var Calendrical = (function(exports) {
"use strict";
exports.astro = exports.astro || {};
var astro = exports.astro;var Calendrical = (function(exports) {
"use strict";
exports.astro = exports.astro || {};
var astro = exports.astro; astro.constants = {Julian day of J2000 epoch
J2000: 2451545.0,Days in Julian century
JULIAN_CENTURY: 36525.0,Days in Julian millennium
JULIAN_MILLENIUM: (36525.0 * 10),Astronomical unit in kilometres
ASTRONOMICAL_UNIT: 149597870.0,Mean solar tropical year
TROPICAL_YEAR: 365.24219878,Weekdays
WEEKDAYS: ["Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"],Terms used in calculating the obliquity of the ecliptic from Astronomy and Astrophysics, Vol 157, p68 (1986), New Formulas for the Precession, Valid Over 10000 years, Table 8.
O_TERMS: [-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.
Argument of Multiple
NUT_ARG_MULT: [
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
],Coefficient of the sine of the argument and Coefficient of the cosine of the argument
NUT_ARG_COEFF: [
-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
],Table of observed Delta T values at the beginning of even numbered years from 1620 through 2002.
DELTA_T_TAB: [
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
],Periodic terms to obtain true time
EQUINOX_P_TERMS: [
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
],
JDE0_TAB_1000: [
[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]
],
JDE0_TAB_2000: [
[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]
]
}Arc-seconds to radians
astro.astor = function(a) {
return a * (Math.PI / (180.0 * 3600.0));
}Degrees to radians
astro.dtr = function(d) {
return (d * Math.PI) / 180.0;
}Radians to degrees
astro.rtd = function(r) {
return (r * 180.0) / Math.PI;
}Range reduce angle in degrees
astro.fixangle = function(a) {
return a - 360.0 * (Math.floor(a / 360.0));
}Range reduce angle in radians
astro.fixangr = function(a) {
return a - (2 * Math.PI) * (Math.floor(a / (2 * Math.PI)));
}Sine of an angle in degrees
astro.dsin = function(d) {
return Math.sin(this.dtr(d));
}Cosine of an angle in degrees
astro.dcos = function(d) {
return Math.cos(this.dtr(d));
}Modulus function which works for non-integers
astro.mod = function(a, b) {
return a - (b * Math.floor(a / b));
}Modulus function which returns numerator if modulus is zero
astro.amod = function(a, b) {
return this.mod(a - 1, b) + 1;
}Convert Julian time to hour, minutes, and seconds, returned as a three-element array
astro.jhms = function(j) {
var ij;Astronomical to civil
j += 0.5;
ij = ((j - Math.floor(j)) * 86400.0) + 0.5;
return [
Math.floor(ij / 3600),
Math.floor((ij / 60) % 60),
Math.floor(ij % 60)
];
}Calculate day of week from Julian day
astro.jwday = function(j) {
return this.mod(Math.floor((j + 1.5)), 7);
}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.
astro.obliqeq = function(jd) {
var eps, u, v, i;
v = u = (jd - this.constants.J2000) / (this.constants.JULIAN_CENTURY * 100);
eps = 23 + (26 / 60.0) + (21.448 / 3600.0);
if (Math.abs(u) < 1.0) {
for (i = 0; i < 10; i++) {
eps += (this.constants.O_TERMS[i] / 3600.0) * v;
v *= u;
}
}
return eps;
}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.
astro.nutation = function(jd) {
var deltaPsi, deltaEpsilon,
i, j,
t = (jd - 2451545.0) / 36525.0,
t2, t3, to10,
ta = [],
dp = 0,
de = 0,
ang;
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] = this.dtr(297.850363 + 445267.11148 * t - 0.0019142 * t2 +
t3 / 189474.0);
ta[1] = this.dtr(357.52772 + 35999.05034 * t - 0.0001603 * t2 -
t3 / 300000.0);
ta[2] = this.dtr(134.96298 + 477198.867398 * t + 0.0086972 * t2 +
t3 / 56250.0);
ta[3] = this.dtr(93.27191 + 483202.017538 * t - 0.0036825 * t2 +
t3 / 327270);
ta[4] = this.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 (i = 0; i < 5; i++) {
ta[i] = this.fixangr(ta[i]);
}
to10 = t / 10.0;
for (i = 0; i < 63; i++) {
ang = 0;
for (j = 0; j < 5; j++) {
if (this.constants.NUT_ARG_MULT[(i * 5) + j] != 0) {
ang += this.constants.NUT_ARG_MULT[(i * 5) + j] * ta[j];
}
}
dp += (this.constants.NUT_ARG_COEFF[(i * 4) + 0] + this.constants.NUT_ARG_COEFF[(i * 4) + 1] * to10) * Math.sin(ang);
de += (this.constants.NUT_ARG_COEFF[(i * 4) + 2] + this.constants.NUT_ARG_COEFF[(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 [deltaPsi, deltaEpsilon];
}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.
