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rappaurio-sae501_502/app/node_modules/cejs/application/astronomy.js
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/**
* @name CeL function for astronomical calculations.
* @fileoverview 本檔案包含了天文演算用的日期轉換功能。
*
* @since 2015/3/20 23:5:43
*
* TODO:
*
* 1. 座標全改 radians
*
* 2. 黃→視黃→赤→(視)赤→地平座標
*
* http://eclipse.gsfc.nasa.gov/JSEX/JSEX-index.html
* https://web.archive.org/web/http://www.chris.obyrne.com/Eclipses/calculator.html
* https://en.wikipedia.org/wiki/Astronomical_symbols
*
* calculate Halley's Comet 哈雷彗星
*
* Software & coded<br />
* http://www.kentauren.info/menu/index1.htm?page=/cgi-bin/planeph_VSOP87d.pl
* https://pypi.python.org/pypi/astronomia
* https://github.com/Hedwig1958/libastro/blob/master/astro.c
* https://github.com/soniakeys/meeus/blob/master/solar/solar.go
* https://github.com/hkuno9000/sunmoon/blob/master/acoord.cpp
* http://www.timeanddate.com/calendar/moonphases.html
* http://eco.mtk.nao.ac.jp/koyomi/
*
* 大地測量:給定地球表面兩個點的經緯度,計算兩點間之距離<br />
* 天球上天體/星體距離<br />
* http://geographiclib.sourceforge.net/scripts/geod-calc.html
* http://wywu.pixnet.net/blog/post/27459116
* http://iotresearch.wikispaces.com/GPS<br />
* Andoyer 方法最大的誤差約為50公尺，Lambert 方法最大的誤差約30m。
* http://usenrong.iteye.com/blog/2147341
* http://en.wikipedia.org/wiki/Haversine_formula
* http://en.wikipedia.org/wiki/Spherical_law_of_cosines
* http://en.wikipedia.org/wiki/Vincenty's_formulae
*
* LUNAR SOLUTION ELP version ELP/MPP02
*
* 未來發展：<br />
*
* @see <a href="http://www.nongli.com/item2/index.html" accessdate="2013/5/2
* 20:23">农历知识:传统节日,24节气，农历历法，三九，三伏，天文历法,天干地支阴阳五行</a>
* @see <a href="http://www.chinesefortunecalendar.com/CLC/clcBig5.htm"
* accessdate="2013/5/2 20:23">如何轉換陰陽曆</a>
*
* 簡易朔望/天象計算功能/千年 節氣 計算。<br />
* http://bieyu.com/<br />
* http://www.fjptsz.com/xxjs/xjw/rj/117/index.htm
*
* 通用万年历 寿星万年历 择吉老黄历 http://www.todayonhistory.com/wnl/lhl.htm
*
*/
'use strict';
// 'use asm';
// More examples: see /_test suite/test.js
// ------------------------------------------------------------------------------------------------------------------//
// 不採用 if 陳述式，可以避免 Eclipse JSDoc 與 format 多縮排一層。
typeof CeL === 'function' && CeL.run({
// module name
name : 'application.astronomy',
require : 'data.code.compatibility.'
// data.math.find_root()
// data.date.Date_to_JD()
+ '|data.math.polynomial_value|data.date.',
// 為了方便格式化程式碼，因此將 module 函式主體另外抽出。
code : module_code
});
function module_code(library_namespace) {
// requiring
var polynomial_value = this.r('polynomial_value');
/**
* full module name.
*
* @type {String}
*/
var module_name = this.id;
/**
* null module constructor
*
* @class astronomical calculations 的 functions
*/
var _// JSDT:_module_
= function() {
// null module constructor
};
/**
* for JSDT: 有 prototype 才會將之當作 Class
*/
_// JSDT:_module_
.prototype = {};
// ------------------------------------------------------------------------------------------------------//
// basic constants. 定義基本常數。
var
/** {Number}未發現之index。 const: 基本上與程式碼設計合一，僅表示名義，不可更改。(=== -1) */
NOT_FOUND = ''.indexOf('_'),
/**
* 周角 = 360°, 1 turn, 1 revolution, 1 perigon, full circle, complete
* rotation, a full rotation in degrees.
*
* @type {Number}
*/
TURN_TO_DEGREES = 360 | 0,
/**
* 周角.
*
* TURN_TO_RADIANS = 2πr/r = 2π =
* 6.283185307179586476925286766559005768394338798750211641949889...
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Radian
*/
TURN_TO_RADIANS = 2 * Math.PI,
/**
* degrees * DEGREES_TO_RADIANS = radians.
*
* DEGREES_TO_RADIANS = 2π/360 =
* 0.017453292519943295769236907684886127134428718885417254560971... ≈
* 1.745329251994329576923691e-2
*
* @type {Number}
*/
DEGREES_TO_RADIANS = TURN_TO_RADIANS / TURN_TO_DEGREES,
/**
* degrees * DEGREES_TO_ARCSECONDS = arcseconds.
*
* DEGREES_TO_ARCSECONDS = 3600
*
* @type {Number}
*/
DEGREES_TO_ARCSECONDS = 60 * 60 | 0,
/**
* Arcseconds in a full circle. 角秒
*
* TURN_TO_ARCSECONDS = 1296000
*
* @type {Number}
*/
TURN_TO_ARCSECONDS = TURN_TO_DEGREES * DEGREES_TO_ARCSECONDS,
/**
* arcseconds * ARCSECONDS_TO_RADIANS = radians.
*
* ARCSECONDS_TO_RADIANS = 2π/360/3600 =
* 0.0000048481368110953599358991410235794797595635330237270151558... ≈
* 4.848136811095359935899141e-6
*
* @type {Number}
*/
ARCSECONDS_TO_RADIANS = DEGREES_TO_RADIANS / DEGREES_TO_ARCSECONDS,
/**
* 24: 24 hours @ 1 day
*/
ONE_DAY_HOURS = 24,
/**
* Seconds per day. 每一天 86400 秒鐘。
*
* @type {Number}
*/
ONE_DAY_SECONDS = ONE_DAY_HOURS * 60 * 60 | 0;
// ---------------------------------------------------------------------//
// 天文相關定常數。
var
/**
* 每年 2 分點 + 2 至點。
*
* EQUINOX_SOLSTICE_COUNT = 4
*
* @type {Number}
*/
EQUINOX_SOLSTICE_COUNT = 2 + 2,
/**
* 每分至點 90°。
*
* EQUINOX_SOLSTICE_DEGREES = 90
*
* @type {Number}
*/
EQUINOX_SOLSTICE_DEGREES
//
= TURN_TO_DEGREES / EQUINOX_SOLSTICE_COUNT,
/** {Array}二十四節氣名。每月有一個節氣，一個中氣，分別發生在每月的7日和22日前後。 */
SOLAR_TERMS_NAME =
// Chinese name: 中氣,節氣,中氣,節氣,...
'春分,清明,穀雨,立夏,小滿,芒種,夏至,小暑,大暑,立秋,處暑,白露,秋分,寒露,霜降,立冬,小雪,大雪,冬至,小寒,大寒,立春,雨水,驚蟄'
.split(','),
/**
* 每年 24節氣。
*
* SOLAR_TERMS_COUNT = 24
*
* @type {Number}
*/
SOLAR_TERMS_COUNT = SOLAR_TERMS_NAME.length,
/**
* 每節氣 15°。
*
* DEGREES_BETWEEN_SOLAR_TERMS = 15
*
* @type {Number}
*/
DEGREES_BETWEEN_SOLAR_TERMS = TURN_TO_DEGREES / SOLAR_TERMS_COUNT,
// 🌑NEW MOON SYMBOL
// 🌒WAXING CRESCENT MOON SYMBOL
// ☽FIRST QUARTER MOON
// 🌓FIRST QUARTER MOON SYMBOL
// 🌔WAXING GIBBOUS MOON SYMBOL
// 🌕FULL MOON SYMBOL
// 🌖WANING GIBBOUS MOON SYMBOL
// 🌙CRESCENT MOON
// ☾LAST QUARTER MOON
// 🌗LAST QUARTER MOON SYMBOL
// 🌘WANING CRESCENT MOON SYMBOL
// 🌚NEW MOON WITH FACE
/**
* 各種月相: 新月、上弦月、滿月、下弦月。
*/
LUNAR_PHASE_NAME = [
// gettext_config:{"id":"new-moon"}
"朔",
// gettext_config:{"id":"first-quarter"}
"上弦",
// gettext_config:{"id":"full-moon"}
"望",
// gettext_config:{"id":"last-quarter"}
"下弦" ],
/**
* 本地之 time zone / time offset (UTC offset by minutes)。<br />
* e.g., UTC+8: 8 * 60 = +480<br />
* e.g., UTC-5: -5 * 60
*
* @type {Number}
*/
default_offset = library_namespace.String_to_Date
//
&& library_namespace.String_to_Date.default_offset
|| -(new Date).getTimezoneOffset() || 0;
_.SOLAR_TERMS = SOLAR_TERMS_NAME;
// ---------------------------------------------------------------------//
// Astronomical constant 天文常數。
// @see https://en.wikipedia.org/wiki/Astronomical_constant
// @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/sofam.h
// @see
// http://asa.usno.navy.mil/static/files/2015/Astronomical_Constants_2015.txt
var
/**
* Reference epoch (J2000.0), Julian Date. J2000.0 曆元。
*
* DAYS_OF_JULIAN_CENTURY = (365 + 1/4) * 100
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Epoch_%28astronomy%29#Julian_years_and_J2000
*/
J2000_epoch = 2451545.0,
/**
* Days per Julian century. 儒略世紀.
*
* DAYS_OF_JULIAN_CENTURY = (365 + 1/4) * 100
*
* @type {Number}
*/
DAYS_OF_JULIAN_CENTURY = 36525,
/**
* speed of light in vacuum (m/s), c 光速.
*
* @type {Number}
*/
CELERITAS = 299792458,
/**
* Astronomical unit (meters).<br />
* 1 astronomical unit = 149597870700 meters (exactly)
*
* Astronomical Almanac 2011:<br />
* au = A = 149597870700 ± 3 m
*
* @type {Number}
*/
AU_TO_METERS = 149597870700,
/**
* Light-time for unit (AU) distance (in days).<br />
* AU_LIGHT_TIME = 149597870700/299792458/86400 ≈ 0.005775518331436995
*
* @type {Number}
*/
AU_LIGHT_TIME = AU_TO_METERS / CELERITAS / ONE_DAY_SECONDS,
/**
* Earth mean radius (meter). 地球平均半徑(公尺)。地球半徑6,357km到6,378km。
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Earth_radius#Mean_radius
*/
TERRA_RADIUS_M = 6371009,
/**
* Equatorial radius of Earth (meter). 地球赤道半徑(公尺)。
*
* IERS (2003),<br />
* Astronomical Almanac 2011:<br />
* a_E = a_e = 6378136.6 ± 0.10 m
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids
*/
TERRA_EQUATORIAL_RADIUS_M = 6378136.6,
/**
* Polar radius of Earth (meter). 地球極半徑(公尺)。
*
* IERS (2003):<br />
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids
*/
TERRA_POLAR_RADIUS_M = 6356751.9,
/**
* Earth's flattening = 1 / (Reciprocal of flattening).<br />
* 地球偏率 = 1 - 極半徑/赤道半徑
*
* IERS (2003): 1 / 298.25642
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids
*/
TERRA_FLATTENING = 1 / 298.25642,
/**
* 月球平均半徑 in meter (公尺)。
*
* @type {Number}
*
* @see http://en.wikipedia.org/wiki/Moon
*/
LUNAR_RADIUS_M = 1737100,
/**
* 地月平均距離 in meter (公尺)。
*
* 平均距離 mean distance: 384400 km (公里)<br />
* 半長軸 Semi-major axis: 384748 km (公里)<br />
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Lunar_distance_%28astronomy%29
* @see http://en.wikipedia.org/wiki/Orbit_of_the_Moon
* @see http://solarsystem.nasa.gov/planets/profile.cfm?Display=Facts&Object=Moon
*/
LUNAR_DISTANCE_M = 384400000,
/**
* Geocentric semi-diameter of the Sun (in radians) 日面的平均地心視半徑。
* 960″.12±0″.09 (696, 342±65km).
