astronomia
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An astronomical library
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JavaScript
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module jupitermoons
*/
/**
* Jupitermoons: Chapter 44, Positions of the Satellites of Jupiter.
*/
import base from './base.js'
import planetelements from './planetelements.js'
import solar from './solar.js'
import { Planet } from './planetposition.js' // eslint-disable-line no-unused-vars
// Moon names in order of position in Array
export const io = 0
export const europa = 1
export const ganymede = 2
export const callisto = 3
const 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) {
const d = jde - base.J2000
const p = Math.PI / 180
const V = 172.74 * p + 0.00111588 * p * d
const M = 357.529 * p + 0.9856003 * p * d
const sV = Math.sin(V)
const N = 20.02 * p + 0.0830853 * p * d + 0.329 * p * sV
const J = 66.115 * p + 0.9025179 * p * d - 0.329 * p * sV
const [sM, cM] = base.sincos(M)
const [sN, cN] = base.sincos(N)
const [s2M, c2M] = base.sincos(2 * M)
const [s2N, c2N] = base.sincos(2 * N)
const A = 1.915 * p * sM + 0.02 * p * s2M
const B = 5.555 * p * sN + 0.168 * p * s2N
const K = J + A - B
const R = 1.00014 - 0.01671 * cM - 0.00014 * c2M
const r = 5.20872 - 0.25208 * cN - 0.00611 * c2N
const [sK, cK] = base.sincos(K)
const Δ = Math.sqrt(r * r + R * R - 2 * r * R * cK)
const ψ = Math.asin(R / Δ * sK)
const λ = 34.35 * p + 0.083091 * p * d + 0.329 * p * sV + B
const DS = 3.12 * p * Math.sin(λ + 42.8 * p)
const 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)
const dd = d - Δ / 173
const u1 = 163.8069 * p + 203.4058646 * p * dd + ψ - B
const u2 = 358.414 * p + 101.2916335 * p * dd + ψ - B
const u3 = 5.7176 * p + 50.234518 * p * dd + ψ - B
const u4 = 224.8092 * p + 21.48798 * p * dd + ψ - B
const G = 331.18 * p + 50.310482 * p * dd
const H = 87.45 * p + 21.569231 * p * dd
const [s212, c212] = base.sincos(2 * (u1 - u2))
const [s223, c223] = base.sincos(2 * (u2 - u3))
const [sG, cG] = base.sincos(G)
const [sH, cH] = base.sincos(H)
const c1 = 0.473 * p * s212
const c2 = 1.065 * p * s223
const c3 = 0.165 * p * sG
const c4 = 0.843 * p * sH
const r1 = 5.9057 - 0.0244 * c212
const r2 = 9.3966 - 0.0882 * c223
const r3 = 14.9883 - 0.0216 * cG
const r4 = 26.3627 - 0.1939 * cH
const sDE = Math.sin(DE)
const xy = function (u, r) {
const [su, cu] = base.sincos(u)
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 {Planet} earth - VSOP87 Planet earth
* @param {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
let λ0, β0, t
let Δ = 5.0
;(function () {
const { lon, lat, range } = solar.trueVSOP87(earth, jde)
const [s, β, R] = [lon, lat, range]
const [ss, cs] = base.sincos(s)
const sβ = Math.sin(β)
let τ = base.lightTime(Δ)
let x = 0
let y = 0
let z = 0
function f () {
const { lon, lat, range } = jupiter.position(jde - τ)
const [sl, cl] = base.sincos(lon)
const [sb, cb] = base.sincos(lat)
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
})()
const p = Math.PI / 180
const l1 = 106.07719 * p + 203.48895579 * p * t
const l2 = 175.73161 * p + 101.374724735 * p * t
const l3 = 120.55883 * p + 50.317609207 * p * t
const l4 = 84.44459 * p + 21.571071177 * p * t
const π1 = 97.0881 * p + 0.16138586 * p * t
const π2 = 154.8663 * p + 0.04726307 * p * t
const π3 = 188.184 * p + 0.00712734 * p * t
const π4 = 335.2868 * p + 0.00184 * p * t
const ω1 = 312.3346 * p - 0.13279386 * p * t
const ω2 = 100.4411 * p - 0.03263064 * p * t
const ω3 = 119.1942 * p - 0.00717703 * p * t
const ω4 = 322.6186 * p - 0.00175934 * p * t
const 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)
const Φλ = 199.6766 * p + 0.1737919 * p * t
let ψ = 316.5182 * p - 0.00000208 * p * t
const G = 30.23756 * p + 0.0830925701 * p * t + Γ
const Gʹ = 31.97853 * p + 0.0334597339 * p * t
const Π = 13.469942 * p
const 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)
const 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))
const 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))
const 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)
const L1 = l1 + Σ1
const L2 = l2 + Σ2
const L3 = l3 + Σ3
const L4 = l4 + Σ4
// variables assigned in following block
let I
const X = new Array(5).fill(0)
const Y = new Array(5).fill(0)
const Z = new Array(5).fill(0)
let R
;(function () {
const L = [L1, L2, L3, L4]
const 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
const T0 = (jde - 2433282.423) / base.JulianCentury
const P = (1.3966626 * p + 0.0003088 * p * T0) * T0
for (const i in L) {
L[i] += P
}
ψ += P
const T = (jde - base.J1900) / base.JulianCentury
I = 3.120262 * p + 0.0006 * p * T
for (const i in L) {
const [sLψ, cLψ] = base.sincos(L[i] - ψ)
const [sB, cB] = base.sincos(B[i])
X[i] = R[i] * cLψ * cB
Y[i] = R[i] * sLψ * cB
Z[i] = R[i] * sB
}
})()
Z[4] = 1
// p. 312
const A = new Array(5).fill(0)
const B = new Array(5).fill(0)
const C = new Array(5).fill(0)
const [sI, cI] = base.sincos(I)
const Ω = planetelements.node(planetelements.jupiter, jde)
const [sΩ, cΩ] = base.sincos(Ω)
const [sΦ, cΦ] = base.sincos(ψ - Ω)
const [si, ci] = base.sincos(planetelements.inc(planetelements.jupiter, jde))
const [sλ0, cλ0] = base.sincos(λ0)
const [sβ0, cβ0] = base.sincos(β0)
for (const i in A) {
let a0
// step 1
let a = X[i]
let b = Y[i] * cI - Z[i] * sI
let c = Y[i] * sI + Z[i] * cI
// step 2
a0 = a * cΦ - b * sΦ
b = a * sΦ + b * cΦ
a = a0
// step 3
const 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
}
const [sD, cD] = base.sincos(Math.atan2(A[4], C[4]))
// p. 313
for (let i = 0; i < 4; i++) {
let x = A[i] * cD - C[i] * sD
const y = A[i] * sD + C[i] * cD
const z = B[i]
// differential light time
const d = x / R[i]
x += Math.abs(z) / k[i] * Math.sqrt(1 - d * d)
// perspective effect
const W = Δ / (Δ + z / 2095)
pos[i] = new XY(x * W, y * W)
}
return pos
}
export default {
io,
europa,
ganymede,
callisto,
positions,
e5
}