astronomia/es/jupitermoons.js

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module jupitermoons
 */
/**
 * Jupitermoons: Chapter 44, Positions of the Satellites of Jupiter.
 */

import base from './base';
import planetelements from './planetelements';
import solar from './solar';

// Moon names in order of position in Array
export var io = 0;
export var europa = 1;
export var ganymede = 2;
export var callisto = 3;

var k = [17295, 21819, 27558, 36548];

/**
 * XY used for returning coordinates of moons.
 * @param {number} x - in units of Jupiter radii
 * @param {number} y - in units of Jupiter radii
 */
function XY(x, y) {
  this.x = x;
  this.y = y;
}

/**
 * Positions computes positions of moons of Jupiter.
 *
 * Returned coordinates are in units of Jupiter radii.
 *
 * @param {Number} jde - Julian ephemeris day
 * @return {Array} x, y - coordinates of the 4 Satellites of jupiter
 */
export function positions(jde) {
  var d = jde - base.J2000;
  var p = Math.PI / 180;
  var V = 172.74 * p + 0.00111588 * p * d;
  var M = 357.529 * p + 0.9856003 * p * d;
  var sV = Math.sin(V);
  var N = 20.02 * p + 0.0830853 * p * d + 0.329 * p * sV;
  var J = 66.115 * p + 0.9025179 * p * d - 0.329 * p * sV;

  var _base$sincos = base.sincos(M),
      sM = _base$sincos[0],
      cM = _base$sincos[1];

  var _base$sincos2 = base.sincos(N),
      sN = _base$sincos2[0],
      cN = _base$sincos2[1];

  var _base$sincos3 = base.sincos(2 * M),
      s2M = _base$sincos3[0],
      c2M = _base$sincos3[1];

  var _base$sincos4 = base.sincos(2 * N),
      s2N = _base$sincos4[0],
      c2N = _base$sincos4[1];

  var A = 1.915 * p * sM + 0.02 * p * s2M;
  var B = 5.555 * p * sN + 0.168 * p * s2N;
  var K = J + A - B;
  var R = 1.00014 - 0.01671 * cM - 0.00014 * c2M;
  var r = 5.20872 - 0.25208 * cN - 0.00611 * c2N;

  var _base$sincos5 = base.sincos(K),
      sK = _base$sincos5[0],
      cK = _base$sincos5[1];

  var Δ = Math.sqrt(r * r + R * R - 2 * r * R * cK);
  var ψ = Math.asin(R / Δ * sK);
  var λ = 34.35 * p + 0.083091 * p * d + 0.329 * p * sV + B;
  var DS = 3.12 * p * Math.sin(λ + 42.8 * p);
  var DE = DS - 2.22 * p * Math.sin(ψ) * Math.cos(λ + 22 * p) - 1.3 * p * (r - Δ) / Δ * Math.sin(λ - 100.5 * p);
  var dd = d - Δ / 173;
  var u1 = 163.8069 * p + 203.4058646 * p * dd + ψ - B;
  var u2 = 358.414 * p + 101.2916335 * p * dd + ψ - B;
  var u3 = 5.7176 * p + 50.234518 * p * dd + ψ - B;
  var u4 = 224.8092 * p + 21.48798 * p * dd + ψ - B;
  var G = 331.18 * p + 50.310482 * p * dd;
  var H = 87.45 * p + 21.569231 * p * dd;

  var _base$sincos6 = base.sincos(2 * (u1 - u2)),
      s212 = _base$sincos6[0],
      c212 = _base$sincos6[1];

  var _base$sincos7 = base.sincos(2 * (u2 - u3)),
      s223 = _base$sincos7[0],
      c223 = _base$sincos7[1];

  var _base$sincos8 = base.sincos(G),
      sG = _base$sincos8[0],
      cG = _base$sincos8[1];

  var _base$sincos9 = base.sincos(H),
      sH = _base$sincos9[0],
      cH = _base$sincos9[1];

  var c1 = 0.473 * p * s212;
  var c2 = 1.065 * p * s223;
  var c3 = 0.165 * p * sG;
  var c4 = 0.843 * p * sH;
  var r1 = 5.9057 - 0.0244 * c212;
  var r2 = 9.3966 - 0.0882 * c223;
  var r3 = 14.9883 - 0.0216 * cG;
  var r4 = 26.3627 - 0.1939 * cH;
  var sDE = Math.sin(DE);
  var xy = function xy(u, r) {
    var _base$sincos10 = base.sincos(u),
        su = _base$sincos10[0],
        cu = _base$sincos10[1];

    return new XY(r * su, -r * cu * sDE);
  };
  return [xy(u1 + c1, r1), xy(u2 + c2, r2), xy(u3 + c3, r3), xy(u4 + c4, r4)];
}

