247 lines
7.8 KiB
JavaScript
247 lines
7.8 KiB
JavaScript
'use strict';
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Object.defineProperty(exports, '__esModule', { value: true });
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var base = require('./base.cjs');
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var sexagesimal = require('./sexagesimal.cjs');
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/**
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* @copyright 2013 Sonia Keys
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* @copyright 2016 commenthol
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* @license MIT
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* @module nutation
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*/
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// Nutation: Chapter 22, Nutation and the Obliquity of the Ecliptic.
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/**
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* Nutation returns nutation in longitude (Δψ) and nutation in obliquity (Δε)
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* for a given JDE.
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*
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* JDE = UT + ΔT, see package.
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*
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* Computation is by 1980 IAU theory, with terms < .0003″ neglected.
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*
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* Result units are radians.
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*
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* @param {number} jde - Julian ephemeris day
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* @return {number[]} [Δψ, Δε] - [longitude, obliquity] in radians
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*/
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function nutation (jde) {
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const T = base["default"].J2000Century(jde);
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// Mean elongation of the Moon from the sun
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const D = base["default"].horner(T,
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297.85036, 445267.11148, -0.0019142, 1.0 / 189474) * Math.PI / 180;
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// Mean anomaly of the Sun (Earth)
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const M = base["default"].horner(T,
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357.52772, 35999.050340, -0.0001603, -1.0 / 300000) * Math.PI / 180;
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// Mean anomaly of the Moon
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const N = base["default"].horner(T,
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134.96298, 477198.867398, 0.0086972, 1.0 / 56250) * Math.PI / 180;
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// Moon's argument of latitude
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const F = base["default"].horner(T,
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93.27191, 483202.017538, -0.0036825, 1.0 / 327270) * Math.PI / 180;
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// Longitude of the ascending node of the Moon's mean orbit on the ecliptic, measured from mean equinox of date
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const Ω = base["default"].horner(T,
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125.04452, -1934.136261, 0.0020708, 1.0 / 450000) * Math.PI / 180;
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let Δψ = 0;
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let Δε = 0;
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// sum in reverse order to accumulate smaller terms first
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for (let i = table22A.length - 1; i >= 0; i--) {
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const row = table22A[i];
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const arg = row.d * D + row.m * M + row.n * N + row.f * F + row.ω * Ω;
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const [s, c] = base["default"].sincos(arg);
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Δψ += s * (row.s0 + row.s1 * T);
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Δε += c * (row.c0 + row.c1 * T);
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}
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Δψ *= 0.0001 / 3600 * (Math.PI / 180);
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Δε *= 0.0001 / 3600 * (Math.PI / 180);
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return [Δψ, Δε] // (Δψ, Δε float)
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}
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/**
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* ApproxNutation returns a fast approximation of nutation in longitude (Δψ)
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* and nutation in obliquity (Δε) for a given JDE.
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*
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* Accuracy is 0.5″ in Δψ, 0.1″ in Δε.
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*
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* Result units are radians.
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*
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* @param {number} jde - Julian ephemeris day
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* @return {number[]} [Δψ, Δε] - [longitude, obliquity] in radians
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*/
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function approxNutation (jde) {
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const T = (jde - base["default"].J2000) / 36525;
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const Ω = (125.04452 - 1934.136261 * T) * Math.PI / 180;
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const L = (280.4665 + 36000.7698 * T) * Math.PI / 180;
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const N = (218.3165 + 481267.8813 * T) * Math.PI / 180;
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const [sΩ, cΩ] = base["default"].sincos(Ω);
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const [s2L, c2L] = base["default"].sincos(2 * L);
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const [s2N, c2N] = base["default"].sincos(2 * N);
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const [s2Ω, c2Ω] = base["default"].sincos(2 * Ω);
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const Δψ = (-17.2 * sΩ - 1.32 * s2L - 0.23 * s2N + 0.21 * s2Ω) / 3600 * (Math.PI / 180);
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const Δε = (9.2 * cΩ + 0.57 * c2L + 0.1 * c2N - 0.09 * c2Ω) / 3600 * (Math.PI / 180);
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return [Δψ, Δε] // (Δψ, Δε float)
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}
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/**
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* MeanObliquity returns mean obliquity (ε₀) following the IAU 1980
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* polynomial.
