astronomia/es/illum.js

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module illum
 */
/**
 * Illum: Chapter 41, Illuminated Fraction of the Disk and Magnitude of a Planet.
 *
 * Also see functions `illuminated` and `limb` in package base.  While this
 * chapter title includes "illumnated fraction," the function for computing
 * illuminated fraction given a phase angle is `base.illuminated`.
 * `base.limb` is the function mentioned at the bottom of p. 283.0
 */

import base from './base';

/**
 * PhaseAngle computes the phase angle of a planet.
 *
 * Argument r is planet's distance to Sun, Δ its distance to Earth, and R
 * the distance from Sun to Earth.  All distances in AU.
 *
 * Result in radians.
 */
export function phaseAngle(r, Δ, R) {
  // (r, Δ, R float64)  float64
  return Math.acos((r * r + Δ * Δ - R * R) / (2 * r * Δ));
}

/**
 * Fraction computes the illuminated fraction of the disk of a planet.
 *
 * Argument r is planet's distance to Sun, Δ its distance to Earth, and R
 * the distance from Sun to Earth.  All distances in AU.
 */
export function fraction(r, Δ, R) {
  // (r, Δ, R float64)  float64
  // (41.2) p. 283
  var s = r + Δ;
  return (s * s - R * R) / (4 * r * Δ);
}

/**
 * PhaseAngle2 computes the phase angle of a planet.
 *
 * Arguments L, B, R are heliocentric ecliptical coordinates of the planet.
 * L0, R0 are longitude and radius for Earth, Δ is distance from Earth to
 * the planet.  All distances in AU, angles in radians.
 *
 * The phase angle result is in radians.
 */
export function phaseAngle2(L, B, R, L0, R0, Δ) {
  // (L, B, R, L0, R0, Δ float64)  float64
  // (41.3) p. 283
  return Math.acos((R - R0 * Math.cos(B) * Math.cos(L - L0)) / Δ);
}

/**
 * PhaseAngle3 computes the phase angle of a planet.
 *
 * Arguments L, B are heliocentric ecliptical longitude and latitude of the
 * planet.  x, y, z are cartesian coordinates of the planet, Δ is distance
 * from Earth to the planet.  All distances in AU, angles in radians.
 *
 * The phase angle result is in radians.
 */
export function phaseAngle3(L, B, x, y, z, Δ) {
  // (L, B, x, y, z, Δ float64)  float64
  // (41.4) p. 283
  var _base$sincos = base.sincos(L),
      sL = _base$sincos[0],
      cL = _base$sincos[1];

  var _base$sincos2 = base.sincos(B),
      sB = _base$sincos2[0],
      cB = _base$sincos2[1];

  return Math.acos((x * cB * cL + y * cB * sL + z * sB) / Δ);
}

var p = Math.PI / 180;

/**
 * FractionVenus computes an approximation of the illumanted fraction of Venus.
 */
export function fractionVenus(jde) {
  // (jde float64)  float64
  var T = base.J2000Century(jde);
  var V = 261.51 * p + 22518.443 * p * T;
  var M = 177.53 * p + 35999.05 * p * T;
  var N = 50.42 * p + 58517.811 * p * T;
  var W = V + 1.91 * p * Math.sin(M) + 0.78 * p * Math.sin(N);
  var Δ = Math.sqrt(1.52321 + 1.44666 * Math.cos(W));
  var s = 0.72333 + Δ;
  return (s * s - 1) / 2.89332 / Δ;
}

/**
 * Mercury computes the visual magnitude of Mercury.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function mercury(r, Δ, i) {
  // (r, Δ, i float64)  float64
  var s = i - 50 * p;
  return 1.16 + 5 * Math.log10(r * Δ) + 0.02838 / p * s + 0.0001023 / p / p * s * s;
}

/**
 * Venus computes the visual magnitude of Venus.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function venus(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return -4 + 5 * Math.log10(r * Δ) + (0.01322 / p + 0.0000004247 / p / p / p * i * i) * i;
}

/**
 * Mars computes the visual magnitude of Mars.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function mars(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return -1.3 + 5 * Math.log10(r * Δ) + 0.01486 / p * i;
}