/**
 * Positions computes positions of moons of Jupiter.
 *
 * High accuracy method based on theory "E5"  Results returned in
 * argument pos, which must not be undefined.  Returned coordinates in units
 * of Jupiter radii.
 *
 * @param {Number} jde - Julian ephemeris day
 * @param {planetposition.Planet} earth - VSOP87 Planet earth
 * @param {planetposition.Planet} jupiter - VSOP87 Planet jupiter
 * @param {Array} [pos] - reference to array of positions (same as return value)
 * @return {Array} x, y - coordinates of the 4 Satellites of jupiter
 */
export function e5(jde, earth, jupiter, pos) {
  pos = pos || new Array(4);

  // variables assigned in following block
  var λ0 = void 0,
      β0 = void 0,
      t = void 0;
  var Δ = 5.0;(function () {
    var _solar$trueVSOP = solar.trueVSOP87(earth, jde),
        lon = _solar$trueVSOP.lon,
        lat = _solar$trueVSOP.lat,
        range = _solar$trueVSOP.range;

    var s = lon,
        β = lat,
        R = range;

    var _base$sincos11 = base.sincos(s),
        ss = _base$sincos11[0],
        cs = _base$sincos11[1];

    var sβ = Math.sin(β);
    var τ = base.lightTime(Δ);
    var x = void 0,
        y = void 0,
        z = void 0;
    function f() {
      var _jupiter$position = jupiter.position(jde - τ),
          lon = _jupiter$position.lon,
          lat = _jupiter$position.lat,
          range = _jupiter$position.range;

      var _base$sincos12 = base.sincos(lon),
          sl = _base$sincos12[0],
          cl = _base$sincos12[1];

      var _base$sincos13 = base.sincos(lat),
          sb = _base$sincos13[0],
          cb = _base$sincos13[1];

      x = range * cb * cl + R * cs;
      y = range * cb * sl + R * ss;
      z = range * sb + R * sβ;
      Δ = Math.sqrt(x * x + y * y + z * z);
      τ = base.lightTime(Δ);
    }

    f();
    f();

    λ0 = Math.atan2(y, x);
    β0 = Math.atan(z / Math.hypot(x, y));
    t = jde - 2443000.5 - τ;
  })();

  var p = Math.PI / 180;
  var l1 = 106.07719 * p + 203.48895579 * p * t;
  var l2 = 175.73161 * p + 101.374724735 * p * t;
  var l3 = 120.55883 * p + 50.317609207 * p * t;
  var l4 = 84.44459 * p + 21.571071177 * p * t;
  var π1 = 97.0881 * p + 0.16138586 * p * t;
  var π2 = 154.8663 * p + 0.04726307 * p * t;
  var π3 = 188.184 * p + 0.00712734 * p * t;
  var π4 = 335.2868 * p + 0.00184 * p * t;
  var ω1 = 312.3346 * p - 0.13279386 * p * t;
  var ω2 = 100.4411 * p - 0.03263064 * p * t;
  var ω3 = 119.1942 * p - 0.00717703 * p * t;
  var ω4 = 322.6186 * p - 0.00175934 * p * t;
  var Γ = 0.33033 * p * Math.sin(163.679 * p + 0.0010512 * p * t) + 0.03439 * p * Math.sin(34.486 * p - 0.0161731 * p * t);
  var Φλ = 199.6766 * p + 0.1737919 * p * t;
  var ψ = 316.5182 * p - 0.00000208 * p * t;
  var G = 30.23756 * p + 0.0830925701 * p * t + Γ;
  var Gʹ = 31.97853 * p + 0.0334597339 * p * t;
  var Π = 13.469942 * p;

