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meeus algorithm
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meeus.js
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/* 0 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module base
*/
/**
* Base: Functions and other definitions useful with multiple packages.
*
* Base contains various definitions and support functions useful in multiple
* chapters.
*
* Bessellian and Julian Year
*
* Chapter 21, Precession actually contains these definitions. They are moved
* here because of their general utility.
*
* Chapter 22, Nutation contains the function for Julian centuries since J2000.
*
* Phase angle functions
*
* Two functions, Illuminated and Limb, concern the illumnated phase of a body
* and are given in two chapters, 41 an 48. They are collected here because
* the identical functions apply in both chapters.
*
* General purpose math functions
*
* SmallAngle is recommended in chapter 17, p. 109.
*
* PMod addresses the issue on p. 7, chapter 1, in the section "Trigonometric
* functions of large angles", but the function is not written to be specific
* to angles and so has more general utility.
*
* Horner is described on p. 10, chapter 1.
*
* FloorDiv and FloorDiv64 are optimizations for the INT function described
* on p. 60, chapter 7.
*/
var M = exports;
// ---- constants ----
/** K is the Gaussian gravitational constant. */
M.K = 0.01720209895;
// K from ch 33, p. 228, for example
/** AU is one astronomical unit in km. */
M.AU = 149597870;
// from Appendix I, p, 407.
/** SOblJ2000 sine obliquity at J2000. */
M.SOblJ2000 = 0.397777156;
/** COblJ2000 cosine obliquity at J2000. */
M.COblJ2000 = 0.917482062;
// SOblJ2000, COblJ2000 from ch 33, p. 228, for example
/**
* lightTime returns time for light to travel a given distance.
* `dist` is distance in to earth in AU. √(x² + y² + z²)
* Result in seconds of time.
* @param {Number} dist - distance in to earth in AU
* @returns {Number} time for light to travel a given distance in seconds
*/
M.lightTime = function (dist) {
// Formula given as (33.3) p. 224.
return 0.0057755183 * dist;
};
// ---- julian ----
/**
* Julian and Besselian years described in chapter 21, Precession.
* T, Julian centuries since J2000 described in chapter 22, Nutation.
*/
/** JMod is the Julian date of the modified Julian date epoch. */
M.JMod = 2400000.5;
/** J2000 is the Julian date corresponding to January 1.5, year 2000. */
M.J2000 = 2451545.0;
// Julian days of common epochs.
// B1900, B1950 from p. 133
/** Julian days of Julian epoch 1900 */
M.J1900 = 2415020.0;
/** Julian days of Besselian epoch 1900 */
M.B1900 = 2415020.3135;
/** Julian days of Besselian epoch 1950 */
M.B1950 = 2433282.4235;
// JulianYear and other common periods
/** JulianYear in days */
M.JulianYear = 365.25; // days
/** JulianCentury in days */
M.JulianCentury = 36525; // days
/** BesselianYear in days; equals mean tropical year */
M.BesselianYear = 365.2421988; // days
/** Mean sidereal year */
M.meanSiderealYear = 365.25636; // days
/**
* JulianYearToJDE returns the Julian ephemeris day for a Julian year.
* @param {Number} jy - Julian year
* @returns {Number} jde - Julian ephemeris day
*/
M.JulianYearToJDE = function (jy) {
return M.J2000 + M.JulianYear * (jy - 2000);
};
/**
* JDEToJulianYear returns a Julian year for a Julian ephemeris day.
* @param {Number} jde - Julian ephemeris day
* @returns {Number} jy - Julian year
*/
M.JDEToJulianYear = function (jde) {
return 2000 + (jde - M.J2000) / M.JulianYear;
};
/**
* BesselianYearToJDE returns the Julian ephemeris day for a Besselian year.
* @param {Number} by - Besselian year
* @returns {Number} jde - Julian ephemeris day
*/
M.BesselianYearToJDE = function (by) {
return M.B1900 + M.BesselianYear * (by - 1900);
};
/**
* JDEToBesselianYear returns the Besselian year for a Julian ephemeris day.
* @param {Number} jde - Julian ephemeris day
* @returns {Number} by - Besselian year
*/
M.JDEToBesselianYear = function (jde) {
return 1900 + (jde - M.B1900) / M.BesselianYear;
};
/**
* J2000Century returns the number of Julian centuries since J2000.
*
* The quantity appears as T in a number of time series.
* @param {Number} jde - Julian ephemeris day
* @returns {Number} number of Julian centuries since J2000
*/
M.J2000Century = function (jde) {
// The formula is given in a number of places in the book, for example
// (12.1) p. 87.
// (22.1) p. 143.
// (25.1) p. 163.
return (jde - M.J2000) / M.JulianCentury;
};
// ---- phase ----
/**
* illuminated returns the illuminated fraction of a body's disk.
*
* The illuminated body can be the Moon or a planet.
*
* @param {Number} i - phase angle in radians.
* @returns {Number} illuminated fraction of a body's disk.
*/
M.illuminated = function (i) {
// (41.1) p. 283, also (48.1) p. 345.
return (1 + Math.cos(i)) * 0.5;
};
/**
* celestial coordinates in right ascension and declination
* or ecliptic coordinates in longitude and latitude
*
* @param {number} ra - right ascension (or longitude)
* @param {number} dec - declination (or latitude)
* @param {number} [range] - distance
* @param {number} [elongation] - elongation
*/
function Coord(ra /* lon */, dec /* lat */, range, elongation) {
this._ra = ra || 0;
this._dec = dec || 0;
this.range = range;
this.elongation = elongation;
Object.defineProperties(this, {
ra: {
get: function get() {
return this._ra;
},
set: function set(ra) {
this._ra = ra;
}
},
dec: {
get: function get() {
return this._dec;
},
set: function set(dec) {
this._dec = dec;
}
},
lon: {
get: function get() {
return this._ra;
},
set: function set(ra) {
this._ra = ra;
}
},
lat: {
get: function get() {
return this._dec;
},
set: function set(dec) {
this._dec = dec;
}
}
});
}
M.Coord = Coord;
/**
* Limb returns the position angle of the midpoint of an illuminated limb.
*
* The illuminated body can be the Moon or a planet.
*
* @param {base.Coord} equ - equatorial coordinates of the body `{ra, dec}` (in radians)
* @param {base.Coord} appSun - apparent coordinates of the Sun `{ra, dec}` (In radians).
* @returns {Number} position angle of the midpoint (in radians).
*/
M.limb = function (equ, appSun) {
var α = equ.ra;
var δ = equ.dec;
var α0 = appSun.ra;
var δ0 = appSun.dec;
// Mentioned in ch 41, p. 283. Formula (48.5) p. 346
var sδ = Math.sin(δ);
var cδ = Math.cos(δ);
var sδ0 = Math.sin(δ0);
var cδ0 = Math.cos(δ0);
var sα0α = Math.sin(α0 - α);
var cα0α = Math.cos(α0 - α);
var χ = Math.atan2(cδ0 * sα0α, sδ0 * cδ - cδ0 * sδ * cα0α);
if (χ < 0) {
χ += 2 * Math.PI;
}
return χ;
};
// ---- math ----
// In chapter 17, p. 109, Meeus recommends 10′.
/**
* SmallAngle is threshold used by various routines for switching between
* trigonometric functions and Pythagorean approximations.
*/
M.SmallAngle = 10 * Math.PI / 180 / 60; // about .003 radians
/** cosine of SmallAngle */
M.CosSmallAngle = Math.cos(M.SmallAngle); // about .999996
/**
* pmod returns a positive floating-point x mod y.
*
* For a positive argument y, it returns a value in the range [0,y).
*
* @param {Number} x
* @param {Number} y
* @returns {Number} x % y - The result may not be useful if y is negative.
*/
M.pmod = function (x, y) {
var r = x % y;
if (r < 0) {
r += y;
}
return r;
};
/**
* horner evaluates a polynomal with coefficients c at x. The constant
* term is c[0].
* @param {Number} x
* @param {Number|Number[]} c - coefficients
* @returns {Number}
*/
M.horner = function (x) {
for (var _len = arguments.length, c = Array(_len > 1 ? _len - 1 : 0), _key = 1; _key < _len; _key++) {
c[_key - 1] = arguments[_key];
}
if (Array.isArray(c[0])) {
c = c[0];
}
var i = c.length - 1;
var y = c[i];
while (i > 0) {
i--;
y = y * x + c[i];
}
return y;
};
/**
* FloorDiv returns the integer floor of the fractional value (x / y).
* @param {Number} x
* @param {Number} y
* @returns {Number} (int)
*/
M.floorDiv = function (x, y) {
var q = x / y;
return Math.floor(q);
};
/**
* Cmp compares two float64s and returns -1, 0, or 1 if a is <, ==, or > b,
* respectively.
* .
* @param {Number} a
* @param {Number} b
* @returns {Number} comparison result
*/
M.cmp = function (a, b) {
if (a < b) return -1;
if (a > b) return 1;
return 0;
};
/**
* shorthand function for Math.sin, Math.cos
* @param {Number} ε
* @returns {Number[]} [sin(ε), cos(ε)]
*/
M.sincos = function (ε) {
return [Math.sin(ε), Math.cos(ε)];
};
/**
* Convert degrees to radians
* @param {Number} deg - Angle in degrees
* @return {Number} Angle in radians
*/
M.toRad = function (deg) {
return Math.PI / 180.0 * deg;
};
/**
* Convert radians to degrees
* @param {Number} rad - Angle in radians
* @return {Number} Angle in degrees
*/
M.toDeg = function (rad) {
return 180.0 / Math.PI * rad;
};
/**
* separate fix `i` from fraction `f`
* @param {Number} float
* @returns {Array} [i, f]
* {Number} i - (int) fix value
* {Number} f - (float) fractional portion; always > 1
*/
M.modf = function (float) {
var i = Math.trunc(float);
var f = Math.abs(float - i);
return [i, f];
};
/**
* Rounds `float` value by precision
* @param {Number} float - value to round
* @param {Number} precision - (int) number of post decimal positions
* @return {Number} rounded `float`
*/
M.round = function (float, precision) {
precision = precision == undefined ? 14 : precision; // eslint-disable-line eqeqeq
return parseFloat(float.toFixed(precision), 10);
};
M.errorCode = function (msg, code) {
var err = new Error(msg);
err.code = code;
return err;
};
/***/ }),
/* 1 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module nutation
*/
/**
* Nutation: Chapter 22, Nutation and the Obliquity of the Ecliptic.
*/
var base = __webpack_require__(0);
var sexa = __webpack_require__(4);
var M = exports;
// Nutation: Chapter 22, Nutation and the Obliquity of the Ecliptic.
/**
* Nutation returns nutation in longitude (Δψ) and nutation in obliquity (Δε)
* for a given JDE.
*
* JDE = UT + ΔT, see package.
*
* Computation is by 1980 IAU theory, with terms < .0003″ neglected.
*
* Result units are radians.
*
* @param {number} jde - Julian ephemeris day
* @return {number[]} [Δψ, Δε] - [longitude, obliquity] in radians
*/
M.nutation = function (jde) {
var T = base.J2000Century(jde);
var D = base.horner(T, 297.85036, 445267.11148, -0.0019142, 1.0 / 189474) * Math.PI / 180;
var M = base.horner(T, 357.52772, 35999.050340, -0.0001603, -1.0 / 300000) * Math.PI / 180;
var N = base.horner(T, 134.96298, 477198.867398, 0.0086972, 1.0 / 5620) * Math.PI / 180;
var F = base.horner(T, 93.27191, 483202.017538, -0.0036825, 1.0 / 327270) * Math.PI / 180;
var Ω = base.horner(T, 125.04452, -1934.136261, 0.0020708, 1.0 / 450000) * Math.PI / 180;
var Δψ = 0;
var Δε = 0;
// sum in reverse order to accumulate smaller terms first
for (var i = table22A.length - 1; i >= 0; i--) {
var row = table22A[i];
var arg = row.d * D + row.m * M + row.n * N + row.f * F + row.ω * Ω;
var _base$sincos = base.sincos(arg),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
s = _base$sincos2[0],
c = _base$sincos2[1];
Δψ += s * (row.s0 + row.s1 * T);
Δε += c * (row.c0 + row.c1 * T);
}
Δψ *= 0.0001 / 3600 * (Math.PI / 180);
Δε *= 0.0001 / 3600 * (Math.PI / 180);
return [Δψ, Δε]; // (Δψ, Δε float)
};
/**
* ApproxNutation returns a fast approximation of nutation in longitude (Δψ)
* and nutation in obliquity (Δε) for a given JDE.
*
* Accuracy is 0.5″ in Δψ, 0.1″ in Δε.
*
* Result units are radians.
*
* @param {number} jde - Julian ephemeris day
* @return {number[]} [Δψ, Δε] - [longitude, obliquity] in radians
*/
M.approxNutation = function (jde) {
var T = (jde - base.J2000) / 36525;
var Ω = (125.04452 - 1934.136261 * T) * Math.PI / 180;
var L = (280.4665 + 36000.7698 * T) * Math.PI / 180;
var N = (218.3165 + 481267.8813 * T) * Math.PI / 180;
var _base$sincos3 = base.sincos(Ω),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sΩ = _base$sincos4[0],
cΩ = _base$sincos4[1];
var _base$sincos5 = base.sincos(2 * L),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
s2L = _base$sincos6[0],
c2L = _base$sincos6[1];
var _base$sincos7 = base.sincos(2 * N),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
s2N = _base$sincos8[0],
c2N = _base$sincos8[1];
var _base$sincos9 = base.sincos(2 * Ω),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
s2Ω = _base$sincos10[0],
c2Ω = _base$sincos10[1];
var Δψ = (-17.2 * sΩ - 1.32 * s2L - 0.23 * s2N + 0.21 * s2Ω) / 3600 * (Math.PI / 180);
var Δε = (9.2 * cΩ + 0.57 * c2L + 0.1 * c2N - 0.09 * c2Ω) / 3600 * (Math.PI / 180);
return [Δψ, Δε]; // (Δψ, Δε float)
};
/**
* MeanObliquity returns mean obliquity (ε₀) following the IAU 1980
* polynomial.
*
* Accuracy is 1″ over the range 1000 to 3000 years and 10″ over the range
* 0 to 4000 years.
*
* Result unit is radians.
*
* @param {number} jde - Julian ephemeris day
* @return {number} mean obliquity (ε₀)
*/
M.meanObliquity = function (jde) {
// (22.2) p. 147
return base.horner(base.J2000Century(jde), new sexa.Angle(false, 23, 26, 21.448).rad(), -46.815 / 3600 * (Math.PI / 180), -0.00059 / 3600 * (Math.PI / 180), 0.001813 / 3600 * (Math.PI / 180));
};
/**
* MeanObliquityLaskar returns mean obliquity (ε₀) following the Laskar
* 1986 polynomial.
*
* Accuracy over the range 1000 to 3000 years is .01″.
*
* Accuracy over the valid date range of -8000 to +12000 years is
* "a few seconds."
*
* Result unit is radians.
*
* @param {number} jde - Julian ephemeris day
* @return {number} mean obliquity (ε₀)
*/
M.meanObliquityLaskar = function (jde) {
// (22.3) p. 147
return base.horner(base.J2000Century(jde) * 0.01, new sexa.Angle(false, 23, 26, 21.448).rad(), -4680.93 / 3600 * (Math.PI / 180), -1.55 / 3600 * (Math.PI / 180), 1999.25 / 3600 * (Math.PI / 180), -51.38 / 3600 * (Math.PI / 180), -249.67 / 3600 * (Math.PI / 180), -39.05 / 3600 * (Math.PI / 180), 7.12 / 3600 * (Math.PI / 180), 27.87 / 3600 * (Math.PI / 180), 5.79 / 3600 * (Math.PI / 180), 2.45 / 3600 * (Math.PI / 180));
};
/**
* NutationInRA returns "nutation in right ascension" or "equation of the
* equinoxes."
*
* Result is an angle in radians.
*
* @param {number} jde - Julian ephemeris day
* @return {number} nutation in right ascension
*/
M.nutationInRA = function (jde) {
var _M$nutation = M.nutation(jde),
_M$nutation2 = _slicedToArray(_M$nutation, 2),
Δψ = _M$nutation2[0],
Δε = _M$nutation2[1];
var ε0 = M.meanObliquity(jde);
return Δψ * Math.cos(ε0 + Δε);
};
var table22A = function () {
var PROPS = 'd,m,n,f,ω,s0,s1,c0,c1'.split(',');
var tab = [[0, 0, 0, 0, 1, -171996, -174.2, 92025, 8.9], [-2, 0, 0, 2, 2, -13187, -1.6, 5736, -3.1], [0, 0, 0, 2, 2, -2274, -0.2, 977, -0.5], [0, 0, 0, 0, 2, 2062, 0.2, -895, 0.5], [0, 1, 0, 0, 0, 1426, -3.4, 54, -0.1], [0, 0, 1, 0, 0, 712, 0.1, -7, 0], [-2, 1, 0, 2, 2, -517, 1.2, 224, -0.6], [0, 0, 0, 2, 1, -386, -0.4, 200, 0], [0, 0, 1, 2, 2, -301, 0, 129, -0.1], [-2, -1, 0, 2, 2, 217, -0.5, -95, 0.3], [-2, 0, 1, 0, 0, -158, 0, 0, 0], [-2, 0, 0, 2, 1, 129, 0.1, -70, 0], [0, 0, -1, 2, 2, 123, 0, -53, 0], [2, 0, 0, 0, 0, 63, 0, 0, 0], [0, 0, 1, 0, 1, 63, 0.1, -33, 0], [2, 0, -1, 2, 2, -59, 0, 26, 0], [0, 0, -1, 0, 1, -58, -0.1, 32, 0], [0, 0, 1, 2, 1, -51, 0, 27, 0], [-2, 0, 2, 0, 0, 48, 0, 0, 0], [0, 0, -2, 2, 1, 46, 0, -24, 0], [2, 0, 0, 2, 2, -38, 0, 16, 0], [0, 0, 2, 2, 2, -31, 0, 13, 0], [0, 0, 2, 0, 0, 29, 0, 0, 0], [-2, 0, 1, 2, 2, 29, 0, -12, 0], [0, 0, 0, 2, 0, 26, 0, 0, 0], [-2, 0, 0, 2, 0, -22, 0, 0, 0], [0, 0, -1, 2, 1, 21, 0, -10, 0], [0, 2, 0, 0, 0, 17, -0.1, 0, 0], [2, 0, -1, 0, 1, 16, 0, -8, 0], [-2, 2, 0, 2, 2, -16, 0.1, 7, 0], [0, 1, 0, 0, 1, -15, 0, 9, 0], [-2, 0, 1, 0, 1, -13, 0, 7, 0], [0, -1, 0, 0, 1, -12, 0, 6, 0], [0, 0, 2, -2, 0, 11, 0, 0, 0], [2, 0, -1, 2, 1, -10, 0, 5, 0], [2, 0, 1, 2, 2, -8, 0, 3, 0], [0, 1, 0, 2, 2, 7, 0, -3, 0], [-2, 1, 1, 0, 0, -7, 0, 0, 0], [0, -1, 0, 2, 2, -7, 0, 3, 0], [2, 0, 0, 2, 1, -7, 0, 3, 0], [2, 0, 1, 0, 0, 6, 0, 0, 0], [-2, 0, 2, 2, 2, 6, 0, -3, 0], [-2, 0, 1, 2, 1, 6, 0, -3, 0], [2, 0, -2, 0, 1, -6, 0, 3, 0], [2, 0, 0, 0, 1, -6, 0, 3, 0], [0, -1, 1, 0, 0, 5, 0, 0, 0], [-2, -1, 0, 2, 1, -5, 0, 3, 0], [-2, 0, 0, 0, 1, -5, 0, 3, 0], [0, 0, 2, 2, 1, -5, 0, 3, 0], [-2, 0, 2, 0, 1, 4, 0, 0, 0], [-2, 1, 0, 2, 1, 4, 0, 0, 0], [0, 0, 1, -2, 0, 4, 0, 0, 0], [-1, 0, 1, 0, 0, -4, 0, 0, 0], [-2, 1, 0, 0, 0, -4, 0, 0, 0], [1, 0, 0, 0, 0, -4, 0, 0, 0], [0, 0, 1, 2, 0, 3, 0, 0, 0], [0, 0, -2, 2, 2, -3, 0, 0, 0], [-1, -1, 1, 0, 0, -3, 0, 0, 0], [0, 1, 1, 0, 0, -3, 0, 0, 0], [0, -1, 1, 2, 2, -3, 0, 0, 0], [2, -1, -1, 2, 2, -3, 0, 0, 0], [0, 0, 3, 2, 2, -3, 0, 0, 0], [2, -1, 0, 2, 2, -3, 0, 0, 0]];
return tab.map(function (row) {
var o = {};
PROPS.forEach(function (p, i) {
o[p] = row[i];
});
return o;
});
}();
/***/ }),
/* 2 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _typeof = typeof Symbol === "function" && typeof Symbol.iterator === "symbol" ? function (obj) { return typeof obj; } : function (obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; };
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module coord
*/
/**
* Coord: Chapter 13, Transformation of Coordinates.
*
* Transforms in this package are provided in two forms, function and method.
* The results of the two forms should be identical.
