 * 3600.0));
}
/* DTR -- Degrees to radians. */
protected virtual double Dtr(double d)
{
return (d * Math.PI) / 180.0;
}
/* RTD -- Radians to degrees. */
protected virtual double Rtd(double r)
{
return (r * 180.0) / Math.PI;
}
/* FIXANGLE -- Range reduce angle in degrees. */
protected virtual double Fixangle(double a)
{
return a - 360.0 * (Math.Floor(a / 360.0));
}
/* FIXANGR -- Range reduce angle in radians. */
protected virtual double Fixangr(double a)
{
return a - (2 * Math.PI) * (Math.Floor(a / (2 * Math.PI)));
}
// DSIN -- Sine of an angle in degrees
protected virtual double Dsin(double d)
{
return Math.Sin(Dtr(d));
}
// DCOS -- Cosine of an angle in degrees
protected virtual double Dcos(double d)
{
return Math.Cos(Dtr(d));
}
/* EQUINOX -- Determine the Julian Ephemeris Day of an
equinox or solstice. The "which" argument
selects the item to be computed:
0 March equinox
1 June solstice
2 September equinox
3 December solstice
*/
// Periodic terms to obtain true time
private readonly double[] _equinoxpTerms = {
485, 324.96, 1934.136,
203, 337.23, 32964.467,
199, 342.08, 20.186,
182, 27.85, 445267.112,
156, 73.14, 45036.886,
136, 171.52, 22518.443,
77, 222.54, 65928.934,
74, 296.72, 3034.906,
70, 243.58, 9037.513,
58, 119.81, 33718.147,
52, 297.17, 150.678,
50, 21.02, 2281.226,
45, 247.54, 29929.562,
44, 325.15, 31555.956,
29, 60.93, 4443.417,
18, 155.12, 67555.328,
17, 288.79, 4562.452,
16, 198.04, 62894.029,
14, 199.76, 31436.921,
12, 95.39, 14577.848,
12, 287.11, 31931.756,
12, 320.81, 34777.259,
9, 227.73, 1222.114,
8, 15.45, 16859.074
};
private readonly double[,] _jde0Tab1000 = {
{1721139.29189, 365242.13740, 0.06134, 0.00111, -0.00071},
{1721233.25401, 365241.72562, -0.05323, 0.00907, 0.00025},
{1721325.70455, 365242.49558, -0.11677, -0.00297, 0.00074},
{1721414.39987, 365242.88257, -0.00769, -0.00933, -0.00006}
};
private readonly double[,] _jde0Tab2000 = {
{2451623.80984, 365242.37404, 0.05169, -0.00411, -0.00057},
{2451716.56767, 365241.62603, 0.00325, 0.00888, -0.00030},
{2451810.21715, 365242.01767, -0.11575, 0.00337, 0.00078},
{2451900.05952, 365242.74049, -0.06223, -0.00823, 0.00032}
};
/* OBLIQEQ -- Calculate the obliquity of the ecliptic for a given
Julian date. This uses Laskar's tenth-degree
polynomial fit (J. Laskar, Astronomy and
Astrophysics, Vol. 157, page 68 [1986]) which is
accurate to within 0.01 arc second between AD 1000
and AD 3000, and within a few seconds of arc for
+/-10000 years around AD 2000. If we're outside the
range in which this fit is valid (deep time) we
simply return the J2000 value of the obliquity, which
happens to be almost precisely the mean. */
readonly double[] _oterms = {
-4680.93,
-1.55,
1999.25,
-51.38,
-249.67,