  var Σ1 = 0.47259 * p * Math.sin(2 * (l1 - l2)) + -0.03478 * p * Math.sin(π3 - π4) + 0.01081 * p * Math.sin(l2 - 2 * l3 + π3) + 0.00738 * p * Math.sin(Φλ) + 0.00713 * p * Math.sin(l2 - 2 * l3 + π2) + -0.00674 * p * Math.sin(π1 + π3 - 2 * Π - 2 * G) + 0.00666 * p * Math.sin(l2 - 2 * l3 + π4) + 0.00445 * p * Math.sin(l1 - π3) + -0.00354 * p * Math.sin(l1 - l2) + -0.00317 * p * Math.sin(2 * ψ - 2 * Π) + 0.00265 * p * Math.sin(l1 - π4) + -0.00186 * p * Math.sin(G) + 0.00162 * p * Math.sin(π2 - π3) + 0.00158 * p * Math.sin(4 * (l1 - l2)) + -0.00155 * p * Math.sin(l1 - l3) + -0.00138 * p * Math.sin(ψ + ω3 - 2 * Π - 2 * G) + -0.00115 * p * Math.sin(2 * (l1 - 2 * l2 + ω2)) + 0.00089 * p * Math.sin(π2 - π4) + 0.00085 * p * Math.sin(l1 + π3 - 2 * Π - 2 * G) + 0.00083 * p * Math.sin(ω2 - ω3) + 0.00053 * p * Math.sin(ψ - ω2);
  var Σ2 = 1.06476 * p * Math.sin(2 * (l2 - l3)) + 0.04256 * p * Math.sin(l1 - 2 * l2 + π3) + 0.03581 * p * Math.sin(l2 - π3) + 0.02395 * p * Math.sin(l1 - 2 * l2 + π4) + 0.01984 * p * Math.sin(l2 - π4) + -0.01778 * p * Math.sin(Φλ) + 0.01654 * p * Math.sin(l2 - π2) + 0.01334 * p * Math.sin(l2 - 2 * l3 + π2) + 0.01294 * p * Math.sin(π3 - π4) + -0.01142 * p * Math.sin(l2 - l3) + -0.01057 * p * Math.sin(G) + -0.00775 * p * Math.sin(2 * (ψ - Π)) + 0.00524 * p * Math.sin(2 * (l1 - l2)) + -0.0046 * p * Math.sin(l1 - l3) + 0.00316 * p * Math.sin(ψ - 2 * G + ω3 - 2 * Π) + -0.00203 * p * Math.sin(π1 + π3 - 2 * Π - 2 * G) + 0.00146 * p * Math.sin(ψ - ω3) + -0.00145 * p * Math.sin(2 * G) + 0.00125 * p * Math.sin(ψ - ω4) + -0.00115 * p * Math.sin(l1 - 2 * l3 + π3) + -0.00094 * p * Math.sin(2 * (l2 - ω2)) + 0.00086 * p * Math.sin(2 * (l1 - 2 * l2 + ω2)) + -0.00086 * p * Math.sin(5 * Gʹ - 2 * G + 52.225 * p) + -0.00078 * p * Math.sin(l2 - l4) + -0.00064 * p * Math.sin(3 * l3 - 7 * l4 + 4 * π4) + 0.00064 * p * Math.sin(π1 - π4) + -0.00063 * p * Math.sin(l1 - 2 * l3 + π4) + 0.00058 * p * Math.sin(ω3 - ω4) + 0.00056 * p * Math.sin(2 * (ψ - Π - G)) + 0.00056 * p * Math.sin(2 * (l2 - l4)) + 0.00055 * p * Math.sin(2 * (l1 - l3)) + 0.00052 * p * Math.sin(3 * l3 - 7 * l4 + π3 + 3 * π4) + -0.00043 * p * Math.sin(l1 - π3) + 0.00041 * p * Math.sin(5 * (l2 - l3)) + 0.00041 * p * Math.sin(π4 - Π) + 0.00032 * p * Math.sin(ω2 - ω3) + 0.00032 * p * Math.sin(2 * (l3 - G - Π));