*
* old: 959.63 arcseconds.<br />
* 0°16′ should be added for the semidiameter.<br />
* average apparent radius of the Sun (16 arcminutes)
*
* @type {Number}
*
* @see http://arxiv.org/pdf/1203.4898v1.pdf
* @see http://arxiv.org/pdf/1106.2537.pdf
* @see http://aa.usno.navy.mil/faq/docs/RST_defs.php
* @see https://en.wikipedia.org/wiki/Solar_radius
*/
SOLAR_RADIUS_ARCSECONDS = 960.12,
//
SOLAR_RADIUS_RADIANS = SOLAR_RADIUS_ARCSECONDS * ARCSECONDS_TO_RADIANS,
/**
* Geocentric semi-diameter of the Sun (in m) 日面的平均地心視半徑。
*
* Math.atan(696342000 / 149597870700) / (2 * Math.PI) * 360 * 60 ≈ 16′
*
* @type {Number}
*/
SOLAR_RADIUS_M = 696342000,
/**
* Constant of aberration (arcseconds). κ 光行差常數
*
* 天文學中定義周年光行差常數（簡稱光行差常數）為κ=v/c，其中c是光速，v是地球繞太陽公轉的平均速度
*
* Astronomical Almanac 2011:<br />
* Constant of aberration at epoch J2000.0:<br />
* kappa = 20.49551″
*
* @type {Number}
*
* @see https://zh.wikipedia.org/wiki/%E5%85%89%E8%A1%8C%E5%B7%AE
*/
ABERRATION_κ = 20.49551;
// ---------------------------------------------------------------------//
// 初始調整並規範基本常數。
// ---------------------------------------------------------------------//
// private tool functions. 工具函數
/**
* 經緯度 pattern [ , °, ′, ″, ″., NEWS ]
*
* @type {RegExp}
*/
var LATITUDE_PATTERN, LONGITUDE_PATTERN;
(function() {
/**
* 經緯度 pattern [ , °, ′, ″, ″., NEWS ]
* <q>/([+-]?\d+(?:\.\d+)?)°\s*(?:(\d+)[′']\s*(?:(\d+(?:\.\d+)?)(?:″|"|'')(\.\d+)?\s*)?)?([NEWS])/i</q>
*/
var d = /([+-]?\d+(?:\.\d+)?)°\s*/, ms =
//
/(?:(\d+)[′']\s*(?:(\d+(?:\.\d+)?)(?:″|"|'')(\.\d+)?\s*)?)?/;
LATITUDE_PATTERN = new RegExp(d.source + ms.source + '([NS])', 'i');
LONGITUDE_PATTERN = new RegExp(d.source + ms.source + '([EW])', 'i');
})();
// 經緯度
// [ {Number}latitude 緯度, {Number}longitude 經度 ]
function parse_coordinates(coordinates) {
var latitude, longitude,
// e.g., '25.032969, 121.565418'
matched = coordinates.match(
//
/([+-]?\d+(?:\.\d+)?)(?:\s+|\s*,\s*)([+-]?\d+(?:\.\d+)?)/);
if (matched)
return [ +matched[1], +matched[2] ];
// e.g., 25° 1′ 58.6884″ N 121° 33′ 55.5048″ E
// e.g., 25° 1' 58.6884'' N 121° 33' 55.5048'' E
matched = coordinates.match(LATITUDE_PATTERN);
if (matched) {
latitude = +matched[1] + (matched[2] ? matched[2] / 60 : 0)
+ (matched[3] ? matched[3] / 60 / 60 : 0)
+ (matched[4] ? matched[4] / 60 / 60 : 0);
if (matched[5].toUpperCase() === 'S')
latitude = -latitude;
}
matched = coordinates.match(LONGITUDE_PATTERN);
if (matched) {
longitude = +matched[1] + (matched[2] ? matched[2] / 60 : 0)
+ (matched[3] ? matched[3] / 60 / 60 : 0)
+ (matched[4] ? matched[4] / 60 / 60 : 0);
if (matched[5].toUpperCase() === 'W')
longitude = -longitude;
}
if (latitude || longitude)
return [ latitude, longitude ];
}
_.parse_coordinates = parse_coordinates;
/**
* get Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.<br />
* Interval between fundamental date J2000.0 and given date.
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number} Julian centuries of JD from J2000.0
*/
function Julian_century(TT_JD) {
return (TT_JD - J2000_epoch) / DAYS_OF_JULIAN_CENTURY;
}
_.Julian_century = Julian_century;
// normalize degrees
// to proper degrees 0–less than 360
// near_0: −180–less than 180
function normalize_degrees(degrees, near_0) {
if (!degrees)
return degrees;
if ((degrees %= TURN_TO_DEGREES) < 0)
degrees += TURN_TO_DEGREES;
if (near_0 && degrees >= TURN_TO_DEGREES / 2)
degrees -= TURN_TO_DEGREES;
return degrees;
}
_.normalize_degrees = normalize_degrees;
function normalize_radians(radians, near_0) {
if (!radians)
return radians;
radians = radians.mod(TURN_TO_RADIANS);
if (near_0 && radians >= TURN_TO_RADIANS / 2)
radians -= TURN_TO_RADIANS;
return radians;
}
_.normalize_radians = normalize_radians;
/**
* 將時分秒轉成 radians。
*
* @param {Number}hours
* @param {Number}minutes
* @param {Number}seconds
* @param {Boolean}to_days
* 轉成 days (turns)。
* @param {Boolean}is_degrees
* 輸入的是 degrees
*
* @returns {Number}radians
*/
function time_to_radians(hours, minutes, seconds, to_days, is_degrees) {
if (seconds)
minutes = (minutes || 0) + seconds / 60;
hours = ((hours || 0) + (minutes ? minutes / 60 : 0))
// to days
/ (is_degrees ? TURN_TO_DEGREES : ONE_DAY_HOURS);
if (!to_days)
hours *= TURN_TO_RADIANS;
return hours;
}
_.time_to_radians = time_to_radians;
/**
* 將 degrees 轉成 radians。
*
* @param {Number}degrees
* degrees
* @param {Number}arcminutes
* arcminutes
* @param {Number}arcseconds
* arcseconds
* @param {Boolean}to_days
* 轉成 days (turns)。
*
* @returns {Number}radians
*/
function degrees_to_radians(degrees, arcminutes, arcseconds, to_days) {
if (degrees < 0) {
if (arcminutes)
arcminutes = -arcminutes, arcseconds = -arcseconds;
if (arcseconds)
arcseconds = -arcseconds;
}
return time_to_radians(degrees, arcminutes, arcseconds, to_days, true);
}
_.degrees_to_radians = degrees_to_radians;
/**
* 計算角度差距(減法)。 return (base - target), target 會先趨近於 base。或是說結果會向 0 趨近。
*
* subtract_degrees(base,target)>0: base>target, base-target>0
*
* @param {Object}base
* base coordinates
* @param {Object}target
* target coordinates
*
* @returns {Number}
*/
function subtract_degrees(base, target) {
if (Math.abs(base = (base - target) % TURN_TO_DEGREES)
//
>= TURN_TO_DEGREES / 2)
if (base > 0)
base -= TURN_TO_DEGREES;
else
base += TURN_TO_DEGREES;
return base;
}
/**
* show degrees / sexagesimal system. 顯示易懂角度。
*
* @param {Number}degrees
* degrees
* @param {Integer}padding
* 小數要取的位數。
*
* @returns {String}易懂角度。
*
* @see https://en.wikipedia.org/wiki/Minute_and_second_of_arc
*/
function format_degrees(degree, padding) {
if (!degree)
return '0°';
// is negative.
var minus = degree < 0;
// 處理負數。
if (minus)
degree = -degree;
var value = Math.floor(degree),
//
show = '';
if (value > 0) {
degree -= value;
// 限制範圍在0至360度內。
value %= TURN_TO_DEGREES;
if (padding >= 0 && value < 100)
show = value > 9 ? ' ' : ' ';
show += value + '° ';
}
if (degree > 0) {
value = (degree *= 60) | 0;
if (value || show)
show += (padding && value < 10 ? ' ' : '')
//
+ value + '′ ';
if (degree -= value) {
degree *= 60;
degree = padding >= 0 ? (degree < 10 ? ' ' : '')
+ degree.toFixed(padding) : String(degree);
show += degree.includes('.') ? degree.replace('.', '″.')
// arcseconds
: degree + '″';
}
}
// 處理負數。
if (minus)
show = '-' + show;
return show.replace(/ $/, '');
}
_.format_degrees = format_degrees;
/**
* show time angle. 顯示易懂時角。
*
* @param {Number}days
* days / turns
*
* @returns {String}易懂時角。
*
* @see https://en.wikipedia.org/wiki/Unicode_subscripts_and_superscripts
*/
function days_to_time(days) {
var show = '', minus = days < 0;
// 處理負數。
if (minus)
days = -days;
// time: hours
var time = (days % 1) * ONE_DAY_HOURS;
if (days |= 0)
show += days + 'ᵈ';
days = time | 0;
if (days || show)
show += days + 'ʰ';
// time: minutes
time = (time % 1) * 60;
days = time | 0;
if (days || show)
show += days + 'ᵐ';
// time: seconds
time = (time % 1) * 60;
if (days || show)
show += days + 'ˢ';
// time <= 1e-10: 當作 error。
// 1e-11: -Math.log10((1/2-1/3-1/6)*86400)|0
if ((time %= 1) > 1e-11) {
// 去首尾之 0。
time = time.toPrecision(11).replace(/0+$/, '').replace(/^0+/, '');
if (show)
show += time;
else
show = '0ˢ' + time;
} else if (!show) {
show = '0';
}
// 收尾。
// 處理負數。
if (minus)
show = '-' + show;
return show;
}
_.days_to_time = days_to_time;
/**
* format radians
*
* @param {Number}radians
* radians to format
* @param {String}[to_type]
* to what type: decimal degrees, degrees, time, radians, turns
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
*
* @returns {String}formatted radians
*/
function format_radians(radians, to_type, options) {
if (!to_type)
// default: degrees of sexagesimal measure
to_type = 'degrees';
switch (to_type) {
case 'decimal':
case 'decimal degrees':
return radians / DEGREES_TO_RADIANS;
case 'degrees':
return format_degrees(radians / DEGREES_TO_RADIANS, options
&& options.padding);
case 'turns':
return radians / TURN_TO_RADIANS;
case 'time':
return days_to_time(radians / TURN_TO_RADIANS);
}
// default
return radians;
}
_.format_radians = format_radians;
// ------------------------------------------------------------------------------------------------------//
// semi-diameter of objects
/**
* 天體的中心視半徑 (in arcseconds)。
*
* e.g., Geocentric semi-diameter of the Sun, apparent radius, 日面的地心視半徑。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 390. Chapter 55 Semidiameters of the Sun, Moon, and Planets
*
* @param {Object|Number}coordinates
* coordinates or distance (in AU) of object
* @param {Number|String}[radius]
* object radius (in arcseconds) or object name. default: sun
* @param {Number}[latitude]
* object-centric latitude of the Earth.<br />
* e.g., Saturnicentric latitude of the Earth (see Chapter 45).<br />
* “以土星為中心”的緯度(詳見《天文算法》第45章)。
*
* @returns {Number}semi-diameter (in arcseconds)
*
* @see https://github.com/soniakeys/meeus/blob/master/semidiameter/semidiameter.go
*/
function semidiameter(coordinates, radius, latitude) {
var object = coordinates && coordinates.object
|| (isNaN(radius) ? radius : SUN_NAME);
if (!radius)
radius = object;
if (radius in semidiameter.apparent)
radius = semidiameter.apparent[object = radius];
else if (radius === SUN_NAME)
object = radius, radius = SOLAR_RADIUS_ARCSECONDS;
// assert: radius is in arcseconds now.
var distance = typeof coordinates === 'number' && coordinates > 0 ? coordinates
: coordinates.Δ
|| (object === MOON_NAME ? LUNAR_DISTANCE_M
/ AU_TO_METERS
// 1: default: 1 AU
: 1);
// assert: distance is in AU now.
if (object === MOON_NAME) {
if (false && coordinates.Δ > 0) {
radius = Math.atan(LUNAR_RADIUS_M / AU_TO_METERS
/ coordinates.Δ)
/ ARCSECONDS_TO_RADIANS;
if (latitude)
// → 以觀測者為中心的座標中看到的月亮視半徑
radius += radius * Math.sin(latitude * DEGREES_TO_RADIANS)
* TERRA_RADIUS_M / LUNAR_DISTANCE_M;
return radius;
}
// 設Δ是地球中心到月球中心到的距離(單位是千米)，
distance *= AU_TO_METERS / 1000;
/**
* π是月球的赤道地平視差，s是月亮的地心視半徑，k是月亮平均半徑與地球赤道半徑的比值。在1963到1968年的天文曆書中，日月食計算中取k=0.272481
*
* Explanatory Supplement to the Astronomical Ephemeris. Third
* impression 1974.<br />
* p. 213.<br />
* As from 1963, the value of k is taken as 0.2724807, which leads
* to the same value of the semi-diameter as in the lunar ephemeris.
* The value 0.272274 for k is retained, however, in the calculation
* of duration on the central line of total solar eclipses, by way
* of applying an approximate correction for the irregularities of
* the lunar limb.
*
* Explanatory Supplement to the Astronomical Almanac.<br />
* p. 425.<br />
* The lAU adopted a new value of k (k = 0.2725076) in August 1982.