*
* The function forms pass all arguments and results as single values. These
* forms are best used when you are transforming a single pair of coordinates
* and wish to avoid memory allocation.
*
* The method forms take and return pointers to structs. These forms are best
* used when you are transforming multiple coordinates and can reuse one or
* more of the structs. In this case reuse of structs will minimize
* allocations, and the struct pointers will pass more efficiently on the
* stack. These methods transform their arguments, placing the result in
* the receiver. The receiver is then returned for convenience.
*
* A number of the functions take sine and cosine of the obliquity of the
* ecliptic. This becomes an advantage when you doing multiple transformations
* with the same obliquity. The efficiency of computing sine and cosine once
* and reuse these values far outweighs the overhead of passing one number as
* opposed to two.
*/
var base = __webpack_require__(0);
var sexa = __webpack_require__(4);
var M = exports;
/**
* Ecliptic coordinates are referenced to the plane of the ecliptic.
*/
var Ecliptic = function () {
/**
* IMPORTANT: Longitudes are measured *positively* westwards
* e.g. Washington D.C. +77°04; Vienna -16°23'
* @param {Number} lon - Longitude (λ) in radians
* @param {Number} lat - Latitude (β) in radians
*/
function Ecliptic(lon, lat) {
_classCallCheck(this, Ecliptic);
if ((typeof lon === 'undefined' ? 'undefined' : _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}
*/
_createClass(Ecliptic, [{
key: 'toEquatorial',
value: function toEquatorial(ε) {
var _base$sincos = base.sincos(ε),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
εsin = _base$sincos2[0],
εcos = _base$sincos2[1];
var _base$sincos3 = base.sincos(this.lat),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sβ = _base$sincos4[0],
cβ = _base$sincos4[1];
var _base$sincos5 = base.sincos(this.lon),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
sλ = _base$sincos6[0],
cλ = _base$sincos6[1];
var ra = Math.atan2(sλ * εcos - sβ / cβ * εsin, cλ); // (13.3) p. 93
if (ra < 0) {
ra += 2 * Math.PI;
}
var dec = Math.asin(sβ * εcos + cβ * εsin * sλ); // (13.4) p. 93
return new Equatorial(ra, dec);
}
}]);
return Ecliptic;
}();
M.Ecliptic = Ecliptic;
/**
* Equatorial coordinates are referenced to the Earth's rotational axis.
*/
var Equatorial = function () {
/**
* @param {Number} ra - (float) Right ascension (α) in radians
* @param {Number} dec - (float) Declination (δ) in radians
*/
function Equatorial() {
var ra = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var dec = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
_classCallCheck(this, Equatorial);
this.ra = ra;
this.dec = dec;
}
/**
* EqToEcl converts equatorial coordinates to ecliptic coordinates.
* @param {Number} ε - Obliquity
* @returns {Ecliptic}
*/
_createClass(Equatorial, [{
key: 'toEcliptic',
value: function toEcliptic(ε) {
var _base$sincos7 = base.sincos(ε),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
εsin = _base$sincos8[0],
εcos = _base$sincos8[1];
var _base$sincos9 = base.sincos(this.ra),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sα = _base$sincos10[0],
cα = _base$sincos10[1];
var _base$sincos11 = base.sincos(this.dec),
_base$sincos12 = _slicedToArray(_base$sincos11, 2),
sδ = _base$sincos12[0],
cδ = _base$sincos12[1];
var lon = Math.atan2(sα * εcos + sδ / cδ * εsin, cα); // (13.1) p. 93
var 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 {Equatorial} eq - equatorial coordinates (right ascension, declination)
* @param {globe.Coord} g - coordinates of observer on Earth
* @param {Number} st - sidereal time at Greenwich at time of observation
* @returns {Horizontal}
*/
}, {
key: 'toHorizontal',
value: function toHorizontal(g, st) {
var H = new sexa.Time(st).rad() - g.lon - this.ra;
var _base$sincos13 = base.sincos(H),
_base$sincos14 = _slicedToArray(_base$sincos13, 2),
sH = _base$sincos14[0],
cH = _base$sincos14[1];
var _base$sincos15 = base.sincos(g.lat),
_base$sincos16 = _slicedToArray(_base$sincos15, 2),
sφ = _base$sincos16[0],
cφ = _base$sincos16[1];
var _base$sincos17 = base.sincos(this.dec),
_base$sincos18 = _slicedToArray(_base$sincos17, 2),
sδ = _base$sincos18[0],
cδ = _base$sincos18[1];
var azimuth = Math.atan2(sH, cH * sφ - sδ / cδ * cφ); // (13.5) p. 93
var altitude = Math.asin(sφ * sδ + cφ * cδ * cH); // (13.6) p. 93
return new Horizontal(azimuth, altitude);
}
/**
* EqToGal converts equatorial coordinates to galactic coordinates.
*
* Equatorial coordinates must be referred to the standard equinox of B1950.0.
* For conversion to B1950, see package precess and utility functions in
* package "common".
*
* @param {Equatorial} eq
* @returns {Galactic}
*/
}, {
key: 'toGalactic',
value: function toGalactic() {
var _base$sincos19 = base.sincos(galacticNorth1950.ra - this.ra),
_base$sincos20 = _slicedToArray(_base$sincos19, 2),
sdα = _base$sincos20[0],
cdα = _base$sincos20[1];
var _base$sincos21 = base.sincos(galacticNorth1950.dec),
_base$sincos22 = _slicedToArray(_base$sincos21, 2),
sgδ = _base$sincos22[0],
cgδ = _base$sincos22[1];
var _base$sincos23 = base.sincos(this.dec),
_base$sincos24 = _slicedToArray(_base$sincos23, 2),
sδ = _base$sincos24[0],
cδ = _base$sincos24[1];
var x = Math.atan2(sdα, cdα * sgδ - sδ / cδ * cgδ); // (13.7) p. 94
// (galactic0Lon1950 + 1.5*math.Pi) = magic number of 303 deg
var lon = (galactic0Lon1950 + 1.5 * Math.PI - x) % (2 * Math.PI); // (13.8) p. 94
var lat = Math.asin(sδ * sgδ + cδ * cgδ * cdα);
return new Galactic(lon, lat);
}
}]);
return Equatorial;
}();
M.Equatorial = Equatorial;
/**
* 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
*/
var Horizontal = function () {
function Horizontal() {
var az = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var alt = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
_classCallCheck(this, Horizontal);
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 {globe.Coord} g - coordinates of observer on Earth (lat, lon)
* @param {Number} st - sidereal time at Greenwich at time of observation.
* @returns {Equatorial} (right ascension, declination)
*/
_createClass(Horizontal, [{
key: 'toEquatorial',
value: function toEquatorial(g, st) {
var _base$sincos25 = base.sincos(this.az),
_base$sincos26 = _slicedToArray(_base$sincos25, 2),
sA = _base$sincos26[0],
cA = _base$sincos26[1];
var _base$sincos27 = base.sincos(this.alt),
_base$sincos28 = _slicedToArray(_base$sincos27, 2),
sh = _base$sincos28[0],
ch = _base$sincos28[1];
var _base$sincos29 = base.sincos(g.lat),
_base$sincos30 = _slicedToArray(_base$sincos29, 2),
sφ = _base$sincos30[0],
cφ = _base$sincos30[1];
var H = Math.atan2(sA, cA * sφ + sh / ch * cφ);
var ra = base.pmod(new sexa.Time(st).rad() - g.lon - H, 2 * Math.PI);
var dec = Math.asin(sφ * sh - cφ * ch * cA);
return new Equatorial(ra, dec);
}
}]);
return Horizontal;
}();
M.Horizontal = Horizontal;
/**
* Galactic coordinates are referenced to the plane of the Milky Way.
* @param {Number} lon - Longitude (l) in radians
* @param {Number} lat - Latitude (b) in radians
*/
var Galactic = function () {
function Galactic() {
var lon = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var lat = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
_classCallCheck(this, Galactic);
this.lon = lon;
this.lat = lat;
}
/**
* GalToEq converts galactic coordinates to equatorial coordinates.
*
* Resulting equatorial coordinates will be referred to the standard equinox of
* B1950.0. For subsequent conversion to other epochs, see package precess and
* utility functions in package meeus.
*
* @returns {Equatorial} (right ascension, declination)
*/
_createClass(Galactic, [{
key: 'toEquatorial',
value: function toEquatorial() {
// (-galactic0Lon1950 - math.Pi/2) = magic number of -123 deg
var _base$sincos31 = base.sincos(this.lon - galactic0Lon1950 - Math.PI / 2),
_base$sincos32 = _slicedToArray(_base$sincos31, 2),
sdLon = _base$sincos32[0],
cdLon = _base$sincos32[1];
var _base$sincos33 = base.sincos(galacticNorth1950.dec),
_base$sincos34 = _slicedToArray(_base$sincos33, 2),
sgδ = _base$sincos34[0],
cgδ = _base$sincos34[1];
var _base$sincos35 = base.sincos(this.lat),
_base$sincos36 = _slicedToArray(_base$sincos35, 2),
sb = _base$sincos36[0],
cb = _base$sincos36[1];
var y = Math.atan2(sdLon, cdLon * sgδ - sb / cb * cgδ);
// (galacticNorth1950.RA.Rad() - math.Pi) = magic number of 12.25 deg
var ra = base.pmod(y + galacticNorth1950.ra - Math.PI, 2 * Math.PI);
var dec = Math.asin(sb * sgδ + cb * cgδ * cdLon);
return new Equatorial(ra, dec);
}
}]);
return Galactic;
}();
M.Galactic = Galactic;
/**
* equatorial coords for galactic north
* IAU B1950.0 coordinates of galactic North Pole
*/
var galacticNorth1950 = M.galacticNorth1950 = M.galacticNorth = new Equatorial(new sexa.RA(12, 49, 0).rad(), 27.4 * Math.PI / 180);
/**
* 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.
*/
var galactic0Lon1950 = M.galactic0Lon1950 = M.galacticLon0 = 33 * Math.PI / 180;
/***/ }),
/* 3 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module solar
*/
/**
* Solar: Chapter 25, Solar Coordinates.
*
* Partial implementation:
*
* 1. Higher accuracy positions are not computed with Appendix III but with
* full VSOP87 as implemented in package planetposition.
*
* 2. Higher accuracy correction for aberration (using the formula for
* variation Δλ on p. 168) is not implemented. Results for example 25.b
* already match the full VSOP87 values on p. 165 even with the low accuracy
* correction for aberration, thus there are no more significant digits that
* would check a more accurate result. Also the size of the formula presents
* significant chance of typographical error.
*/
var base = __webpack_require__(0);
var coord = __webpack_require__(2);
var nutation = __webpack_require__(1);
var M = exports;
/**
* True returns true geometric longitude and anomaly of the sun referenced to the mean equinox of date.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Object}
* {Number} lon = true geometric longitude, ☉, in radians
* {Number} ano = true anomaly in radians
*/
M.true = function (T) {
// (25.2) p. 163
var L0 = base.horner(T, 280.46646, 36000.76983, 0.0003032) * Math.PI / 180;
var m = M.meanAnomaly(T);
var C = (base.horner(T, 1.914602, -0.004817, -0.000014) * Math.sin(m) + (0.019993 - 0.000101 * T) * Math.sin(2 * m) + 0.000289 * Math.sin(3 * m)) * Math.PI / 180;
var lon = base.pmod(L0 + C, 2 * Math.PI);
var ano = base.pmod(m + C, 2 * Math.PI);
return { lon: lon, ano: ano };
};
/**
* meanAnomaly returns the mean anomaly of Earth at the given T.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Number} Result is in radians and is not normalized to the range 0..2π.
*/
M.meanAnomaly = function (T) {
// (25.3) p. 163
return base.horner(T, 357.52911, 35999.05029, -0.0001537) * Math.PI / 180;
};
/**
* eccentricity returns eccentricity of the Earth's orbit around the sun.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Number} eccentricity of the Earth's orbit around the sun.
*/
M.eccentricity = function (T) {
// (25.4) p. 163
return base.horner(T, 0.016708634, -0.000042037, -0.0000001267);
};
/**
* Radius returns the Sun-Earth distance in AU.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Number} Sun-Earth distance in AU
*/
M.radius = function (T) {
var _M$true = M.true(T),
lon = _M$true.lon,
ano = _M$true.ano; // eslint-disable-line
var e = M.eccentricity(T);
// (25.5) p. 164
return 1.000001018 * (1 - e * e) / (1 + e * Math.cos(ano));
};
/**
* ApparentLongitude returns apparent longitude of the Sun referenced to the true equinox of date.
* Result includes correction for nutation and aberration. Unit is radians.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Number} apparent longitude of the Sun referenced to the true equinox of date.
*/
M.apparentLongitude = function (T) {
var Ω = node(T);
var _M$true2 = M.true(T),
lon = _M$true2.lon,
ano = _M$true2.ano; // eslint-disable-line
return lon - 0.00569 * Math.PI / 180 - 0.00478 * Math.PI / 180 * Math.sin(Ω);
};
/**
* @private
*/
function node(T) {
return 125.04 * Math.PI / 180 - 1934.136 * Math.PI / 180 * T;
}
/**
* true2000 returns true geometric longitude and anomaly of the sun referenced to equinox J2000.
* Results are accurate to .01 degree for years 1900 to 2100.
*
* @param {Number} T - number of Julian centuries since J2000. See base.J2000Century.
* @returns {Object}
* {Number} lon - true geometric longitude, ☉, in radians
* {Number} ano - true anomaly in radians
*/
M.true2000 = function (T) {
var _M$true3 = M.true(T),
lon = _M$true3.lon,
ano = _M$true3.ano;
lon -= 0.01397 * Math.PI / 180 * T * 100;
return { lon: lon, ano: ano };
};
/**
* trueEquatorial returns the true geometric position of the Sun as equatorial coordinates.
*
* @param {Number} jde - Julian ephemeris day
* @returns {base.Coord}
* {Number} ra - right ascension in radians
* {Number} dec - declination in radians
*/
M.trueEquatorial = function (jde) {
var _M$true4 = M.true(base.J2000Century(jde)),
lon = _M$true4.lon,
ano = _M$true4.ano; // eslint-disable-line
var ε = nutation.meanObliquity(jde);
var _base$sincos = base.sincos(lon),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
ss = _base$sincos2[0],
cs = _base$sincos2[1];
var _base$sincos3 = base.sincos(ε),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sε = _base$sincos4[0],
cε = _base$sincos4[1];
// (25.6, 25.7) p. 165
var ra = Math.atan2(cε * ss, cs);
var dec = sε * ss;
return new base.Coord(ra, dec);
};
/**
* apparentEquatorial returns the apparent position of the Sun as equatorial coordinates.
*
* @param {Number} jde - Julian ephemeris day
* @returns {base.Coord}
* {Number} ra - right ascension in radians
* {Number} dec - declination in radians
*/
M.apparentEquatorial = function (jde) {
var T = base.J2000Century(jde);
var λ = M.apparentLongitude(T);
var ε = nutation.meanObliquity(jde);
var _base$sincos5 = base.sincos(λ),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
sλ = _base$sincos6[0],
cλ = _base$sincos6[1];
// (25.8) p. 165
var _base$sincos7 = base.sincos(ε + 0.00256 * Math.PI / 180 * Math.cos(node(T))),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
sε = _base$sincos8[0],
cε = _base$sincos8[1];
var ra = Math.atan2(cε * sλ, cλ);
var dec = Math.asin(sε * sλ);
return new base.Coord(ra, dec);
};
/**
* trueVSOP87 returns the true geometric position of the sun as ecliptic coordinates.
*
* Result computed by full VSOP87 theory. Result is at equator and equinox
* of date in the FK5 frame. It does not include nutation or aberration.
*
* @param {planetposition.Planet} planet
* @param {Number} jde - Julian ephemeris day
* @returns {Object}
* {Number} lon - ecliptic longitude in radians
* {Number} lat - ecliptic latitude in radians
* {Number} range - range in AU
*/
M.trueVSOP87 = function (planet, jde) {
var _planet$position = planet.position(jde),
lon = _planet$position.lon,
lat = _planet$position.lat,
range = _planet$position.range;
var s = lon + Math.PI;
// FK5 correction.
var λp = base.horner(base.J2000Century(jde), s, -1.397 * Math.PI / 180, -0.00031 * Math.PI / 180);
var _base$sincos9 = base.sincos(λp),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sλp = _base$sincos10[0],
cλp = _base$sincos10[1];
var Δβ = 0.03916 / 3600 * Math.PI / 180 * (cλp - sλp);
// (25.9) p. 166
lon = base.pmod(s - 0.09033 / 3600 * Math.PI / 180, 2 * Math.PI);
lat = Δβ - lat;
return new base.Coord(lon, lat, range);
};
/**
* apparentVSOP87 returns the apparent position of the sun as ecliptic coordinates.
*
* Result computed by VSOP87, at equator and equinox of date in the FK5 frame,
* and includes effects of nutation and aberration.
*
* @param {planetposition.Planet} planet
* @param {Number} jde - Julian ephemeris day
* @returns {base.Coord}
* {Number} lon - ecliptic longitude in radians
* {Number} lat - ecliptic latitude in radians
* {Number} range - range in AU
*/
M.apparentVSOP87 = function (planet, jde) {
// note: see duplicated code in ApparentEquatorialVSOP87.
var _M$trueVSOP = M.trueVSOP87(planet, jde),
lon = _M$trueVSOP.lon,
lat = _M$trueVSOP.lat,
range = _M$trueVSOP.range;
var Δψ = nutation.nutation(jde)[0];
var a = M.aberration(range);
lon = lon + Δψ + a;
return new base.Coord(lon, lat, range);
};
/**
* apparentEquatorialVSOP87 returns the apparent position of the sun as equatorial coordinates.
*
* Result computed by VSOP87, at equator and equinox of date in the FK5 frame,
* and includes effects of nutation and aberration.
*
* @param {planetposition.Planet} planet
* @param {Number} jde - Julian ephemeris day
* @returns
* {Number} ra - right ascension in radians
* {Number} dec - declination in radians
* {Number} range - range in AU
*/
M.apparentEquatorialVSOP87 = function (planet, jde) {
// note: duplicate code from ApparentVSOP87 so we can keep Δε.
// see also duplicate code in time.E().
var _M$trueVSOP2 = M.trueVSOP87(planet, jde),
lon = _M$trueVSOP2.lon,
lat = _M$trueVSOP2.lat,
range = _M$trueVSOP2.range;
var _nutation$nutation = nutation.nutation(jde),
_nutation$nutation2 = _slicedToArray(_nutation$nutation, 2),
Δψ = _nutation$nutation2[0],
Δε = _nutation$nutation2[1];
var a = M.aberration(range);
var λ = lon + Δψ + a;
var ε = nutation.meanObliquity(jde) + Δε;
var _toEquatorial = new coord.Ecliptic(λ, lat).toEquatorial(ε),
ra = _toEquatorial.ra,
dec = _toEquatorial.dec;
return new base.Coord(ra, dec, range);
};
/**
* Low precision formula. The high precision formula is not implemented
* because the low precision formula already gives position results to the
* accuracy given on p. 165. The high precision formula represents lots
* of typing with associated chance of typos, and no way to test the result.
* @param {Number} range
* @returns {Number} aberation
*/
M.aberration = function (range) {
// (25.10) p. 167
return -20.4898 / 3600 * Math.PI / 180 / range;
};
/***/ }),
/* 4 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
function _possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
function _inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module sexagesimal
*/
/**
* Sexagesimal functions
*/
var M = exports;
/**
* Angle represents a general purpose angle.
* Unit is radians.
*/
var Angle = function () {
/**
* constructs a new Angle value from sign, degree, minute, and second
* components.
* __One argument__
* @param {Number} angle - (float) angle in radians
* __Four arguments__
* @param {Boolean} neg - sign, true if negative
* @param {Number} d - (int) degree
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
*/
function Angle(neg, d, m, s) {
_classCallCheck(this, Angle);
if (arguments.length === 1) {
this.angle = neg;
} else {
this.setDMS(neg, d, m, s);
}
}
/**
* SetDMS sets the value of an FAngle from sign, degree, minute, and second
* components.
* The receiver is returned as a convenience.
* @param {Boolean} neg - sign, true if negative
* @param {Number} d - (int) degree
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
* @returns {Angle}
*/
_createClass(Angle, [{
key: 'setDMS',
value: function setDMS() {
var neg = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var d = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
var m = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 0;
var s = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : 0.0;
this.angle = M.DMSToDeg(neg, d, m, s) * Math.PI / 180;
return this;
}
/**
* sets angle
* @param {Number} angle - (float) angle in radians
* @returns {Angle}
*/
}, {
key: 'setAngle',
value: function setAngle(rad) {
this.angle = rad;
return this;
}
/**
* Rad returns the angle in radians.
* @returns {Number} angle in radians
*/
}, {
key: 'rad',
value: function rad() {
return this.angle;
}
/**
* Deg returns the angle in degrees.
* @returns {Number} angle in degree
*/
}, {
key: 'deg',
value: function deg() {
return this.angle * 180 / Math.PI;
}
/**
* toDMS converts to parsed sexagesimal angle component.