  var Σ3 = 0.1649 * p * Math.sin(l3 - π3) + 0.09081 * p * Math.sin(l3 - π4) + -0.06907 * p * Math.sin(l2 - l3) + 0.03784 * p * Math.sin(π3 - π4) + 0.01846 * p * Math.sin(2 * (l3 - l4)) + -0.0134 * p * Math.sin(G) + -0.01014 * p * Math.sin(2 * (ψ - Π)) + 0.00704 * p * Math.sin(l2 - 2 * l3 + π3) + -0.0062 * p * Math.sin(l2 - 2 * l3 + π2) + -0.00541 * p * Math.sin(l3 - l4) + 0.00381 * p * Math.sin(l2 - 2 * l3 + π4) + 0.00235 * p * Math.sin(ψ - ω3) + 0.00198 * p * Math.sin(ψ - ω4) + 0.00176 * p * Math.sin(Φλ) + 0.0013 * p * Math.sin(3 * (l3 - l4)) + 0.00125 * p * Math.sin(l1 - l3) + -0.00119 * p * Math.sin(5 * Gʹ - 2 * G + 52.225 * p) + 0.00109 * p * Math.sin(l1 - l2) + -0.001 * p * Math.sin(3 * l3 - 7 * l4 + 4 * π4) + 0.00091 * p * Math.sin(ω3 - ω4) + 0.0008 * p * Math.sin(3 * l3 - 7 * l4 + π3 + 3 * π4) + -0.00075 * p * Math.sin(2 * l2 - 3 * l3 + π3) + 0.00072 * p * Math.sin(π1 + π3 - 2 * Π - 2 * G) + 0.00069 * p * Math.sin(π4 - Π) + -0.00058 * p * Math.sin(2 * l3 - 3 * l4 + π4) + -0.00057 * p * Math.sin(l3 - 2 * l4 + π4) + 0.00056 * p * Math.sin(l3 + π3 - 2 * Π - 2 * G) + -0.00052 * p * Math.sin(l2 - 2 * l3 + π1) + -0.00050 * p * Math.sin(π2 - π3) + 0.00048 * p * Math.sin(l3 - 2 * l4 + π3) + -0.00045 * p * Math.sin(2 * l2 - 3 * l3 + π4) + -0.00041 * p * Math.sin(π2 - π4) + -0.00038 * p * Math.sin(2 * G) + -0.00037 * p * Math.sin(π3 - π4 + ω3 - ω4) + -0.00032 * p * Math.sin(3 * l3 - 7 * l4 + 2 * π3 + 2 * π4) + 0.0003 * p * Math.sin(4 * (l3 - l4)) + 0.00029 * p * Math.sin(l3 + π4 - 2 * Π - 2 * G) + -0.00028 * p * Math.sin(ω3 + ψ - 2 * Π - 2 * G) + 0.00026 * p * Math.sin(l3 - Π - G) + 0.00024 * p * Math.sin(l2 - 3 * l3 + 2 * l4) + 0.00021 * p * Math.sin(2 * (l3 - Π - G)) + -0.00021 * p * Math.sin(l3 - π2) + 0.00017 * p * Math.sin(2 * (l3 - π3));