-39.05,
7.12,
27.87,
5.79,
2.45
};
/* Periodic terms for nutation in longiude (delta \Psi) and
obliquity (delta \Epsilon) as given in table 21.A of
Meeus, "Astronomical Algorithms", first edition. */
private double[] _nutArgMult = {
0, 0, 0, 0, 1,
-2, 0, 0, 2, 2,
0, 0, 0, 2, 2,
0, 0, 0, 0, 2,
0, 1, 0, 0, 0,
0, 0, 1, 0, 0,
-2, 1, 0, 2, 2,
0, 0, 0, 2, 1,
0, 0, 1, 2, 2,
-2, -1, 0, 2, 2,
-2, 0, 1, 0, 0,
-2, 0, 0, 2, 1,
0, 0, -1, 2, 2,
2, 0, 0, 0, 0,
0, 0, 1, 0, 1,
2, 0, -1, 2, 2,
0, 0, -1, 0, 1,
0, 0, 1, 2, 1,
-2, 0, 2, 0, 0,
0, 0, -2, 2, 1,
2, 0, 0, 2, 2,
0, 0, 2, 2, 2,
0, 0, 2, 0, 0,
-2, 0, 1, 2, 2,
0, 0, 0, 2, 0,
-2, 0, 0, 2, 0,
0, 0, -1, 2, 1,
0, 2, 0, 0, 0,
2, 0, -1, 0, 1,
-2, 2, 0, 2, 2,
0, 1, 0, 0, 1,
-2, 0, 1, 0, 1,
0, -1, 0, 0, 1,
0, 0, 2, -2, 0,
2, 0, -1, 2, 1,
2, 0, 1, 2, 2,
0, 1, 0, 2, 2,
-2, 1, 1, 0, 0,
0, -1, 0, 2, 2,
2, 0, 0, 2, 1,
2, 0, 1, 0, 0,
-2, 0, 2, 2, 2,
-2, 0, 1, 2, 1,
2, 0, -2, 0, 1,
2, 0, 0, 0, 1,
0, -1, 1, 0, 0,
-2, -1, 0, 2, 1,
-2, 0, 0, 0, 1,
0, 0, 2, 2, 1,
-2, 0, 2, 0, 1,
-2, 1, 0, 2, 1,
0, 0, 1, -2, 0,
-1, 0, 1, 0, 0,
-2, 1, 0, 0, 0,
1, 0, 0, 0, 0,
0, 0, 1, 2, 0,
-1, -1, 1, 0, 0,
0, 1, 1, 0, 0,
0, -1, 1, 2, 2,
2, -1, -1, 2, 2,
0, 0, -2, 2, 2,
0, 0, 3, 2, 2,
2, -1, 0, 2, 2
};
readonly double[] _nutArgCoeff = {
-171996, -1742, 92095, 89, /* 0, 0, 0, 0, 1 */
-13187, -16, 5736, -31, /* -2, 0, 0, 2, 2 */
-2274, -2, 977, -5, /* 0, 0, 0, 2, 2 */
2062, 2, -895, 5, /* 0, 0, 0, 0, 2 */
1426, -34, 54, -1, /* 0, 1, 0, 0, 0 */
712, 1, -7, 0, /* 0, 0, 1, 0, 0 */
-517, 12, 224, -6, /* -2, 1, 0, 2, 2 */
-386, -4, 200, 0, /* 0, 0, 0, 2, 1 */
-301, 0, 129, -1, /* 0, 0, 1, 2, 2 */
217, -5, -95, 3, /* -2, -1, 0, 2, 2 */
-158, 0, 0, 0, /* -2, 0, 1, 0, 0 */
129, 1, -70, 0, /* -2, 0, 0, 2, 1 */
123, 0, -53, 0, /* 0, 0, -1, 2, 2 */
63, 0, 0, 0, /* 2, 0, 0, 0, 0 */
63, 1, -33, 0, /* 0, 0, 1, 0, 1 */
-59, 0, 26, 0, /* 2, 0, -1, 2, 2 */
-58, -1, 32, 0, /* 0, 0, -1, 0, 1 */
-51, 0, 27, 0, /* 0, 0, 1, 2, 1 */
48, 0, 0, 0, /* -2, 0, 2, 0, 0 */
46, 0, -24, 0, /* 0, 0, -2, 2, 1 */
-38, 0, 16, 0, /* 2, 0, 0, 2, 2 */
-31, 0, 13, 0, /* 0, 0, 2, 2, 2 */
29, 0, 0, 0, /* 0, 0, 2, 0, 0 */
29, 0, -12, 0, /* -2, 0, 1, 2, 2 */
26, 0, 0, 0, /* 0, 0, 0, 2, 0 */
-22, 0, 0, 0, /* -2, 0, 0, 2, 0 */
21, 0, -10, 0, /* 0, 0, -1, 2, 1 */
17, -1, 0, 0, /* 0, 2, 0, 0, 0 */
16, 0, -8, 0, /* 2, 0, -1, 0, 1 */
-16, 1, 7, 0, /* -2, 2, 0, 2, 2 */
-15, 0, 9, 0, /* 0, 1, 0, 0, 1 */
-13, 0, 7, 0, /* -2, 0, 1, 0, 1 */
-12, 0, 6, 0, /* 0, -1, 0, 0, 1 */
11, 0, 0, 0, /* 0, 0, 2, -2, 0 */
-10, 0, 5, 0, /* 2, 0, -1, 2, 1 */
-8, 0, 3, 0, /* 2, 0, 1, 2, 2 */
7, 0, -3, 0, /* 0, 1, 0, 2, 2 */
-7, 0, 0, 0, /* -2, 1, 1, 0, 0 */
-7, 0, 3, 0, /* 0, -1, 0, 2, 2 */
-7, 0, 3, 0, /* 2, 0, 0, 2, 1 */