*/
}, {
key: 'toDMS',
value: function toDMS() {
return M.degToDMS(this.deg());
}
/**
* Print angle in degree using `d°m´s.ss″`
* @param {Number} precision - precision of `s.ss`
* @returns {String}
*/
}, {
key: 'toString',
value: function toString(precision) {
var _toDMS = this.toDMS(),
_toDMS2 = _slicedToArray(_toDMS, 4),
neg = _toDMS2[0],
d = _toDMS2[1],
m = _toDMS2[2],
s = _toDMS2[3];
s = round(s, precision).toString().replace(/^0\./, '.');
var str = (neg ? '-' : '') + (d + '°') + (m + '′') + (s + '″');
return str;
}
/**
* Print angle in degree using `d°.ff`
* @param {Number} precision - precision of `.ff`
* @returns {String}
*/
}, {
key: 'toDegString',
value: function toDegString(precision) {
var _modf = modf(this.deg()),
_modf2 = _slicedToArray(_modf, 2),
i = _modf2[0],
s = _modf2[1];
s = round(s, precision).toString().replace(/^0\./, '.');
var str = i + '°' + s;
return str;
}
}]);
return Angle;
}();
M.Angle = Angle;
/**
* HourAngle represents an angle corresponding to angular rotation of
* the Earth in a specified time.
*
* Unit is radians.
*/
var HourAngle = function (_Angle) {
_inherits(HourAngle, _Angle);
function HourAngle() {
_classCallCheck(this, HourAngle);
return _possibleConstructorReturn(this, (HourAngle.__proto__ || Object.getPrototypeOf(HourAngle)).apply(this, arguments));
}
_createClass(HourAngle, [{
key: 'setDMS',
/**
* NewHourAngle constructs a new HourAngle value from sign, hour, minute,
* and second components.
* @param {Boolean} neg
* @param {Number} h - (int)
* @param {Number} m - (int)
* @param {Number} s - (float)
*/
// constructor (neg, h, m, s) {
// super(neg, h, m, s)
// }
/**
* SetDMS sets the value of an FAngle from sign, degree, minute, and second
* components.
* The receiver is returned as a convenience.
* @param {Boolean} neg - sign, true if negative
* @param {Number} h - (int) hour
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
* @returns {Angle}
*/
value: function setDMS() {
var neg = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var h = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
var m = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 0;
var s = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : 0.0;
this.angle = M.DMSToDeg(neg, h, m, s) * 15 * Math.PI / 180;
return this;
}
/**
* Hour returns the hour angle as hours of time.
* @returns hour angle
*/
}, {
key: 'hour',
value: function hour() {
return this.angle * 12 / Math.PI; // 12 = 180 / 15
}
}, {
key: 'deg',
value: function deg() {
return this.hour();
}
/**
* Print angle in `HʰMᵐs.ssˢ`
* @param {Number} precision - precision of `s.ss`
* @returns {String}
*/
}, {
key: 'toString',
value: function toString(precision) {
var _toDMS3 = this.toDMS(),
_toDMS4 = _slicedToArray(_toDMS3, 4),
neg = _toDMS4[0],
h = _toDMS4[1],
m = _toDMS4[2],
s = _toDMS4[3];
s = round(s, precision).toString().replace(/^0\./, '.');
var str = (neg ? '-' : '') + (h + 'ʰ') + (m + 'ᵐ') + (s + 'ˢ');
return str;
}
}]);
return HourAngle;
}(Angle);
M.HourAngle = HourAngle;
/**
* DMSToDeg converts from parsed sexagesimal angle components to decimal
* degrees.
* @param {Boolean} neg - sign, true if negative
* @param {Number} d - (int) degree
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
* @returns {Number} angle in degree
*/
M.DMSToDeg = function (neg, d, m, s) {
s = ((d * 60 + m) * 60 + s) / 3600;
if (neg) {
return -s;
}
return s;
};
/**
* DegToDMS converts from decimal degrees to parsed sexagesimal angle component.
* @param {Number} deg - angle in degree
* @returns {Array} [neg, d, m, s]
* {Boolean} neg - sign, true if negative
* {Number} d - (int) degree
* {Number} m - (int) minute
* {Number} s - (float) second
*/
M.degToDMS = function (deg) {
var neg = deg < 0;
deg = Math.abs(deg);
var _modf3 = modf(deg % 360),
_modf4 = _slicedToArray(_modf3, 2),
d = _modf4[0],
s = _modf4[1];
var _modf5 = modf(s * 60),
_modf6 = _slicedToArray(_modf5, 2),
m = _modf6[0],
s1 = _modf6[1];
s = round(s1 * 60); // may introduce an error < 1e13
return [neg, d, m, s];
};
/**
* TODO
*/
var RA = function (_HourAngle) {
_inherits(RA, _HourAngle);
/**
* constructs a new RA value from hour, minute, and second components.
* Negative values are not supported, RA wraps values larger than 24
* to the range [0,24) hours.
* @param {Number} h - (int) hour
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
*/
function RA() {
var h = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var m = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
var s = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 0;
_classCallCheck(this, RA);
var _this2 = _possibleConstructorReturn(this, (RA.__proto__ || Object.getPrototypeOf(RA)).call(this));
var args = [].slice.call(arguments);
if (args.length === 1) {
_this2.angle = h;
} else {
var hr = M.DMSToDeg(false, h, m, s) % 24;
_this2.angle = hr * 15 * Math.PI / 180;
}
return _this2;
}
_createClass(RA, [{
key: 'hour',
value: function hour() {
var h = this.angle * 12 / Math.PI;
return (24 + h % 24) % 24;
}
}]);
return RA;
}(HourAngle);
M.RA = RA;
/**
* TODO
*/
var Time = function () {
/**
* @param {Boolean} neg - set `true` if negative
* @param {Number} h - (int) hour
* @param {Number} m - (int) minute
* @param {Number} s - (float) second
*/
function Time(neg, h, m, s) {
_classCallCheck(this, Time);
if (arguments.length === 1) {
this.time = neg;
} else {
this.setHMS(neg, h, m, s);
}
}
_createClass(Time, [{
key: 'setHMS',
value: function setHMS() {
var neg = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : false;
var h = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
var m = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 0;
var s = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : 0;
s += (h * 60 + m) * 60;
if (neg) {
s = -s;
}
this.time = s;
}
/**
* @returns {Number} time in seconds.
*/
}, {
key: 'sec',
value: function sec() {
return this.time;
}
/**
* @returns {Number} time in minutes.
*/
}, {
key: 'min',
value: function min() {
return this.time / 60;
}
/**
* @returns {Number} time in hours.
*/
}, {
key: 'hour',
value: function hour() {
return this.time / 3600;
}
/**
* @returns {Number} time in days.
*/
}, {
key: 'day',
value: function day() {
return this.time / 3600 / 24;
}
/**
* @returns {Number} time in radians, where 1 day = 2 Pi radians.
*/
}, {
key: 'rad',
value: function rad() {
return this.time * Math.PI / 12 / 3600;
}
/**
* convert time to HMS
* @returns {Array} [neg, h, m, s]
* {Boolean} neg - sign, true if negative
* {Number} h - (int) hour
* {Number} m - (int) minute
* {Number} s - (float) second
*/
}, {
key: 'toHMS',
value: function toHMS() {
var t = this.time;
var neg = t < 0;
t = neg ? -t : t;
var h = Math.trunc(t / 3600);
t = t - h * 3600;
var m = Math.trunc(t / 60);
var s = t - m * 60;
return [neg, h, m, s];
}
/**
* Print time using `HʰMᵐsˢ.ss`
* @param {Number} precision - precision of `.ss`
* @returns {String}
*/
}, {
key: 'toString',
value: function toString(precision) {
var _toHMS = this.toHMS(),
_toHMS2 = _slicedToArray(_toHMS, 4),
neg = _toHMS2[0],
h = _toHMS2[1],
m = _toHMS2[2],
s = _toHMS2[3];
var _modf7 = modf(s),
_modf8 = _slicedToArray(_modf7, 2),
si = _modf8[0],
sf = _modf8[1];
if (precision === 0) {
si = round(s, 0);
sf = 0;
} else {
sf = round(sf, precision).toString().substr(1);
}
var str = (neg ? '-' : '') + (h + 'ʰ') + (m + 'ᵐ') + (si + 'ˢ') + (sf || '');
return str;
}
}]);
return Time;
}();
M.Time = Time;
/**
* separate fix `i` from fraction `f`
* @private
* @param {Number} float
* @returns {Array} [i, f]
* {Number} i - (int) fix value
* {Number} f - (float) fractional portion; always > 1
*/
function modf(float) {
var i = Math.trunc(float);
var f = Math.abs(float - i);
return [i, f];
}
/**
* Rounds `float` value by precision
* @private
* @param {Number} float - value to round
* @param {Number} precision - (int) number of post decimal positions
* @return {Number} rounded `float`
*/
function round(float, precision) {
precision = precision === undefined ? 10 : precision;
return parseFloat(float.toFixed(precision), 10);
}
/***/ }),
/* 5 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
function _toConsumableArray(arr) { if (Array.isArray(arr)) { for (var i = 0, arr2 = Array(arr.length); i < arr.length; i++) { arr2[i] = arr[i]; } return arr2; } else { return Array.from(arr); } }
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module interpolation
*/
/**
* Interp: Chapter 3, Interpolation.
*
* Len3 and Len5 types
*
* These types allow interpolation from a table of equidistant x values
* and corresponding y values. Since the x values are equidistant,
* only the first and last values are supplied as arguments to the
* constructors. The interior x values are implicit. All y values must be
* supplied however. They are passed as a slice, and the length of y is fixed.
* For Len3 it must be 3 and for (Len5 it must be 5.0
*
* For these Len3 and Len5 functions, Meeus notes the importance of choosing
* the 3 or 5 rows of a larger table that will minimize the interpolating
* factor n. He does not provide algorithms for doing this however.
*
* For an example of a selection function, see len3ForInterpolateX. This
* was useful for computing Delta T.
*/
var base = __webpack_require__(0);
var M = exports;
var int = Math.trunc;
/**
* Error values returned by functions and methods in this package.
* Defined here to help testing for specific errors.
*/
var errorNot3 = M.errorNot3 = new Error('Argument y must be length 3');
var errorNot4 = M.errorNot4 = new Error('Argument y must be length 4');
var errorNot5 = M.errorNot5 = new Error('Argument y must be length 5');
var errorNoXRange = M.errorNoXRange = new Error('Argument x3 (or x5) cannot equal x1');
var errorNOutOfRange = M.errorNOutOfRange = new Error('Interpolating factor n must be in range -1 to 1');
var errorNoExtremum = M.errorNoExtremum = new Error('No extremum in table');
var errorExtremumOutside = M.errorExtremumOutside = new Error('Extremum falls outside of table');
var errorZeroOutside = M.errorZeroOutside = new Error('Zero falls outside of table');
var errorNoConverge = M.errorNoConverge = new Error('Failure to converge');
/**
* Len3 allows second difference interpolation.
*/
var Len3 = function () {
/**
* NewLen3 prepares a Len3 object from a table of three rows of x and y values.
*
* X values must be equally spaced, so only the first and last are supplied.
* X1 must not equal to x3. Y must be a slice of three y values.
*
* @throws Error
* @param {Number} x1 - is the x value corresponding to the first y value of the table.
* @param {Number} x3 - is the x value corresponding to the last y value of the table.
* @param {Number[]} y - is all y values in the table. y.length should be >= 3.0
*/
function Len3(x1, x3, y) {
_classCallCheck(this, Len3);
if (y.length !== 3) {
throw errorNot3;
}
if (x3 === x1) {
throw errorNoXRange;
}
this.x1 = x1;
this.x3 = x3;
this.y = y;
// differences. (3.1) p. 23
this.a = y[1] - y[0];
this.b = y[2] - y[1];
this.c = this.b - this.a;
// other intermediate values
this.abSum = this.a + this.b;
this.xSum = x3 + x1;
this.xDiff = x3 - x1;
}
/**
* InterpolateX interpolates for a given x value.
*/
_createClass(Len3, [{
key: 'interpolateX',
value: function interpolateX(x) {
var n = (2 * x - this.xSum) / this.xDiff;
return this.interpolateN(n);
}
/**
* InterpolateXStrict interpolates for a given x value,
* restricting x to the range x1 to x3 given to the constructor NewLen3.
*/
}, {
key: 'interpolateXStrict',
value: function interpolateXStrict(x) {
var n = (2 * x - this.xSum) / this.xDiff;
var y = this.interpolateNStrict(n, true);
return y;
}
/**
* InterpolateN interpolates for (a given interpolating factor n.
*
* This is interpolation formula (3.3)
*
* The interpolation factor n is x-x2 in units of the tabular x interval.
* (See Meeus p. 24.)
*/
}, {
key: 'interpolateN',
value: function interpolateN(n) {
return this.y[1] + n * 0.5 * (this.abSum + n * this.c);
}
/**
* InterpolateNStrict interpolates for (a given interpolating factor n.
*
* N is restricted to the range [-1..1] corresponding to the range x1 to x3
* given to the constructor of Len3.
*/
}, {
key: 'interpolateNStrict',
value: function interpolateNStrict(n) {
if (n < -1 || n > 1) {
throw errorNOutOfRange;
}
return this.interpolateN(n);
}
/**
* Extremum returns the x and y values at the extremum.
*
* Results are restricted to the range of the table given to the constructor
* new Len3.
*/
}, {
key: 'extremum',
value: function extremum() {
if (this.c === 0) {
throw errorNoExtremum;
}
var n = this.abSum / (-2 * this.c); // (3.5), p. 25
if (n < -1 || n > 1) {
throw errorExtremumOutside;
}
var x = 0.5 * (this.xSum + this.xDiff * n);
var y = this.y[1] - this.abSum * this.abSum / (8 * this.c); // (3.4), p. 25
return [x, y];
}
/**
* Len3Zero finds a zero of the quadratic function represented by the table.
*
* That is, it returns an x value that yields y=0.
*
* Argument strong switches between two strategies for the estimation step.
* when iterating to converge on the zero.
*
* Strong=false specifies a quick and dirty estimate that works well
* for gentle curves, but can work poorly or fail on more dramatic curves.
*
* Strong=true specifies a more sophisticated and thus somewhat more
* expensive estimate. However, if the curve has quick changes, This estimate
* will converge more reliably and in fewer steps, making it a better choice.
*
* Results are restricted to the range of the table given to the constructor
* NewLen3.
*/
}, {
key: 'zero',
value: function zero(strong) {
var _this = this;
var f = void 0;
if (strong) {
// (3.7), p. 27
f = function f(n0) {
return n0 - (2 * _this.y[1] + n0 * (_this.abSum + _this.c * n0)) / (_this.abSum + 2 * _this.c * n0);
};
} else {
// (3.6), p. 26
f = function f(n0) {
return -2 * _this.y[1] / (_this.abSum + _this.c * n0);
};
}
var _iterate = iterate(0, f),
_iterate2 = _slicedToArray(_iterate, 2),
n0 = _iterate2[0],
ok = _iterate2[1];
if (!ok) {
throw errorNoConverge;
}
if (n0 > 1 || n0 < -1) {
throw errorZeroOutside;
}
return 0.5 * (this.xSum + this.xDiff * n0); // success
}
}]);
return Len3;
}();
M.Len3 = Len3;
/**
* Len3ForInterpolateX is a special purpose Len3 constructor.
*
* Like NewLen3, it takes a table of x and y values, but it is not limited
* to tables of 3 rows. An X value is also passed that represents the
* interpolation target x value. Len3ForInterpolateX will locate the
* appropriate three rows of the table for interpolating for x, and initialize
* the Len3 object for those rows.
*
* @param {Number} x - is the target for interpolation
* @param {Number} x1 - is the x value corresponding to the first y value of the table.
* @param {Number} xn - is the x value corresponding to the last y value of the table.
* @param {Number[]} y - is all y values in the table. y.length should be >= 3.0
* @returns {Number} interpolation value
*/
M.len3ForInterpolateX = function (x, x1, xN, y) {
var y3 = y;
if (y.length > 3) {
var interval = (xN - x1) / (y.length - 1);
if (interval === 0) {
throw errorNoXRange;
}
var nearestX = int((x - x1) / interval + 0.5);
if (nearestX < 1) {
nearestX = 1;
} else if (nearestX > y.length - 2) {
nearestX = y.length - 2;
}
y3 = y.slice(nearestX - 1, nearestX + 2);
xN = x1 + (nearestX + 1) * interval;
x1 = x1 + (nearestX - 1) * interval;
}
return new Len3(x1, xN, y3);
};
/**
* @private
* @param {Number} n0
* @param {Function} f
* @returns {Array}
* {Number} n1
* {Boolean} ok - if `false` failure to converge
*/
var iterate = M.iterate = function (n0, f) {
for (var limit = 0; limit < 50; limit++) {
var n1 = f(n0);
if (!isFinite(n1) || isNaN(n1)) {
break; // failure to converge
}
if (Math.abs((n1 - n0) / n0) < 1e-15) {
return [n1, true]; // success
}
n0 = n1;
}
return [0, false]; // failure to converge
};
/**
* Len4Half interpolates a center value from a table of four rows.
* @param {Number[]} y - 4 values
* @returns {Number} interpolation result
*/
M.len4Half = function (y) {
if (y.length !== 4) {
throw errorNot4;
}
// (3.12) p. 32
return (9 * (y[1] + y[2]) - y[0] - y[3]) / 16;
};
/**
* Len5 allows fourth Difference interpolation.
*/
var Len5 = function () {
/**
* NewLen5 prepares a Len5 object from a table of five rows of x and y values.
*
* X values must be equally spaced, so only the first and last are suppliethis.
* X1 must not equal x5. Y must be a slice of five y values.
*/
function Len5(x1, x5, y) {
_classCallCheck(this, Len5);
if (y.length !== 5) {
throw errorNot5;
}
if (x5 === x1) {
throw errorNoXRange;
}
this.x1 = x1;
this.x5 = x5;
this.y = y;
this.y3 = y[2];
// differences
this.a = y[1] - y[0];
this.b = y[2] - y[1];
this.c = y[3] - y[2];
this.d = y[4] - y[3];
this.e = this.b - this.a;
this.f = this.c - this.b;
this.g = this.d - this.c;
this.h = this.f - this.e;
this.j = this.g - this.f;
this.k = this.j - this.h;
// other intermediate values
this.xSum = x5 + x1;
this.xDiff = x5 - x1;
this.interpCoeff = [// (3.8) p. 28
this.y3, (this.b + this.c) / 2 - (this.h + this.j) / 12, this.f / 2 - this.k / 24, (this.h + this.j) / 12, this.k / 24];
}
/**
* InterpolateX interpolates for (a given x value.
*/
_createClass(Len5, [{
key: 'interpolateX',
value: function interpolateX(x) {
var n = (4 * x - 2 * this.xSum) / this.xDiff;
return this.interpolateN(n);
}
/**
* InterpolateXStrict interpolates for a given x value,
* restricting x to the range x1 to x5 given to the the constructor NewLen5.
*/
}, {
key: 'interpolateXStrict',
value: function interpolateXStrict(x) {
var n = (4 * x - 2 * this.xSum) / this.xDiff;
var y = this.interpolateNStrict(n);
return y;
}
/**
* InterpolateN interpolates for (a given interpolating factor n.
*
* The interpolation factor n is x-x3 in units of the tabular x interval.
* (See Meeus p. 28.)
*/
}, {
key: 'interpolateN',
value: function interpolateN(n) {
return base.horner.apply(base, [n].concat(_toConsumableArray(this.interpCoeff)));
}
/**
* InterpolateNStrict interpolates for (a given interpolating factor n.
*
* N is restricted to the range [-1..1]. This is only half the range given
* to the constructor NewLen5, but is the recommendation given on p. 31.0
*/
}, {
key: 'interpolateNStrict',
value: function interpolateNStrict(n) {
if (n < -1 || n > 1) {
throw errorNOutOfRange;
}
return base.horner.apply(base, [n].concat(_toConsumableArray(this.interpCoeff)));
}
/**
* Extremum returns the x and y values at the extremum.
*
* Results are restricted to the range of the table given to the constructor
* NewLen5. (Meeus actually recommends restricting the range to one unit of
* the tabular interval, but that seems a little harsh.)
*/
}, {
key: 'extremum',
value: function extremum() {
// (3.9) p. 29
var nCoeff = [6 * (this.b + this.c) - this.h - this.j, 0, 3 * (this.h + this.k), 2 * this.k];
var den = this.k - 12 * this.f;
if (den === 0) {
throw errorExtremumOutside;
}
var _iterate3 = iterate(0, function (n0) {
return base.horner.apply(base, [n0].concat(nCoeff)) / den;
}),
_iterate4 = _slicedToArray(_iterate3, 2),
n0 = _iterate4[0],
ok = _iterate4[1];
if (!ok) {
throw errorNoConverge;
}
if (n0 < -2 || n0 > 2) {
throw errorExtremumOutside;
}
var x = 0.5 * this.xSum + 0.25 * this.xDiff * n0;
var y = base.horner.apply(base, [n0].concat(_toConsumableArray(this.interpCoeff)));
return [x, y];
}
/**
* Len5Zero finds a zero of the quartic function represented by the table.
*
* That is, it returns an x value that yields y=0.