  var Σ4 = 0.84287 * p * Math.sin(l4 - π4) + 0.03431 * p * Math.sin(π4 - π3) + -0.03305 * p * Math.sin(2 * (ψ - Π)) + -0.03211 * p * Math.sin(G) + -0.01862 * p * Math.sin(l4 - π3) + 0.01186 * p * Math.sin(ψ - ω4) + 0.00623 * p * Math.sin(l4 + π4 - 2 * G - 2 * Π) + 0.00387 * p * Math.sin(2 * (l4 - π4)) + -0.00284 * p * Math.sin(5 * Gʹ - 2 * G + 52.225 * p) + -0.00234 * p * Math.sin(2 * (ψ - π4)) + -0.00223 * p * Math.sin(l3 - l4) + -0.00208 * p * Math.sin(l4 - Π) + 0.00178 * p * Math.sin(ψ + ω4 - 2 * π4) + 0.00134 * p * Math.sin(π4 - Π) + 0.00125 * p * Math.sin(2 * (l4 - G - Π)) + -0.00117 * p * Math.sin(2 * G) + -0.00112 * p * Math.sin(2 * (l3 - l4)) + 0.00107 * p * Math.sin(3 * l3 - 7 * l4 + 4 * π4) + 0.00102 * p * Math.sin(l4 - G - Π) + 0.00096 * p * Math.sin(2 * l4 - ψ - ω4) + 0.00087 * p * Math.sin(2 * (ψ - ω4)) + -0.00085 * p * Math.sin(3 * l3 - 7 * l4 + π3 + 3 * π4) + 0.00085 * p * Math.sin(l3 - 2 * l4 + π4) + -0.00081 * p * Math.sin(2 * (l4 - ψ)) + 0.00071 * p * Math.sin(l4 + π4 - 2 * Π - 3 * G) + 0.00061 * p * Math.sin(l1 - l4) + -0.00056 * p * Math.sin(ψ - ω3) + -0.00054 * p * Math.sin(l3 - 2 * l4 + π3) + 0.00051 * p * Math.sin(l2 - l4) + 0.00042 * p * Math.sin(2 * (ψ - G - Π)) + 0.00039 * p * Math.sin(2 * (π4 - ω4)) + 0.00036 * p * Math.sin(ψ + Π - π4 - ω4) + 0.00035 * p * Math.sin(2 * Gʹ - G + 188.37 * p) + -0.00035 * p * Math.sin(l4 - π4 + 2 * Π - 2 * ψ) + -0.00032 * p * Math.sin(l4 + π4 - 2 * Π - G) + 0.0003 * p * Math.sin(2 * Gʹ - 2 * G + 149.15 * p) + 0.00029 * p * Math.sin(3 * l3 - 7 * l4 + 2 * π3 + 2 * π4) + 0.00028 * p * Math.sin(l4 - π4 + 2 * ψ - 2 * Π) + -0.00028 * p * Math.sin(2 * (l4 - ω4)) + -0.00027 * p * Math.sin(π3 - π4 + ω3 - ω4) + -0.00026 * p * Math.sin(5 * Gʹ - 3 * G + 188.37 * p) + 0.00025 * p * Math.sin(ω4 - ω3) + -0.00025 * p * Math.sin(l2 - 3 * l3 + 2 * l4) + -0.00023 * p * Math.sin(3 * (l3 - l4)) + 0.00021 * p * Math.sin(2 * l4 - 2 * Π - 3 * G) + -0.00021 * p * Math.sin(2 * l3 - 3 * l4 + π4) + 0.00019 * p * Math.sin(l4 - π4 - G) + -0.00019 * p * Math.sin(2 * l4 - π3 - π4) + -0.00018 * p * Math.sin(l4 - π4 + G) + -0.00016 * p * Math.sin(l4 + π3 - 2 * Π - 2 * G);
  var L1 = l1 + Σ1;
  var L2 = l2 + Σ2;
  var L3 = l3 + Σ3;
  var L4 = l4 + Σ4;