*/
var k = 0.272481, sin_π = 6378.14 / distance;
if (coordinates && coordinates.LHA) {
// p. 280. formula 40.7
var A = Math.cos(coordinates.δ) * Math.sin(coordinates.LHA),
//
B = Math.cos(coordinates.δ) * Math.cos(coordinates.LHA)
- coordinates.ρcos_φp * sin_π,
//
C = Math.sin(coordinates.δ) - coordinates.ρsin_φp * sin_π;
/**
* the topocentric distance of the Moon (that is, the distance
* from the observer to the center of the Moon) is Δ′=q*Δ, q
* being given by formula (40.7).
*/
distance *= Math.sqrt(A * A + B * B + C + C);
sin_π = 6378.14 / distance;
}
radius = Math.asin(k * sin_π) / ARCSECONDS_TO_RADIANS;
} else {
radius /= distance;
if (latitude && object
&& ((object + '_polar') in semidiameter.apparent)) {
// 極半徑/赤道半徑
var k = semidiameter.apparent[object + '_polar']
/ semidiameter.apparent[object];
k = 1 - k * k;
latitude = Math.cos(latitude * DEGREES_TO_RADIANS);
radius *= Math.sqrt(1 - k * latitude * latitude);
}
}
return radius;
}
_.semidiameter = semidiameter;
/**
* apparent radius (arcseconds). 距離 1 AU 時的太陽和行星的視半徑。
*
* @type {Object}
*/
semidiameter.apparent = {
mercury : 3.36,
venus_surface : 8.34,
// +cloud
// 對於金星，值8″.34，指從地球上看它的地殼半徑，而不是指它的雲層。由於這個原因，當計算諸如中天、淩日、星食等天文現象時，我們採用舊值8″.41。
venus : 8.41,
mars : 4.68,
// equatorial
jupiter : 98.44,
jupiter_polar : 92.06,
// equatorial
saturn : 82.73,
saturn_polar : 73.82,
uranus : 35.02,
neptune : 33.50,
pluto : 2.07
};
// ------------------------------------------------------------------------------------------------------//
// coordinate transformations 座標變換
// @see
// https://en.wikipedia.org/wiki/List_of_common_coordinate_transformations
/**
* auto detect time zone. 自動判別時區。
*
* @param {Array}local
* the observer's geographic location [ latitude (°), longitude
* (°), time zone (e.g., UTC+8: 8), elevation or geometric height
* (m) ]<br />
* 觀測者 [ 緯度（北半球為正,南半球為負）, 經度（從Greenwich向東為正，西為負）, 時區,
* 海拔標高(觀測者距海平面的高度) ]
*
* @returns {Number}time zone. UTC+8: 8
*/
function get_time_zone(local) {
return isNaN(local[2]) ? Math.round(local[1]
/ (TURN_TO_DEGREES / ONE_DAY_HOURS)) : local[2];
}
/**
* 此函數為為了舊曆元所做的修正。
*
* longitude λ must be converted to the ephemeris longitude λ* by increasing
* it by 1.002738 ΔT, the sidereal equivalent of ΔT.
*
* 星曆用的經度從Greenwich向西為正，東為負，與向東為正的一般地理經度用法相反。
*
* Reference 資料來源/資料依據:<br />
* Explanatory Supplement to the Astronomical Ephemeris. Third impression
* 1974.<br />
* p. 241.
*
* The ephemeris meridian is 1.002 738 ΔT east of the Greenwich meridian,
* where ΔT=TT−UT1.
*
* @param {Number}longitude
* longitude of geographic coordinate in degrees, 一般地理經度
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}ephemeris longitude in radians, 星曆用的經度
*
* @see http://asa.usno.navy.mil/SecM/Glossary.html
*/
function to_ephemeris_longitude(longitude, TT_JD) {
return -longitude * DEGREES_TO_RADIANS;
return ((TT_JD ? 1.002738 * ΔT_of_JD(TT_JD) : 0) - longitude)
* DEGREES_TO_RADIANS;
}
/**
* ephemeris longitude → geographic longitude
*
* @param {Number}longitude
* ephemeris longitude in radians, 星曆用的經度
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}geographic longitude in degrees
*/
function from_ephemeris_longitude(longitude, TT_JD) {
return normalize_radians(-longitude, true) /
//
DEGREES_TO_RADIANS;
return (TT_JD ? -1.002738 * ΔT_of_JD(TT_JD) : 0) - longitude
/ DEGREES_TO_RADIANS;
}
/**
* 計算角距離 angular distance (in radians)
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 109. formula 17.1
*
* @param {Object}coordinates_1
* apparent geocentric ecliptical coordinates<br /> { longitude
* α , latitude δ } in radians
* @param {Object}coordinates_2
* apparent geocentric ecliptical coordinates<br /> { longitude
* α , latitude δ } in radians
*
* @returns {Number}angular distance in radians
*/
function angular_distance(coordinates_1, coordinates_2, no_minor_squre) {
var Δα = Math.abs(coordinates_1.α - coordinates_2.α), Δδ,
//
δ1 = coordinates_1.δ, δ2 = coordinates_2.δ;
// 10 / 60 / 360 * (2 * Math.PI) = 0.0029088820866572155
if (!no_minor_squre && Δα < .001 && (Δδ = Math.abs(δ1 - δ2)) < .001) {
// 角度差接近於0或180度時，求取近似值。
Δα *= Math.cos((δ1 + δ2) / 2);
return Math.sqrt(Δα * Δα + Δδ * Δδ);
}
if (false)
console.log(Math.sin(δ1) * Math.sin(δ2) + Math.cos(δ1)
* Math.cos(δ2) * Math.cos(Δα));
return Math.acos(Math.sin(δ1) * Math.sin(δ2) + Math.cos(δ1)
* Math.cos(δ2) * Math.cos(Δα));
}
_.angular_distance = angular_distance;
/**
* 向量長度，與原點距離。
*
* @param {Array}rectangular
* 直角座標 [ x, y, z ]
*
* @returns {Number}distance
*/
function distance_of_rectangular(rectangular) {
var x = rectangular[0], y = rectangular[1], z = rectangular[2];
return Math.sqrt(x * x + y * y + z * z);
}
/**
* spherical coordinates → rectangular coordinates. 球座標系(日心座標)轉為直角座標系。
*
* @param {Number}longitude
* longitude (L) of spherical 球座標
* @param {Number}latitude
* latitude (B) of spherical 球座標
* @param {Number}radius
* radius (R) of spherical 球座標
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.unit_radius: 若為 true，則將 .R 當作 1。<br />
* {Object}options.base: base spherical coordinates. {L,B,R}
* 基準球座標.
*
* @returns {Object}rectangular coordinates [ x, y, z ]
*
* @see https://en.wikipedia.org/wiki/Ecliptic_coordinate_system#Rectangular_coordinates
* https://en.wikipedia.org/wiki/Equatorial_coordinate_system#Geocentric_equatorial_coordinates
*/
function spherical_to_rectangular(longitude, latitude, radius, options) {
if (library_namespace.is_Object(longitude)) {
options = latitude;
radius = longitude.R;
latitude = longitude.B;
longitude = longitude.L;
}
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var tmp, cos_B = Math.cos(latitude),
//
x = cos_B * Math.cos(longitude), y = cos_B * Math.sin(longitude), z = Math
.sin(latitude);
if (!options.unit_radius && radius) {
x *= radius;
y *= radius;
z *= radius;
}
if (tmp = options.base) {
tmp = spherical_to_rectangular(tmp, options.unit_radius ? {
unit_radius : true
} : null);
x -= tmp[0];
y -= tmp[1];
z -= tmp[2];
}
tmp = [ x, y, z ];
if (options.distance)
tmp.distance = Math.sqrt(x * x + y * y + z * z);
// return rectangular
return tmp;
}
/**
* rectangular coordinates → spherical coordinates. 直角座標系轉為球座標系(黃道座標)。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 223. formula 33.2 座標變換
*
* @param {Array}rectangular
* 直角座標 [ x, y, z ]
* @param {Boolean}get_radius
* 亦生成 radius
*
* @returns {Object}spherical coordinates { λ , β }
*/
function rectangular_to_spherical(rectangular, get_radius) {
var x = rectangular[0], y = rectangular[1], z = rectangular[2],
// ecliptical (or celestial) [ longitude 黃經, latitude 黃緯 ]。
spherical = [ Math.atan2(y, x), Math.atan2(z, Math.sqrt(x * x, y * y)) ];
if (get_radius)
spherical.push(Math.sqrt(x * x + y * y + z * z));
return spherical;
}
/**
* Transformation from ecliptical into equatorial coordinates. G地心視黃道座標轉到
* E地心赤道座標(視赤經及視赤緯)
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 93. formula 13.3, 13.4
*
* @param {Object}coordinates
* apparent geocentric ecliptical coordinates<br /> { longitude
* λ , latitude β }
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Object}equatorial coordinates { right ascension α , declination
* δ }
*/
function ecliptical_to_equatorial(coordinates, TT_JD, options) {
var ε = obliquity(TT_JD),
// G地心視黃道 apparent geocentric ecliptic coordinates:
// longitude λ and latitude β in radians
λ = coordinates.λ, β = coordinates.β,
// cache
sin_λ = Math.sin(λ), cos_ε = Math.cos(ε), sin_ε = Math.sin(ε);
// geocentric right ascension 地心赤經。
coordinates.α = Math.atan2(sin_λ * cos_ε - Math.tan(β) * sin_ε, Math
.cos(λ));
// geocentric declination 地心赤緯。
coordinates.δ = Math.asin(Math.sin(β) * cos_ε + Math.cos(β) * sin_ε
* sin_λ);
// 因為 equatorial_to_horizontal() 可能會再利用，這裡不處理 options.degrees。
return coordinates;
}
/**
* equatorial coordinates → local horizontal coordinates.
* 依據觀測者的位置和時間，轉換地心視赤道座標到本地站心地平座標系。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 93. formula 13.5, 13.6 座標變換<br />
* Chapter 40: Correction for Parallax
*
* @param {Object}coordinates
* equatorial coordinates { right ascension α , declination δ }
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Array}local
* the observer's geographic location [ latitude (°), longitude
* (°), time zone (e.g., UTC+8: 8), elevation or geometric height
* (m) ]<br />
* 觀測者 [ 緯度（北半球為正,南半球為負）, 經度（從Greenwich向東為正，西為負）, 時區,
* 海拔標高(觀測者距海平面的高度) ]
*
* @returns {Object}horizontal { Alt:altitude (radians) , Az:azimuth
* (radians) }
*
* @see https://en.wikipedia.org/wiki/Horizontal_coordinate_system
*/
function equatorial_to_horizontal(coordinates, TT_JD, local) {
/**
* 地心赤緯δ。
*
* @type {Number}
*/
var δ = coordinates.δ;
if (isNaN(δ))
// 先算出地心視赤道座標。
// 一般已在 function get_horizontal() 中處理。
δ = ecliptical_to_equatorial(coordinates, TT_JD).δ;
/**
* 地心赤經α。
*
* @type {Number}
*/
var α = coordinates.α,
/**
* Phi: lower-case letter φ (or often its variant, ϕ) 觀測者緯度（北半球為正,南半球為負）
*
* @type {Number}
*/
φ = local[0] * DEGREES_TO_RADIANS,
// p. 92.
/**
* Greenwich視恆星時θ0
*
* @type {Number} in radians
*/
θ0 = GAST(TT_of(TT_JD, true), TT_JD),
/**
* 本地恆星時θ = Greenwich視恆星時θ0 - L觀測者星曆經度
*
* @type {Number} in radians
*/
θ = θ0 - to_ephemeris_longitude(local[1], TT_JD),
/**
* local hour angle (in radians)
* 本地地心時角。一個天體的時角是2.5HA，就表示他已經在2.5個小時之前通過當地的子午圈，並且在當地子午圈的西方37.5度的距離上。負數則表示在多少小時之後將通過當地的子午圈。
*
* LHA = 本地恆星時θ − 地心赤經α = Greenwich視恆星時θ0 - L觀測者星曆經度 − 地心赤經α
*
* @type {Number} in radians
*/
LHA = θ - α,
// cache
sin_φ = Math.sin(φ), cos_φ = Math.cos(φ),
// cache
cos_H = Math.cos(LHA),
// p. 82.
// tmp
u = Math.atan(TERRA_POLAR_RADIUS_M / TERRA_EQUATORIAL_RADIUS_M
* Math.tan(φ));
// tmp
LHA /= TERRA_EQUATORIAL_RADIUS_M;
/**
* 計算周日視差、日月食、星蝕所需要的量ρsin(φ′)
*
* @type {Number}
*/
var ρsin_φp = TERRA_POLAR_RADIUS_M / TERRA_EQUATORIAL_RADIUS_M
* Math.sin(u) + LHA * sin_φ,
/**
* 計算周日視差、日月食、星蝕所需要的量ρcos(φ′)
*
* @type {Number}
*/
ρcos_φp = Math.cos(u) + LHA * cos_φ;
coordinates.ρsin_φp = ρsin_φp;
coordinates.ρcos_φp = ρcos_φp;
// p. 279.