*
* Argument strong switches between two strategies for the estimation step.
* when iterating to converge on the zero.
*
* Strong=false specifies a quick and dirty estimate that works well
* for gentle curves, but can work poorly or fail on more dramatic curves.
*
* Strong=true specifies a more sophisticated and thus somewhat more
* expensive estimate. However, if the curve has quick changes, This estimate
* will converge more reliably and in fewer steps, making it a better choice.
*
* Results are restricted to the range of the table given to the constructor
* NewLen5.
*/
}, {
key: 'zero',
value: function zero(strong) {
var f;
if (strong) {
// (3.11), p. 29
var _M = this.k / 24;
var N = (this.h + this.j) / 12;
var P = this.f / 2 - _M;
var Q = (this.b + this.c) / 2 - N;
var numCoeff = [this.y3, Q, P, N, _M];
var denCoeff = [Q, 2 * P, 3 * N, 4 * _M];
f = function f(n0) {
return n0 - base.horner.apply(base, [n0].concat(numCoeff)) / base.horner.apply(base, [n0].concat(denCoeff));
};
} else {
// (3.10), p. 29
var _numCoeff = [-24 * this.y3, 0, this.k - 12 * this.f, -2 * (this.h + this.j), -this.k];
var den = 12 * (this.b + this.c) - 2 * (this.h + this.j);
f = function f(n0) {
return base.horner.apply(base, [n0].concat(_numCoeff)) / den;
};
}
var _iterate5 = iterate(0, f),
_iterate6 = _slicedToArray(_iterate5, 2),
n0 = _iterate6[0],
ok = _iterate6[1];
if (!ok) {
throw errorNoConverge;
}
if (n0 > 2 || n0 < -2) {
throw errorZeroOutside;
}
var x = 0.5 * this.xSum + 0.25 * this.xDiff * n0;
return x;
}
}]);
return Len5;
}();
M.Len5 = Len5;
/**
* Lagrange performs interpolation with unequally-spaced abscissae.
*
* Given a table of X and Y values, interpolate a new y value for argument x.
*
* X values in the table do not have to be equally spaced; they do not even
* have to be in order. They must however, be distinct.
*
* @param {Number} x - x-value of interpolation
* @param {Array} table - `[[x0, y0], ... [xN, yN]]` of x, y values
* @returns {Number} interpolation result `y` of `x`
*/
M.lagrange = function (x, table) {
// method of BASIC program, p. 33.0
var sum = 0;
table.forEach(function (ti, i) {
var xi = ti[0];
var prod = 1.0;
table.forEach(function (tj, j) {
if (i !== j) {
var xj = tj[0];
prod *= (x - xj) / (xi - xj);
}
});
sum += ti[1] * prod;
});
return sum;
};
/**
* LagrangePoly uses the formula of Lagrange to produce an interpolating
* polynomial.
*
* X values in the table do not have to be equally spaced; they do not even
* have to be in order. They must however, be distinct.
*
* The returned polynomial will be of degree n-1 where n is the number of rows
* in the table. It can be evaluated for x using base.horner.
*
* @param {Array} table - `[[x0, y0], ... [xN, yN]]`
* @returns {Array} - polynomial array
*/
M.lagrangePoly = function (table) {
// Method not fully described by Meeus, but needed for (numerical solution
// to Example 3.g.
var sum = new Array(table.length).fill(0);
var prod = new Array(table.length).fill(0);
var last = table.length - 1;
var _loop = function _loop() {
var xi = table[i][0] || table[i].x || 0;
var yi = table[i][1] || table[i].y || 0;
prod[last] = 1;
var den = 1.0;
var n = last;
for (j = 0; j < table.length; j++) {
if (i !== j) {
var xj = table[j][0] || table[j].x || 0;
prod[n - 1] = prod[n] * -xj;
for (k = n; k < last; k++) {
prod[k] -= prod[k + 1] * xj;
}
n--;
den *= xi - xj;
}
}
prod.forEach(function (pj, j) {
sum[j] += yi * pj / den;
});
};
for (var i = 0; i < table.length; i++) {
var j;
var k;
_loop();
}
return sum;
};
/**
* Linear Interpolation of x
*/
M.linear = function (x, x1, xN, y) {
var interval = (xN - x1) / (y.length - 1);
if (interval === 0) {
throw errorNoXRange;
}
var nearestX = Math.floor((x - x1) / interval);
if (nearestX < 0) {
nearestX = 0;
} else if (nearestX > y.length - 2) {
nearestX = y.length - 2;
}
var y2 = y.slice(nearestX, nearestX + 2);
var x01 = x1 + nearestX * interval;
return y2[0] + (y[1] - y[0]) * (x - x01) / interval;
};
/***/ }),
/* 6 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module planetposition
*/
/**
* Planetposition: Chapter 32, Positions of the Planets.
*
* Incomplete:
*
* 1. The package does not implement algorithms that use appendix III,
* but instead implements a full VSOP87 solution. I do not have a copy
* of the supplimentary disk with appendix III in machine readable form
* and as the appendix is rather large, retyping it by hand is problematic.
* The full VSOP87 data set on the other hand is freely downloadable from
* the internet, so I implement here code that can use that data directly.
*
* 2. The formula for accuracy of results is not implemented. It is
* not needed for full VSOP87 solutions.
*
* 3. Polynomial expressions are not implemented. Again, implementation
* would involve typing rather large tables of numbers with associated
* risk of typographical errors.
*/
var base = __webpack_require__(0);
var coord = __webpack_require__(2);
var precess = __webpack_require__(8);
var M = exports;
// planet names used in Planet
M.mercury = 'mercury';
M.venus = 'venus';
M.earth = 'earth';
M.mars = 'mars';
M.jupiter = 'jupiter';
M.saturn = 'saturn';
M.uranus = 'uranus';
M.neptune = 'neptune';
function sum(t, series) {
var coeffs = [];
Object.keys(series).forEach(function (x) {
coeffs[x] = 0;
var y = series[x].length - 1;
for (y; y >= 0; y--) {
var term = {
a: series[x][y][0],
b: series[x][y][1],
c: series[x][y][2]
};
coeffs[x] += term.a * Math.cos(term.b + term.c * t);
}
});
var res = base.horner(t, coeffs);
return res;
}
var Planet = function () {
/**
* VSOP87 representation of a Planet
* @constructs Planet
* @param {string|object} planet - name of planet or data series
* @example
* ```js
* // for use in browser
* const earthData = require('astronomia/data/vsop87Bearth')
* const earth = new planetposition.Planet(earthData)
* // otherwise
* const saturn = new planetposition.Planet(planetposition.saturn)
* ```
*/
function Planet(planet) {
_classCallCheck(this, Planet);
if (typeof planet === 'string') {
this.name = planet.toLowerCase();
this.series = __webpack_require__(42)("./vsop87B" + this.name);
} else {
this.name = planet.name;
this.series = planet;
}
}
/**
* Position2000 returns ecliptic position of planets by full VSOP87 theory.
*
* @param {Number} jde - the date for which positions are desired.
* @returns {base.Coord} Results are for the dynamical equinox and ecliptic J2000.
* {Number} lon - heliocentric longitude in radians.
* {Number} lat - heliocentric latitude in radians.
* {Number} range - heliocentric range in AU.
*/
_createClass(Planet, [{
key: 'position2000',
value: function position2000(jde) {
var T = base.J2000Century(jde);
var τ = T * 0.1;
var lon = base.pmod(sum(τ, this.series.L), 2 * Math.PI);
var lat = sum(τ, this.series.B);
var range = sum(τ, this.series.R);
return new base.Coord(lon, lat, range);
}
/**
* Position returns ecliptic position of planets at equinox and ecliptic of date.
*
* @param {Number} jde - the date for which positions are desired.
* @returns {base.Coord} Results are positions consistent with those from Meeus's
* Apendix III, that is, at equinox and ecliptic of date.
* {Number} lon - heliocentric longitude in radians.
* {Number} lat - heliocentric latitude in radians.
* {Number} range - heliocentric range in AU.
*/
}, {
key: 'position',
value: function position(jde) {
var _position = this.position2000(jde),
lat = _position.lat,
lon = _position.lon,
range = _position.range;
var eclFrom = new coord.Ecliptic(lon, lat);
var epochFrom = 2000.0;
var epochTo = base.JDEToJulianYear(jde);
var eclTo = precess.eclipticPosition(eclFrom, epochFrom, epochTo, 0, 0);
return new base.Coord(eclTo.lon, eclTo.lat, range);
}
}]);
return Planet;
}();
M.Planet = Planet;
/**
* ToFK5 converts ecliptic longitude and latitude from dynamical frame to FK5.
*
* @param {Number} lon - ecliptic longitude
* @param {Number} lat - ecliptic latitude
* @param {Number} jde - Julian ephemeris day
* @return {base.Coord}
* {Number} lon - FK5 longitude
* {Number} lat - FK5 latitude
*/
M.toFK5 = function (lon, lat, jde) {
// formula 32.3, p. 219.
var T = base.J2000Century(jde);
var Lp = lon - 1.397 * Math.PI / 180 * T - 0.00031 * Math.PI / 180 * T * T;
var _base$sincos = base.sincos(Lp),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
sLp = _base$sincos2[0],
cLp = _base$sincos2[1];
// (32.3) p. 219
var L5 = lon + -0.09033 / 3600 * Math.PI / 180 + 0.03916 / 3600 * Math.PI / 180 * (cLp + sLp) * Math.tan(lat);
var B5 = lat + 0.03916 / 3600 * Math.PI / 180 * (cLp - sLp);
return new base.Coord(L5, B5);
};
/***/ }),
/* 7 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
function _possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
function _inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module julian
*/
/**
* Julian: Chapter 7, Julian day.
*/
var base = __webpack_require__(0);
var sexa = __webpack_require__(4);
var deltat = __webpack_require__(9);
var _padstart = __webpack_require__(41);
var M = exports;
var int = Math.trunc;
/** 1582-10-05 Julian Date is 1st Gregorian Date (1582-10-15) */
var GREGORIAN0JD = M.GREGORIAN0JD = 2299160.5;
var DAYS_OF_YEAR = [0, 0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334];
var SECS_OF_DAY = 86400; // 24 * 60 * 60
/**
* Base class for CalendarJulian and CalendarGregorian
* Respects the start of the Gregorian Calendar at `GREGORIAN0JD`
*/
var Calendar = function () {
/**
* @param {number|Date} year - If `Date` is given then year, month, day is taken from that. Shortcut to `new Calendar().fromDate(date)`
* @param {number} month
* @param {number} day
*/
function Calendar(year) {
var month = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 1;
var day = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 1;
_classCallCheck(this, Calendar);
this.year = year;
this.month = month;
this.day = day;
if (year instanceof Date) {
this.fromDate(year);
}
}
_createClass(Calendar, [{
key: 'getDate',
value: function getDate() {
return {
year: this.year,
month: this.month,
day: Math.floor(this.day)
};
}
}, {
key: 'getTime',
value: function getTime() {
var t = new sexa.Time(this.day * SECS_OF_DAY);
var _t$toHMS = t.toHMS(),
_t$toHMS2 = _slicedToArray(_t$toHMS, 4),
neg = _t$toHMS2[0],
h = _t$toHMS2[1],
m = _t$toHMS2[2],
_s = _t$toHMS2[3]; // eslint-disable-line no-unused-vars
var _base$modf = base.modf(_s),
_base$modf2 = _slicedToArray(_base$modf, 2),
s = _base$modf2[0],
ms = _base$modf2[1];
ms = Math.trunc(ms * 1000);
return {
hour: h % 24,
minute: m,
second: s,
millisecond: ms
};
}
}, {
key: 'toISOString',
value: function toISOString() {
var _getDate = this.getDate(),
year = _getDate.year,
month = _getDate.month,
day = _getDate.day;
var _getTime = this.getTime(),
hour = _getTime.hour,
minute = _getTime.minute,
second = _getTime.second,
millisecond = _getTime.millisecond;
return pad(year, 4) + '-' + pad(month) + '-' + pad(day) + 'T' + (pad(hour) + ':' + pad(minute) + ':' + pad(second) + '.' + pad(millisecond, 3) + 'Z');
}
}, {
key: 'isGregorian',
value: function isGregorian() {
return M.isCalendarGregorian(this.year, this.month, this.day);
}
/**
* Note: Take care for dates < GREGORIAN0JD as `date` is always within the
* proleptic Gregorian Calender
* @param {Date} date - proleptic Gregorian date
*/
}, {
key: 'fromDate',
value: function fromDate(date) {
this.year = date.getUTCFullYear();
this.month = date.getUTCMonth() + 1;
var day = date.getUTCDate();
var hour = date.getUTCHours();
var minute = date.getUTCMinutes();
var second = date.getUTCSeconds();
var ms = date.getMilliseconds();
this.day = day + (hour + (minute + (second + ms / 1000) / 60) / 60) / 24;
return this;
}
/**
* Note: Take care for dates < GREGORIAN0JD as `date` is always within the
* proleptic Gregorian Calender
* @returns {Date} proleptic Gregorian date
*/
}, {
key: 'toDate',
value: function toDate() {
var _base$modf3 = base.modf(this.day),
_base$modf4 = _slicedToArray(_base$modf3, 2),
day = _base$modf4[0],
fhour = _base$modf4[1];
var _base$modf5 = base.modf(fhour * 24),
_base$modf6 = _slicedToArray(_base$modf5, 2),
hour = _base$modf6[0],
fminute = _base$modf6[1];
var _base$modf7 = base.modf(fminute * 60),
_base$modf8 = _slicedToArray(_base$modf7, 2),
minute = _base$modf8[0],
fsecond = _base$modf8[1];
var _base$modf9 = base.modf(fsecond * 60),
_base$modf10 = _slicedToArray(_base$modf9, 2),
second = _base$modf10[0],
fms = _base$modf10[1];
var date = new Date(Date.UTC(this.year, this.month - 1, day, hour, minute, second, Math.round(fms * 1000)));
date.setUTCFullYear(this.year);
return date;
}
/**
* converts a calendar date to decimal year
* @returns {number} decimal year
*/
}, {
key: 'toYear',
value: function toYear() {
var _base$modf11 = base.modf(this.day),
_base$modf12 = _slicedToArray(_base$modf11, 2),
d = _base$modf12[0],
f = _base$modf12[1]; // eslint-disable-line no-unused-vars
var n = this.dayOfYear() - 1 + f;
var days = this.isLeapYear() ? 366 : 365;
var decYear = this.year + n / days;
return decYear;
}
/**
* converts a decimal year to a calendar date
* @param {number} decimal year
*/
}, {
key: 'fromYear',
value: function fromYear(year) {
var _base$modf13 = base.modf(year),
_base$modf14 = _slicedToArray(_base$modf13, 2),
y = _base$modf14[0],
f = _base$modf14[1];
this.year = y;
var days = this.isLeapYear() ? 366 : 365;
var dayOfYear = base.round(f * days, 5);
var m = 12;
while (m > 0 && DAYS_OF_YEAR[m] > dayOfYear) {
m--;
}
this.month = m;
this.day = 1 + dayOfYear - DAYS_OF_YEAR[this.month];
return this;
}
}, {
key: 'isLeapYear',
value: function isLeapYear() {
if (this.isGregorian()) {
return M.LeapYearGregorian(this.year);
} else {
return M.LeapYearJulian(this.year);
}
}
}, {
key: 'toJD',
value: function toJD() {
return M.CalendarToJD(this.year, this.month, this.day, !this.isGregorian());
}
}, {
key: 'fromJD',
value: function fromJD(jd) {
var isJulian = !M.isJDCalendarGregorian(jd);
var _M$JDToCalendar = M.JDToCalendar(jd, isJulian),
year = _M$JDToCalendar.year,
month = _M$JDToCalendar.month,
day = _M$JDToCalendar.day;
this.year = year;
this.month = month;
this.day = day;
return this;
}
}, {
key: 'fromJDE',
value: function fromJDE(jde) {
this.fromJD(jde);
var dT = deltat.deltaT(this.toYear()); // in seconds
this.day -= dT / 86400;
return this;
}
}, {
key: 'toJDE',
value: function toJDE() {
var dT = deltat.deltaT(this.toYear()); // in seconds
this.day += dT / 86400;
return this.toJD();
}
/**
* set date to midnight UTC
*/
}, {
key: 'midnight',
value: function midnight() {
this.day = Math.floor(this.day);
return this;
}
/**
* set date to noon UTC
*/
}, {
key: 'noon',
value: function noon() {
this.day = Math.floor(this.day) + 0.5;
return this;
}
/**
* @param {Boolean} td - if `true` calendar instance is in TD; date gets converted to UT
* true - `UT = TD - ΔT`
* false - `TD = UT + ΔT`
*/
}, {
key: 'deltaT',
value: function deltaT(td) {
var dT = deltat.deltaT(this.toYear()); // in seconds
if (td) {
this.day -= dT / 86400;
} else {
this.day += dT / 86400;
}
return this;
}
}, {
key: 'dayOfWeek',
value: function dayOfWeek() {
return M.DayOfWeek(this.toJD());
}
}, {
key: 'dayOfYear',
value: function dayOfYear() {
if (this.isGregorian()) {
return M.DayOfYearGregorian(this.year, this.month, this.day);
} else {
return M.DayOfYearJulian(this.year, this.month, this.day);
}
}
}]);
return Calendar;
}();
M.Calendar = Calendar;
var CalendarJulian = function (_Calendar) {
_inherits(CalendarJulian, _Calendar);
function CalendarJulian() {
_classCallCheck(this, CalendarJulian);
return _possibleConstructorReturn(this, (CalendarJulian.__proto__ || Object.getPrototypeOf(CalendarJulian)).apply(this, arguments));
}
_createClass(CalendarJulian, [{
key: 'toJD',
value: function toJD() {
return M.CalendarJulianToJD(this.year, this.month, this.day);
}
}, {
key: 'fromJD',
value: function fromJD(jd) {
var _M$JDToCalendarJulian = M.JDToCalendarJulian(jd),
year = _M$JDToCalendarJulian.year,
month = _M$JDToCalendarJulian.month,
day = _M$JDToCalendarJulian.day;
this.year = year;
this.month = month;
this.day = day;
return this;
}
}, {
key: 'isLeapYear',
value: function isLeapYear() {
return M.LeapYearJulian(this.year);
}
}, {
key: 'dayOfYear',
value: function dayOfYear() {
return M.DayOfYearJulian(this.year, this.month, this.day);
}
/**
* toGregorian converts a Julian calendar date to a year, month, and day
* in the Gregorian calendar.
* @returns {CalendarGregorian}
*/
}, {
key: 'toGregorian',
value: function toGregorian() {
var jd = this.toJD();
return new CalendarGregorian().fromJD(jd);
}
}]);
return CalendarJulian;
}(Calendar);
M.CalendarJulian = CalendarJulian;
var CalendarGregorian = function (_Calendar2) {
_inherits(CalendarGregorian, _Calendar2);
function CalendarGregorian() {
_classCallCheck(this, CalendarGregorian);
return _possibleConstructorReturn(this, (CalendarGregorian.__proto__ || Object.getPrototypeOf(CalendarGregorian)).apply(this, arguments));
}
_createClass(CalendarGregorian, [{
key: 'toJD',
value: function toJD() {
return M.CalendarGregorianToJD(this.year, this.month, this.day);
}
}, {
key: 'fromJD',
value: function fromJD(jd) {
var _M$JDToCalendarGregor = M.JDToCalendarGregorian(jd),
year = _M$JDToCalendarGregor.year,
month = _M$JDToCalendarGregor.month,
day = _M$JDToCalendarGregor.day;
this.year = year;
this.month = month;
this.day = day;
return this;
}
}, {
key: 'isLeapYear',
value: function isLeapYear() {
return M.LeapYearGregorian(this.year);
}
}, {
key: 'dayOfYear',
value: function dayOfYear() {
return M.DayOfYearGregorian(this.year, this.month, this.day);
}
/*
* toJulian converts a Gregorian calendar date to a year, month, and day
* in the Julian calendar.
* @returns {CalendarJulian}
*/
}, {
key: 'toJulian',
value: function toJulian() {
var jd = this.toJD();
return new CalendarJulian().fromJD(jd);
}
}]);
return CalendarGregorian;
}(Calendar);
M.CalendarGregorian = CalendarGregorian;
// -----------------------------------------------------------------------------
/**
* base conversion from calendar date to julian day
*/
M.CalendarToJD = function (y, m, d, isJulian) {
var b = 0;
if (m < 3) {
y--;
m += 12;
}
if (!isJulian) {
var a = base.floorDiv(y, 100);
b = 2 - a + base.floorDiv(a, 4);
}
// (7.1) p. 61
var jd = base.floorDiv(36525 * int(y + 4716), 100) + (base.floorDiv(306 * (m + 1), 10) + b) + d - 1524.5;
return jd;
};
/**
* CalendarGregorianToJD converts a Gregorian year, month, and day of month
* to Julian day.
*
* Negative years are valid, back to JD 0. The result is not valid for
* dates before JD 0.
* @param {number} y - year (int)
* @param {number} m - month (int)
* @param {number} d - day (float)
* @returns {number} jd - Julian day (float)
*/
M.CalendarGregorianToJD = function (y, m, d) {
return M.CalendarToJD(y, m, d, false);
};
/**
* CalendarJulianToJD converts a Julian year, month, and day of month to Julian day.