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*
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* Accuracy is 1″ over the range 1000 to 3000 years and 10″ over the range
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* 0 to 4000 years.
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*
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* Result unit is radians.
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*
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* @param {number} jde - Julian ephemeris day
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* @return {number} mean obliquity (ε₀)
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*/
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function meanObliquity (jde) {
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// (22.2) p. 147
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return base["default"].horner(
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base["default"].J2000Century(jde),
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new sexagesimal["default"].Angle(false, 23, 26, 21.448).rad(),
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-46.815 / 3600 * (Math.PI / 180),
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-0.00059 / 3600 * (Math.PI / 180),
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0.001813 / 3600 * (Math.PI / 180)
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)
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}
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/**
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* MeanObliquityLaskar returns mean obliquity (ε₀) following the Laskar
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* 1986 polynomial.
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*
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* Accuracy over the range 1000 to 3000 years is .01″.
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*
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* Accuracy over the valid date range of -8000 to +12000 years is
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* "a few seconds."
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*
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* Result unit is radians.
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*
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* @param {number} jde - Julian ephemeris day
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* @return {number} mean obliquity (ε₀)
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*/
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function meanObliquityLaskar (jde) {
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// (22.3) p. 147
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return base["default"].horner(
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base["default"].J2000Century(jde) * 0.01,
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new sexagesimal["default"].Angle(false, 23, 26, 21.448).rad(),
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-4680.93 / 3600 * (Math.PI / 180),
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-1.55 / 3600 * (Math.PI / 180),
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1999.25 / 3600 * (Math.PI / 180),
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-51.38 / 3600 * (Math.PI / 180),
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-249.67 / 3600 * (Math.PI / 180),
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-39.05 / 3600 * (Math.PI / 180),
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7.12 / 3600 * (Math.PI / 180),
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27.87 / 3600 * (Math.PI / 180),
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5.79 / 3600 * (Math.PI / 180),
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2.45 / 3600 * (Math.PI / 180)
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)
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}
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/**
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* NutationInRA returns "nutation in right ascension" or "equation of the
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* equinoxes."
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*
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* Result is an angle in radians.
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*
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* @param {number} jde - Julian ephemeris day
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* @return {number} nutation in right ascension
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*/
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function nutationInRA (jde) {
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const [Δψ, Δε] = nutation(jde);
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const ε0 = meanObliquity(jde);
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return Δψ * Math.cos(ε0 + Δε)
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}
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const table22A = (function () {
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const PROPS = 'd,m,n,f,ω,s0,s1,c0,c1'.split(',');
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const tab = [
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[0, 0, 0, 0, 1, -171996, -174.2, 92025, 8.9],
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[-2, 0, 0, 2, 2, -13187, -1.6, 5736, -3.1],
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[0, 0, 0, 2, 2, -2274, -0.2, 977, -0.5],
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[0, 0, 0, 0, 2, 2062, 0.2, -895, 0.5],
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[0, 1, 0, 0, 0, 1426, -3.4, 54, -0.1],
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[0, 0, 1, 0, 0, 712, 0.1, -7, 0],
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[-2, 1, 0, 2, 2, -517, 1.2, 224, -0.6],
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[0, 0, 0, 2, 1, -386, -0.4, 200, 0],
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[0, 0, 1, 2, 2, -301, 0, 129, -0.1],