// 地心視赤道座標轉到本地站心赤道座標:
// 修正 planet's parallax (行星視差)
var
/**
* the equatorial horizontal parallax of the body in radians. 天體的赤道地平視差.
*
* Math.sin(8.794 * ARCSECONDS_TO_RADIANS) ≈ 0.0000426345
*
* @type {Number} in radians
*/
π = Math.asin(Math.sin(8.794 * ARCSECONDS_TO_RADIANS)
// coordinates.Δ: apparent distance at TT_JD in AU in radians
// 對於太陽、行星和慧星，經常適合使用它們到地球的距離Δ替代視差
/ coordinates.Δ),
// cache
sin_π = Math.sin(π), cos_δ = Math.cos(δ);
coordinates.π = π;
// tmp
u = ρcos_φp * sin_π;
π = cos_δ - u * cos_H;
var Δα = Math.atan2(-u * Math.sin(LHA), π);
// 對於赤緯，不必計算Δδ，用下式可直接算出δ′：
// apply new value to (δ, α, LHA).
δ = Math.atan2((Math.sin(δ) - ρsin_φp * sin_π) * Math.cos(Δα), π);
α += Δα;
// T站心赤道 topocentric equatorial coordinate system
// @see function Coordinates()
coordinates.T = [ α, δ ];
// coordinates.θ0 = θ0;
// coordinates.θ = θ;
// LHA: local hour angle (in radians) 本地地心時角。
coordinates.LHA = LHA = θ - α;
// re-cache
cos_H = Math.cos(LHA);
// p. 93.
// 站心赤道座標轉到站心地平座標 (radians)
// Altitude (Alt) 高度角或仰角又稱地平緯度。
// 修正大氣折射的影響
// TODO: 考慮 dip of the horizon (地平俯角, 海岸視高差)
// @see
// https://en.wikipedia.org/wiki/Horizon#Effect_of_atmospheric_refraction
// http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/altitudes.html
coordinates.Alt = refraction(Math.asin(sin_φ * Math.sin(δ) + cos_φ
* Math.cos(δ) * cos_H)
/ DEGREES_TO_RADIANS)
* DEGREES_TO_RADIANS;
// Azimuth (Az) 方位角又稱地平經度。
coordinates.Az = Math.atan2(Math.sin(LHA), cos_H * sin_φ - Math.tan(δ)
* cos_φ);
// parallactic angle
// https://en.wikipedia.org/wiki/Parallactic_angle
// Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版
// p. 98. formula 14.1
if (false
// 當天體正好在天頂，則沒有定義。
&& (π = Math.tan(φ) * Math.cos(δ) - Math.sin(δ) * cos_H))
coordinates.parallactic = Math.atan2(Math.sin(LHA), π);
// 因為可能會再利用，這裡不處理 options.degrees。
return coordinates;
}
/**
* ecliptical → equatorial coordinates → local horizontal coordinates.
*
* @param {Object}coordinates
* apparent geocentric ecliptical coordinates<br /> { longitude
* λ , latitude β }
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*/
function get_horizontal(coordinates, TT_JD, options) {
var local = Array.isArray(options.local) && options.local;
if (local || options.equatorial) {
// 地心視黃道座標轉到視赤道座標(視赤經及視赤緯)。
ecliptical_to_equatorial(coordinates, TT_JD, options);
// 需要保證有 coordinates.Δ
if (local && coordinates.Δ)
equatorial_to_horizontal(coordinates, TT_JD, local);
// 單位轉換。
if (options.degrees) {
if (local) {
coordinates.Alt /= DEGREES_TO_RADIANS;
coordinates.Az /= DEGREES_TO_RADIANS;
}
coordinates.α /= DEGREES_TO_RADIANS;
coordinates.δ /= DEGREES_TO_RADIANS;
}
}
// elongation Ψ of the planet, its angular distance to the Sun
// https://en.wikipedia.org/wiki/Elongation_%28astronomy%29
// 行星的距角，即地心看行星與太陽的角距離 (angular distance)。
// Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版
// Chapter 48 Illuminated Fraction of the Moon's Disk
if (options.elongation) {
// the Sun's apparent longitude in degrees → radians.
var solar = solar_coordinates(TT_JD, {
equatorial : true
}),
//
λ0 = solar.apparent * DEGREES_TO_RADIANS,
//
cos_Ψ = Math.cos(coordinates.β) * Math.cos(coordinates.λ - λ0);
// The Sun's latitude, which is always smaller than 1.2
// arcsecond, may be neglected here.
// 地心座標下的月球距角ψ
coordinates.Ψ = Math.acos(cos_Ψ);
// 月心座標下的地球距角i
coordinates.i = Math.atan2(solar.Δ * Math.sin(coordinates.Ψ),
coordinates.Δ - solar.Δ * cos_Ψ);
// ψ和i在均在0到180度之間。
// 月亮明亮邊緣的位置角
coordinates.χ = Math.atan2(Math.cos(solar.δ)
* Math.sin(solar.α - coordinates.α), Math.sin(solar.δ)
* Math.cos(coordinates.δ) - Math.cos(solar.δ)
* Math.sin(coordinates.δ)
* Math.cos(solar.α - coordinates.α));
// 單位轉換。
if (options.degrees) {
coordinates.Ψ /= DEGREES_TO_RADIANS;
coordinates.i /= DEGREES_TO_RADIANS;
coordinates.χ /= DEGREES_TO_RADIANS;
}
}
}
// ------------------------------------------------------------------------------------------------------//
// ΔT
/**
* get ΔT of year.<br />
* ΔT = TT - UT<br />
* <br />
* 天文計算/星曆表使用 Terrestrial Time (TT, 地球時標)，<br />
* 日常生活中使用 UTC, 接近 Universal Time (UT, 世界時標), 主要為 UT1。<br />
* <br />
* 簡略的說，天文計算用時間 TT = 日常生活時間 UT + ΔT
*
* ΔT is NOT △T
*
* @param {Number}year
* the year value of time = year + (month - 0.5) / 12
* @param {Number}[month]
* the month of time.
*
* @returns {Number} ΔT of year in seconds.
*
* @see https://en.wikipedia.org/wiki/%CE%94T
* @see <a href="http://www.cv.nrao.edu/~rfisher/Ephemerides/times.html"
* accessdate="2015/3/25 20:35">Astronomical Times</a>
* @see http://njsas.org/projects/speed_of_light/roemer/tt-utc.html
*
* @since 2015/3/21 9:23:32
*/
function ΔT(year, month) {
if (month > 0)
year += (month - 0.5) / 12;
var index = 0;
while (true) {
if (year >= ΔT_year_start[index])
break;
if (++index === ΔT_year_start.length) {
// before −500: the same as after 2150.
index = 0;
break;
}
}
var deltaT = polynomial_value(ΔT_coefficients[index],
(year - ΔT_year_base[index]) / 100);
library_namespace.debug('ΔT of year ' + year + ': ' + deltaT
+ ' seconds', 3);
return deltaT;
}
_.deltaT = _.ΔT = ΔT;
/**
* get ΔT of JD.<br />
* ΔT = TT - UT<br />
* <br />
* 天文計算/星曆表使用 Terrestrial Time (TT, 地球時標)，<br />
* 日常生活中使用 UTC, 接近 Universal Time (UT, 世界時標), 主要為 UT1。<br />
* <br />
* 簡略的說，天文計算用時間 TT = 日常生活時間 UT + ΔT
*
* @param {Number}JD
* Julian date
*
* @returns {Number} ΔT of year in seconds.
*/
function ΔT_of_JD(JD) {
// + 2000: Julian_century(JD) starts from year 2000.
return ΔT(Julian_century(JD) * 100 + 2000);
}
_.deltaT.JD = ΔT_of_JD;
/**
* get Terrestrial Time of Universal Time JD, apply ΔT to UT.
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Boolean}[TT_to_UT]
* reverse, TT → UT. treat JD as 天文計算用時間 TT.
*
* @returns {Number}JD of TT
*/
function TT_of(UT_JD, TT_to_UT) {
if (library_namespace.is_Date(UT_JD))
UT_JD = library_namespace.Date_to_JD(UT_JD);
var deltaT = ΔT_of_JD(UT_JD) / ONE_DAY_SECONDS;
// normal: UT → TT.
// TT_to_UT: TT → UT.
// 簡略的說，日常生活時間 UT = 天文計算用時間 TT - ΔT
return TT_to_UT ? UT_JD - deltaT : UT_JD + deltaT;
}
/**
* Translate Terrestrial Time JD → Universal Time JD.
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}JD of UT
*/
function UT_of(TT_JD) {
return TT_of(TT_JD, true);
}
_.TT = TT_of;
_.UT = UT_of;
// ------------------------------------------------------------------------------------------------------//
// Atmospheric refraction 大氣折射又稱蒙氣差、折光差（蒙氣即行星的大氣）
/**
* true apparent in degrees ← apparent altitude.<br />
* 大氣折射公式: 真地平緯度 ← 視地平緯度<br />
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 大氣折射.<br />
* based on: G. G. Bennett. (1982). "The Calculation of Astronomical
* Refraction in Marine Navigation".
*
* @param {Number}apparent
* apparent altitude in degrees. 視地平緯度/高度角或仰角，單位是度。
* @param {Number}[Celsius]
* temperature in degree Celsius. 攝氏度氣溫
* @param {Number}[pressure]
* pressure in kPa. 地表氣壓
*
* @returns {Number} degrees of true apparent. 單位是度
*
* @since 2015/3/21 21:31:17
*
* @see https://en.wikipedia.org/wiki/Atmospheric_refraction#Calculating_refraction
* @see http://www.astro.com/ftp/swisseph/src/swecl.c
*/
function refraction_to_real(apparent, Celsius, pressure) {
// (86.63175) get 4.186767499821572e-10
// 經測試，再多就變負數。
if (apparent > 86.63175)
// Jean Meeus: 在90°時，不作第二項修正反而更好。
return apparent;
// refraction in arcminutes. 折射角單位是分。
var refraction = 1 / Math.tan((apparent + 7.31 / (apparent + 4.4))
* DEGREES_TO_RADIANS);
// 第二項公式修正
refraction -= 0.06 * Math.sin(14.7 * refraction + 13);
// assert: refraction > 0
// Jean Meeus: 大約修正。折射率還與光的波長有關。這些運算式適用于黃光，它對人眼的靈敏度最高。
// @see
// http://www.iausofa.org/2015_0209_C/sofa/sofa_ast_c.pdf#75
// 常規條件: Both formulas assume an atmospheric pressure
// of 101.0 kPa and a temperature of 10 °C
if (!isNaN(Celsius))
// [K] = [°C] + 273.15
refraction *= (273 + 10) / (273 + refraction);
if (pressure >= 0)
refraction *= pressure / 101;
// 1度 = 60分
return apparent - refraction / 60;
}
/**
* apparent altitude in degrees ← true altitude.<br />
* 大氣折射公式: 視地平緯度 ← 真地平緯度
*
* @param {Number}real
* real altitude in degrees. 真地平緯度/高度角或仰角，單位是度。
* @param {Number}[Celsius]
* temperature in degree Celsius. 攝氏度氣溫
* @param {Number}[pressure]
* pressure in kPa. 地表氣壓
*
* @returns {Number} degrees of apparent altitude. 單位是度
*
* @since 2015/3/21 21:31:17
*
* @see https://en.wikipedia.org/wiki/Atmospheric_refraction#Calculating_refraction
* @see http://www.astro.com/ftp/swisseph/src/swecl.c
*/
function refraction(real, Celsius, pressure) {
// (89.891580) get 2.226931796052203e-10
// 經測試，再多就變負數。
if (real > 89.89158)
// Jean Meeus: h=90°時，該式算得R不等於零。
return real;
// refraction in arcminutes. 折射角單位是分.
var refraction = 1.02 / Math.tan((real + 10.3 / (real + 5.11))
* DEGREES_TO_RADIANS);
// assert: refraction > 0
// Jean Meeus: 大約修正。折射率還與光的波長有關。這些運算式適用于黃光，它對人眼的靈敏度最高。
// 常規條件: Both formulas assume an atmospheric pressure
// of 101.0 kPa and a temperature of 10 °C
if (!isNaN(Celsius))
// [K] = [°C] + 273.15
refraction *= (273 + 10) / (273 + refraction);
if (pressure >= 0)
refraction *= pressure / 101;
// 1度 = 60分
return real + refraction / 60;
}
refraction.to_real = refraction_to_real;
_.refraction = refraction;
// ------------------------------------------------------------------------------------------------------//
// obliquity 轉軸傾角。
/**
* 地球的平均轉軸傾角，平黃赤交角。 get mean obliquity of the ecliptic (Earth's axial tilt),
* IAU 2006 precession model.
*
* Reference 資料來源/資料依據:
* https://github.com/kanasimi/IAU-SOFA/blob/master/src/obl06.c
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number} obliquity in radians
*/
function mean_obliquity_IAU2006(TT_JD) {
return polynomial_value(IAU2006_obliquity_coefficients,
// Interval between fundamental date J2000.0
// and given date (JC).