*
* Negative years are valid, back to JD 0. The result is not valid for
* dates before JD 0.
* @param {number} y - year (int)
* @param {number} m - month (int)
* @param {number} d - day (float)
* @returns {number} jd - Julian day (float)
*/
M.CalendarJulianToJD = function (y, m, d) {
return M.CalendarToJD(y, m, d, true);
};
/**
* LeapYearJulian returns true if year y in the Julian calendar is a leap year.
* @param {number} y - year (int)
* @returns {boolean} true if leap year in Julian Calendar
*/
M.LeapYearJulian = function (y) {
return y % 4 === 0;
};
/**
* LeapYearGregorian returns true if year y in the Gregorian calendar is a leap year.
* @param {number} y - year (int)
* @returns {boolean} true if leap year in Gregorian Calendar
*/
M.LeapYearGregorian = function (y) {
return y % 4 === 0 && y % 100 !== 0 || y % 400 === 0;
};
/**
* JDToCalendar returns the calendar date for the given jd.
*
* Note that this function returns a date in either the Julian or Gregorian
* Calendar, as appropriate.
* @param {number} jd - Julian day (float)
* @param {boolean} isJulian - set true for Julian Calendar, otherwise Gregorian is used
* @returns {object} `{ (int) year, (int) month, (float) day }`
*/
M.JDToCalendar = function (jd, isJulian) {
var _base$modf15 = base.modf(jd + 0.5),
_base$modf16 = _slicedToArray(_base$modf15, 2),
z = _base$modf16[0],
f = _base$modf16[1];
var a = z;
if (!isJulian) {
var α = base.floorDiv(z * 100 - 186721625, 3652425);
a = z + 1 + α - base.floorDiv(α, 4);
}
var b = a + 1524;
var c = base.floorDiv(b * 100 - 12210, 36525);
var d = base.floorDiv(36525 * c, 100);
var e = int(base.floorDiv((b - d) * 1e4, 306001));
// compute return values
var year;
var month;
var day = int(b - d) - base.floorDiv(306001 * e, 1e4) + f;
if (e === 14 || e === 15) {
month = e - 13;
} else {
month = e - 1;
}
if (month < 3) {
year = int(c) - 4715;
} else {
year = int(c) - 4716;
}
return { year: year, month: month, day: day };
};
/**
* JDToCalendarGregorian returns the calendar date for the given jd in the Gregorian Calendar.
*
* @param {number} jd - Julian day (float)
* @returns {object} `{ (int) year, (int) month, (float) day }`
*/
M.JDToCalendarGregorian = function (jd) {
return M.JDToCalendar(jd, false);
};
/**
* JDToCalendarJulian returns the calendar date for the given jd in the Julian Calendar.
*
* @param {number} jd - Julian day (float)
* @returns {object} { (int) year, (int) month, (float) day }
*/
M.JDToCalendarJulian = function (jd) {
return M.JDToCalendar(jd, true);
};
/**
* isJDCalendarGregorian tests if Julian day `jd` falls into the Gregorian calendar
* @param {number} jd - Julian day (float)
* @returns {boolean} true for Gregorian, false for Julian calendar
*/
M.isJDCalendarGregorian = function (jd) {
return jd >= GREGORIAN0JD;
};
/**
* isCalendarGregorian tests if date falls into the Gregorian calendar
* @param {number} year - julian/gregorian year
* @param {number} [month] - month of julian/gregorian year
* @param {number} [day] - day of julian/gregorian year
* @returns {boolean} true for Gregorian, false for Julian calendar
*/
M.isCalendarGregorian = function (year) {
var month = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 1;
var day = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 1;
return year > 1582 || year === 1582 && month > 10 || year === 1582 && month === 10 && day >= 15;
};
/**
* JDToDate converts a Julian day `jd` to a Date Object (Gregorian Calendar)
*
* Note: Javascript uses the the ISO-8601 calendar, which is a proleptic Gregorian
* calendar, i.e. it acts as if this calendar was always in effect, even before
* its year of introduction in 1582. Therefore dates between 1582-10-05 and
* 1582-10-14 exists.
*
* @param {number} jd - Julian day (float)
* @returns {Date}
*/
M.JDToDate = function (jd) {
return new CalendarGregorian().fromJD(jd).toDate();
};
/**
* DateToJD converts a proleptic Gregorian Date into a Julian day `jd`
* @param {Date} date
* @returns {number} jd - Julian day (float)
*/
M.DateToJD = function (date) {
return new CalendarGregorian().fromDate(date).toJD();
};
/**
* JDEToDate converts a Julian ephemeris day `jde` to a Date Object (Gregorian Calendar)
* To obtain "Universal Time" (UT) from "Dynamical Time" (TD) the correction ΔT (in seconds) gets applied
* ```
* UT = TD - ΔT
* ```
* If your use case does not require such accuracy converting `jde` using `JDToDate` is fine.
*
* Note: Javascript uses the the ISO-8601 calendar, which is a proleptic Gregorian
* calendar, i.e. it acts as if this calendar was always in effect, even before
* its year of introduction in 1582. Therefore dates between 1582-10-05 and
* 1582-10-14 exists.
*
* @param {number} jde - Julian ephemeris day
* @returns {Date} Javascript Date Object
*/
M.JDEToDate = function (jde) {
return new CalendarGregorian().fromJDE(jde).toDate();
};
/**
* DateToJDE converts a Date Object (Gregorian Calendar) to a Julian ephemeris day `jde`
* To obtain "Dynamical Time" (TD) from "Universal Time" (UT) the correction ΔT (in seconds) gets applied
* ```
* TD = UT + ΔT
* ```
* If your use case does not require such accuracy converting `Date` using `DateToJD` is fine.
*
* @param {Date} date - Javascript Date Object
* @returns {number} jde - Julian ephemeris day (float)
*/
M.DateToJDE = function (date) {
return new CalendarGregorian().fromDate(date).toJDE();
};
/**
* converts Modified Julian Day `mjd` to Julian Day `jd`
* @param {Number} mjd - Modified Julian Day
* @returns {Number} jd - Julian Day
*/
M.MJDToJD = function (mjd) {
return mjd - base.JMod;
};
/**
* converts Julian Day `jd` to Modified Julian Day `mjd`
* @param {Number} jd - Julian Day
* @returns {Number} mjd - Modified Julian Day
*/
M.JDToMJD = function (jd) {
return jd + base.JMod;
};
/**
* DayOfWeek determines the day of the week for a given JD.
*
* The value returned is an integer in the range 0 to 6, where 0 represents
* Sunday. This is the same convention followed in the time package of the
* Javascript standard library.
* @param {number} jd - Julian day (float)
* @returns {number} (int) 0 == sunday; ...; 6 == saturday
*/
M.DayOfWeek = function (jd) {
return int(jd + 1.5) % 7;
};
/**
* DayOfYearGregorian computes the day number within the year of the Gregorian
* calendar.
* @param {number} y - year (int)
* @param {number} m - month (int)
* @param {number} d - day (float)
* @returns {number} day of year
*/
M.DayOfYearGregorian = function (y, m, d) {
return M.DayOfYear(y, m, int(d), M.LeapYearGregorian(y));
};
/**
* DayOfYearJulian computes the day number within the year of the Julian
* calendar.
* @param {number} y - year (int)
* @param {number} m - month (int)
* @param {number} d - day (float)
* @returns {number} day of year
*/
M.DayOfYearJulian = function (y, m, d) {
return M.DayOfYear(y, m, int(d), M.LeapYearJulian(y));
};
/**
* DayOfYear computes the day number within the year.
*
* This form of the function is not specific to the Julian or Gregorian
* calendar, but you must tell it whether the year is a leap year.
* @param {number} y - year (int)
* @param {number} m - month (int)
* @param {number} d - day (float)
* @param {boolean} leap - set `true` if `y` is leap year
* @returns {number} day of year
*/
M.DayOfYear = function (y, m, d, leap) {
var k = 0;
if (leap && m > 1) {
k = 1;
}
return k + DAYS_OF_YEAR[m] + int(d);
};
/**
* DayOfYearToCalendar returns the calendar month and day for a given
* day of year and leap year status.
* @param {number} n - day of year (int)
* @param {boolean} leap - set `true` if `y` is leap year
* @returns {object} `{ (int) month, (float) day }`
*/
M.DayOfYearToCalendar = function (n, leap) {
var month;
var k = 0;
if (leap) {
k = 1;
}
for (month = 1; month <= 12; month++) {
if (k + DAYS_OF_YEAR[month] > n) {
month = month - 1;
break;
}
}
var day = n - k - DAYS_OF_YEAR[month];
return { month: month, day: day };
};
/**
* DayOfYearToCalendarGregorian returns the calendar month and day for a given
* day of year.
* @param {number} year
* @param {number} n - day of year (int)
* @returns {CalendarGregorian} { (int) year, (int) month, (float) day }
*/
M.DayOfYearToCalendarGregorian = function (year, n) {
var _M$DayOfYearToCalenda = M.DayOfYearToCalendar(n, M.LeapYearGregorian(year)),
month = _M$DayOfYearToCalenda.month,
day = _M$DayOfYearToCalenda.day;
return new CalendarGregorian(year, month, day);
};
/**
* DayOfYearToCalendarJulian returns the calendar month and day for a given
* day of year.
* @param {number} year
* @param {number} n - day of year (int)
* @returns {CalendarJulian} { (int) year, (int) month, (float) day }
*/
M.DayOfYearToCalendarJulian = function (year, n) {
var _M$DayOfYearToCalenda2 = M.DayOfYearToCalendar(n, M.LeapYearJulian(year)),
month = _M$DayOfYearToCalenda2.month,
day = _M$DayOfYearToCalenda2.day;
return new CalendarJulian(year, month, day);
};
function pad(num, len) {
len = len || 2;
var neg = num < 0 ? '-' : '';
num = Math.abs(num);
return neg + _padstart(num, len, '0');
}
/***/ }),
/* 8 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module precess
*/
/**
* Precession: Chapter 21, Precession.
*
* Functions in this package take Julian epoch argurments rather than Julian
* days. Use base.JDEToJulianYear() to convert.
*
* Also in package base are some definitions related to the Besselian and
* Julian Year.
*
* Partial: Precession from FK4 not implemented. Meeus gives no test cases.
* It's a fair amount of code and data, representing significant chances for
* errors. And precession from FK4 would seem to be of little interest today.
*
* Proper motion units
*
* Meeus gives some example annual proper motions in units of seconds of
* right ascension and seconds of declination. To make units clear,
* functions in this package take proper motions with argument types of
* sexa.HourAngle and sexa.Angle respectively. Error-prone conversions
* can be avoided by using the constructors for these base types.
*
* For example, given an annual proper motion in right ascension of -0ˢ.03847,
* rather than
*
* mra = -0.03847 / 13751 // as Meeus suggests
*
* or
*
* mra = -0.03847 * (15/3600) * (pi/180) // less magic
*
* use
*
* mra = new sexa.HourAngle(false, 0, 0, -0.03847)
*
* Unless otherwise indicated, functions in this library expect proper motions
* to be annual proper motions, so the unit denominator is years.
* (The code, following Meeus's example, technically treats it as Julian years.)
*/
var base = __webpack_require__(0);
var coord = __webpack_require__(2);
var elementequinox = __webpack_require__(13);
var nutation = __webpack_require__(1);
var sexa = __webpack_require__(4);
var M = exports;
/**
* approxAnnualPrecession returns approximate annual precision in right
* ascension and declination.
*
* The two epochs should be within a few hundred years.
* The declinations should not be too close to the poles.
*
* @param {coord.Equatorial} eqFrom
* @param {Number} epochFrom - use `base.JDEToJulianYear(year)` to get epoch
* @param {Number} epochTo - use `base.JDEToJulianYear(year)` to get epoch
* @returns {Array}
* {sexa.HourAngle} seconds of right ascension
* {sexa.Angle} seconds of Declination
*/
M.approxAnnualPrecession = function (eqFrom, epochFrom, epochTo) {
var _mn = mn(epochFrom, epochTo),
_mn2 = _slicedToArray(_mn, 3),
m = _mn2[0],
na = _mn2[1],
nd = _mn2[2];
var _base$sincos = base.sincos(eqFrom.ra),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
sa = _base$sincos2[0],
ca = _base$sincos2[1];
// (21.1) p. 132
var Δαs = m + na * sa * Math.tan(eqFrom.dec); // seconds of RA
var Δδs = nd * ca; // seconds of Dec
var ra = new sexa.HourAngle(false, 0, 0, Δαs).rad();
var dec = new sexa.Angle(false, 0, 0, Δδs).rad();
return { ra: ra, dec: dec };
};
/**
* @param {Number} epochFrom - use `base.JDEToJulianYear(year)` to get epoch
* @param {Number} epochTo - use `base.JDEToJulianYear(year)` to get epoch
*/
function mn(epochFrom, epochTo) {
var T = (epochTo - epochFrom) * 0.01;
var m = 3.07496 + 0.00186 * T;
var na = 1.33621 - 0.00057 * T;
var nd = 20.0431 - 0.0085 * T;
return [m, na, nd];
}
M.mn = mn;
/**
* ApproxPosition uses ApproxAnnualPrecession to compute a simple and quick
* precession while still considering proper motion.
*
* @param {coord.Equatorial} eqFrom
* @param {Number} epochFrom
* @param {Number} epochTo
* @param {Number} mα - in radians
* @param {Number} mδ - in radians
* @returns {coord.Equatorial} eqTo
*/
M.approxPosition = function (eqFrom, epochFrom, epochTo, mα, mδ) {
var _M$approxAnnualPreces = M.approxAnnualPrecession(eqFrom, epochFrom, epochTo),
ra = _M$approxAnnualPreces.ra,
dec = _M$approxAnnualPreces.dec;
var dy = epochTo - epochFrom;
var eqTo = new coord.Equatorial();
eqTo.ra = eqFrom.ra + (ra + mα) * dy;
eqTo.dec = eqFrom.dec + (dec + mδ) * dy;
return eqTo;
};
// constants
var d = Math.PI / 180;
var s = d / 3600;
// coefficients from (21.2) p. 134
var ζT = [2306.2181 * s, 1.39656 * s, -0.000139 * s];
var zT = [2306.2181 * s, 1.39656 * s, -0.000139 * s];
var θT = [2004.3109 * s, -0.8533 * s, -0.000217 * s];
// coefficients from (21.3) p. 134
var ζt = [2306.2181 * s, 0.30188 * s, 0.017998 * s];
var zt = [2306.2181 * s, 1.09468 * s, 0.018203 * s];
var θt = [2004.3109 * s, -0.42665 * s, -0.041833 * s];
/**
* Precessor represents precession from one epoch to another.
*
* Construct with NewPrecessor, then call method Precess.
* After construction, Precess may be called multiple times to precess
* different coordinates with the same initial and final epochs.
*/
var Precessor = function () {
/**
* constructs a Precessor object and initializes it to precess
* coordinates from epochFrom to epochTo.
* @param {Number} epochFrom
* @param {Number} epochTo
*/
function Precessor(epochFrom, epochTo) {
_classCallCheck(this, Precessor);
// (21.2) p. 134
var ζCoeff = ζt;
var zCoeff = zt;
var θCoeff = θt;
if (epochFrom !== 2000) {
var T = (epochFrom - 2000) * 0.01;
ζCoeff = [base.horner(T, ζT), 0.30188 * s - 0.000344 * s * T, 0.017998 * s];
zCoeff = [base.horner(T, zT), 1.09468 * s + 0.000066 * s * T, 0.018203 * s];
θCoeff = [base.horner(T, θT), -0.42665 * s - 0.000217 * s * T, -0.041833 * s];
}
var t = (epochTo - epochFrom) * 0.01;
this.ζ = base.horner(t, ζCoeff) * t;
this.z = base.horner(t, zCoeff) * t;
var θ = base.horner(t, θCoeff) * t;
this.sθ = Math.sin(θ);
this.cθ = Math.cos(θ);
}
/**
* Precess precesses coordinates eqFrom, leaving result in eqTo.
*
* @param {coord.Equatorial} eqFrom
* @returns {coord.Equatorial} eqTo
*/
_createClass(Precessor, [{
key: 'precess',
value: function precess(eqFrom) {
// (21.4) p. 134
var _base$sincos3 = base.sincos(eqFrom.dec),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sδ = _base$sincos4[0],
cδ = _base$sincos4[1];
var _base$sincos5 = base.sincos(eqFrom.ra + this.ζ),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
sαζ = _base$sincos6[0],
cαζ = _base$sincos6[1];
var A = cδ * sαζ;
var B = this.cθ * cδ * cαζ - this.sθ * sδ;
var C = this.sθ * cδ * cαζ + this.cθ * sδ;
var eqTo = new coord.Equatorial();
eqTo.ra = Math.atan2(A, B) + this.z;
if (C < base.CosSmallAngle) {
eqTo.dec = Math.asin(C);
} else {
eqTo.dec = Math.acos(Math.hypot(A, B)); // near pole
}
return eqTo;
}
}]);
return Precessor;
}();
M.Precessor = Precessor;
/**
* Position precesses equatorial coordinates from one epoch to another,
* including proper motions.
*
* If proper motions are not to be considered or are not applicable, pass 0, 0
* for mα, mδ
*
* Both eqFrom and eqTo must be non-nil, although they may point to the same
* struct. EqTo is returned for convenience.
* @param {coord.Equatorial} eqFrom
* @param {coord.Equatorial} eqTo
* @param {Number} epochFrom
* @param {Number} epochTo
* @param {Number} mα - in radians
* @param {Number} mδ - in radians
* @returns {coord.Equatorial} [eqTo]
*/
M.position = function (eqFrom, epochFrom, epochTo, mα, mδ) {
var p = new Precessor(epochFrom, epochTo);
var t = epochTo - epochFrom;
var eqTo = new coord.Equatorial();
eqTo.ra = eqFrom.ra + mα * t;
eqTo.dec = eqFrom.dec + mδ * t;
return p.precess(eqTo);
};
// coefficients from (21.5) p. 136
var ηT = [47.0029 * s, -0.06603 * s, 0.000598 * s];
var πT = [174.876384 * d, 3289.4789 * s, 0.60622 * s];
var pT = [5029.0966 * s, 2.22226 * s, -0.000042 * s];
var ηt = [47.0029 * s, -0.03302 * s, 0.000060 * s];
var πt = [174.876384 * d, -869.8089 * s, 0.03536 * s];
var pt = [5029.0966 * s, 1.11113 * s, -0.000006 * s];
/**
* EclipticPrecessor represents precession from one epoch to another.
*
* Construct with NewEclipticPrecessor, then call method Precess.
* After construction, Precess may be called multiple times to precess
* different coordinates with the same initial and final epochs.
*/
var EclipticPrecessor = function () {
/**
* constructs an EclipticPrecessor object and initializes
* it to precess coordinates from epochFrom to epochTo.
* @param {Number} epochFrom
* @param {Number} epochTo
*/
function EclipticPrecessor(epochFrom, epochTo) {
_classCallCheck(this, EclipticPrecessor);
// (21.5) p. 136
var ηCoeff = ηt;
var πCoeff = πt;
var pCoeff = pt;
if (epochFrom !== 2000) {
var T = (epochFrom - 2000) * 0.01;
ηCoeff = [base.horner(T, ηT), -0.03302 * s + 0.000598 * s * T, 0.000060 * s];
πCoeff = [base.horner(T, πT), -869.8089 * s - 0.50491 * s * T, 0.03536 * s];
pCoeff = [base.horner(T, pT), 1.11113 * s - 0.000042 * s * T, -0.000006 * s];
}
var t = (epochTo - epochFrom) * 0.01;
this.π = base.horner(t, πCoeff);
this.p = base.horner(t, pCoeff) * t;
var η = base.horner(t, ηCoeff) * t;
this.sη = Math.sin(η);
this.cη = Math.cos(η);
}
/**
* EclipticPrecess precesses coordinates eclFrom, leaving result in eclTo.
*
* The same struct may be used for eclFrom and eclTo.
* EclTo is returned for convenience.
* @param {coord.Ecliptic} eclFrom
* @param {coord.Ecliptic} eclTo
* @returns {coord.Ecliptic} [eclTo]
*/
_createClass(EclipticPrecessor, [{
key: 'precess',
value: function precess(eclFrom) {
// (21.7) p. 137
var _base$sincos7 = base.sincos(eclFrom.lat),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
sβ = _base$sincos8[0],
cβ = _base$sincos8[1];
var _base$sincos9 = base.sincos(this.π - eclFrom.lon),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sd = _base$sincos10[0],
cd = _base$sincos10[1];
var A = this.cη * cβ * sd - this.sη * sβ;
var B = cβ * cd;
var C = this.cη * sβ + this.sη * cβ * sd;
var eclTo = new coord.Ecliptic();
eclTo.lon = this.p + this.π - Math.atan2(A, B);
if (C < base.CosSmallAngle) {
eclTo.lat = Math.asin(C);
} else {
eclTo.lat = Math.acos(Math.hypot(A, B)); // near pole
}
return eclTo;
}
/**
* ReduceElements reduces orbital elements of a solar system body from one
* equinox to another.
