astronomia/es/moonmaxdec.js

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module moonmaxdec
 */
/**
 * Moonmaxdec: Chapter 52, Maximum Declinations of the Moon
 */

import base from './base';

/**
 * North computes the maximum northern declination of the Moon near a given date.
 *
 * Argument year is a decimal year specifying a date near the event.
 *
 * Returned is the jde of the event nearest the given date and the declination
 * of the Moon at that time.
 */
export function north(y) {
  // (y float64)  (jde, δ float64)
  return max(y, nc);
}

/**
 * South computes the maximum southern declination of the Moon near a given date.
 *
 * Argument year is a decimal year specifying a date near the event.
 *
 * Returned is the jde of the event nearest the given date and the declination
 * of the Moon at that time.
 */
export function south(y) {
  // (y float64)  (jde, δ float64)
  return max(y, sc);
}

var p = Math.PI / 180;
var ck = 1 / 1336.86;

/**
 * @private
 */
function max(y, c) {
  // (y float64, c *mc)  (jde, δ float64)
  var k = (y - 2000.03) * 13.3686; // (52.1) p. 367
  k = Math.floor(k + 0.5);
  var T = k * ck;
  var D = base.horner(T, c.D, 333.0705546 * p / ck, -0.0004214 * p, 0.00000011 * p);
  var m = base.horner(T, c.m, 26.9281592 * p / ck, -0.0000355 * p, -0.0000001 * p);
  var m_ = base.horner(T, c.m_, 356.9562794 * p / ck, 0.0103066 * p, 0.00001251 * p);
  var f = base.horner(T, c.f, 1.4467807 * p / ck, -0.002069 * p, -0.00000215 * p);
  var E = base.horner(T, 1, -0.002516, -0.0000074);
  var jde = base.horner(T, c.JDE, 27.321582247 / ck, 0.000119804, -0.000000141) + c.tc[0] * Math.cos(f) + c.tc[1] * Math.sin(m_) + c.tc[2] * Math.sin(2 * f) + c.tc[3] * Math.sin(2 * D - m_) + c.tc[4] * Math.cos(m_ - f) + c.tc[5] * Math.cos(m_ + f) + c.tc[6] * Math.sin(2 * D) + c.tc[7] * Math.sin(m) * E + c.tc[8] * Math.cos(3 * f) + c.tc[9] * Math.sin(m_ + 2 * f) + c.tc[10] * Math.cos(2 * D - f) + c.tc[11] * Math.cos(2 * D - m_ - f) + c.tc[12] * Math.cos(2 * D - m_ + f) + c.tc[13] * Math.cos(2 * D + f) + c.tc[14] * Math.sin(2 * m_) + c.tc[15] * Math.sin(m_ - 2 * f) + c.tc[16] * Math.cos(2 * m_ - f) + c.tc[17] * Math.sin(m_ + 3 * f) + c.tc[18] * Math.sin(2 * D - m - m_) * E + c.tc[19] * Math.cos(m_ - 2 * f) + c.tc[20] * Math.sin(2 * (D - m_)) + c.tc[21] * Math.sin(f) + c.tc[22] * Math.sin(2 * D + m_) + c.tc[23] * Math.cos(m_ + 2 * f) + c.tc[24] * Math.sin(2 * D - m) * E + c.tc[25] * Math.sin(m_ + f) + c.tc[26] * Math.sin(m - m_) * E + c.tc[27] * Math.sin(m_ - 3 * f) + c.tc[28] * Math.sin(2 * m_ + f) + c.tc[29] * Math.cos(2 * (D - m_) - f) + c.tc[30] * Math.sin(3 * f) + c.tc[31] * Math.cos(m_ + 3 * f) + c.tc[32] * Math.cos(2 * m_) + c.tc[33] * Math.cos(2 * D - m_) + c.tc[34] * Math.cos(2 * D + m_ + f) + c.tc[35] * Math.cos(m_) + c.tc[36] * Math.sin(3 * m_ + f) + c.tc[37] * Math.sin(2 * D - m_ + f) + c.tc[38] * Math.cos(2 * (D - m_)) + c.tc[39] * Math.cos(D + f) + c.tc[40] * Math.sin(m + m_) * E + c.tc[41] * Math.sin(2 * (D - f)) + c.tc[42] * Math.cos(2 * m_ + f) + c.tc[43] * Math.cos(3 * m_ + f);
  var δ = 23.6961 * p - 0.013004 * p * T + c.dc[0] * Math.sin(f) + c.dc[1] * Math.cos(2 * f) + c.dc[2] * Math.sin(2 * D - f) + c.dc[3] * Math.sin(3 * f) + c.dc[4] * Math.cos(2 * (D - f)) + c.dc[5] * Math.cos(2 * D) + c.dc[6] * Math.sin(m_ - f) + c.dc[7] * Math.sin(m_ + 2 * f) + c.dc[8] * Math.cos(f) + c.dc[9] * Math.sin(2 * D + m - f) * E + c.dc[10] * Math.sin(m_ + 3 * f) + c.dc[11] * Math.sin(D + f) + c.dc[12] * Math.sin(m_ - 2 * f) + c.dc[13] * Math.sin(2 * D - m - f) * E + c.dc[14] * Math.sin(2 * D - m_ - f) + c.dc[15] * Math.cos(m_ + f) + c.dc[16] * Math.cos(m_ + 2 * f) + c.dc[17] * Math.cos(2 * m_ + f) + c.dc[18] * Math.cos(m_ - 3 * f) + c.dc[19] * Math.cos(2 * m_ - f) + c.dc[20] * Math.cos(m_ - 2 * f) + c.dc[21] * Math.sin(2 * m_) + c.dc[22] * Math.sin(3 * m_ + f) + c.dc[23] * Math.cos(2 * D + m - f) * E + c.dc[24] * Math.cos(m_ - f) + c.dc[25] * Math.cos(3 * f) + c.dc[26] * Math.sin(2 * D + f) + c.dc[27] * Math.cos(m_ + 3 * f) + c.dc[28] * Math.cos(D + f) + c.dc[29] * Math.sin(2 * m_ - f) + c.dc[30] * Math.cos(3 * m_ + f) + c.dc[31] * Math.cos(2 * (D + m_) + f) + c.dc[32] * Math.sin(2 * (D - m_) - f) + c.dc[33] * Math.cos(2 * m_) + c.dc[34] * Math.cos(m_) + c.dc[35] * Math.sin(2 * f) + c.dc[36] * Math.sin(m_ + f);
  return { jde: jde, dec: c.s * δ };
}