  // variables assigned in following block
  var I = void 0;
  var X = new Array(5).fill(0);
  var Y = new Array(5).fill(0);
  var Z = new Array(5).fill(0);
  var R = void 0;(function () {
    var L = [L1, L2, L3, L4];
    var B = [Math.atan(0.0006393 * Math.sin(L1 - ω1) + 0.0001825 * Math.sin(L1 - ω2) + 0.0000329 * Math.sin(L1 - ω3) + -0.0000311 * Math.sin(L1 - ψ) + 0.0000093 * Math.sin(L1 - ω4) + 0.0000075 * Math.sin(3 * L1 - 4 * l2 - 1.9927 * Σ1 + ω2) + 0.0000046 * Math.sin(L1 + ψ - 2 * Π - 2 * G)), Math.atan(0.0081004 * Math.sin(L2 - ω2) + 0.0004512 * Math.sin(L2 - ω3) + -0.0003284 * Math.sin(L2 - ψ) + 0.0001160 * Math.sin(L2 - ω4) + 0.0000272 * Math.sin(l1 - 2 * l3 + 1.0146 * Σ2 + ω2) + -0.0000144 * Math.sin(L2 - ω1) + 0.0000143 * Math.sin(L2 + ψ - 2 * Π - 2 * G) + 0.0000035 * Math.sin(L2 - ψ + G) + -0.0000028 * Math.sin(l1 - 2 * l3 + 1.0146 * Σ2 + ω3)), Math.atan(0.0032402 * Math.sin(L3 - ω3) + -0.0016911 * Math.sin(L3 - ψ) + 0.0006847 * Math.sin(L3 - ω4) + -0.0002797 * Math.sin(L3 - ω2) + 0.0000321 * Math.sin(L3 + ψ - 2 * Π - 2 * G) + 0.0000051 * Math.sin(L3 - ψ + G) + -0.0000045 * Math.sin(L3 - ψ - G) + -0.0000045 * Math.sin(L3 + ψ - 2 * Π) + 0.0000037 * Math.sin(L3 + ψ - 2 * Π - 3 * G) + 0.000003 * Math.sin(2 * l2 - 3 * L3 + 4.03 * Σ3 + ω2) + -0.0000021 * Math.sin(2 * l2 - 3 * L3 + 4.03 * Σ3 + ω3)), Math.atan(-0.0076579 * Math.sin(L4 - ψ) + 0.0044134 * Math.sin(L4 - ω4) + -0.0005112 * Math.sin(L4 - ω3) + 0.0000773 * Math.sin(L4 + ψ - 2 * Π - 2 * G) + 0.0000104 * Math.sin(L4 - ψ + G) + -0.0000102 * Math.sin(L4 - ψ - G) + 0.0000088 * Math.sin(L4 + ψ - 2 * Π - 3 * G) + -0.0000038 * Math.sin(L4 + ψ - 2 * Π - G))];
    R = [5.90569 * (1 + -0.0041339 * Math.cos(2 * (l1 - l2)) + -0.0000387 * Math.cos(l1 - π3) + -0.0000214 * Math.cos(l1 - π4) + 0.000017 * Math.cos(l1 - l2) + -0.0000131 * Math.cos(4 * (l1 - l2)) + 0.0000106 * Math.cos(l1 - l3) + -0.0000066 * Math.cos(l1 + π3 - 2 * Π - 2 * G)), 9.39657 * (1 + 0.0093848 * Math.cos(l1 - l2) + -0.0003116 * Math.cos(l2 - π3) + -0.0001744 * Math.cos(l2 - π4) + -0.0001442 * Math.cos(l2 - π2) + 0.0000553 * Math.cos(l2 - l3) + 0.0000523 * Math.cos(l1 - l3) + -0.0000290 * Math.cos(2 * (l1 - l2)) + 0.0000164 * Math.cos(2 * (l2 - ω2)) + 0.0000107 * Math.cos(l1 - 2 * l3 + π3) + -0.0000102 * Math.cos(l2 - π1) + -0.0000091 * Math.cos(2 * (l1 - l3))), 14.98832 * (1 + -0.0014388 * Math.cos(l3 - π3) + -0.0007917 * Math.cos(l3 - π4) + 0.0006342 * Math.cos(l2 - l3) + -0.0001761 * Math.cos(2 * (l3 - l4)) + 0.0000294 * Math.cos(l3 - l4) + -0.0000156 * Math.cos(3 * (l3 - l4)) + 0.0000156 * Math.cos(l1 - l3) + -0.0000153 * Math.cos(l1 - l2) + 0.000007 * Math.cos(2 * l2 - 3 * l3 + π3) + -0.0000051 * Math.cos(l3 + π3 - 2 * Π - 2 * G)), 26.36273 * (1 + -0.0073546 * Math.cos(l4 - π4) + 0.0001621 * Math.cos(l4 - π3) + 0.0000974 * Math.cos(l3 - l4) + -0.0000543 * Math.cos(l4 + π4 - 2 * Π - 2 * G) + -0.0000271 * Math.cos(2 * (l4 - π4)) + 0.0000182 * Math.cos(l4 - Π) + 0.0000177 * Math.cos(2 * (l3 - l4)) + -0.0000167 * Math.cos(2 * l4 - ψ - ω4) + 0.0000167 * Math.cos(ψ - ω4) + -0.0000155 * Math.cos(2 * (l4 - Π - G)) + 0.0000142 * Math.cos(2 * (l4 - ψ)) + 0.0000105 * Math.cos(l1 - l4) + 0.0000092 * Math.cos(l2 - l4) + -0.0000089 * Math.cos(l4 - Π - G) + -0.0000062 * Math.cos(l4 + π4 - 2 * Π - 3 * G) + 0.0000048 * Math.cos(2 * (l4 - ω4)))];
    // p. 311
    var T0 = (jde - 2433282.423) / base.JulianCentury;
    var P = (1.3966626 * p + 0.0003088 * p * T0) * T0;
    for (var i in L) {
      L[i] += P;
    }
    ψ += P;
    var T = (jde - base.J1900) / base.JulianCentury;
    I = 3.120262 * p + 0.0006 * p * T;
    for (var _i in L) {
      var _base$sincos14 = base.sincos(L[_i] - ψ),
          sLψ = _base$sincos14[0],
          cLψ = _base$sincos14[1];