*
* This function is described in chapter 24, but is located in this
* package so it can be a method of EclipticPrecessor.
*
* @param {elementequinox.Elements} eFrom
* @returns {elementequinox.Elements} eTo
*/
}, {
key: 'reduceElements',
value: function reduceElements(eFrom) {
var ψ = this.π + this.p;
var _base$sincos11 = base.sincos(eFrom.inc),
_base$sincos12 = _slicedToArray(_base$sincos11, 2),
si = _base$sincos12[0],
ci = _base$sincos12[1];
var _base$sincos13 = base.sincos(eFrom.node - this.π),
_base$sincos14 = _slicedToArray(_base$sincos13, 2),
snp = _base$sincos14[0],
cnp = _base$sincos14[1];
var eTo = new elementequinox.Elements();
// (24.1) p. 159
eTo.inc = Math.acos(ci * this.cη + si * this.sη * cnp);
// (24.2) p. 159
eTo.node = Math.atan2(si * snp, this.cη * si * cnp - this.sη * ci) + ψ;
// (24.3) p. 159
eTo.peri = Math.atan2(-this.sη * snp, si * this.cη - ci * this.sη * cnp) + eFrom.peri;
return eTo;
}
}]);
return EclipticPrecessor;
}();
M.EclipticPrecessor = EclipticPrecessor;
/**
* eclipticPosition precesses ecliptic coordinates from one epoch to another,
* including proper motions.
* While eclFrom is given as ecliptic coordinates, proper motions mα, mδ are
* still expected to be equatorial. If proper motions are not to be considered
* or are not applicable, pass 0, 0.
* Both eclFrom and eclTo must be non-nil, although they may point to the same
* struct. EclTo is returned for convenience.
*
* @param {coord.Ecliptic} eclFrom,
* @param {Number} epochFrom
* @param {Number} epochTo
* @param {sexa.HourAngle} mα
* @param {sexa.Angle} mδ
* @returns {coord.Ecliptic} eclTo
*/
M.eclipticPosition = function (eclFrom, epochFrom, epochTo, mα, mδ) {
var p = new EclipticPrecessor(epochFrom, epochTo);
if (mα !== 0 || mδ !== 0) {
var _M$properMotion = M.properMotion(mα.rad(), mδ.rad(), epochFrom, eclFrom),
lon = _M$properMotion.lon,
lat = _M$properMotion.lat;
var t = epochTo - epochFrom;
eclFrom.lon += lon * t;
eclFrom.lat += lat * t;
}
return p.precess(eclFrom);
};
/**
* @param {Number} mα - anual proper motion (ra)
* @param {Number} mδ - anual proper motion (dec)
* @param {Number} epoch
* @param {coord.Ecliptic} ecl
* @returns {Number[]} [mλ, mβ]
*/
M.properMotion = function (mα, mδ, epoch, ecl) {
var ε = nutation.meanObliquity(base.JulianYearToJDE(epoch));
var _base$sincos15 = base.sincos(ε),
_base$sincos16 = _slicedToArray(_base$sincos15, 2),
εsin = _base$sincos16[0],
εcos = _base$sincos16[1];
var _ecl$toEquatorial = ecl.toEquatorial(ε),
ra = _ecl$toEquatorial.ra,
dec = _ecl$toEquatorial.dec;
var _base$sincos17 = base.sincos(ra),
_base$sincos18 = _slicedToArray(_base$sincos17, 2),
sα = _base$sincos18[0],
cα = _base$sincos18[1];
var _base$sincos19 = base.sincos(dec),
_base$sincos20 = _slicedToArray(_base$sincos19, 2),
sδ = _base$sincos20[0],
cδ = _base$sincos20[1];
var cβ = Math.cos(ecl.lat);
var lon = (mδ * εsin * cα + mα * cδ * (εcos * cδ + εsin * sδ * sα)) / (cβ * cβ);
var lat = (mδ * (εcos * cδ + εsin * sδ * sα) - mα * εsin * cα * cδ) / cβ;
return new coord.Ecliptic(lon, lat);
};
/**
* ProperMotion3D takes the 3D equatorial coordinates of an object
* at one epoch and computes its coordinates at a new epoch, considering
* proper motion and radial velocity.
*
* Radial distance (r) must be in parsecs, radial velocitiy (mr) in
* parsecs per year.
*
* Both eqFrom and eqTo must be non-nil, although they may point to the same
* struct. EqTo is returned for convenience.
*
* @param {coord.Equatorial} eqFrom,
* @param {Number} epochFrom
* @param {Number} r
* @param {Number} mr
* @param {sexa.HourAngle} mα
* @param {sexa.Angle} mδ
* @returns {coord.Equatorial} eqTo
*/
M.properMotion3D = function (eqFrom, epochFrom, epochTo, r, mr, mα, mδ) {
var _base$sincos21 = base.sincos(eqFrom.ra),
_base$sincos22 = _slicedToArray(_base$sincos21, 2),
sα = _base$sincos22[0],
cα = _base$sincos22[1];
var _base$sincos23 = base.sincos(eqFrom.dec),
_base$sincos24 = _slicedToArray(_base$sincos23, 2),
sδ = _base$sincos24[0],
cδ = _base$sincos24[1];
var x = r * cδ * cα;
var y = r * cδ * sα;
var z = r * sδ;
var mrr = mr / r;
var zmδ = z * mδ.rad();
var mx = x * mrr - zmδ * cα - y * mα.rad();
var my = y * mrr - zmδ * sα + x * mα.rad();
var mz = z * mrr + r * mδ.rad() * cδ;
var t = epochTo - epochFrom;
var xp = x + t * mx;
var yp = y + t * my;
var zp = z + t * mz;
var eqTo = new coord.Equatorial();
eqTo.ra = Math.atan2(yp, xp);
eqTo.dec = Math.atan2(zp, Math.hypot(xp, yp));
return eqTo;
};
/***/ }),
/* 9 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module deltat
*/
/**
* DeltaT: Chapter 10, Dynamical Time and Universal Time.
*
* This package uses no functions from the Chapter. Polynoms are from
* <http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html>, data sets are from
* <http://maia.usno.navy.mil/ser7/>
*
* Functions in this package compute ΔT for various ranges of dates.
*
* ΔT = TD - UT1
*
* TD = "Dynamical Time", which is related to:
* ET "Ephermis Time", an older term.
* TDB "Barycentric Dynamical Time", very close to TD.
* TDT "Terrestrial Dynamical Time", a more correct term.
* TT "Terrestrial Time", a newer and more correct term.
*
* UT = "Universal Time", which is related (if ambiguously) to GMT "Greenwich
* Mean Time".
*
* Terrestrial Time is effectively equal to International Atomic Time (TAI)
* plus 32.184 seconds exactly: TT = TAI + 32.184
* The epoch designated "J2000.0" is specified as Julian date 2451545.0 TT,
* or 2000 January 1, 12h TT. This epoch can also be expressed as
* 2000 January 1, 11:59:27.816 TAI or 2000 January 1, 11:58:55.816 UTC.
*/
var base = __webpack_require__(0);
var interp = __webpack_require__(5);
var deltat = __webpack_require__(40);
var M = exports;
/**
* deltaT returns the difference ΔT = TD - UT between Dynamical Time TD and
* Univeral Time (GMT+12) in seconds
*
* Polynoms are from <http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html>
* and <http://www.staff.science.uu.nl/~gent0113/deltat/deltat_old.htm>
*
* @param {Number} dyear - decimal year
* @returns {Number} ΔT in seconds.
*/
M.deltaT = function (dyear) {
var ΔT = void 0;
if (dyear < -500) {
ΔT = base.horner((dyear - 1820) * 0.01, -20, 0, 32);
} else if (dyear < 500) {
ΔT = base.horner(dyear * 0.01, 10583.6, -1014.41, 33.78311, -5.952053, -0.1798452, 0.022174192, 0.0090316521);
} else if (dyear < 1600) {
ΔT = base.horner((dyear - 1000) * 0.01, 1574.2, -556.01, 71.23472, 0.319781, -0.8503463, -0.005050998, 0.0083572073);
} else if (dyear < deltat.historic.first) {
ΔT = base.horner(dyear - 1600, 120, -0.9808, -0.01532, 1 / 7129);
} else if (dyear < deltat.data.first) {
ΔT = interpolate(dyear, deltat.historic);
} else if (dyear < deltat.data.last - 0.25) {
// -0.25 ~= do not consider last 3 months in dataset
ΔT = interpolateData(dyear, deltat.data);
} else if (dyear < deltat.prediction.last) {
ΔT = interpolate(dyear, deltat.prediction);
} else if (dyear < 2050) {
ΔT = base.horner((dyear - 2000) / 100, 62.92, 32.217, 55.89);
} else if (dyear < 2150) {
ΔT = base.horner((dyear - 1820) / 100, -205.72, 56.28, 32);
} else {
var u = (dyear - 1820) / 100;
ΔT = -20 + 32 * u * u;
}
return ΔT;
};
/**
* interpolation of dataset
* @private
* @param {Number} dyear - julian year
* @returns {Number} ΔT in seconds.
*/
function interpolate(dyear, data) {
var d3 = interp.len3ForInterpolateX(dyear, data.first, data.last, data.table);
return d3.interpolateX(dyear);
}
/**
* interpolation of dataset from finals2000A with is one entry per month
* linear interpolation over whole dataset is inaccurate as points per month
* are not equidistant. Therefore points are approximated using 2nd diff. interpolation
* from current month using the following two points
*
* @private
* @param {Number} dyear - julian year
* @returns {Number} ΔT in seconds.
*/
function interpolateData(dyear, data) {
var _data$firstYM = _slicedToArray(data.firstYM, 2),
fyear = _data$firstYM[0],
fmonth = _data$firstYM[1];
var _monthOfYear = monthOfYear(dyear),
year = _monthOfYear.year,
month = _monthOfYear.month,
first = _monthOfYear.first,
last = _monthOfYear.last;
var pos = 12 * (year - fyear) + (month - fmonth);
var table = data.table.slice(pos, pos + 3);
var d3 = new interp.Len3(first, last, table);
return d3.interpolateX(dyear);
}
/**
* Get month of Year from fraction. Fraction differs at leap years.
* @private
* @param {Number} dyear - decimal year
* @return {Object} `{year: Number, month: Number, first: Number, last}`
*/
function monthOfYear(dyear) {
var _require = __webpack_require__(7),
Calendar = _require.Calendar,
LeapYearGregorian = _require.LeapYearGregorian; // need to include this here due to cyclic require
if (!monthOfYear.data) {
// memoize yearly fractions per month
monthOfYear.data = { 0: [], 1: [] };
for (var m = 0; m <= 12; m++) {
monthOfYear.data[0][m] = new Calendar(1999, m, 1).toYear() - 1999; // non leap year
monthOfYear.data[1][m] = new Calendar(2000, m, 1).toYear() - 2000; // leap year
}
}
var year = dyear | 0;
var f = dyear - year;
var d = LeapYearGregorian(year) ? 1 : 0;
var data = monthOfYear.data[d];
var month = 12; // TODO loop could be improved
while (month > 0 && data[month] > f) {
month--;
}
var first = year + data[month];
var last = month < 11 ? year + data[month + 2] : year + 1 + data[(month + 2) % 12];
return { year: year, month: month, first: first, last: last };
}
/***/ }),
/* 10 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _typeof = typeof Symbol === "function" && typeof Symbol.iterator === "symbol" ? function (obj) { return typeof obj; } : function (obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; };
var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module elliptic
*/
/**
* Elliptic: Chapter 33, Elliptic Motion.
*
* Partial: Various formulas and algorithms are unimplemented for lack of
* examples or test cases.
*/
var apparent = __webpack_require__(12);
var base = __webpack_require__(0);
var coord = __webpack_require__(2);
var kepler = __webpack_require__(15);
var nutation = __webpack_require__(1);
var planetposition = __webpack_require__(6);
var solarxyz = __webpack_require__(25);
var M = exports;
/**
* Position returns observed equatorial coordinates of a planet at a given time.
*
* Argument p must be a valid V87Planet object for the observed planet.
* Argument earth must be a valid V87Planet object for Earth.
*
* Results are right ascension and declination, α and δ in radians.
*/
M.position = function (planet, earth, jde) {
// (p, earth *pp.V87Planet, jde float64) (α, δ float64)
var x = void 0;
var y = void 0;
var z = void 0;
var posEarth = earth.position(jde);
var _ref = [posEarth.lon, posEarth.lat, posEarth.range],
L0 = _ref[0],
B0 = _ref[1],
R0 = _ref[2];
var _base$sincos = base.sincos(B0),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
sB0 = _base$sincos2[0],
cB0 = _base$sincos2[1];
var _base$sincos3 = base.sincos(L0),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sL0 = _base$sincos4[0],
cL0 = _base$sincos4[1];
function pos() {
var τ = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
var pos = planet.position(jde - τ);
var _ref2 = [pos.lon, pos.lat, pos.range],
L = _ref2[0],
B = _ref2[1],
R = _ref2[2];
var _base$sincos5 = base.sincos(B),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
sB = _base$sincos6[0],
cB = _base$sincos6[1];
var _base$sincos7 = base.sincos(L),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
sL = _base$sincos8[0],
cL = _base$sincos8[1];
x = R * cB * cL - R0 * cB0 * cL0;
y = R * cB * sL - R0 * cB0 * sL0;
z = R * sB - R0 * sB0;
}
pos();
var Δ = Math.sqrt(x * x + y * y + z * z); // (33.4) p. 224
var τ = base.lightTime(Δ);
// repeating with jde-τ
pos(τ);
var λ = Math.atan2(y, x); // (33.1) p. 223
var β = Math.atan2(z, Math.hypot(x, y)); // (33.2) p. 223
var _apparent$eclipticAbe = apparent.eclipticAberration(λ, β, jde),
_apparent$eclipticAbe2 = _slicedToArray(_apparent$eclipticAbe, 2),
Δλ = _apparent$eclipticAbe2[0],
Δβ = _apparent$eclipticAbe2[1];
var fk5 = planetposition.toFK5(λ + Δλ, β + Δβ, jde);
λ = fk5.lon;
β = fk5.lat;
var _nutation$nutation = nutation.nutation(jde),
_nutation$nutation2 = _slicedToArray(_nutation$nutation, 2),
Δψ = _nutation$nutation2[0],
Δε = _nutation$nutation2[1];
λ += Δψ;
var ε = nutation.meanObliquity(jde) + Δε;
return new coord.Ecliptic(λ, β).toEquatorial(ε);
// Meeus gives a formula for elongation but doesn't spell out how to
// obtaion term λ0 and doesn't give an example solution.
};
/**
* Elements holds keplerian elements.
*/
var Elements = function () {
/*
Axis float64 // Semimajor axis, a, in AU
Ecc float64 // Eccentricity, e
Inc float64 // Inclination, i, in radians
ArgP float64 // Argument of perihelion, ω, in radians
Node float64 // Longitude of ascending node, Ω, in radians
TimeP float64 // Time of perihelion, T, as jde
*/
function Elements(axis, ecc, inc, argP, node, timeP) {
_classCallCheck(this, Elements);
var o = {};
if ((typeof axis === 'undefined' ? 'undefined' : _typeof(axis)) === 'object') {
o = axis;
}
this.axis = o.axis || axis;
this.ecc = o.ecc || ecc;
this.inc = o.inc || inc;
this.argP = o.argP || argP;
this.node = o.node || node;
this.timeP = o.timeP || timeP;
}
/**
* Position returns observed equatorial coordinates of a body with Keplerian elements.
*
* Argument e must be a valid V87Planet object for Earth.
*
* Results are right ascension and declination α and δ, and elongation ψ,
* all in radians.
*/
_createClass(Elements, [{
key: 'position',
value: function position(jde, earth) {
var _this = this;
// (α, δ, ψ float64) {
// (33.6) p. 227
var n = base.K / this.axis / Math.sqrt(this.axis);
var sε = base.SOblJ2000;
var cε = base.COblJ2000;
var _base$sincos9 = base.sincos(this.node),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sΩ = _base$sincos10[0],
cΩ = _base$sincos10[1];
var _base$sincos11 = base.sincos(this.inc),
_base$sincos12 = _slicedToArray(_base$sincos11, 2),
si = _base$sincos12[0],
ci = _base$sincos12[1];
// (33.7) p. 228
var F = cΩ;
var G = sΩ * cε;
var H = sΩ * sε;
var P = -sΩ * ci;
var Q = cΩ * ci * cε - si * sε;
var R = cΩ * ci * sε + si * cε;
// (33.8) p. 229
var A = Math.atan2(F, P);
var B = Math.atan2(G, Q);
var C = Math.atan2(H, R);
var a = Math.hypot(F, P);
var b = Math.hypot(G, Q);
var c = Math.hypot(H, R);
var f = function f(jde) {
// (x, y, z float64) {
var M = n * (jde - _this.timeP);
var E = void 0;
try {
E = kepler.kepler2b(_this.ecc, M, 15);
} catch (e) {
E = kepler.kepler3(_this.ecc, M);
}
var ν = kepler.true(E, _this.ecc);
var r = kepler.radius(E, _this.ecc, _this.axis);
// (33.9) p. 229
var x = r * a * Math.sin(A + _this.argP + ν);
var y = r * b * Math.sin(B + _this.argP + ν);
var z = r * c * Math.sin(C + _this.argP + ν);
return { x: x, y: y, z: z };
};
return M.astrometricJ2000(f, jde, earth);
}
}]);
return Elements;
}();
M.Elements = Elements;
/**
* AstrometricJ2000 is a utility function for computing astrometric coordinates.
*
* It is used internally and only exported so that it can be used from
* multiple packages. It is not otherwise expected to be used.
*
* Argument f is a function that returns J2000 equatorial rectangular
* coodinates of a body.
*
* Results are J2000 right ascention, declination, and elongation.
*/
M.astrometricJ2000 = function (f, jde, earth) {
// (f func(float64) (x, y, z float64), jde float64, e *pp.V87Planet) (α, δ, ψ float64)
var sol = solarxyz.positionJ2000(earth, jde);
var _ref3 = [sol.x, sol.y, sol.z],
X = _ref3[0],
Y = _ref3[1],
Z = _ref3[2];
var ξ = void 0;
var η = void 0;
var ζ = void 0;
var Δ = void 0;
function fn() {
var τ = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 0;
// (33.10) p. 229
var _f = f(jde - τ),
x = _f.x,
y = _f.y,
z = _f.z;
ξ = X + x;
η = Y + y;
ζ = Z + z;
Δ = Math.sqrt(ξ * ξ + η * η + ζ * ζ);
}
fn();
var τ = base.lightTime(Δ);
fn(τ);
var α = Math.atan2(η, ξ);
if (α < 0) {
α += 2 * Math.PI;
}
var δ = Math.asin(ζ / Δ);
var R0 = Math.sqrt(X * X + Y * Y + Z * Z);
var ψ = Math.acos((ξ * X + η * Y + ζ * Z) / R0 / Δ);
return new base.Coord(α, δ, undefined, ψ);
};
/**
* Velocity returns instantaneous velocity of a body in elliptical orbit around the Sun.
*
* Argument a is the semimajor axis of the body, r is the instaneous distance
* to the Sun, both in AU.
*
* Result is in Km/sec.
*/
M.velocity = function (a, r) {
// (a, r float64) float64
return 42.1219 * Math.sqrt(1 / r - 0.5 / a);
};
/**
* Velocity returns the velocity of a body at aphelion.
*
* Argument a is the semimajor axis of the body in AU, e is eccentricity.
*
* Result is in Km/sec.
*/
M.vAphelion = function (a, e) {
// (a, e float64) float64
return 29.7847 * Math.sqrt((1 - e) / (1 + e) / a);
};
/**
* Velocity returns the velocity of a body at perihelion.
*
* Argument a is the semimajor axis of the body in AU, e is eccentricity.
*
* Result is in Km/sec.
*/
M.vPerihelion = function (a, e) {
// (a, e float64) float64
return 29.7847 * Math.sqrt((1 + e) / (1 - e) / a);
};
/**
* Length1 returns Ramanujan's approximation for the length of an elliptical
* orbit.
*
* Argument a is semimajor axis, e is eccentricity.
*
* Result is in units used for semimajor axis, typically AU.
*/
M.length1 = function (a, e) {
// (a, e float64) float64
var b = a * Math.sqrt(1 - e * e);
return Math.PI * (3 * (a + b) - Math.sqrt((a + 3 * b) * (3 * a + b)));
};
/**
* Length2 returns an alternate approximation for the length of an elliptical
* orbit.
*
* Argument a is semimajor axis, e is eccentricity.
*
* Result is in units used for semimajor axis, typically AU.
*/
M.length2 = function (a, e) {
// (a, e float64) float64
var b = a * Math.sqrt(1 - e * e);
var s = a + b;
var p = a * b;
var A = s * 0.5;
var G = Math.sqrt(p);
var H = 2 * p / s;
return Math.PI * (21 * A - 2 * G - 3 * H) * 0.125;
};
/**
* Length3 returns the length of an elliptical orbit.
*
* Argument a is semimajor axis, e is eccentricity.
*
* Result is exact, and in units used for semimajor axis, typically AU.
