astronomia/lib/coord.cjs

An astronomical library

'use strict';

Object.defineProperty(exports, '__esModule', { value: true });

var base = require('./base.cjs');
var sexagesimal = require('./sexagesimal.cjs');
require('./globe.cjs');

/**
 * @copyright 2013 Sonia Keys
 * @copyright 2016 commenthol
 * @license MIT
 * @module coord
 */

/**
 * @typedef {object} LonLat
 * @property {Number} lon - Longitude (λ) in radians
 * @property {Number} lat - Latitude (β) in radians
 */

/**
* Ecliptic coordinates are referenced to the plane of the ecliptic.
*/
class Ecliptic {
  /**
   * IMPORTANT: Longitudes are measured *positively* westwards
   * e.g. Washington D.C. +77°04; Vienna -16°23'
   * @param {Number|LonLat} [lon] - Longitude (λ) in radians
   * @param {Number} [lat] - Latitude (β) in radians
   */
  constructor (lon, lat) {
    if (typeof lon === 'object') {
      lat = lon.lat;
      lon = lon.lon;
    }
    this.lon = lon || 0;
    this.lat = lat || 0;
  }

  /**
   * converts ecliptic coordinates to equatorial coordinates.
   * @param {Number} ε - Obliquity
   * @returns {Equatorial}
   */
  toEquatorial (ε) {
    const [εsin, εcos] = base["default"].sincos(ε);
    const [sβ, cβ] = base["default"].sincos(this.lat);
    const [sλ, cλ] = base["default"].sincos(this.lon);
    let ra = Math.atan2(sλ * εcos - (sβ / cβ) * εsin, cλ); // (13.3) p. 93
    if (ra < 0) {
      ra += 2 * Math.PI;
    }
    const dec = Math.asin(sβ * εcos + cβ * εsin * sλ); // (13.4) p. 93
    return new Equatorial(ra, dec)
  }
}

/**
 * Equatorial coordinates are referenced to the Earth's rotational axis.
 */
class Equatorial {
  /**
   * @param {Number} ra - (float) Right ascension (α) in radians
   * @param {Number} dec - (float) Declination (δ) in radians
   */
  constructor (ra = 0, dec = 0) {
    this.ra = ra;
    this.dec = dec;
  }

  /**
   * EqToEcl converts equatorial coordinates to ecliptic coordinates.
   * @param {Number} ε - Obliquity
   * @returns {Ecliptic}
   */
  toEcliptic (ε) {
    const [εsin, εcos] = base["default"].sincos(ε);
    const [sα, cα] = base["default"].sincos(this.ra);
    const [sδ, cδ] = base["default"].sincos(this.dec);
    const lon = Math.atan2(sα * εcos + (sδ / cδ) * εsin, cα); // (13.1) p. 93
    const lat = Math.asin(sδ * εcos - cδ * εsin * sα); // (13.2) p. 93
    return new Ecliptic(lon, lat)
  }

  /**
   * EqToHz computes Horizontal coordinates from equatorial coordinates.
   *
   * Argument g is the location of the observer on the Earth.  Argument st
   * is the sidereal time at Greenwich.
   *
   * Sidereal time must be consistent with the equatorial coordinates.
   * If coordinates are apparent, sidereal time must be apparent as well.
   *
   * @param {GlobeCoord} g - coordinates of observer on Earth
   * @param {Number} st - sidereal time at Greenwich at time of observation
   * @returns {Horizontal}
   */
  toHorizontal (g, st) {
    const H = new sexagesimal["default"].Time(st).rad() - g.lon - this.ra;
    const [sH, cH] = base["default"].sincos(H);
    const [sφ, cφ] = base["default"].sincos(g.lat);
    const [sδ, cδ] = base["default"].sincos(this.dec);
    const azimuth = Math.atan2(sH, cH * sφ - (sδ / cδ) * cφ); // (13.5) p. 93
    const altitude = Math.asin(sφ * sδ + cφ * cδ * cH); // (13.6) p. 93
    return new Horizontal(azimuth, altitude)
  }

  /**
   * EqToGal converts equatorial coordinates to galactic coordinates.
   *
   * Equatorial coordinates must be referred to the standard equinox of B1950.0.
   * For conversion to B1950, see package precess and utility functions in
   * package "common".
   *
   * @returns {Galactic}
   */
  toGalactic () {
    const [sdα, cdα] = base["default"].sincos(galacticNorth1950.ra - this.ra);
    const [sgδ, cgδ] = base["default"].sincos(galacticNorth1950.dec);
    const [sδ, cδ] = base["default"].sincos(this.dec);
    const x = Math.atan2(sdα, cdα * sgδ - (sδ / cδ) * cgδ); // (13.7) p. 94
    // (galactic0Lon1950 + 1.5*math.Pi) = magic number of 303 deg
    const lon = (galactic0Lon1950 + 1.5 * Math.PI - x) % (2 * Math.PI); // (13.8) p. 94
    const lat = Math.asin(sδ * sgδ + cδ * cgδ * cdα);
    return new Galactic(lon, lat)
  }
}