6, 0, 0, 0, /* 2, 0, 1, 0, 0 */
6, 0, -3, 0, /* -2, 0, 2, 2, 2 */
6, 0, -3, 0, /* -2, 0, 1, 2, 1 */
-6, 0, 3, 0, /* 2, 0, -2, 0, 1 */
-6, 0, 3, 0, /* 2, 0, 0, 0, 1 */
5, 0, 0, 0, /* 0, -1, 1, 0, 0 */
-5, 0, 3, 0, /* -2, -1, 0, 2, 1 */
-5, 0, 3, 0, /* -2, 0, 0, 0, 1 */
-5, 0, 3, 0, /* 0, 0, 2, 2, 1 */
4, 0, 0, 0, /* -2, 0, 2, 0, 1 */
4, 0, 0, 0, /* -2, 1, 0, 2, 1 */
4, 0, 0, 0, /* 0, 0, 1, -2, 0 */
-4, 0, 0, 0, /* -1, 0, 1, 0, 0 */
-4, 0, 0, 0, /* -2, 1, 0, 0, 0 */
-4, 0, 0, 0, /* 1, 0, 0, 0, 0 */
3, 0, 0, 0, /* 0, 0, 1, 2, 0 */
-3, 0, 0, 0, /* -1, -1, 1, 0, 0 */
-3, 0, 0, 0, /* 0, 1, 1, 0, 0 */
-3, 0, 0, 0, /* 0, -1, 1, 2, 2 */
-3, 0, 0, 0, /* 2, -1, -1, 2, 2 */
-3, 0, 0, 0, /* 0, 0, -2, 2, 2 */
-3, 0, 0, 0, /* 0, 0, 3, 2, 2 */
-3, 0, 0, 0 /* 2, -1, 0, 2, 2 */
};
public virtual double Obliqeq(double jd)
{
double eps;
double u;
double v;
v = u = (jd - J2000) / (JulianCentury * 100);
eps = 23 + (26 / 60.0) + (21.448 / 3600.0);
if (Math.Abs(u) < 1.0)
{
for (var i = 0; i < 10; i++)
{
eps += (_oterms[i] / 3600.0) * v;
v *= u;
}
}
return eps;
}
/* NUTATION -- Calculate the nutation in longitude, deltaPsi, and
obliquity, deltaEpsilon for a given Julian date
jd. Results are returned as a two element Array
giving (deltaPsi, deltaEpsilon) in degrees. */
public double[] Nutation(double jd)
{
double deltaPsi;
double deltaEpsilon;
var t = (jd - 2451545.0) / 36525.0;
double t2;
double t3;
double to10;
double dp = 0;
double de = 0;
double ang;
var ta = new double[5];
t3 = t * (t2 = t * t);
/* Calculate angles. The correspondence between the elements
of our array and the terms cited in Meeus are:
ta[0] = D ta[0] = M ta[2] = M' ta[3] = F ta[4] = \Omega
*/
ta[0] = Dtr(297.850363 + 445267.11148 * t - 0.0019142 * t2 +
t3 / 189474.0);
ta[1] = Dtr(357.52772 + 35999.05034 * t - 0.0001603 * t2 -
t3 / 300000.0);
ta[2] = Dtr(134.96298 + 477198.867398 * t + 0.0086972 * t2 +
t3 / 56250.0);
ta[3] = Dtr(93.27191 + 483202.017538 * t - 0.0036825 * t2 +
t3 / 327270);
ta[4] = Dtr(125.04452 - 1934.136261 * t + 0.0020708 * t2 +
t3 / 450000.0);
/* Range reduce the angles in case the sine and Cosine functions
don't do it as accurately or quickly. */
for (var i = 0; i < 5; i++)
{
ta[i] = Fixangr(ta[i]);
}
to10 = t / 10.0;
for (var i = 0; i < 63; i++)
{
ang = 0;
for (var j = 0; j < 5; j++)
{
if (_nutArgMult[(i * 5) + j] != 0)
{
ang += _nutArgMult[(i * 5) + j] * ta[j];
}
}
dp += (_nutArgCoeff[(i * 4) + 0] + _nutArgCoeff[(i * 4) + 1] * to10) * Math.Sin(ang);
de += (_nutArgCoeff[(i * 4) + 2] + _nutArgCoeff[(i * 4) + 3] * to10) * Math.Cos(ang);
}
/* Return the result, converting from ten thousandths of arc
seconds to radians in the process. */
deltaPsi = dp / (3600.0 * 10000.0);
deltaEpsilon = de / (3600.0 * 10000.0);