astro.ecliptoeq = function(jd, Lambda, Beta) {
var eps, Ra, Dec;Obliquity of the ecliptic
eps = this.dtr(this.obliqeq(jd));
Ra = this.rtd(Math.atan2((Math.cos(eps) * Math.sin(this.dtr(Lambda)) -
(Math.tan(this.dtr(Beta)) * Math.sin(eps))),
Math.cos(this.dtr(Lambda))));
Ra = this.fixangle(this.rtd(Math.atan2((Math.cos(eps) * Math.sin(this.dtr(Lambda)) -
(Math.tan(this.dtr(Beta)) * Math.sin(eps))),
Math.cos(this.dtr(Lambda)))));
Dec = this.rtd(Math.asin((Math.sin(eps) * Math.sin(this.dtr(Lambda)) * Math.cos(this.dtr(Beta))) +
(Math.sin(this.dtr(Beta)) * Math.cos(eps))));
return [Ra, Dec];
}Determine the difference, in seconds, between Dynamical time and Universal time.
astro.deltat = function(year) {
var dt, f, i, t;
if ((year >= 1620) && (year <= 2000)) {
i = Math.floor((year - 1620) / 2);Fractional part of year
f = ((year - 1620) / 2) - i;
dt = this.constants.DELTA_T_TAB[i] + ((this.constants.DELTA_T_TAB[i + 1] - this.constants.DELTA_T_TAB[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;
}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
astro.equinox = function(year, which) {
var deltaL, i, j, JDE0, JDE, JDE0tab, S, T, W, Y;Initialise terms for mean equinox and solstices. We have two sets: one for years prior to 1000 and a second for subsequent years.
if (year < 1000) {
JDE0tab = this.constants.JDE0_TAB_1000;
Y = year / 1000;
} else {
JDE0tab = this.constants.JDE0_TAB_2000;
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);
T = (JDE0 - 2451545.0) / 36525;
W = (35999.373 * T) - 2.47;
deltaL = 1 + (0.0334 * this.dcos(W)) + (0.0007 * this.dcos(2 * W));Sum the periodic terms for time T
S = 0;
for (i = j = 0; i < 24; i++) {
S += this.constants.EQUINOX_P_TERMS[j] * this.dcos(this.constants.EQUINOX_P_TERMS[j + 1] + (this.constants.EQUINOX_P_TERMS[j + 2] * T));
j += 3;
}
JDE = JDE0 + ((S * 0.00001) / deltaL);
return JDE;
}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.
astro.sunpos = function(jd) {
var T, T2, L0, M, e, C, sunLong, sunAnomaly, sunR,
Omega, Lambda, epsilon, epsilon0, Alpha, Delta,
AlphaApp, DeltaApp;
T = (jd - this.constants.J2000) / this.constants.JULIAN_CENTURY;
T2 = T * T;
L0 = 280.46646 + (36000.76983 * T) + (0.0003032 * T2);
L0 = this.fixangle(L0);
M = 357.52911 + (35999.05029 * T) + (-0.0001537 * T2);
M = this.fixangle(M);
e = 0.016708634 + (-0.000042037 * T) + (-0.0000001267 * T2);
C = ((1.914602 + (-0.004817 * T) + (-0.000014 * T2)) * this.dsin(M)) +
((0.019993 - (0.000101 * T)) * this.dsin(2 * M)) +
(0.000289 * this.dsin(3 * M));
sunLong = L0 + C;
sunAnomaly = M + C;
sunR = (1.000001018 * (1 - (e * e))) / (1 + (e * this.dcos(sunAnomaly)));
Omega = 125.04 - (1934.136 * T);
Lambda = sunLong + (-0.00569) + (-0.00478 * this.dsin(Omega));
epsilon0 = this.obliqeq(jd);
epsilon = epsilon0 + (0.00256 * this.dcos(Omega));
Alpha = this.rtd(Math.atan2(this.dcos(epsilon0) * this.dsin(sunLong), this.dcos(sunLong)));
Alpha = this.fixangle(Alpha);
Delta = this.rtd(Math.asin(this.dsin(epsilon0) * this.dsin(sunLong)));
AlphaApp = this.rtd(Math.atan2(this.dcos(epsilon) * this.dsin(Lambda), this.dcos(Lambda)));
AlphaApp = this.fixangle(AlphaApp);
DeltaApp = this.rtd(Math.asin(this.dsin(epsilon) * this.dsin(Lambda)));Angular quantities are expressed in decimal degrees
return [[0] Geometric mean longitude of the Sun
L0,[1] Mean anomaly of the Sun
M,[2] Eccentricity of the Earth's orbit
e,[3] Sun's equation of the Centre
C,[4] Sun's true longitude
sunLong,[5] Sun's true anomaly
sunAnomaly,[6] Sun's radius vector in AU
sunR,[7] Sun's apparent longitude at true equinox of the date
Lambda,[8] Sun's true right ascension
Alpha,[9] Sun's true declination
Delta,[10] Sun's apparent right ascension
AlphaApp,[11] Sun's apparent declination
DeltaApp
];
}Compute equation of time for a given moment. Returns the equation of time as a fraction of a day.
astro.equationOfTime = function(jd) {
var alpha, deltaPsi, E, epsilon, L0, tau;
tau = (jd - this.constants.J2000) / this.constants.JULIAN_MILLENIUM;
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));
L0 = this.fixangle(L0);
alpha = this.sunpos(jd)[10];
deltaPsi = this.nutation(jd)[0];
epsilon = this.obliqeq(jd) + this.nutation(jd)[1];
E = L0 + (-0.0057183) + (-alpha) + (deltaPsi * this.dcos(epsilon));
E = E - 20.0 * (Math.floor(E / 20.0));
E = E / (24 * 60);
return E;
}
return exports;
}(Calendrical || {}));