      var _base$sincos15 = base.sincos(B[_i]),
          sB = _base$sincos15[0],
          cB = _base$sincos15[1];

      X[_i] = R[_i] * cLψ * cB;
      Y[_i] = R[_i] * sLψ * cB;
      Z[_i] = R[_i] * sB;
    }
  })();

  Z[4] = 1;
  // p. 312
  var A = new Array(5).fill(0);
  var B = new Array(5).fill(0);
  var C = new Array(5).fill(0);

  var _base$sincos16 = base.sincos(I),
      sI = _base$sincos16[0],
      cI = _base$sincos16[1];

  var Ω = planetelements.node(planetelements.jupiter, jde);

  var _base$sincos17 = base.sincos(Ω),
      sΩ = _base$sincos17[0],
      cΩ = _base$sincos17[1];

  var _base$sincos18 = base.sincos(ψ - Ω),
      sΦ = _base$sincos18[0],
      cΦ = _base$sincos18[1];

  var _base$sincos19 = base.sincos(planetelements.inc(planetelements.jupiter, jde)),
      si = _base$sincos19[0],
      ci = _base$sincos19[1];

  var _base$sincos20 = base.sincos(λ0),
      sλ0 = _base$sincos20[0],
      cλ0 = _base$sincos20[1];

  var _base$sincos21 = base.sincos(β0),
      sβ0 = _base$sincos21[0],
      cβ0 = _base$sincos21[1];

  for (var i in A) {
    var a0 = void 0,
        b0 = void 0;
    // step 1
    var a = X[i];
    var b = Y[i] * cI - Z[i] * sI;
    var c = Y[i] * sI + Z[i] * cI;
    // step 2
    a0 = a * cΦ - b * sΦ;
    b = a * sΦ + b * cΦ;
    a = a0;
    // step 3
    b0 = b * ci - c * si;
    c = b * si + c * ci;
    b = b0;
    // step 4
    a0 = a * cΩ - b * sΩ;
    b = a * sΩ + b * cΩ;
    a = a0;
    // step 5
    a0 = a * sλ0 - b * cλ0;
    b = a * cλ0 + b * sλ0;
    a = a0;
    // step 6
    A[i] = a;
    B[i] = c * sβ0 + b * cβ0;
    C[i] = c * cβ0 - b * sβ0;
  }

  var _base$sincos22 = base.sincos(Math.atan2(A[4], C[4])),
      sD = _base$sincos22[0],
      cD = _base$sincos22[1];
  // p. 313


  for (var _i2 = 0; _i2 < 4; _i2++) {
    var x = A[_i2] * cD - C[_i2] * sD;
    var y = A[_i2] * sD + C[_i2] * cD;
    var z = B[_i2];
    // differential light time
    var d = x / R[_i2];
    x += Math.abs(z) / k[_i2] * Math.sqrt(1 - d * d);
    // perspective effect
    var W = Δ / (Δ + z / 2095);
    pos[_i2] = new XY(x * W, y * W);
  }
  return pos;
}

export default {
  io: io,
  europa: europa,
  ganymede: ganymede,
  callisto: callisto,
  positions: positions,
  e5: e5
};