return new[] { deltaPsi, deltaEpsilon };
}
/* ECLIPTOEQ -- Convert celestial (ecliptical) longitude and
latitude into right ascension (in degrees) and
declination. We must supply the time of the
conversion in order to compensate correctly for the
varying obliquity of the ecliptic over time.
The right ascension and declination are returned
as a two-element Array in that order. */
protected virtual double[] Ecliptoeq(double jd, double Lambda, double Beta)
{
double eps;
double Ra;
double Dec;
/* Obliquity of the ecliptic. */
eps = Dtr(Obliqeq(jd));
Ra = Rtd(Math.Atan2((Math.Cos(eps) * Math.Sin(Dtr(Lambda)) -
(Math.Tan(Dtr(Beta)) * Math.Sin(eps))),
Math.Cos(Dtr(Lambda))));
Ra = Fixangle(Rtd(Math.Atan2((Math.Cos(eps) * Math.Sin(Dtr(Lambda)) -
(Math.Tan(Dtr(Beta)) * Math.Sin(eps))),
Math.Cos(Dtr(Lambda)))));
Dec = Rtd(Math.Asin((Math.Sin(eps) * Math.Sin(Dtr(Lambda)) * Math.Cos(Dtr(Beta))) +
(Math.Sin(Dtr(Beta)) * Math.Cos(eps))));
return new[] { Ra, Dec };
}
/* DELTAT -- Determine the difference, in seconds, between
Dynamical time and Universal time. */
/* Table of observed Delta T values at the beginning of
even numbered years from 1620 through 2002. */
readonly double[] _deltaTtab = {
121, 112, 103, 95, 88, 82, 77, 72, 68, 63, 60, 56, 53, 51, 48, 46,
44, 42, 40, 38, 35, 33, 31, 29, 26, 24, 22, 20, 18, 16, 14, 12,
11, 10, 9, 8, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10,
10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13,
13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16,
16, 16, 15, 15, 14, 13, 13.1, 12.5, 12.2, 12, 12, 12, 12, 12, 12,
11.9, 11.6, 11, 10.2, 9.2, 8.2, 7.1, 6.2, 5.6, 5.4, 5.3, 5.4, 5.6,
5.9, 6.2, 6.5, 6.8, 7.1, 7.3, 7.5, 7.6, 7.7, 7.3, 6.2, 5.2, 2.7,
1.4, -1.2, -2.8, -3.8, -4.8, -5.5, -5.3, -5.6, -5.7, -5.9, -6,
-6.3, -6.5, -6.2, -4.7, -2.8, -0.1, 2.6, 5.3, 7.7, 10.4, 13.3, 16,
18.2, 20.2, 21.1, 22.4, 23.5, 23.8, 24.3, 24, 23.9, 23.9, 23.7,
24, 24.3, 25.3, 26.2, 27.3, 28.2, 29.1, 30, 30.7, 31.4, 32.2,
33.1, 34, 35, 36.5, 38.3, 40.2, 42.2, 44.5, 46.5, 48.5, 50.5,
52.2, 53.8, 54.9, 55.8, 56.9, 58.3, 60, 61.6, 63, 65, 66.6
};
protected virtual double Deltat(double year)
{
double dt;
double f;
double t;
int i;
if ((year >= 1620) && (year <= 2000))
{
i = (int)Math.Floor((year - 1620) / 2);
f = ((year - 1620) / 2) - i; /* Fractional part of year */
dt = _deltaTtab[i] + ((_deltaTtab[i + 1] - _deltaTtab[i]) * f);
}
else
{
t = (year - 2000) / 100;
if (year < 948)
{
dt = 2177 + (497 * t) + (44.1 * t * t);
}
else
{
dt = 102 + (102 * t) + (25.3 * t * t);
if ((year > 2000) && (year < 2100))
{
dt += 0.37 * (year - 2100);
}
}
}
return dt;
}
protected virtual double Equinox(double year, int which)
{
double deltaL, JDE0, JDE, S, T, W, Y;