*/
/* As Meeus notes, Length4 converges faster. There is no reason to use
this function
M.length3 = function (a, e) { // (a, e float64) float64
let sum0 = 1.0
let e2 = e * e
let term = e2 * 0.25
let sum1 = 1.0 - term
let nf = 1.0
let df = 2.0
while (sum1 !== sum0) {
term *= nf
nf += 2
df += 2
term *= nf * e2 / (df * df)
sum0 = sum1
sum1 -= term
}
return 2 * Math.PI * a * sum0
} */
/**
* Length4 returns the length of an elliptical orbit.
*
* Argument a is semimajor axis, e is eccentricity.
*
* Result is exact, and in units used for semimajor axis, typically AU.
*/
M.length4 = function (a, e) {
// (a, e float64) float64
var b = a * Math.sqrt(1 - e * e);
var m = (a - b) / (a + b);
var m2 = m * m;
var sum0 = 1.0;
var term = m2 * 0.25;
var sum1 = 1.0 + term;
var nf = -1.0;
var df = 2.0;
while (sum1 !== sum0) {
nf += 2;
df += 2;
term *= nf * nf * m2 / (df * df);
sum0 = sum1;
sum1 += term;
}
return 2 * Math.PI * a * sum0 / (1 + m);
};
/***/ }),
/* 11 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module sidereal
*/
/**
* Sidereal: Chapter 12, Sidereal Time at Greenwich.
*/
var base = __webpack_require__(0);
var nutation = __webpack_require__(1);
var M = exports;
/**
* JDToCFrac returns values for use in computing sidereal time at Greenwich.
*
* Cen is centuries from J2000 of the JD at 0h UT of argument jd. This is
* the value to use for evaluating the IAU sidereal time polynomial.
* DayFrac is the fraction of jd after 0h UT. It is used to compute the
* final value of sidereal time.
*
* @param {number} jd - Julian Days
* @return {number[]} [century, fraction] century and fraction of jd after 0h UT
*/
M.JDToCFrac = function (jd) {
var _base$modf = base.modf(jd + 0.5),
_base$modf2 = _slicedToArray(_base$modf, 2),
j0 = _base$modf2[0],
f = _base$modf2[1];
return [base.J2000Century(j0 - 0.5), f]; // (cen, dayFrac /* float */)
};
/**
* iau82 is a polynomial giving mean sidereal time at Greenwich at 0h UT.
*
* The polynomial is in centuries from J2000.0, as given by JDToCFrac.
* Coefficients are those adopted in 1982 by the International Astronomical
* Union and are given in (12.2) p. 87.
*/
var iau82 = M.iau82 = [24110.54841, 8640184.812866, 0.093104, 0.0000062];
/**
* Mean returns mean sidereal time at Greenwich for a given JD.
*
* Computation is by IAU 1982 coefficients. The result is in seconds of
* time and is in the range [0,86400).
*
* @param {number} jd - Julian Days
* @return {number}
*/
M.mean = function (jd) {
return base.pmod(_mean(jd), 86400);
};
/**
* @private
*/
function _mean(jd) {
var _mean0UT2 = _mean0UT(jd),
_mean0UT3 = _slicedToArray(_mean0UT2, 2),
s = _mean0UT3[0],
f = _mean0UT3[1];
return s + f * 1.00273790935 * 86400;
}
/**
* Mean0UT returns mean sidereal time at Greenwich at 0h UT on the given JD.
*
* The result is in seconds of time and is in the range [0,86400).
*
* @param {number} jd - Julian Days
* @return {number}
*/
M.mean0UT = function (jd /* float */) {
var _mean0UT4 = _mean0UT(jd),
_mean0UT5 = _slicedToArray(_mean0UT4, 2),
s = _mean0UT5[0],
_ = _mean0UT5[1]; // eslint-disable-line
return base.pmod(s, 86400);
};
/**
* @private
*/
function _mean0UT(jd /* float */) {
var _M$JDToCFrac = M.JDToCFrac(jd),
_M$JDToCFrac2 = _slicedToArray(_M$JDToCFrac, 2),
cen = _M$JDToCFrac2[0],
f = _M$JDToCFrac2[1];
// (12.2) p. 87
return [base.horner.apply(base, [cen].concat(iau82)), f]; // (sidereal, dayFrac /* float */)
}
/**
* Apparent returns apparent sidereal time at Greenwich for the given JD.
*
* Apparent is mean plus the nutation in right ascension.
*
* The result is in seconds of time and is in the range [0,86400).
*
* @param {number} jd - Julian Days
* @return {number}
*/
M.apparent = function (jd) {
var s = _mean(jd); // seconds of time
var n = nutation.nutationInRA(jd); // angle (radians) of RA
var ns = n * 3600 * 180 / Math.PI / 15; // convert RA to time in seconds
return base.pmod(s + ns, 86400);
};
/**
* Apparent0UT returns apparent sidereal time at Greenwich at 0h UT
* on the given JD.
*
* The result is in seconds of time and is in the range [0,86400).
*
* @param {number} jd - Julian Days
* @return {number}
*/
M.apparent0UT = function (jd) {
var _base$modf3 = base.modf(jd + 0.5),
_base$modf4 = _slicedToArray(_base$modf3, 2),
j0 = _base$modf4[0],
f = _base$modf4[1];
var cen = (j0 - 0.5 - base.J2000) / 36525;
var s = base.horner.apply(base, [cen].concat(iau82)) + f * 1.00273790935 * 86400;
var n = nutation.nutationInRA(j0); // angle (radians) of RA
var ns = n * 3600 * 180 / Math.PI / 15; // convert RA to time in seconds
return base.pmod(s + ns, 86400);
};
/***/ }),
/* 12 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module apparent
*/
/**
* Apparent: Chapter 23, Apparent Place of a Star
*/
var base = __webpack_require__(0);
var coord = __webpack_require__(2);
var nutation = __webpack_require__(1);
var precess = __webpack_require__(8);
var solar = __webpack_require__(3);
var cos = Math.cos,
tan = Math.tan;
var M = exports;
/**
* Nutation returns corrections due to nutation for equatorial coordinates
* of an object.
*
* Results are invalid for objects very near the celestial poles.
* @param {Number} α - right ascension
* @param {Number} δ - declination
* @param {Number} jd - Julian Day
* @return {Number[]} [Δα1, Δδ1] -
*/
M.nutation = function (α, δ, jd) {
// (α, δ, jd float64) (Δα1, Δδ1 float64)
var ε = nutation.meanObliquity(jd);
var _base$sincos = base.sincos(ε),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
sinε = _base$sincos2[0],
cosε = _base$sincos2[1];
var _nutation$nutation = nutation.nutation(jd),
_nutation$nutation2 = _slicedToArray(_nutation$nutation, 2),
Δψ = _nutation$nutation2[0],
Δε = _nutation$nutation2[1];
var _base$sincos3 = base.sincos(α),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sinα = _base$sincos4[0],
cosα = _base$sincos4[1];
var tanδ = tan(δ);
// (23.1) p. 151
var Δα1 = (cosε + sinε * sinα * tanδ) * Δψ - cosα * tanδ * Δε;
var Δδ1 = sinε * cosα * Δψ + sinα * Δε;
return [Δα1, Δδ1];
};
/**
* κ is the constant of aberration in radians.
*/
var κ = 20.49552 * Math.PI / 180 / 3600;
/**
* longitude of perihelian of Earth's orbit.
*/
M.perihelion = function (T) {
// (T float64) float64
return base.horner(T, 102.93735, 1.71946, 0.00046) * Math.PI / 180;
};
/**
* EclipticAberration returns corrections due to aberration for ecliptic
* coordinates of an object.
*/
M.eclipticAberration = function (λ, β, jd) {
// (λ, β, jd float64) (Δλ, Δβ float64)
var T = base.J2000Century(jd);
var _solar$true = solar.true(T),
lon = _solar$true.lon,
ano = _solar$true.ano; // eslint-disable-line no-unused-vars
var e = solar.eccentricity(T);
var π = M.perihelion(T);
var _base$sincos5 = base.sincos(β),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
sβ = _base$sincos6[0],
cβ = _base$sincos6[1];
var _base$sincos7 = base.sincos(lon - λ),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
ssλ = _base$sincos8[0],
csλ = _base$sincos8[1];
var _base$sincos9 = base.sincos(π - λ),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sinπλ = _base$sincos10[0],
cosπλ = _base$sincos10[1];
// (23.2) p. 151
var Δλ = κ * (e * cosπλ - csλ) / cβ;
var Δβ = -κ * sβ * (ssλ - e * sinπλ);
return [Δλ, Δβ];
};
/**
* Aberration returns corrections due to aberration for equatorial
* coordinates of an object.
*/
M.aberration = function (α, δ, jd) {
// (α, δ, jd float64) (Δα2, Δδ2 float64)
var ε = nutation.meanObliquity(jd);
var T = base.J2000Century(jd);
var _solar$true2 = solar.true(T),
lon = _solar$true2.lon,
ano = _solar$true2.ano; // eslint-disable-line no-unused-vars
var e = solar.eccentricity(T);
var π = M.perihelion(T);
var _base$sincos11 = base.sincos(α),
_base$sincos12 = _slicedToArray(_base$sincos11, 2),
sinα = _base$sincos12[0],
cosα = _base$sincos12[1];
var _base$sincos13 = base.sincos(δ),
_base$sincos14 = _slicedToArray(_base$sincos13, 2),
sinδ = _base$sincos14[0],
cosδ = _base$sincos14[1];
var _base$sincos15 = base.sincos(lon),
_base$sincos16 = _slicedToArray(_base$sincos15, 2),
sins = _base$sincos16[0],
coss = _base$sincos16[1];
var _base$sincos17 = base.sincos(π),
_base$sincos18 = _slicedToArray(_base$sincos17, 2),
sinπ = _base$sincos18[0],
cosπ = _base$sincos18[1];
var cosε = cos(ε);
var q1 = cosα * cosε;
// (23.3) p. 152
var Δα2 = κ * (e * (q1 * cosπ + sinα * sinπ) - (q1 * coss + sinα * sins)) / cosδ;
var q2 = cosε * (tan(ε) * cosδ - sinα * sinδ);
var q3 = cosα * sinδ;
var Δδ2 = κ * (e * (cosπ * q2 + sinπ * q3) - (coss * q2 + sins * q3));
return [Δα2, Δδ2];
};
/**
* Position computes the apparent position of an object.
*
* Position is computed for equatorial coordinates in eqFrom, considering
* proper motion, precession, nutation, and aberration. Result is in
* eqTo. EqFrom and eqTo must be non-nil, but may point to the same struct.
*/
M.position = function (eqFrom, epochFrom, epochTo, mα, mδ) {
// (eqFrom, eqTo *coord.Equatorial, epochFrom, epochTo float64, mα sexa.HourAngle, mδ sexa.Angle) *coord.Equatorial
var eqTo = precess.position(eqFrom, epochFrom, epochTo, mα, mδ);
var jd = base.JulianYearToJDE(epochTo);
var _M$nutation = M.nutation(eqTo.ra, eqTo.dec, jd),
_M$nutation2 = _slicedToArray(_M$nutation, 2),
Δα1 = _M$nutation2[0],
Δδ1 = _M$nutation2[1];
var _M$aberration = M.aberration(eqTo.ra, eqTo.dec, jd),
_M$aberration2 = _slicedToArray(_M$aberration, 2),
Δα2 = _M$aberration2[0],
Δδ2 = _M$aberration2[1];
eqTo.ra += Δα1 + Δα2;
eqTo.dec += Δδ1 + Δδ2;
return eqTo;
};
/**
* AberrationRonVondrak uses the Ron-Vondrák expression to compute corrections
* due to aberration for equatorial coordinates of an object.
*/
M.aberrationRonVondrak = function (α, δ, jd) {
// (α, δ, jd float64) (Δα, Δδ float64)
var T = base.J2000Century(jd);
var r = {
T: T,
L2: 3.1761467 + 1021.3285546 * T,
L3: 1.7534703 + 628.3075849 * T,
L4: 6.2034809 + 334.0612431 * T,
L5: 0.5995465 + 52.9690965 * T,
L6: 0.8740168 + 21.3299095 * T,
L7: 5.4812939 + 7.4781599 * T,
L8: 5.3118863 + 3.8133036 * T,
Lp: 3.8103444 + 8399.6847337 * T,
D: 5.1984667 + 7771.3771486 * T,
Mp: 2.3555559 + 8328.6914289 * T,
F: 1.6279052 + 8433.4661601 * T
};
var Xp = 0;
var Yp = 0;
var Zp = 0;
// sum smaller terms first
for (var i = 35; i >= 0; i--) {
var _rvTerm$i = rvTerm[i](r),
_rvTerm$i2 = _slicedToArray(_rvTerm$i, 3),
x = _rvTerm$i2[0],
y = _rvTerm$i2[1],
z = _rvTerm$i2[2];
Xp += x;
Yp += y;
Zp += z;
}
var _base$sincos19 = base.sincos(α),
_base$sincos20 = _slicedToArray(_base$sincos19, 2),
sinα = _base$sincos20[0],
cosα = _base$sincos20[1];
var _base$sincos21 = base.sincos(δ),
_base$sincos22 = _slicedToArray(_base$sincos21, 2),
sinδ = _base$sincos22[0],
cosδ = _base$sincos22[1];
// (23.4) p. 156
return [(Yp * cosα - Xp * sinα) / (c * cosδ), -((Xp * cosα + Yp * sinα) * sinδ - Zp * cosδ) / c];
};
var c = 17314463350; // unit is 1e-8 AU / day
// r = {T, L2, L3, L4, L5, L6, L7, L8, Lp, D, Mp, F}
var rvTerm = [function (r) {
// 1
var _base$sincos23 = base.sincos(r.L3),
_base$sincos24 = _slicedToArray(_base$sincos23, 2),
sinA = _base$sincos24[0],
cosA = _base$sincos24[1];
return [(-1719914 - 2 * r.T) * sinA - 25 * cosA, (25 - 13 * r.T) * sinA + (1578089 + 156 * r.T) * cosA, (10 + 32 * r.T) * sinA + (684185 - 358 * r.T) * cosA];
}, function (r) {
// 2
var _base$sincos25 = base.sincos(2 * r.L3),
_base$sincos26 = _slicedToArray(_base$sincos25, 2),
sinA = _base$sincos26[0],
cosA = _base$sincos26[1];
return [(6434 + 141 * r.T) * sinA + (28007 - 107 * r.T) * cosA, (25697 - 95 * r.T) * sinA + (-5904 - 130 * r.T) * cosA, (11141 - 48 * r.T) * sinA + (-2559 - 55 * r.T) * cosA];
}, function (r) {
// 3
var _base$sincos27 = base.sincos(r.L5),
_base$sincos28 = _slicedToArray(_base$sincos27, 2),
sinA = _base$sincos28[0],
cosA = _base$sincos28[1];
return [715 * sinA, 6 * sinA - 657 * cosA, -15 * sinA - 282 * cosA];
}, function (r) {
// 4
var _base$sincos29 = base.sincos(r.Lp),
_base$sincos30 = _slicedToArray(_base$sincos29, 2),
sinA = _base$sincos30[0],
cosA = _base$sincos30[1];
return [715 * sinA, -656 * cosA, -285 * cosA];
}, function (r) {
// 5
var _base$sincos31 = base.sincos(3 * r.L3),
_base$sincos32 = _slicedToArray(_base$sincos31, 2),
sinA = _base$sincos32[0],
cosA = _base$sincos32[1];
return [(486 - 5 * r.T) * sinA + (-236 - 4 * r.T) * cosA, (-216 - 4 * r.T) * sinA + (-446 + 5 * r.T) * cosA, -94 * sinA - 193 * cosA];
}, function (r) {
// 6
var _base$sincos33 = base.sincos(r.L6),
_base$sincos34 = _slicedToArray(_base$sincos33, 2),
sinA = _base$sincos34[0],
cosA = _base$sincos34[1];
return [159 * sinA, 2 * sinA - 147 * cosA, -6 * sinA - 61 * cosA];
}, function (r) {
// 7
var cosA = Math.cos(r.F);
return [0, 26 * cosA, -59 * cosA];
}, function (r) {
// 8
var _base$sincos35 = base.sincos(r.Lp + r.Mp),
_base$sincos36 = _slicedToArray(_base$sincos35, 2),
sinA = _base$sincos36[0],
cosA = _base$sincos36[1];
return [39 * sinA, -36 * cosA, -16 * cosA];
}, function (r) {
// 9
var _base$sincos37 = base.sincos(2 * r.L5),
_base$sincos38 = _slicedToArray(_base$sincos37, 2),
sinA = _base$sincos38[0],
cosA = _base$sincos38[1];
return [33 * sinA - 10 * cosA, -9 * sinA - 30 * cosA, -5 * sinA - 13 * cosA];
}, function (r) {
// 10
var _base$sincos39 = base.sincos(2 * r.L3 - r.L5),
_base$sincos40 = _slicedToArray(_base$sincos39, 2),
sinA = _base$sincos40[0],
cosA = _base$sincos40[1];
return [31 * sinA + cosA, sinA - 28 * cosA, -12 * cosA];
}, function (r) {
// 11
var _base$sincos41 = base.sincos(3 * r.L3 - 8 * r.L4 + 3 * r.L5),
_base$sincos42 = _slicedToArray(_base$sincos41, 2),
sinA = _base$sincos42[0],
cosA = _base$sincos42[1];
return [8 * sinA - 28 * cosA, 25 * sinA + 8 * cosA, 11 * sinA + 3 * cosA];
}, function (r) {
// 12
var _base$sincos43 = base.sincos(5 * r.L3 - 8 * r.L4 + 3 * r.L5),
_base$sincos44 = _slicedToArray(_base$sincos43, 2),
sinA = _base$sincos44[0],
cosA = _base$sincos44[1];
return [8 * sinA - 28 * cosA, -25 * sinA - 8 * cosA, -11 * sinA + -3 * cosA];
}, function (r) {
// 13
var _base$sincos45 = base.sincos(2 * r.L2 - r.L3),
_base$sincos46 = _slicedToArray(_base$sincos45, 2),
sinA = _base$sincos46[0],
cosA = _base$sincos46[1];
return [21 * sinA, -19 * cosA, -8 * cosA];
}, function (r) {
// 14
var _base$sincos47 = base.sincos(r.L2),
_base$sincos48 = _slicedToArray(_base$sincos47, 2),
sinA = _base$sincos48[0],
cosA = _base$sincos48[1];
return [-19 * sinA, 17 * cosA, 8 * cosA];
}, function (r) {
// 15
var _base$sincos49 = base.sincos(r.L7),
_base$sincos50 = _slicedToArray(_base$sincos49, 2),
sinA = _base$sincos50[0],
cosA = _base$sincos50[1];
return [17 * sinA, -16 * cosA, -7 * cosA];
}, function (r) {
// 16
var _base$sincos51 = base.sincos(r.L3 - 2 * r.L5),
_base$sincos52 = _slicedToArray(_base$sincos51, 2),
sinA = _base$sincos52[0],
cosA = _base$sincos52[1];
return [16 * sinA, 15 * cosA, sinA + 7 * cosA];
}, function (r) {
// 17
var _base$sincos53 = base.sincos(r.L8),
_base$sincos54 = _slicedToArray(_base$sincos53, 2),
sinA = _base$sincos54[0],
cosA = _base$sincos54[1];
return [16 * sinA, sinA - 15 * cosA, -3 * sinA - 6 * cosA];
}, function (r) {
// 18
var _base$sincos55 = base.sincos(r.L3 + r.L5),
_base$sincos56 = _slicedToArray(_base$sincos55, 2),
sinA = _base$sincos56[0],
cosA = _base$sincos56[1];
return [11 * sinA - cosA, -sinA - 10 * cosA, -sinA - 5 * cosA];
}, function (r) {
// 19
var _base$sincos57 = base.sincos(2 * r.L2 - 2 * r.L3),
_base$sincos58 = _slicedToArray(_base$sincos57, 2),
sinA = _base$sincos58[0],
cosA = _base$sincos58[1];
return [-11 * cosA, -10 * sinA, -4 * sinA];
}, function (r) {
// 20
var _base$sincos59 = base.sincos(r.L3 - r.L5),
_base$sincos60 = _slicedToArray(_base$sincos59, 2),
sinA = _base$sincos60[0],
cosA = _base$sincos60[1];
return [-11 * sinA - 2 * cosA, -2 * sinA + 9 * cosA, -sinA + 4 * cosA];
}, function (r) {
// 21
var _base$sincos61 = base.sincos(4 * r.L3),
_base$sincos62 = _slicedToArray(_base$sincos61, 2),
sinA = _base$sincos62[0],
cosA = _base$sincos62[1];
return [-7 * sinA - 8 * cosA, -8 * sinA + 6 * cosA, -3 * sinA + 3 * cosA];
}, function (r) {
// 22
var _base$sincos63 = base.sincos(3 * r.L3 - 2 * r.L5),
_base$sincos64 = _slicedToArray(_base$sincos63, 2),
sinA = _base$sincos64[0],
cosA = _base$sincos64[1];
return [-10 * sinA, 9 * cosA, 4 * cosA];
}, function (r) {
// 23
var _base$sincos65 = base.sincos(r.L2 - 2 * r.L3),
_base$sincos66 = _slicedToArray(_base$sincos65, 2),
sinA = _base$sincos66[0],
cosA = _base$sincos66[1];
return [-9 * sinA, -9 * cosA, -4 * cosA];
}, function (r) {
// 24
var _base$sincos67 = base.sincos(2 * r.L2 - 3 * r.L3),
_base$sincos68 = _slicedToArray(_base$sincos67, 2),
sinA = _base$sincos68[0],
cosA = _base$sincos68[1];
return [-9 * sinA, -8 * cosA, -4 * cosA];
}, function (r) {
// 25
var _base$sincos69 = base.sincos(2 * r.L6),
_base$sincos70 = _slicedToArray(_base$sincos69, 2),
sinA = _base$sincos70[0],
cosA = _base$sincos70[1];
return [-9 * cosA, -8 * sinA, -3 * sinA];
}, function (r) {
// 26
var _base$sincos71 = base.sincos(2 * r.L2 - 4 * r.L3),
_base$sincos72 = _slicedToArray(_base$sincos71, 2),
sinA = _base$sincos72[0],
cosA = _base$sincos72[1];
return [-9 * cosA, 8 * sinA, 3 * sinA];
}, function (r) {
// 27
var _base$sincos73 = base.sincos(3 * r.L3 - 2 * r.L4),
_base$sincos74 = _slicedToArray(_base$sincos73, 2),
sinA = _base$sincos74[0],
cosA = _base$sincos74[1];
return [8 * sinA, -8 * cosA, -3 * cosA];
}, function (r) {
// 28
var _base$sincos75 = base.sincos(r.Lp + 2 * r.D - r.Mp),
_base$sincos76 = _slicedToArray(_base$sincos75, 2),
sinA = _base$sincos76[0],
cosA = _base$sincos76[1];
return [8 * sinA, -7 * cosA, -3 * cosA];
}, function (r) {
// 29
var _base$sincos77 = base.sincos(8 * r.L2 - 12 * r.L3),
_base$sincos78 = _slicedToArray(_base$sincos77, 2),
sinA = _base$sincos78[0],
cosA = _base$sincos78[1];
return [-4 * sinA - 7 * cosA, -6 * sinA + 4 * cosA, -3 * sinA + 2 * cosA];
}, function (r) {
// 30
var _base$sincos79 = base.sincos(8 * r.L2 - 14 * r.L3),
_base$sincos80 = _slicedToArray(_base$sincos79, 2),
sinA = _base$sincos80[0],
cosA = _base$sincos80[1];
return [-4 * sinA - 7 * cosA, 6 * sinA - 4 * cosA, 3 * sinA - 2 * cosA];
}, function (r) {
// 31
var _base$sincos81 = base.sincos(2 * r.L4),
_base$sincos82 = _slicedToArray(_base$sincos81, 2),
sinA = _base$sincos82[0],
cosA = _base$sincos82[1];
return [-6 * sinA - 5 * cosA, -4 * sinA + 5 * cosA, -2 * sinA + 2 * cosA];
}, function (r) {
// 32
var _base$sincos83 = base.sincos(3 * r.L2 - 4 * r.L3),
_base$sincos84 = _slicedToArray(_base$sincos83, 2),
sinA = _base$sincos84[0],
cosA = _base$sincos84[1];
return [-sinA - cosA, -2 * sinA - 7 * cosA, sinA - 4 * cosA];
}, function (r) {
// 33
var _base$sincos85 = base.sincos(2 * r.L3 - 2 * r.L5),
_base$sincos86 = _slicedToArray(_base$sincos85, 2),
sinA = _base$sincos86[0],
cosA = _base$sincos86[1];
return [4 * sinA - 6 * cosA, -5 * sinA - 4 * cosA, -2 * sinA - 2 * cosA];
}, function (r) {
// 34
var _base$sincos87 = base.sincos(3 * r.L2 - 3 * r.L3),
_base$sincos88 = _slicedToArray(_base$sincos87, 2),
sinA = _base$sincos88[0],
cosA = _base$sincos88[1];
return [-7 * cosA, -6 * sinA, -3 * sinA];
}, function (r) {
// 35
var _base$sincos89 = base.sincos(2 * r.L3 - 2 * r.L4),
_base$sincos90 = _slicedToArray(_base$sincos89, 2),
sinA = _base$sincos90[0],
cosA = _base$sincos90[1];
return [5 * sinA - 5 * cosA, -4 * sinA - 5 * cosA, -2 * sinA - 2 * cosA];
}, function (r) {
// 36
var _base$sincos91 = base.sincos(r.Lp - 2 * r.D),
_base$sincos92 = _slicedToArray(_base$sincos91, 2),
sinA = _base$sincos92[0],
cosA = _base$sincos92[1];
return [5 * sinA, -5 * cosA, -2 * cosA];
}];
/**
* PositionRonVondrak computes the apparent position of an object using
* the Ron-Vondrák expression for aberration.