Julian_century(TT_JD)) * ARCSECONDS_TO_RADIANS;
}
/**
* 地球的平均轉軸傾角，平黃赤交角。 get mean obliquity of the ecliptic (Earth's axial tilt).
*
* Reference 資料來源/資料依據: Laskar, J. (1986). "Secular Terms of Classical
* Planetary Theories Using the Results of General Relativity".
*
* J. Laskar computed an expression to order T10 good to 0″.02 over 1000
* years and several arcseconds over 10,000 years.
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT), 適用於J2000.0起算前後各10000年的範圍內。
*
* @returns {Number} obliquity in radians
*/
function mean_obliquity_Laskar(TT_JD) {
return polynomial_value(Laskar_obliquity_coefficients,
// J2000.0 起算的儒略萬年數
Julian_century(TT_JD) / 100) * DEGREES_TO_RADIANS;
}
/**
* 地球的平均轉軸傾角，平黃赤交角。
*
* @type {Function}
*/
var mean_obliquity = mean_obliquity_Laskar;
/**
* 地球的轉軸傾角，真黃赤交角ε。<br />
* get obliquity of the ecliptic (Earth's axial tilt).
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}obliquity in radians
*
* @see https://en.wikipedia.org/wiki/Axial_tilt
*/
function obliquity(TT_JD) {
// 真黃赤交角是ε=ε0+Δε，Δε是交角章動。（詳見第21章 章動及黃赤交角）。
return mean_obliquity(TT_JD) + nutation(TT_JD)[1];
}
_.obliquity = obliquity;
// ------------------------------------------------------------------------------------------------------//
// sidereal time. 恆星時
/**
* Earth rotation angle (IAU 2000 model). 地球自轉角
*
* Reference 資料來源/資料依據:<br />
* IAU-SOFA: /src/era00.c
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
*
* @returns {Number}Earth rotation angle (radians)
*
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/era00.c
*/
function IAU2000_ERA(UT_JD) {
return TURN_TO_RADIANS * (
// Fractional part of T (days).
(UT_JD % 1)
// Astronomical Almanac 2011:
// Earth rotation angle (ERA) at J2000.0 UT1:
// theta_0 = 0.7790572732640 revolutions
+ 0.7790572732640
// Astronomical Almanac 2011:
// Rate of advance of ERA:
// d(theta)/dUT1 = 1.00273781191135448 revs/UT1-day
+ 0.00273781191135448
// Days since fundamental epoch.
* (UT_JD - J2000_epoch));
}
/**
* Earth rotation angle. 地球自轉角
*
* @type {Function}
*/
_.ERA = IAU2000_ERA;
/**
* terms for function IAU2006_GMST()
*
* Reference 資料來源/資料依據:<br />
* IAU-SOFA: /src/gmst06.c
*
* @type {Array}
* @inner
*
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/gmst06.c
*/
var IAU2006_GMST_parameters = [ 0.014506, 4612.156534, 1.3915817,
-0.00000044, -0.000029956, -0.0000000368 ].map(function(p) {
return p * ARCSECONDS_TO_RADIANS;
});
/**
* Greenwich mean sidereal time (consistent with IAU 2006 precession).
*
* Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to
* predict the effects of precession.
*
* his GMST is compatible with the IAU 2006 precession and must not be used
* with other precession models.
*
* Reference 資料來源/資料依據:<br />
* IAU-SOFA: /src/gmst06.c
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}Greenwich mean sidereal time (radians)
*
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/gmst06.c
*/
function IAU2006_GMST(UT_JD, TT_JD) {
if (isNaN(TT_JD))
TT_JD = TT_of(UT_JD);
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(TT_JD);
// Greenwich mean sidereal time, IAU 2006.
return IAU2000_ERA(UT_JD)
+ polynomial_value(IAU2006_GMST_parameters, T);
}
/**
* terms for function Meeus_GMST()
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 88. formula 12.4
*
* @type {Array}
* @inner
*/
var Meeus_GMST_parameters = [ 280.46061837,
360.98564736629 * DAYS_OF_JULIAN_CENTURY, 0.000387933,
-1 / 38710000 ].map(function(p) {
return p * DEGREES_TO_RADIANS;
});
/**
* The mean sidereal time at Greenwich at Oh UT
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 88. formula 12.4
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
*
* @returns {Number}Greenwich mean sidereal time (radians)
*/
function Meeus_GMST(UT_JD) {
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(UT_JD);
return polynomial_value(Meeus_GMST_parameters, T).mod(TURN_TO_RADIANS);
}
/**
* Greenwich mean sidereal time. 平恆星時
*
* @type {Function}
*/
var GMST = IAU2006_GMST;
_.GMST = GMST;
/**
* Greenwich apparent sidereal time, IAU 2006. Greenwich視恆星時
*
* TODO: not yet done
*
* Reference 資料來源/資料依據:<br />
* IAU-SOFA: /src/gst06.c
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}Greenwich apparent sidereal time (radians)
*
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/gst06a.c
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/gst06.c
*/
function IAU2006_GAST(UT_JD, TT_JD) {
if (isNaN(TT_JD))
TT_JD = TT_of(UT_JD);
// Extract from the bias-precession-nutation matrix the X,Y
// coordinates of the Celestial Intermediate Pole.
var xy = iauBpn2xy(rnpb);
// the CIO locator s, given X,Y, IAU 2006
s = iauS06(TT_JD, xy);
return IAU2000_ERA(UT_JD)
// equation of the origins, given NPB matrix and s
- iauEors(rnpb, s);
}
/**
* Greenwich apparent sidereal time. Greenwich視恆星時
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 88.
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number}Greenwich apparent sidereal time (radians)
*/
function Meeus_GAST(UT_JD, TT_JD) {
if (isNaN(TT_JD))
TT_JD = TT_of(UT_JD);
return GMST(UT_JD, TT_JD)
// 赤經章動修正值 Δψ*cos(ε) 也稱作分點方程。
+ nutation(TT_JD, true) * Math.cos(obliquity(TT_JD));
}
/**
* Greenwich apparent sidereal time. Greenwich視恆星時
*
* @type {Function}
*/
var GAST = Meeus_GAST;
_.GAST = GAST;
// ------------------------------------------------------------------------------------------------------//
// Sun's aberration. 太陽地心黃經光行差修正量。
/**
* Sun's aberration. 太陽地心黃經光行差修正量。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 太陽位置計算 "太陽地心黃經光行差修正項" 式.<br />
*
* @param {Number}R
* 日地距離(天文單位 AU), radius vector in AU。
*
* @returns {Number} degree
*
* @see https://en.wikipedia.org/wiki/Aberration_of_light
*/
function sun_aberration_low(R) {
// 式中分子是光行差常數κ乘以a*(1-e²)，與24.5式的分子相同。
// 因此24.10中的分子中其實是一個緩慢變化的數，在0年是20″.4893，在+4000年是20″.4904。
return -20.4898 / DEGREES_TO_ARCSECONDS / R;
// 24.10式本身不是一個嚴格的準確的運算式，因為它是假設地球軌道是不受攝動的標準橢圓。當受到攝動時，月球的攝動可引起0″.01的誤差。
}
/**
* Sun's aberration. 太陽地心黃經光行差修正量。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 167, 168. chapter 太陽位置計算.<br />
*
* @param {Number}R
* 日地距離(天文單位 AU), radius vector in AU。
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
*
* @returns {Number} degree
*
* @see https://en.wikipedia.org/wiki/Aberration_of_light
*/
function sun_aberration_high(R, TT_JD) {
/**
* Julian millennia since J2000.0.<br />
* J2000.0 起算的儒略千年數.
*
* @type {Number}
*/
var τ = Julian_century(TT_JD) / 10,
// coefficients of Δλ
coefficients = [];
sun_aberration_variation.forEach(function(term) {
var coefficient = 0;
term.forEach(function(sub_term) {
coefficient += sub_term[0]
* Math.sin(sub_term[1] + sub_term[2] * τ);
});
coefficients.push(coefficient);
});
/**
* constant term of Sun's aberration
*
* If needed with respect to the mean equinox of the date instead of to
* a fixed reference frame, the constant term 3548.193 should be
* replaced by 3548.330.
* 如果Δλ須是在Date黃道(瞬時黃道/當日黃道?)中的，則應把常數項3548.193換為3548.330
*/
coefficients[0] += sun_aberration_variation_constant;
// Daily variation, in arcseconds, of the geocentric longitude
// of the Sun in a fixed reference frame
var Δλ = polynomial_value(coefficients, τ),
//
aberration = -AU_LIGHT_TIME / DEGREES_TO_ARCSECONDS * R * Δλ;
if (library_namespace.is_debug(3))
library_namespace.debug('aberration of radius vector ' + R
+ ', JD: ' + TT_JD + ': ' + format_degrees(aberration)
+ '. low-precision method: '
+ format_degrees(sun_aberration_low(R)), 0);
return aberration;
}
var sun_aberration = sun_aberration_high;
// ------------------------------------------------------------------------------------------------------//
// precession 歲差
/**
* calculate general precession / precession of the ecliptic
*
* Reference 資料來源/資料依據:<br />
* Kai Tang (2015). A long time span relativistic precession model of the
* Earth.
*
* IAU 2006年將主要的部分重新命名為赤道歲差，而較微弱的成份命名為黃道歲差 (precession of the
* ecliptic)，但是兩者的合稱仍是綜合歲差 (general precession)，取代了分點歲差。
*
* <q>在J2000.0的时候与P03岁差差大概几个角秒，主要由于周期拟合的时候，很难保证长期与短期同时精度很高。</q>
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Boolean}ecliptic
* true: get precession of the ecliptic (黃道歲差). else: general
* precession
*
* @returns {Array} [ P, Q ] in degrees
*/
function precession(TT_JD, ecliptic) {
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(TT_JD),
//
terms = ecliptic ? 唐凯_ecliptic_precession_terms : 唐凯_precession_terms,
//
p_A = polynomial_value(terms.init[0], T),
//
ε_A = polynomial_value(terms.init[1], T);
terms.forEach(function(term) {
var p = term[4] * T;
p_A += term[0] * Math.cos(p) + term[1] * Math.sin(p);
if (term[2])
ε_A += term[2] * Math.cos(p) + term[3] * Math.sin(p);
});
return [ p_A / DEGREES_TO_ARCSECONDS, ε_A / DEGREES_TO_ARCSECONDS ];
}
_.precession = precession;
// ------------------------------------------------------------------------------------------------------//
// nutation 章動
/**
* IAU 2000B model nutation (地球章動) 修正值。
*
* Reference 資料來源/資料依據:<br />
* Nutation, IAU 2000B model.
* https://github.com/kanasimi/IAU-SOFA/blob/master/src/nut00b.c
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Boolean}Δψ_only
* only get 黃經章動Δψ
*
* @returns {Array} [ 黃經章動Δψ, 黃赤交角章動Δε ] (in radians)
*
* @see http://www.neoprogrammics.com/nutations/nutations_1980_2000b/index.php
*/
function IAU2000B_nutation(TT_JD, Δψ_only) {
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(TT_JD),
//
parameters = [], Δψ = 0, Δε = 0;
IAU2000B_nutation_parameters.forEach(function(parameter) {
parameters.push((polynomial_value(parameter, T)
//
% TURN_TO_ARCSECONDS) * ARCSECONDS_TO_RADIANS);
});
library_namespace.debug('Julian centuries since J2000.0: ' + T, 4);
for (var term,
// Summation of luni-solar nutation series
// (smallest terms first).
index = IAU2000B_nutation_terms.length; index > 0;) {
term = IAU2000B_nutation_terms[--index];
var argument = 0;
// 5: length of parameters
for (var i = 0; i < 5; i++)
// term[i] 常為0
argument += term[i] * parameters[i];
var _sin = Math.sin(argument), _cos = Math.cos(argument);
Δψ += (term[5] + term[6] * T) * _sin + term[7] * _cos;
if (!Δψ_only)
Δε += (term[8] + term[9] * T) * _cos + term[10] * _sin;
}
// Convert from 0.1 microarcsec units to radians.
i = ARCSECONDS_TO_RADIANS / 1e7;
// Fixed offsets in lieu of planetary terms
Δψ = Δψ * i + IAU2000B_nutation_offset_Δψ;
if (!Δψ_only)
Δε = Δε * i + IAU2000B_nutation_offset_Δε;
library_namespace
.debug(
//
'IAU2000B nutation 章動修正值 of JD' + TT_JD + ' ('
+ library_namespace.JD_to_Date(TT_JD).format('CE')
+ '): ' + Δψ / DEGREES_TO_RADIANS + '°, ' + Δε
/ DEGREES_TO_RADIANS + '°', 3);
return Δψ_only ? Δψ : [ Δψ, Δε ];
}
/**
* IAU 1980 model nutation (地球章動) 修正值。
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Boolean}Δψ_only
* only get 黃經章動Δψ
*
* @returns {Array} [ 黃經章動Δψ, 黃赤交角章動Δε ] (radians)
*/
function IAU1980_nutation(TT_JD, Δψ_only) {
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(TT_JD),
//
parameters = [], Δψ = 0, Δε = 0;
IAU1980_nutation_parameters.forEach(function(parameter) {
parameters.push((polynomial_value(parameter, T)
//
% TURN_TO_DEGREES) * DEGREES_TO_RADIANS);
});
// IAU1980_nutation_terms[6,8] 有乘以十倍了。
T /= 10;
IAU1980_nutation_terms.forEach(function(term) {
var c, argument = 0, i = 0;
// 5: parameters.length
for (; i < 5; i++)
// 正弦(計算Δψ用sine)的角度參數及餘弦(計算Δε用cosine)的角度參數是D、M、M'、F、Ω這5個基本參數的線性組合。
// c常為0
if (c = term[i])
argument += c * parameters[i];
Δψ += (term[5] + term[6] * T) * Math.sin(argument);
if (!Δψ_only && (c = term[7] + term[8] * T))
Δε += c * Math.cos(argument);
});
// 表中的係數的單位是0″.0001。
T = ARCSECONDS_TO_RADIANS / 1e4;
return Δψ_only ? Δψ * T : [ Δψ * T, Δε * T ];
}
var nutation = IAU2000B_nutation;
_.nutation = nutation;
// ------------------------------------------------------------------------------------------------------//
// VSOP87 planets model
/**
* 座標變換: 轉換動力學Date平黃道座標(Bretagnon的VSOP定義的)到 FK5 (第5基本星表, The Fifth
* Fundamental Catalogue) 坐標系統。<br />
* VSOP87 → FK5: translate VSOP87 coordinates to the FK5 frame.<br />
* 注意:會改變 coordinates!