/**
 * Horizontal coordinates are referenced to the local horizon of an observer
 * on the surface of the Earth.
 * @param {Number} az - Azimuth (A) in radians
 * @param {Number} alt - Altitude (h) in radians
 */
class Horizontal {
  constructor (az = 0, alt = 0) {
    this.az = az;
    this.alt = alt;
  }

  /**
   * transforms horizontal coordinates to equatorial coordinates.
   *
   * Sidereal time must be consistent with the equatorial coordinates.
   * If coordinates are apparent, sidereal time must be apparent as well.
   * @param {GlobeCoord} g - coordinates of observer on Earth (lat, lon)
   * @param {Number} st - sidereal time at Greenwich at time of observation.
   * @returns {Equatorial} (right ascension, declination)
   */
  toEquatorial (g, st) {
    const [sA, cA] = base["default"].sincos(this.az);
    const [sh, ch] = base["default"].sincos(this.alt);
    const [sφ, cφ] = base["default"].sincos(g.lat);
    const H = Math.atan2(sA, cA * sφ + sh / ch * cφ);
    const ra = base["default"].pmod(new sexagesimal["default"].Time(st).rad() - g.lon - H, 2 * Math.PI);
    const dec = Math.asin(sφ * sh - cφ * ch * cA);
    return new Equatorial(ra, dec)
  }
}

/**
 * Galactic coordinates are referenced to the plane of the Milky Way.
 * @param {Number} lon - Longitude (l) in radians
 * @param {Number} lat - Latitude (b) in radians
 */
class Galactic {
  constructor (lon = 0, lat = 0) {
    this.lon = lon;
    this.lat = lat;
  }

  /**
   * GalToEq converts galactic coordinates to equatorial coordinates.
   *
   * Resulting equatorial coordinates will be referred to the standard equinox of
   * B1950.0.  For subsequent conversion to other epochs, see package precess and
   * utility functions in package meeus.
   *
   * @returns {Equatorial} (right ascension, declination)
   */
  toEquatorial () {
    // (-galactic0Lon1950 - math.Pi/2) = magic number of -123 deg
    const [sdLon, cdLon] = base["default"].sincos(this.lon - galactic0Lon1950 - Math.PI / 2);
    const [sgδ, cgδ] = base["default"].sincos(galacticNorth1950.dec);
    const [sb, cb] = base["default"].sincos(this.lat);
    const y = Math.atan2(sdLon, cdLon * sgδ - (sb / cb) * cgδ);
    // (galacticNorth1950.RA.Rad() - math.Pi) = magic number of 12.25 deg
    const ra = base["default"].pmod(y + galacticNorth1950.ra - Math.PI, 2 * Math.PI);
    const dec = Math.asin(sb * sgδ + cb * cgδ * cdLon);
    return new Equatorial(ra, dec)
  }
}

/**
* equatorial coords for galactic north
* IAU B1950.0 coordinates of galactic North Pole
*/
const galacticNorth = new Equatorial(
  new sexagesimal["default"].RA(12, 49, 0).rad(),
  27.4 * Math.PI / 180
);
const galacticNorth1950 = galacticNorth;

/**
* Galactic Longitude 0°
* Meeus gives 33 as the origin of galactic longitudes relative to the
* ascending node of of the galactic equator.  33 + 90 = 123, the IAU
* value for origin relative to the equatorial pole.
*/
const galacticLon0 = 33 * Math.PI / 180;
const galactic0Lon1950 = galacticLon0;

var coord = {
  Ecliptic,
  Equatorial,
  Horizontal,
  Galactic,
  galacticNorth,
  galacticNorth1950,
  galacticLon0,
  galactic0Lon1950
};

exports.Ecliptic = Ecliptic;
exports.Equatorial = Equatorial;
exports.Galactic = Galactic;
exports.Horizontal = Horizontal;
exports["default"] = coord;
exports.galactic0Lon1950 = galactic0Lon1950;
exports.galacticLon0 = galacticLon0;
exports.galacticNorth = galacticNorth;
exports.galacticNorth1950 = galacticNorth1950;