*
* Position is computed for equatorial coordinates in eqFrom, considering
* proper motion, aberration, precession, and nutation. Result is in
* eqTo. EqFrom and eqTo must be non-nil, but may point to the same struct.
*
* Note the Ron-Vondrák expression is only valid for the epoch J2000.
* EqFrom must be coordinates at epoch J2000.
*/
M.positionRonVondrak = function (eqFrom, epochTo, mα, mδ) {
// (eqFrom, eqTo *coord.Equatorial, epochTo float64, mα sexa.HourAngle, mδ sexa.Angle) *coord.Equatorial
var t = epochTo - 2000;
var eqTo = new coord.Equatorial();
eqTo.ra = eqFrom.ra + mα.rad() * t;
eqTo.dec = eqFrom.dec + mδ.rad() * t;
var jd = base.JulianYearToJDE(epochTo);
var _M$aberrationRonVondr = M.aberrationRonVondrak(eqTo.ra, eqTo.dec, jd),
_M$aberrationRonVondr2 = _slicedToArray(_M$aberrationRonVondr, 2),
Δα = _M$aberrationRonVondr2[0],
Δδ = _M$aberrationRonVondr2[1];
eqTo.ra += Δα;
eqTo.dec += Δδ;
eqTo = precess.position(eqTo, 2000, epochTo, 0, 0);
var _M$nutation3 = M.nutation(eqTo.ra, eqTo.dec, jd),
_M$nutation4 = _slicedToArray(_M$nutation3, 2),
Δα1 = _M$nutation4[0],
Δδ1 = _M$nutation4[1];
eqTo.ra += Δα1;
eqTo.dec += Δδ1;
return eqTo;
};
/***/ }),
/* 13 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
var _typeof = typeof Symbol === "function" && typeof Symbol.iterator === "symbol" ? function (obj) { return typeof obj; } : function (obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; };
function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module elementequinox
*/
/**
* Elementequinox: Chapter 24, Reduction of Ecliptical Elements
* from one Equinox to another one.
*
* See package precess for the method EclipticPrecessor.ReduceElements and
* associated example. The method is described in this chapter but located
* in package precess so that it can be a method of EclipticPrecessor.
*/
var base = __webpack_require__(0);
var M = exports;
/**
* Elements are the orbital elements of a solar system object which change
* from one equinox to another.
*
* @param {Number} inc - inclination
* @param {Number} node - longitude of ascending node (Ω)
* @param {Number} peri - argument of perihelion (ω)
*/
var Elements = function Elements(inc, node, peri) {
_classCallCheck(this, Elements);
if ((typeof inc === 'undefined' ? 'undefined' : _typeof(inc)) === 'object') {
node = inc.pode;
peri = inc.peri;
inc = inc.inc;
}
this.inc = inc || 0;
this.node = node || 0;
this.peri = peri || 0;
};
M.Elements = Elements;
// (24.4) p. 161
var S = 0.0001139788;
var C = 0.9999999935;
/**
* ReduceB1950ToJ2000 reduces orbital elements of a solar system body from
* equinox B1950 to J2000.
*
* @param {Elements} eFrom
* @returns {Elements} eTo
*/
M.reduceB1950ToJ2000 = function (eFrom) {
var W = eFrom.node - 174.298782 * Math.PI / 180;
var _base$sincos = base.sincos(eFrom.inc),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
si = _base$sincos2[0],
ci = _base$sincos2[1];
var _base$sincos3 = base.sincos(W),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
sW = _base$sincos4[0],
cW = _base$sincos4[1];
var A = si * sW;
var B = C * si * cW - S * ci;
var eTo = new Elements();
eTo.inc = Math.asin(Math.hypot(A, B));
eTo.node = base.pmod(174.997194 * Math.PI / 180 + Math.atan2(A, B), 2 * Math.PI);
eTo.peri = base.pmod(eFrom.peri + Math.atan2(-S * sW, C * si - S * ci * cW), 2 * Math.PI);
return eTo;
};
var Lp = 4.50001688 * Math.PI / 180;
var L = 5.19856209 * Math.PI / 180;
var J = 0.00651966 * Math.PI / 180;
/**
* ReduceB1950ToJ2000 reduces orbital elements of a solar system body from
* equinox B1950 in the FK4 system to equinox J2000 in the FK5 system.
*
* @param {Elements} eFrom
* @returns {Elements} eTo
*/
M.reduceB1950FK4ToJ2000FK5 = function (eFrom) {
var W = L + eFrom.node;
var _base$sincos5 = base.sincos(eFrom.inc),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
si = _base$sincos6[0],
ci = _base$sincos6[1];
var _base$sincos7 = base.sincos(J),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
sJ = _base$sincos8[0],
cJ = _base$sincos8[1];
var _base$sincos9 = base.sincos(W),
_base$sincos10 = _slicedToArray(_base$sincos9, 2),
sW = _base$sincos10[0],
cW = _base$sincos10[1];
var eTo = new Elements();
eTo.inc = Math.acos(ci * cJ - si * sJ * cW);
eTo.node = base.pmod(Math.atan2(si * sW, ci * sJ + si * cJ * cW) - Lp, 2 * Math.PI);
eTo.peri = base.pmod(eFrom.peri + Math.atan2(sJ * sW, si * cJ + ci * sJ * cW), 2 * Math.PI);
return eTo;
};
/***/ }),
/* 14 */
/***/ (function(module, exports) {
var g;
// This works in non-strict mode
g = (function() {
return this;
})();
try {
// This works if eval is allowed (see CSP)
g = g || Function("return this")() || (1,eval)("this");
} catch(e) {
// This works if the window reference is available
if(typeof window === "object")
g = window;
}
// g can still be undefined, but nothing to do about it...
// We return undefined, instead of nothing here, so it's
// easier to handle this case. if(!global) { ...}
module.exports = g;
/***/ }),
/* 15 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module kepler
*/
/**
* Kepler: Chapter 30, Equation of Kepler.
*/
var base = __webpack_require__(0);
var iterate = __webpack_require__(16);
var M = exports;
/**
* True returns true anomaly ν for given eccentric anomaly E.
*
* @param {number} e - eccentricity
* @param {number} E - eccentric anomaly in radians.
* @return true anomaly ν in radians.
*/
M.true = function (E, e) {
// (30.1) p. 195
return 2 * Math.atan(Math.sqrt((1 + e) / (1 - e)) * Math.tan(E * 0.5));
};
/**
* Radius returns radius distance r for given eccentric anomaly E.
*
* Result unit is the unit of semimajor axis a (typically AU.)
*
* @param {number} e - eccentricity
* @param {number} E - eccentric anomaly in radians
* @param {number} a - semimajor axis
* @return {number} radius distance in unit of `a`
*/
M.radius = function (E, e, a) {
// (E, e, a float64) float64
// (30.2) p. 195
return a * (1 - e * Math.cos(E));
};
/**
* Kepler1 solves Kepler's equation by iteration.
*
* The iterated formula is
*
* E1 = m + e * sin(E0)
*
* For some vaues of e and M it will fail to converge and the
* function will return an error.
*
* @throws Error
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @param {number} places - (int) desired number of decimal places in the result
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler1 = function (e, m, places) {
var f = function f(E0) {
return m + e * Math.sin(E0); // (30.5) p. 195
};
return iterate.decimalPlaces(f, m, places, places * 5);
};
/**
* Kepler2 solves Kepler's equation by iteration.
*
* The iterated formula is
*
* E1 = E0 + (m + e * sin(E0) - E0) / (1 - e * cos(E0))
*
* The function converges over a wider range of inputs than does Kepler1
* but it also fails to converge for some values of e and M.
*
* @throws Error
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @param {number} places - (int) desired number of decimal places in the result
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler2 = function (e, m, places) {
// (e, M float64, places int) (E float64, err error)
var f = function f(E0) {
var _base$sincos = base.sincos(E0),
_base$sincos2 = _slicedToArray(_base$sincos, 2),
se = _base$sincos2[0],
ce = _base$sincos2[1];
return E0 + (m + e * se - E0) / (1 - e * ce); // (30.7) p. 199
};
return iterate.decimalPlaces(f, m, places, places);
};
/**
* Kepler2a solves Kepler's equation by iteration.
*
* The iterated formula is the same as in Kepler2 but a limiting function
* avoids divergence.
*
* @throws Error
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @param {number} places - (int) desired number of decimal places in the result
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler2a = function (e, m, places) {
// (e, M float64, places int) (E float64, err error)
var f = function f(E0) {
var _base$sincos3 = base.sincos(E0),
_base$sincos4 = _slicedToArray(_base$sincos3, 2),
se = _base$sincos4[0],
ce = _base$sincos4[1];
// method of Leingärtner, p. 205
return E0 + Math.asin(Math.sin((m + e * se - E0) / (1 - e * ce)));
};
return iterate.decimalPlaces(f, m, places, places * 5);
};
/**
* Kepler2b solves Kepler's equation by iteration.
*
* The iterated formula is the same as in Kepler2 but a (different) limiting
* function avoids divergence.
*
* @throws Error
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @param {number} places - (int) desired number of decimal places in the result
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler2b = function (e, m, places) {
// (e, M float64, places int) (E float64, err error)
var f = function f(E0) {
var _base$sincos5 = base.sincos(E0),
_base$sincos6 = _slicedToArray(_base$sincos5, 2),
se = _base$sincos6[0],
ce = _base$sincos6[1];
var d = (m + e * se - E0) / (1 - e * ce);
// method of Steele, p. 205
if (d > 0.5) {
d = 0.5;
} else if (d < -0.5) {
d = -0.5;
}
return E0 + d;
};
return iterate.decimalPlaces(f, m, places, places);
};
/**
* Kepler3 solves Kepler's equation by binary search.
*
* @throws Error
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler3 = function (e, m) {
// (e, m float64) (E float64)
// adapted from BASIC, p. 206
m = base.pmod(m, 2 * Math.PI);
var f = 1;
if (m > Math.PI) {
f = -1;
m = 2 * Math.PI - m;
}
var E0 = Math.PI * 0.5;
var d = Math.PI * 0.25;
for (var i = 0; i < 53; i++) {
var M1 = E0 - e * Math.sin(E0);
if (m - M1 < 0) {
E0 -= d;
} else {
E0 += d;
}
d *= 0.5;
}
if (f < 0) {
return -E0;
}
return E0;
};
/**
* Kepler4 returns an approximate solution to Kepler's equation.
*
* It is valid only for small values of e.
*
* @param {number} e - eccentricity
* @param {number} m - mean anomaly in radians
* @return {number} eccentric anomaly `E` in radians.
*/
M.kepler4 = function (e, m) {
// (e, m float64) (E float64)
var _base$sincos7 = base.sincos(m),
_base$sincos8 = _slicedToArray(_base$sincos7, 2),
sm = _base$sincos8[0],
cm = _base$sincos8[1];
return Math.atan2(sm, cm - e); // (30.8) p. 206
};
/***/ }),
/* 16 */
/***/ (function(module, exports, __webpack_require__) {
"use strict";
/**
* @copyright 2013 Sonia Keys
* @copyright 2016 commenthol
* @license MIT
* @module iterate
*/
/**
* Iterate: Chapter 5, Iteration.
*
* This package is best considered illustrative. While the functions are
* usable, they are minimal in showing the points of the chapter text. More
* robust functions would handle more cases of overflow, loss of precision,
* and divergence.
*/
var M = exports;
/**
* decimalPlaces iterates to a fixed number of decimal places.
*
* Inputs are an improvement function, a starting value, the number of
* decimal places desired in the result, and an iteration limit.
*
* @throws Error
* @param {Function} better
* @param {Number} start - (float)
* @param {Number} places - (int)
* @param {Number} maxIterations - (int)
* @returns {Number}
*/
M.decimalPlaces = function (better, start, places, maxIterations) {
var d = Math.pow(10, -places);
for (var i = 0; i < maxIterations; i++) {
var n = better(start);
if (Math.abs(n - start) < d) {
return n;
}
start = n;
}
throw new Error('Maximum iterations reached');
};
/**
* fullPrecison iterates to (nearly) the full precision of a float64.
*
* To allow for a little bit of floating point jitter, FullPrecision iterates
* to 15 significant figures, which is the maximum number of full significant
* figures representable in a float64, but still a couple of bits shy of the
* full representable precision.
*
* @throws Error
* @param {Function} better
* @param {Number} start - (float)
* @param {Number} maxIterations - (int)
* @returns {Number}
*/
M.fullPrecision = function (better, start, maxIterations) {
for (var i = 0; i < maxIterations; i++) {
var n = better(start);
if (Math.abs((n - start) / n) < 1e-15) {
return n;
}
start = n;
}
throw new Error('Maximum iterations reached');
};
/**
* binaryRoot finds a root between given bounds by binary search.
*
* Inputs are a function on x and the bounds on x. A root must exist between
* the given bounds, otherwise the result is not meaningful.
*
* @param {Function} f - root function
* @param {Number} lower - (float)
* @param {Number} upper - (float)
* @returns {Number}
*/
M.binaryRoot = function (f, lower, upper) {
var yLower = f(lower);
var mid = 0;
for (var j = 0; j < 52; j++) {
mid = (lower + upper) / 2;
var yMid = f(mid);
if (yMid === 0) {
break;
}
if (signbit(yLower) === signbit(yMid)) {
lower = mid;
yLower = yMid;
} else {
upper = mid;
}
}
return mid;
};
function signbit(v) {
return v < 0;
}
/***/ }),
/* 17 */
/***/ (function(module, exports) {
module.exports = {
L: {
"0": [
[1.75347045673, 0, 0],
[0.03341656453, 4.66925680415, 6283.0758499914],
[0.00034894275, 4.62610242189, 12566.1516999828],
[0.00003417572, 2.82886579754, 3.523118349],
[0.00003497056, 2.74411783405, 5753.3848848968],
[0.00003135899, 3.62767041756, 77713.7714681205],
[0.00002676218, 4.41808345438, 7860.4193924392],
[0.00002342691, 6.13516214446, 3930.2096962196],
[0.00001273165, 2.03709657878, 529.6909650946],
[0.00001324294, 0.74246341673, 11506.7697697936],
[0.00000901854, 2.04505446477, 26.2983197998],
[0.00001199167, 1.10962946234, 1577.3435424478],
[0.00000857223, 3.50849152283, 398.1490034082],
[0.00000779786, 1.17882681962, 5223.6939198022],
[0.0000099025, 5.23268072088, 5884.9268465832],
[0.00000753141, 2.53339052847, 5507.5532386674],
[0.00000505267, 4.58292599973, 18849.2275499742],
[0.00000492392, 4.20505711826, 775.522611324],
[0.00000356672, 2.91954114478, 0.0673103028],
[0.00000284125, 1.89869240932, 796.2980068164],
[0.00000242879, 0.34481445893, 5486.777843175],
[0.00000317087, 5.84901948512, 11790.6290886588],
[0.00000271112, 0.31486255375, 10977.078804699],
[0.00000206217, 4.80646631478, 2544.3144198834],
[0.00000205478, 1.86953770281, 5573.1428014331],
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[0.00000126225, 1.08295459501, 20.7753954924],
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[0.00000115132, 0.64544911683, 0.9803210682],
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[2.003e-8, 0.38091017375, 6172.869528772],
[2.506e-8, 3.74378169126, 10575.4066829418],
[2.381e-8, 0.10581361289, 7.046236698],
[1.949e-8, 4.86892513469, 36.0278666774],
[2.074e-8, 4.22802468213, 5650.2921106782],
[1.924e-8, 5.59460549844, 6282.0955289232],
[1.949e-8, 1.06999605576, 5230.807466803],
[1.988e-8, 5.19734705445, 6262.300454499],
[1.887e-8, 3.74365662683, 23.8784377478],
[1.787e-8, 1.25929659066, 12559.038152982],
[1.883e-8, 1.90364058477, 15.252471185],
[1.816e-8, 3.68083794819, 15110.4661198662],
[1.701e-8, 4.41109562589, 110.2063212194],
[1.99e-8, 3.93295788548, 6206.8097787158],
[2.103e-8, 0.75354936681, 13521.7514415914],
[1.774e-8, 0.48750515837, 1551.045222648],
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},
name: "earth"
};
/***/ }),
/* 18 */
/***/ (function(module, exports) {
module.exports = {
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},
name: "jupiter"
};
/***/ }),
/* 19 */
/***/ (function(module, exports) {
module.exports = {
L: {
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},
name: "mars"
};
/***/ }),
/* 20 */
/***/ (function(module, exports) {
module.exports = {
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