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 219. formula 32.3
*
* 太陽黃經☉及黃緯β是P.Bretagnon的VSOP行星理論定義的動力學黃道坐標。這個參考系與標準的FK5坐標系統(詳見20章)僅存在很小的差別。
* 可按以下方法把☉、β轉換到FK5坐標系統中,其中T是J2000起算的儒略世紀數,或T=10τ。
* J2000.0的VSOP黃道與J2000.0的FK5黃道存在一個很小的夾角 E = 0″.0554 左右，所以作以上修正。
*
* @param {Object}coordinates {
* L: mean dynamical ecliptical longitude in radians (弧度),<br />
* B: mean dynamical the ecliptical latitude in radians (弧度) }
* @param {Number}τ
* 儒略千年數 Julian millennia since J2000.0.
*
* @returns {Object}FK5 coordinates
*
* @see http://www.astrosurf.com/jephem/astro/ephemeris/et520transfo_en.htm
*/
function dynamical_to_FK5(coordinates, τ) {
// 先計算 L′ = L - 1°.397*T - 0°.00031*T²
var _L = polynomial_value([ coordinates.L, -1.397 * DEGREES_TO_RADIANS,
-0.00031 * DEGREES_TO_RADIANS ], 10 * τ),
// cache
cos_L = Math.cos(_L), sin_L = Math.sin(_L),
// 然後計算L和B的修正值：
ΔL = 0.03916 * ARCSECONDS_TO_RADIANS * (cos_L + sin_L)
* Math.tan(coordinates.B) - 0.09033 * ARCSECONDS_TO_RADIANS;
if (library_namespace.is_debug(3))
library_namespace.debug('FK5 correction of object.L @ ' + τ + ' ≈ '
+ coordinates.L + ' + '
+ format_degrees(ΔL / DEGREES_TO_RADIANS));
coordinates.L += ΔL;
var ΔB = 0.03916 * ARCSECONDS_TO_RADIANS * (cos_L - sin_L);
if (library_namespace.is_debug(3))
library_namespace.debug('FK5 correction of object.B @ ' + τ + ' ≈ '
+ coordinates.B + ' + '
+ format_degrees(ΔB / DEGREES_TO_RADIANS));
coordinates.B += ΔB;
return coordinates;
}
/**
* 無用:因為 items[1,2] 已經是弧度。
*
* @deprecated
*/
function initialize_VSOP87(subterms) {
if (subterms.init)
// 另一 thread 正初始化中。
return;
subterms.init = true;
subterms.forEach(function(series) {
series.forEach(function(items) {
items[1] *= DEGREES_TO_RADIANS;
items[2] *= DEGREES_TO_RADIANS;
});
});
subterms.initialized = true;
delete subterms.init;
}
/**
* terms for VSOP87 planets model used in function VSOP87()
*
* full data:<br />
* ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/README
* ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/VSOP87D.ear
*
* 金文敬. 2015. 太阳系行星和月球历表的发展.<br />
* 球坐標相對於瞬時平黃道和春分點為 VSOP87D 解。
*
* TODO: VSOP2013, DE-431
*
* see also:<br />
* JPL DE422:<br />
* http://ssd.jpl.nasa.gov/?ephemerides
* ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/de422/
*
* @inner
*/
var VSOP87_terms = Object.create(null);
/**
* VSOP87 天體/行星的日心座標位置 (Heliocentric ecliptic spherical coordinates) 計算。<br />
* 得到行星在FK5坐標系統中的日心黃經L、黃緯B。<br />
* <br />
* does not include nutation or aberration.
*
* 依 vsop87.doc 的說法，VSOP87D 已 apply precision:<br />
* ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/vsop87.doc<br />
* The coordinates of the versions C and D are given in the frame defined by
* the mean equinox and ecliptic of the date. This frame is deduced from the
* previous one by precessional moving between J2000 and the epoch of the
* date.
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 太陽位置計算.
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {String}object
* 天體 (planets 行星).
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {String|Array}options.terms: request terms.<br />
* L: 日心黃經 the ecliptical longitude in radians (弧度) 真黃經，不是軌道經度,
* NOT the orbital longitude<br />
* B: 日心黃緯 the ecliptical latitude in radians (弧度)<br />
* R: 行星到太陽的距離 the radius vector (distance to the Sun) in AU
* (Astronomical Units)<br />
* <br />
* {Boolean}options.FK5: translate VSOP87 coordinates to the FK5
* frame. default: true<br />
* <br />
* {Boolean}options.degrees: translate radians to degrees.
*
* @returns {Object}FK5 coordinates { L:longitude in radians, B:latitude in
* radians, R:distance in AU }
*/
function VSOP87(TT_JD, object, options) {
/**
* Julian millennia since J2000.0.<br />
* J2000.0 起算的儒略千年數.
*
* @type {Number}
*/
var τ = Julian_century(TT_JD) / 10,
//
coordinates = Object.create(null),
//
object_terms = VSOP87_terms[VSOP87.object_name(object)];
if (!object_terms)
throw new Error('VSOP87: Invalid object [' + object + ']');
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var terms = options.terms;
if (!terms)
terms = 'LBR'.split('');
else {
if (!Array.isArray(terms))
terms = [ terms ];
if (options.FK5 !== false
&& (terms.includes('L') || terms.includes('R'))) {
if (!terms.includes('L'))
terms.push('L');
if (!terms.includes('B'))
terms.push('B');
}
}
terms.forEach(function(term_name) {
var coefficients = [], subterms = object_terms[term_name];
if (!subterms) {
library_namespace.error('VSOP87: Invalid term name: ['
+ term_name + ']');
return;
}
// 無用:因為 items[1,2] 已經是弧度。
if (false && !subterms.initialized) {
initialize_VSOP87(subterms);
}
// series: 序列 L0,L1,..,B0,B1,..,R0,R1,..
subterms.forEach(function(series) {
coefficients.push(series.reduce(function(value, items) {
if (false && items.length === 1)
return value + items[0];
// assert:
// items.length
// ===
// 3
return value + items[0] * Math.cos(
// items:
// 三個數字項
// [A,B,C]
// 每項(表中各行)的值計算表達式是：
// A*cos(B+C*τ);
items[1] + items[2] * τ);
}, 0));
});
coordinates[term_name] =
// L=(L0+L1*τ+L2*τ²+L3*τ³+L4*τ⁴+L5*τ⁵)/10⁸
// (倍數: 10⁻⁸)
polynomial_value(coefficients, τ);
// 倍數
if (object_terms.multiplier > 0)
coordinates[term_name] *= object_terms.multiplier;
library_namespace.debug(
//
object + '.' + term_name + ' @ ' + TT_JD + ' ≈ '
//
+ (term_name === 'R' ? coordinates[term_name] + ' AU'
//
: format_degrees(normalize_degrees(
//
coordinates[term_name] / DEGREES_TO_RADIANS,
//
term_name === 'B'))) + ' (coefficients: ' + coefficients.join(', ')
+ ')', 3);
});
if (options.FK5 !== false)
dynamical_to_FK5(coordinates, τ);
// 單位轉換。
if (options.degrees) {
if (coordinates.L)
coordinates.L /= DEGREES_TO_RADIANS;
if (coordinates.B)
coordinates.B /= DEGREES_TO_RADIANS;
}
return terms.length > 1 ? coordinates : coordinates[terms[0]];
}
_.VSOP87 = VSOP87;
/**
* 正規化天體/行星名稱。
*
* @param {String}object
* 天體 (planets 行星).
*
* @returns {String|Undefined} 行星名稱
*/
VSOP87.object_name = function(object) {
if (typeof object === 'string')
return object.trim().toLowerCase();
};
/**
* 增加指定天體/行星的計算數據，提供給模組內部函數使用。
*
* @param {String}object
* 天體 (planets 行星).
* @param {Array}terms
* 計算數據.
*/
function VSOP87_add_terms(object, terms) {
object = VSOP87.object_name(object);
if (object === solar_terms_object)
// reset solar_terms_cache
solar_terms_cache = [];
VSOP87_terms[object] = terms;
}
VSOP87.add_terms = VSOP87_add_terms;
/**
* 載入指定天體/行星的計算數據後，執行 callback。提供給模組外部函數使用。
*
* @param {String|Array}object
* 天體 (planets 行星).
* @param {Function}callback
* callback function.
*/
function VSOP87_load_terms(object, callback) {
if (!object)
return callback(succeed);
var paths = [], objects = [];
if (!Array.isArray(object))
object = [ object ];
object.forEach(function(o, index) {
o = VSOP87.object_name(o);
if (!(o in VSOP87_terms)) {
objects.push(o);
paths.push(library_namespace.get_module_path(
//
module_name + library_namespace.env.path_separator + 'VSOP87_'
+ o));
}
});
library_namespace.run(paths, function() {
var failed = [];
objects.forEach(function(o, index) {
if (!VSOP87_terms[o])
failed.push(o);
});
if (failed.length === 0)
failed = undefined;
library_namespace.info(
//
'VSOP87_load_terms: ' + (failed
//
? 'Failed to load [' + failed + ']'
// resources
: 'resource files of [' + objects + '] loaded.'));
if (typeof callback === 'function')
callback(failed);
});
}
VSOP87.load_terms = VSOP87_load_terms;
/**
* 轉換 VSOP87 file @ node.js。
*
* TODO: parse VSOP87 file
*
* @param {String}file_name
* source file name
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @since 2015/4/15 ‏‎17:46:12, 2015/4/18 21:36:12
*/
function convert_VSOP87_file(file_name, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var encoding = options.encoding || 'ascii',
// 需要先設定 fs = require('fs');
// https://nodejs.org/api/fs.html
fs = require('fs');
fs.readFile(file_name, {
encoding : encoding
}, function(error, data) {
if (error)
throw error;
// parse VSOP87 file.
data = data.split(/\n/);
var object, type, group,
//
terms = Object.create(null);
data.forEach(function(line) {
if (!line)
return;
var fields = line.trim().split(/\s+/);
if (isNaN(fields[0])) {
if (!object)
// e.g., 'earth'
object = fields[3].toLowerCase();
// e.g., 'L', 'B',
// 'R'.
var t = fields[6][fields[5]];
group = [];
if (t === type)
terms[type].push(group);
else
terms[type = t] = [ group ];
console.log(object + ' ' + type + ' ' + fields[7] + ' '
+ fields[8] + ' terms');
return;
}
if (false && terms[type].length === 1 && group.length === 0)
console.log(fields);
fields = fields.slice(-3);
fields.forEach(function(f, index) {
fields[index] = +f;
});
// check
if (false && fields.length !== 3)
throw fields;
if (!options.limit || group < options.limit)
group.push(fields);
});
var new_line = '\n', prefix = '// auto-generated from '
//
+ (options.name || 'VSOP87')
// e.g., 'D' for VSOP87D.
+ (options.type || '') + new_line + library_namespace.Class + '.'