/**
 * north coefficients
 */
var nc = {
  D: 152.2029 * p,
  m: 14.8591 * p,
  m_: 4.6881 * p,
  f: 325.8867 * p,
  JDE: 2451562.5897,
  s: 1,
  tc: [0.8975, -0.4726, -0.1030, -0.0976, -0.0462, -0.0461, -0.0438, 0.0162, -0.0157, 0.0145, 0.0136, -0.0095, -0.0091, -0.0089, 0.0075, -0.0068, 0.0061, -0.0047, -0.0043, -0.004, -0.0037, 0.0031, 0.0030, -0.0029, -0.0029, -0.0027, 0.0024, -0.0021, 0.0019, 0.0018, 0.0018, 0.0017, 0.0017, -0.0014, 0.0013, 0.0013, 0.0012, 0.0011, -0.0011, 0.001, 0.001, -0.0009, 0.0007, -0.0007],
  dc: [5.1093 * p, 0.2658 * p, 0.1448 * p, -0.0322 * p, 0.0133 * p, 0.0125 * p, -0.0124 * p, -0.0101 * p, 0.0097 * p, -0.0087 * p, 0.0074 * p, 0.0067 * p, 0.0063 * p, 0.0060 * p, -0.0057 * p, -0.0056 * p, 0.0052 * p, 0.0041 * p, -0.004 * p, 0.0038 * p, -0.0034 * p, -0.0029 * p, 0.0029 * p, -0.0028 * p, -0.0028 * p, -0.0023 * p, -0.0021 * p, 0.0019 * p, 0.0018 * p, 0.0017 * p, 0.0015 * p, 0.0014 * p, -0.0012 * p, -0.0012 * p, -0.001 * p, -0.001 * p, 0.0006 * p]

  /**
   * south coefficients
   */
};var sc = {
  D: 345.6676 * p,
  m: 1.3951 * p,
  m_: 186.21 * p,
  f: 145.1633 * p,
  JDE: 2451548.9289,
  s: -1,
  tc: [-0.8975, -0.4726, -0.1030, -0.0976, 0.0541, 0.0516, -0.0438, 0.0112, 0.0157, 0.0023, -0.0136, 0.011, 0.0091, 0.0089, 0.0075, -0.003, -0.0061, -0.0047, -0.0043, 0.004, -0.0037, -0.0031, 0.0030, 0.0029, -0.0029, -0.0027, 0.0024, -0.0021, -0.0019, -0.0006, -0.0018, -0.0017, 0.0017, 0.0014, -0.0013, -0.0013, 0.0012, 0.0011, 0.0011, 0.001, 0.001, -0.0009, -0.0007, -0.0007],
  dc: [-5.1093 * p, 0.2658 * p, -0.1448 * p, 0.0322 * p, 0.0133 * p, 0.0125 * p, -0.0015 * p, 0.0101 * p, -0.0097 * p, 0.0087 * p, 0.0074 * p, 0.0067 * p, -0.0063 * p, -0.0060 * p, 0.0057 * p, -0.0056 * p, -0.0052 * p, -0.0041 * p, -0.004 * p, -0.0038 * p, 0.0034 * p, -0.0029 * p, 0.0029 * p, 0.0028 * p, -0.0028 * p, 0.0023 * p, 0.0021 * p, 0.0019 * p, 0.0018 * p, -0.0017 * p, 0.0015 * p, 0.0014 * p, 0.0012 * p, -0.0012 * p, 0.001 * p, -0.001 * p, 0.0037 * p]
};

export default {
  north: north,
  south: south
};