double[,] JDE0tab;
/* Initialise terms for mean equinox and solstices. We
have two sets: one for years prior to 1000 and a second
for subsequent years. */
int j;
if (year < 1000)
{
JDE0tab = Jde0Tab1000;
Y = year / 1000;
}
else
{
JDE0tab = Jde0Tab2000;
Y = (year - 2000) / 1000;
}
JDE0 = JDE0tab[which, 0] +
(JDE0tab[which, 1] * Y) +
(JDE0tab[which, 2] * Y * Y) +
(JDE0tab[which, 3] * Y * Y * Y) +
(JDE0tab[which, 4] * Y * Y * Y * Y);
//document.debug.log.value += "JDE0 = " + JDE0 + "\n";
T = (JDE0 - 2451545.0) / 36525;
//document.debug.log.value += "T = " + T + "\n";
W = (35999.373 * T) - 2.47;
//document.debug.log.value += "W = " + W + "\n";
deltaL = 1 + (0.0334 * Dcos(W)) + (0.0007 * Dcos(2 * W));
//document.debug.log.value += "deltaL = " + deltaL + "\n";
// Sum the periodic terms for time T
S = 0;
for (var i = j = 0; i < 24; i++)
{
S += EquinoxpTerms[j] * Dcos(EquinoxpTerms[j + 1] + (EquinoxpTerms[j + 2] * T));
j += 3;
}
//document.debug.log.value += "S = " + S + "\n";
//document.debug.log.value += "Corr = " + ((S * 0.00001) / deltaL) + "\n";
JDE = JDE0 + ((S * 0.00001) / deltaL);
return JDE;
}
/* SUNPOS -- Position of the Sun. Please see the comments
on the return statement at the end of this function
which describe the array it returns. We return
intermediate values because they are useful in a
variety of other contexts. */
protected virtual double[] Sunpos(double jd)
{
double T, T2, L0, M, e, C, sunLong, sunAnomaly, sunR,
Omega, Lambda, epsilon, epsilon0, Alpha, Delta,
AlphaApp, DeltaApp;
T = (jd - J2000) / JulianCentury;
//document.debug.log.value += "Sunpos. T = " + T + "\n";
T2 = T * T;
L0 = 280.46646 + (36000.76983 * T) + (0.0003032 * T2);
//document.debug.log.value += "L0 = " + L0 + "\n";
L0 = Fixangle(L0);
//document.debug.log.value += "L0 = " + L0 + "\n";
M = 357.52911 + (35999.05029 * T) + (-0.0001537 * T2);
//document.debug.log.value += "M = " + M + "\n";
M = Fixangle(M);
//document.debug.log.value += "M = " + M + "\n";
e = 0.016708634 + (-0.000042037 * T) + (-0.0000001267 * T2);
//document.debug.log.value += "e = " + e + "\n";
C = ((1.914602 + (-0.004817 * T) + (-0.000014 * T2)) * Dsin(M)) +
((0.019993 - (0.000101 * T)) * Dsin(2 * M)) +
(0.000289 * Dsin(3 * M));
//document.debug.log.value += "C = " + C + "\n";
sunLong = L0 + C;
//document.debug.log.value += "sunLong = " + sunLong + "\n";
sunAnomaly = M + C;
//document.debug.log.value += "sunAnomaly = " + sunAnomaly + "\n";
sunR = (1.000001018 * (1 - (e * e))) / (1 + (e * Dcos(sunAnomaly)));
//document.debug.log.value += "sunR = " + sunR + "\n";
Omega = 125.04 - (1934.136 * T);
//document.debug.log.value += "Omega = " + Omega + "\n";
Lambda = sunLong + (-0.00569) + (-0.00478 * Dsin(Omega));