+ (options.name || 'VSOP87') + '.add_terms(',
//
postfix = options.postfix || new_line + ');';
fs.writeFile(options.name + '_' + object + '.js', prefix
+ JSON.stringify(object)
+ ','
+ new_line
+ JSON.stringify(terms)
.replace(/(\]\],)/g, '$1' + new_line) + postfix, {
encoding : encoding
});
});
}
VSOP87.convert = convert_VSOP87_file;
// ------------------------------------------------------------------------------------------------------//
// 天體/行星位置計算
/**
* planet / Astronomical objects or celestial objects<br />
* Warning: terms of object and Earth should loaded first.
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 225. Example 33.a with full VSOP87
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {String}object
* 天體 (planets 行星).
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Object}coordinates
*/
function object_coordinates(TT_JD, object, options) {
// 前置處理。
if (!options && library_namespace.is_Object(object) && object.object)
object = (options = object).object;
else if (!library_namespace.is_Object(options))
options = Object.create(null);
var τ0, τ = 0, rectangular, object_heliocentric,
//
coordinates = Object.create(null),
// light-time error in days
error = options.error || 1e-6;
// corrected for the light-time and the aberration together at
// once
// 一次性修正光行時及光行差。
do {
// assert: terms of object and Earth are loaded.
// JD時的天體/行星日心瞬時黃道座標。
object_heliocentric = VSOP87(TT_JD - τ, object, {
FK5 : false
});
// JD時的地球日心黃道座標。
var earth_heliocentric = VSOP87(TT_JD - τ, solar_terms_object, {
FK5 : false
}),
// planet's distance to the Earth, 行星到地球的距離.
Δ = (rectangular = spherical_to_rectangular(object_heliocentric, {
base : earth_heliocentric,
distance : true
})).distance;
if (τ === 0) {
// real distance at TT_JD in AU
coordinates.Δ0 = Δ;
// D日心瞬時黃道
// heliocentric dynamical ecliptic coordinate system
// @see function Coordinates()
coordinates.D = object_heliocentric;
}
τ0 = τ;
// effect of light-time, 光線從行星到達地球所需的時間.
τ = AU_LIGHT_TIME * Δ;
library_namespace.debug('τ-τ0 = ' + Math.abs(τ - τ0));
} while (Math.abs(τ - τ0) > error);
// apparent distance at TT_JD in AU
coordinates.Δ = Δ;
// S日心視黃道 heliocentric ecliptic coordinate system
// @see function Coordinates()
coordinates.S = object_heliocentric;
// rectangular: 該天體的地心直角黃道座標
// → geocentric: 該天體的地心黃道座標(球座標)
var geocentric = rectangular_to_spherical(rectangular);
// corrections for reduction to the FKS system
/**
* Julian millennia since J2000.0.<br />
* J2000.0 起算的儒略千年數.
*
* @type {Number}
*/
τ = Julian_century(TT_JD) / 10;
// replacing L by λ, and B by β.
geocentric = dynamical_to_FK5({
L : geocentric[0],
B : geocentric[1]
}, τ);
// 修正地球章動 nutation。
τ = nutation(TT_JD);
// G地心視黃道 apparent geocentric ecliptic coordinates:
// longitude λ and latitude β in radians
coordinates.λ = geocentric.L + τ[0];
coordinates.β = geocentric.B + τ[1];
get_horizontal(coordinates, TT_JD, options);
// 單位轉換。
if (options.degrees) {
coordinates.λ /= DEGREES_TO_RADIANS;
coordinates.β /= DEGREES_TO_RADIANS;
}
return coordinates;
}
_.object_coordinates = object_coordinates;
// ------------------------------------------------------------------------------------------------------//
// solar coordinates 太陽位置(坐標) & 二十四節氣 (solar terms)
/**
* 低精度分點和至點的時刻, 太陽視黃經λ為0°或90°或180°或270°. 在 1951–2050 CE 的誤差 < 1分.
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 分點和至點.<br />
*
* @param {Integer}year
* 年
* @param {Integer}index
* 0–3: [ 3月春分 0°, 6月夏至 90°, 9月秋分 180°, 12月冬至 270° ]<br />
* aka. [ March equinox, June solstice, September equinox,
* December solstice ]
*
* @returns {Number} Julian date (JD of 天文計算用時間 TT)
*/
function equinox(year, index, no_fix) {
// year is an integer; other values for year, would give
// meaningless results!
var TT_JD = (year |= 0) < 1000 ? equinox_terms_before_1000
: equinox_terms_after_1000;
// 計算相應的"平"分點或"平"至點的時刻。
TT_JD = polynomial_value(TT_JD[index |= 0], (year < 1000 ? year
: year - 2000) / 1000);
if (no_fix)
// get 太陽分點和至點"平"黃經。
return TT_JD;
/**
* Julian centuries since J2000.0.<br />
* J2000.0 起算的儒略世紀數.
*
* @type {Number}
*/
var T = Julian_century(TT_JD),
//
W = (35999.373 * T - 2.47) * DEGREES_TO_RADIANS,
// 太陽平黃經→太陽視黃經
// 要計算的分點或至點時刻(儒略曆書時,即力學時）表達為：
λ = TT_JD + 0.00001 *
// JDE0 + 0.00001 S / Δλ 日
equinox_periodic_terms.reduce(function(S, terms) {
return S + terms[0] * Math.cos(terms[1] + terms[2] * T);
}, 0) /
// Δλ
(1 + 0.0334 * Math.cos(W) + 0.0007 * Math.cos(2 * W));
// λ: 太陽黃經☉是Date黃道分點座標(瞬時黃道/當日黃道?)的真幾何黃經。
// 要取得視黃經λ，還應加上精準的黃經章動及光行差。
// TODO: 黃經周年光行差修正量：-20″.161 (公式(24.10)), 黃經章動效果：Δψ =
// -12″.965
// (詳見第22章), 轉到 FK5 系統的修正值(-0″.09033) (公式(24.9))
// 光行差 aberration
// 章動 nutation
// ΔT(year, month)
λ -= ΔT(year, index * 3 + 3.5) / ONE_DAY_SECONDS;
return λ;
}
_.equinox = equinox;
/**
* solar coordinates 太陽位置(坐標)計算。<br />
* ObsEcLon (Observer ecliptic lon. & lat.) or PAB-LON (PHASE angle &
* bisector) @ HORIZONS?
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 166–169. Example 25.b
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.degrees: translate radians to degrees.<br />
* {Boolean}options.km: translate AU to km.<br />
*
* @returns {Object}coordinates { apparent:太陽視黃經(度), λ:地心黃經(radians),
* β:地心黃緯β(radians), Δ:日地距離(AU), L:黃經 longitude(radians), B:黃緯
* latitude(radians), R:距離 radius vector(AU) }
*/
function solar_coordinates(TT_JD, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
// heliocentric coordinates. 計算日心黃道坐標中地球的位置。
var coordinates = VSOP87(TT_JD, solar_terms_object);
// 日心黃道坐標中地球的位置 → 地心黃道坐標中太陽的位置
// 弧度單位日心黃經L → 地心黃經(geocentric longitude)λ(度)
// Jean Meeus 文中以 "☉" 表示此處之 λ。
var λ = coordinates.L + TURN_TO_RADIANS / 2,
// 弧度單位日心黃緯B → 地心黃緯β(度)
β = -coordinates.B;
// 太陽的視黃經 (apparent longitude)λ(度)（受光行差及章動影響）
// Jean Meeus 文中以 "λ" 表示此處之視黃經 apparent。
//
// https://en.wikipedia.org/wiki/Apparent_longitude
// Apparent longitude is used in the definition of
// equinox and solstice.
// 節氣以太陽視黃經為準。
// ** 問題:但中國古代至點以日長為準。兩者或可能產生出入？
var apparent = λ / DEGREES_TO_RADIANS
// 修正太陽光行差 aberration。
+ sun_aberration(coordinates.R, TT_JD)
// 修正地球章動 nutation。
+ nutation(TT_JD, true) / DEGREES_TO_RADIANS;
// https://en.wikipedia.org/wiki/Ecliptic_coordinate_system#Spherical_coordinates
Object.assign(coordinates, {
// geocentric
λ : normalize_radians(λ),
β : normalize_radians(β, true),
Δ : coordinates.R,
// apparent longitude
apparent : normalize_degrees(apparent)
// TODO: apparent latitude
});
get_horizontal(coordinates, TT_JD, options);
// 單位轉換。
if (options.degrees) {
coordinates.λ /= DEGREES_TO_RADIANS;
coordinates.β /= DEGREES_TO_RADIANS;
coordinates.L /= DEGREES_TO_RADIANS;
coordinates.B /= DEGREES_TO_RADIANS;
}
if (options.km) {
// 1000: 1 km = 1000 m
coordinates.Δ *= AU_TO_METERS / 1000;
coordinates.R *= AU_TO_METERS / 1000;
}
return coordinates;
}
_.solar_coordinates = solar_coordinates;
/**
* 取得指定年分 year 年，指定太陽視黃經角度之 Julian date。
*
* @param {Integer}year
* year 年(CE)
* @param {Number}degrees
* 0–less than 360.<br />
* angle in degrees from March equinox of the year.<br />
* 指定太陽視黃經角度，自當年黃經0度(春分)開始。
*
* @returns {Number} Julian date (JD of 日常生活時間 UT)
*/
function JD_of_solar_angle(year, degrees) {
var offset, apparent,
// index: 下界 index of 分點和至點, 0–3
index = degrees / EQUINOX_SOLSTICE_DEGREES | 0,
// JD 近似值(下界)。
TT_JD = equinox(year, index, true);
// 經測試，有時每天太陽的視黃經 (apparent longitude) 可能會增加近 .95°
// NOT 360/365.25
// 太陽的視黃經最大變化量。
// http://jpkc.haie.edu.cn/jpkc/dqgl/content.asp?classid=17&id=528
// 在遠日點，地球公轉慢，太陽每日黃經差Δλ也慢，為57′
// 在近日點，地球公轉快，太陽每日黃經差Δλ也快，為61′
if (degrees % EQUINOX_SOLSTICE_DEGREES > 0)
TT_JD += ((index === 3 ? equinox(year + 1, 0) : equinox(year,
index + 1)) - TT_JD)
// 以內插法(線性插值)取得近似值。
* (degrees - index * EQUINOX_SOLSTICE_DEGREES)
/ EQUINOX_SOLSTICE_DEGREES;
// 最多趨近 JD_of_solar_angle.max_calculations 次。
for (index = JD_of_solar_angle.max_calculations; index-- > 0;) {
// apparent in degrees.
apparent = solar_coordinates(TT_JD).apparent;
// 由公式(26.1)得到對“大約時間”的修正量。
// +58 sin (k·90° - λ) (26.1)
offset = 58 * Math.sin((degrees - apparent) * DEGREES_TO_RADIANS);
// ↑ 58: maybe 59 = 360/365.25*60 ??
// https://www.ptt.cc/bbs/sky/M.1175584311.A.8B8.html
if (false)
library_namespace.debug('index ' + index + ': apparent: '
+ format_degrees(apparent) + ', offset in days: '
+ offset);
if (Math.abs(offset) < JD_of_solar_angle.error)
// 當 error 設定得很小時，似乎會達到固定循環。
break;
// adapt 修正量。
TT_JD += offset;
}
// apply ΔT: TT → UT.
return UT_of(TT_JD);
}
/**
* 最多計算(趨近) (JD_of_solar_angle.max_calculations) 次。
*
* @type Integer > 0
*/
JD_of_solar_angle.max_calculations = 20 | 0;
/**
* 可接受之最大誤差。<br />
* 即使設為 0，最多也只會計算 (JD_of_solar_angle.max_calculations) 次。<br />
* 當 error 設定得很小時，似乎會達到固定循環。因此此值不應該設為 0，否則以所採用方法將不會收斂。
*
* @type Number > 0
*/
JD_of_solar_angle.error = 2e-10;
_.JD_of_solar_angle = JD_of_solar_angle;
/**
* 定氣：取得指定年分 year 年，指定節氣/分點和至點之 Julian date。
*
* from http://ssd.jpl.nasa.gov/horizons.cgi#results<br />
* DE-0431LE-0431 GEOCENTRIC<br />
* Date__(UT)__HR:MN:SC.fff CT-UT ObsEcLon ObsEcLat<br />
* 0001-Mar-22 21:45:35.500 10518.071036 359.9999962 -0.0001845<br />
* 0001-Mar-22 21:45:36.000 10518.071036 0.0000018 -0.0001845<br />
* <br />
* 2015-Mar-20 22:45:10.000 67.185603 359.9999944 0.0000095<br />
* 2015-Mar-20 22:45:10.500 67.185603 0.0000001 0.0000095
*
* 注意: 1979/1/20 (中曆1978年12月22日) is 大寒 (300°), not 實曆 1979/1/21 (according
* to 中央氣象局 http://www.cwb.gov.tw/V7/astronomy/cdata/calpdf/calpdf.htm,
* 中国科学院紫金山天文台 公农历查询 http://almanac.pmo.ac.cn/cx/gzn/index.htm and 香港天文台
* http://www.weather.gov.hk/gts/time/conversionc.htm ). According to
* HORIZONS (DE-431), it seems at about 1979/1/20 23:59:55.55.