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[-2, -1, 0, 2, 2, 217, -0.5, -95, 0.3],
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[-2, 0, 1, 0, 0, -158, 0, 0, 0],
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[-2, 0, 0, 2, 1, 129, 0.1, -70, 0],
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[0, 0, -1, 2, 2, 123, 0, -53, 0],
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[2, 0, 0, 0, 0, 63, 0, 0, 0],
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[0, 0, 1, 0, 1, 63, 0.1, -33, 0],
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[2, 0, -1, 2, 2, -59, 0, 26, 0],
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[0, 0, -1, 0, 1, -58, -0.1, 32, 0],
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[0, 0, 1, 2, 1, -51, 0, 27, 0],
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[-2, 0, 2, 0, 0, 48, 0, 0, 0],
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[0, 0, -2, 2, 1, 46, 0, -24, 0],
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[2, 0, 0, 2, 2, -38, 0, 16, 0],
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[0, 0, 2, 2, 2, -31, 0, 13, 0],
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[0, 0, 2, 0, 0, 29, 0, 0, 0],
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[-2, 0, 1, 2, 2, 29, 0, -12, 0],
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[0, 0, 0, 2, 0, 26, 0, 0, 0],
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[-2, 0, 0, 2, 0, -22, 0, 0, 0],
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[0, 0, -1, 2, 1, 21, 0, -10, 0],
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[0, 2, 0, 0, 0, 17, -0.1, 0, 0],
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[2, 0, -1, 0, 1, 16, 0, -8, 0],
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[-2, 2, 0, 2, 2, -16, 0.1, 7, 0],
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[0, 1, 0, 0, 1, -15, 0, 9, 0],
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[-2, 0, 1, 0, 1, -13, 0, 7, 0],
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[0, -1, 0, 0, 1, -12, 0, 6, 0],
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[0, 0, 2, -2, 0, 11, 0, 0, 0],
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[2, 0, -1, 2, 1, -10, 0, 5, 0],
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[2, 0, 1, 2, 2, -8, 0, 3, 0],
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[0, 1, 0, 2, 2, 7, 0, -3, 0],
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[-2, 1, 1, 0, 0, -7, 0, 0, 0],
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[0, -1, 0, 2, 2, -7, 0, 3, 0],
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[2, 0, 0, 2, 1, -7, 0, 3, 0],
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[2, 0, 1, 0, 0, 6, 0, 0, 0],
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[-2, 0, 2, 2, 2, 6, 0, -3, 0],
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[-2, 0, 1, 2, 1, 6, 0, -3, 0],
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[2, 0, -2, 0, 1, -6, 0, 3, 0],
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[2, 0, 0, 0, 1, -6, 0, 3, 0],
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[0, -1, 1, 0, 0, 5, 0, 0, 0],
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[-2, -1, 0, 2, 1, -5, 0, 3, 0],
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[-2, 0, 0, 0, 1, -5, 0, 3, 0],
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[0, 0, 2, 2, 1, -5, 0, 3, 0],
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[-2, 0, 2, 0, 1, 4, 0, 0, 0],
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[-2, 1, 0, 2, 1, 4, 0, 0, 0],
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[0, 0, 1, -2, 0, 4, 0, 0, 0],
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[-1, 0, 1, 0, 0, -4, 0, 0, 0],
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[-2, 1, 0, 0, 0, -4, 0, 0, 0],
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[1, 0, 0, 0, 0, -4, 0, 0, 0],
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[0, 0, 1, 2, 0, 3, 0, 0, 0],
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[0, 0, -2, 2, 2, -3, 0, 0, 0],
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[-1, -1, 1, 0, 0, -3, 0, 0, 0],
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[0, 1, 1, 0, 0, -3, 0, 0, 0],
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[0, -1, 1, 2, 2, -3, 0, 0, 0],
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[2, -1, -1, 2, 2, -3, 0, 0, 0],
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[0, 0, 3, 2, 2, -3, 0, 0, 0],
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[2, -1, 0, 2, 2, -3, 0, 0, 0]
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];
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return tab.map((row) => {
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const o = {};
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PROPS.forEach((p, i) => {
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o[p] = row[i];
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});
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return o
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})
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})();
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var nutation$1 = {
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nutation,
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approxNutation,
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meanObliquity,
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meanObliquityLaskar,
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nutationInRA
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};
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exports.approxNutation = approxNutation;
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exports["default"] = nutation$1;
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exports.meanObliquity = meanObliquity;
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exports.meanObliquityLaskar = meanObliquityLaskar;
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exports.nutation = nutation;
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exports.nutationInRA = nutationInRA;
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