//document.debug.log.value += "Lambda = " + Lambda + "\n";
epsilon0 = Obliqeq(jd);
//document.debug.log.value += "epsilon0 = " + epsilon0 + "\n";
epsilon = epsilon0 + (0.00256 * Dcos(Omega));
//document.debug.log.value += "epsilon = " + epsilon + "\n";
Alpha = Rtd(Math.Atan2(Dcos(epsilon0) * Dsin(sunLong), Dcos(sunLong)));
//document.debug.log.value += "Alpha = " + Alpha + "\n";
Alpha = Fixangle(Alpha);
////document.debug.log.value += "Alpha = " + Alpha + "\n";
Delta = Rtd(Math.Asin(Dsin(epsilon0) * Dsin(sunLong)));
////document.debug.log.value += "Delta = " + Delta + "\n";
AlphaApp = Rtd(Math.Atan2(Dcos(epsilon) * Dsin(Lambda), Dcos(Lambda)));
//document.debug.log.value += "AlphaApp = " + AlphaApp + "\n";
AlphaApp = Fixangle(AlphaApp);
//document.debug.log.value += "AlphaApp = " + AlphaApp + "\n";
DeltaApp = Rtd(Math.Asin(Dsin(epsilon) * Dsin(Lambda)));
//document.debug.log.value += "DeltaApp = " + DeltaApp + "\n";
return new[]{ // Angular quantities are expressed in decimal degrees
L0, // [0] Geometric mean longitude of the Sun
M, // [1] Mean anomaly of the Sun
e, // [2] Eccentricity of the Earth's orbit
C, // [3] Sun's equation of the Centre
sunLong, // [4] Sun's true longitude
sunAnomaly, // [5] Sun's true anomaly
sunR, // [6] Sun's radius vector in AU
Lambda, // [7] Sun's apparent longitude at true equinox of the date
Alpha, // [8] Sun's true right ascension
Delta, // [9] Sun's true declination
AlphaApp, // [10] Sun's apparent right ascension
DeltaApp // [11] Sun's apparent declination
};
}
/* EQUATIONOFTIME -- Compute equation of time for a given moment.
Returns the equation of time as a fraction of
a day. */
protected virtual double EquationOfTime(double jd)
{
double alpha, deltaPsi, E, epsilon, L0, tau;
tau = (jd - J2000) / JulianMillennium;
//document.debug.log.value += "equationOfTime. tau = " + tau + "\n";
L0 = 280.4664567 + (360007.6982779 * tau) +
(0.03032028 * tau * tau) +
((tau * tau * tau) / 49931) +
(-((tau * tau * tau * tau) / 15300)) +
(-((tau * tau * tau * tau * tau) / 2000000));
//document.debug.log.value += "L0 = " + L0 + "\n";
L0 = Fixangle(L0);
//document.debug.log.value += "L0 = " + L0 + "\n";
alpha = Sunpos(jd)[10];
//document.debug.log.value += "alpha = " + alpha + "\n";
deltaPsi = Nutation(jd)[0];
//document.debug.log.value += "deltaPsi = " + deltaPsi + "\n";
epsilon = Obliqeq(jd) + Nutation(jd)[1];
//document.debug.log.value += "epsilon = " + epsilon + "\n";
E = L0 + (-0.0057183) + (-alpha) + (deltaPsi * Dcos(epsilon));
//document.debug.log.value += "E = " + E + "\n";
E = E - 20.0 * (Math.Floor(E / 20.0));
//document.debug.log.value += "Efixed = " + E + "\n";
E = E / (24 * 60);
//document.debug.log.value += "Eday = " + E + "\n";
return E;
}
}
}