/**
 * Jupiter computes the visual magnitude of Jupiter.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function jupiter(r, Δ) {
  // (r, Δ float64)  float64
  return -8.93 + 5 * Math.log10(r * Δ);
}

/**
 * Saturn computes the visual magnitude of Saturn.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 * B is the Saturnicentric latitude of the Earth referred to the plane of
 * Saturn's ring. ΔU is the difference between the Saturnicentric longitudes
 * of the Sun and the Earth, measured in the plane of the ring.
 * You can use saturndisk.Disk() to obtain B and ΔU.
 */
export function saturn(r, Δ, B, ΔU) {
  // (r, Δ, B, ΔU float64)  float64
  var s = Math.sin(Math.abs(B));
  return -8.68 + 5 * Math.log10(r * Δ) + 0.044 / p * Math.abs(ΔU) - 2.6 * s + 1.25 * s * s;
}

/**
 * Uranus computes the visual magnitude of Uranus.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function uranus(r, Δ) {
  // (r, Δ float64)  float64
  return -6.85 + 5 * Math.log10(r * Δ);
}

/**
 * Neptune computes the visual magnitude of Neptune.
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function neptune(r, Δ) {
  // (r, Δ float64)  float64
  return -7.05 + 5 * Math.log10(r * Δ);
}

/**
 * Mercury84 computes the visual magnitude of Mercury.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function mercury84(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return base.horner(i, -0.42 + 5 * Math.log10(r * Δ), 0.038 / p, -0.000273 / p / p, 0.000002 / p / p / p);
}

/**
 * Venus84 computes the visual magnitude of Venus.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function venus84(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return base.horner(i, -4.4 + 5 * Math.log10(r * Δ), 0.0009 / p, -0.000239 / p / p, 0.00000065 / p / p / p);
}

/**
 * Mars84 computes the visual magnitude of Mars.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function mars84(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return -1.52 + 5 * Math.log10(r * Δ) + 0.016 / p * i;
}

/**
 * Jupiter84 computes the visual magnitude of Jupiter.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth,
 * and i the phase angle in radians.
 */
export function jupiter84(r, Δ, i) {
  // (r, Δ, i float64)  float64
  return -9.4 + 5 * Math.log10(r * Δ) + 0.005 / p * i;
}

/**
 * Saturn84 computes the visual magnitude of Saturn.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 * B is the Saturnicentric latitude of the Earth referred to the plane of
 * Saturn's ring. ΔU is the difference between the Saturnicentric longitudes
 * of the Sun and the Earth, measured in the plane of the ring.
 */
export function saturn84(r, Δ, B, ΔU) {
  // (r, Δ, B, ΔU float64)  float64
  var s = Math.sin(Math.abs(B));
  return -8.88 + 5 * Math.log10(r * Δ) + 0.044 / p * Math.abs(ΔU) - 2.6 * s + 1.25 * s * s;
}

/**
 * Uranus84 computes the visual magnitude of Uranus.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function uranus84(r, Δ) {
  // (r, Δ float64)  float64
  return -7.19 + 5 * Math.log10(r * Δ);
}

/**
 * Neptune84 computes the visual magnitude of Neptune.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function neptune84(r, Δ) {
  // (r, Δ float64)  float64
  return -6.87 + 5 * Math.log10(r * Δ);
}

/**
 * Pluto84 computes the visual magnitude of Pluto.
 *
 * The formula is that adopted in "Astronomical Almanac" in 1984.0
 *
 * Argument r is the planet's distance from the Sun, Δ the distance from Earth.
 */
export function pluto84(r, Δ) {
  // (r, Δ float64)  float64
  return -1 + 5 * Math.log10(r * Δ);
}

export default {
  phaseAngle: phaseAngle,
  fraction: fraction,
  phaseAngle2: phaseAngle2,
  phaseAngle3: phaseAngle3,
  fractionVenus: fractionVenus,
  mercury: mercury,
  venus: venus,
  mars: mars,
  jupiter: jupiter,
  saturn: saturn,
  uranus: uranus,
  neptune: neptune,
  mercury84: mercury84,
  venus84: venus84,
  mars84: mars84,
  jupiter84: jupiter84,
  saturn84: saturn84,
  uranus84: uranus84,
  neptune84: neptune84,
  pluto84: pluto84
};