*
* @param {Integer}year
* year 年(CE)
* @param {Number|String}index
* index. 0: 春分
* @param {Number}[type]
* 1: 分點和至點, others (default): 二十四節氣，<br />
* 皆自當年黃經0度(春分)開始。
*
* @returns {Number} Julian date (JD of 日常生活時間 UT)
*
* @see http://blog.csdn.net/orbit/article/details/7910220
*/
function solar_term_JD(year, index, type) {
var angle;
if (typeof index === 'string' && NOT_FOUND !==
//
(angle = SOLAR_TERMS_NAME.indexOf(index)))
index = angle, type = 0;
if (type === 1) {
angle = (index | 0) * TURN_TO_DEGREES / EQUINOX_SOLSTICE_COUNT;
} else {
if (!index) {
angle = 0;
} else if (isNaN(angle = index) && (NOT_FOUND ===
//
(angle = SOLAR_TERMS_NAME.indexOf(index)))) {
library_namespace.error(
//
'solar_term_JD: Invalid solar term [' + index + ']!');
return;
}
index = angle;
angle *= DEGREES_BETWEEN_SOLAR_TERMS;
}
// assert:
// angle is now angle (0–less than 360),
// from March equinox of year.
return JD_of_solar_angle(year, angle);
}
_.solar_term_JD = solar_term_JD;
/**
* solar_terms 使用之 object name.
*
* @type {String}
* @inner
*/
var solar_terms_object = 'earth',
/**
* cache.
*
* solar_terms_cache[ year ] = [ 春分JD, 清明JD, 穀雨JD, ... 24個節氣 ]
*
* @type {Array}
* @inner
*/
solar_terms_cache = [];
/**
* 取得指定 Julian date 之二十四節氣名，或已經過日數、物候(七十二候, 初候/二候/三候, 初候/次候/末候)。
*
* TODO: 候應, 二十四番花信風 http://baike.baidu.com/view/54438.htm
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* options.days: 回傳 [ 節氣年 year (以"春分"分年, 非立春後才過年!), 節氣序 index,
* 已經過日數/剩下幾日 ]。<br />
* options.pentads: 亦標示七十二候 (物候, 72 pentads)<br />
* options.time: 取得節氣名時，亦取得交節時刻。
*
* @returns {String|Undefined|Array}
*
* @see http://koyomi8.com/24sekki.htm
*/
function solar_term_of_JD(UT_JD, options) {
// return the nearest (test_next: thie next one) solar
// term JD.
function get_cache(test_next) {
if (!date)
date = library_namespace.JD_to_Date(UT_JD);
year = date.getFullYear();
index = apparent / DEGREES_BETWEEN_SOLAR_TERMS | 0;
if (test_next && ++index === SOLAR_TERMS_COUNT)
// 本年春分
index = 0;
// 17: SOLAR_TERMS_NAME.indexOf('大雪')
// assert: 大雪以及之前的節氣，都會落在本年度內。
// 2000 CE 前後千年間，小寒或大寒之前分年。
else if (index > 17
// 3: assert: 要算作前一年的節氣，都會在3月前。
&& date.getMonth() <= 3 - 1)
// 每一年春分前末幾個節氣，算前一年的。
year--;
var cache = solar_terms_cache[year], term_JD;
if (!cache)
// 初始化本年度資料。
solar_terms_cache[year] = cache = [];
if (!(term_JD = cache[index]))
// 填入節氣JD
cache[index] = term_JD = solar_term_JD(year, index);
return term_JD;
}
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var index, days, date, year,
// apparent in degrees
apparent = solar_coordinates(TT_of(UT_JD)).apparent;
// get days, 回傳已經過幾日。
if (options.days) {
// 先取得 距離上一節氣之日數。
days = get_cache(true) - UT_JD | 0;
// days === 0: 當天交節。
if (days !== 0 && options.days !== 'next')
// 'next': 距離下一節氣之日數。天文節氣 剩餘日數。
index--, days = Math.ceil(UT_JD - get_cache());
// others (passed days): 距離上一節氣之日數。天文節氣 經過日數。
return [ year, index, days ];
}
if (DEGREES_BETWEEN_SOLAR_TERMS
// assert: 超過2度，就不會是在同一天。
- (apparent % DEGREES_BETWEEN_SOLAR_TERMS) < 2) {
// UT_JD 再過一下下便是節氣。
// 測試本日0時是否距離下一節氣發生時間1天內。
// assert: 此範圍內不可能為物候。
days = get_cache(true) - UT_JD;
// UT_JD 將被視為當地時間當日0時!
if (0 <= days && days < 1) {
// 初候
index = SOLAR_TERMS_NAME[index];
if (options.time) {
index += ' ' + ((days *= ONE_DAY_HOURS) | 0) + ':';
// options.time > 1 : add seconds.
if (options.time > 1)
index += ((days = (days % 1) * 60) | 0) + ':';
// index += ((days % 1) * 60).to_fixed(1);
index += Math.round((days % 1) * 60);
}
return index;
}
return;
}
if (options.pentads
// UT_JD 將被視為當地時間當日0時，因此只要節氣在 UT_JD 之前，皆表示本日非節氣，僅能測試物候。
// || (apparent % DEGREES_BETWEEN_SOLAR_TERMS < 2)
) {
// days = 與前一個節氣之間距。
days = UT_JD - get_cache();
// 七十二候 (物候, 72 pentads)
// 初候 二候 三候
// 初候 中候 末候
// http://koyomi8.com/sub/72kou.htm
// 5: 又五日
// 節氣之後每五日一候，非採用 360/72 = 5° 一候。
if (days <= 5 && 4 < days)
return SOLAR_TERMS_NAME[index] + ' 二候';
if (4 + 5 < days && days <= 5 + 5)
return SOLAR_TERMS_NAME[index] + ' 三候';
// return;
}
}
_.solar_term_of_JD = solar_term_of_JD;
// ----------------------------------------------------------------------------------------------------------------------------------------------//
// 應用功能:輔助以節氣為年首之曆法
var
// copy from CeL.data.date.
/** {Number}一整天的 time 值。should be 24 * 60 * 60 * 1000 = 86400000. */
ONE_DAY_LENGTH_VALUE = new Date(0, 0, 2) - new Date(0, 0, 1);
var
// 小寒(19) 1月5-7日交節，以春分分年的情況，已在下一年。
solar_term_starts_year = SOLAR_TERMS_NAME.indexOf('小寒'),
// solar_term_calendar_cache[term index / minute_offset]
// = { CE year : Date value }
solar_term_calendar_cache = [];
/**
* 取得 calendar 年首。
*
* @param {Integer}CE_year
* CE year
*
* @returns {Integer} Date value
*/
function solar_term_calendar_year_start(CE_year) {
var year_start = this.cache[CE_year |= 0];
if (year_start)
return year_start;
year_start = midnight_of(solar_term_JD(
// 保證 year_start 與 CE_year 在同一年:
// 小寒(19) 1月5-7日交節，之後應該計算前一年的節氣。
// 警告:此演算法於小寒不在隔年的情況，將失效。
this.term_index < solar_term_starts_year ? CE_year : CE_year - 1,
this.term_index), this.minute_offset, true);
library_namespace.debug('CE ' + CE_year + ' '
+ SOLAR_TERMS_NAME[this.term_index] + ' begins on '
+ year_start.format(), 2);
return this.cache[CE_year]
// cache[CE year] = term Date value of year
= year_start = year_start.getTime();
}
/**
* Date → [ year, days of year ]
*
* @param {Date}date
* 指定日期。
*
* @returns {Array} [ (CE year), (days counts from the first day) ]
*/
function solar_term_calendar_year_of(date) {
var CE_year = date.getFullYear(),
//
month = date.getMonth(), days;
// (this.month_start) 月之前，位在前一年。
if (month < this.month_start
//
|| (days = date - this.year_starts(CE_year)) < 0)
days = date - this.year_starts(--CE_year);
// assert: days >= 0
// [ CE_year, (days counts from the first day) ]
return [ CE_year, days / ONE_DAY_LENGTH_VALUE ];
}
/**
* 輔助以節氣為年首曆法之 handler。
*
* handler(year) → start of year
*
* handler.year_of(date) → [ year, days]
*
* @param {String|Integer}term
* solar term name / index
* @param {Integer}[minute_offset]
* indicate the time zone
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Function} handler
*
* @see solar_term_calendar_year_start(CE_year),
* solar_term_calendar_year_of(date)
*/
function solar_term_calendar(term, minute_offset, options) {
var term_index = typeof term === 'string' ? SOLAR_TERMS_NAME
.indexOf(term) : term;
if (!SOLAR_TERMS_NAME[term_index]) {
library_namespace.error(
//
'solar_term_calendar: Invalid term: [' + term + ']');
return;
}
var cache = term_index + '/' + (minute_offset |= 0);
cache = solar_term_calendar_cache[cache]
//
|| (solar_term_calendar_cache[cache]
//
= Object.create(null));
// 不動到原 options。
options = Object.assign(Object.create(null), options);
var handler = solar_term_calendar_year_start.bind(options);
handler.year_of = solar_term_calendar_year_of.bind(options);
Object.assign(options, {
term_index : term_index,
minute_offset : minute_offset,
cache : cache,
year_starts : handler,
month_start : (term_index - solar_term_starts_year)
.mod(SOLAR_TERMS_NAME.length) / 2 | 0
});
return handler;
}
_.solar_term_calendar = solar_term_calendar;
// ----------------------------------------------------------------------------------------------------------------------------------------------//
// 應用功能:需配合 'data.date'。
var
// 起始年月日。年月日 starts form 1.
// 基本上與程式碼設計合一，僅表示名義，不可更改。
START_YEAR = 1, START_MONTH = 1, START_DATE = 1,
// set normal month count of a year.
// 月數12: 每年有12個月。
MONTH_COUNT = 12,
// = 2. assert: 為整數
SOLAR_TERMS_MONTH_RATE = SOLAR_TERMS_NAME.length / MONTH_COUNT | 0,
// 21
立春NO = SOLAR_TERMS_NAME.indexOf('立春') | 0,
// 立春年_OFFSET = 5
立春年_OFFSET = (MONTH_COUNT + START_MONTH) * SOLAR_TERMS_MONTH_RATE - 立春NO
| 0;
/**
* 取得立春年歲首。
*
* TODO: 以立春與節氣排曆。計算以節氣(實為十二節)分年月。每年以立春交節時刻為界。<br />
* 十二節年月, 節氣年月, 立春年月
*
* 立春，指太陽到達黃經315°時，屬相（生肖）以立春作為起始點。 中國古時春節曾專指立春，也被視為一年的開始。
*
* @param {Date|Integer}date
* 指定年份或日期
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Date} 指定年份或日期所在立春年之歲首(立春時刻)
*/
function 立春年(date, options) {
if (!isNaN(date) && -1000 < date && date < 3000) {
// get JD of CE year (date)
date = [ date, 1 ];
}
if (Array.isArray(date)) {
// [ CE 立春節氣年, 立春節氣月 ]
// get JD of CE year (date)
if ((date[1] = date[1] * SOLAR_TERMS_MONTH_RATE - 立春年_OFFSET) < 0)
date[1] += SOLAR_TERMS_NAME.length, date[0]--;
date = solar_term_JD(date[0], date[1]);
// options: return JD
return options ? date : library_namespace.JD_to_Date(date);
}
if (!library_namespace.is_Date(date))
return;
if (options) {
// options: return [ CE 立春節氣年, 立春節氣月 ]
date = solar_term_of_JD(
// 回傳 [ 節氣年 year (以"春分"分年, 非立春後才過年!),
// 節氣序 index, 已經過日數/剩下幾日 ]。
library_namespace.Date_to_JD(date), {
days : true
});
date.pop();
date[1] = (date[1] + 立春年_OFFSET) / SOLAR_TERMS_MONTH_RATE | 0;
// 月數12: 每年有12個月
if (date[1] > MONTH_COUNT)
date[1] -= MONTH_COUNT, date[0]++;
return date;
}
// options: return (CE 立春節氣年)
var year = date.getFullYear(), month = date.getMonth();
// 快速判別:立春為公曆每年2月3至5日之間
if (month !== 1)
return month < 1 ? year - 1 : year;
// +1: 當天24時之前交節，依舊得算在當日。
return library_namespace.Date_to_JD(date) + 1
// 就算正好等於，本日JD也應該算前一年的。
<= solar_term_JD(year - 1, 立春NO) ? year - 1 : year;
}
// CeL.立春年(2001).format('CE');
_.立春年 = 立春年;
// ------------------------------------------------------------------------------------------------------//
var TYPE_SOLAR = 1, TYPE_LUNAR = 2,
// 89: Lunar Eclipses Saros Series 7
MAX_SAROS_SERIES = 89;
/**
* Get the saros series index of JD.
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Number}[type]
* type = 1(TYPE_SOLAR): solar, 2(TYPE_LUNAR): lunar
*
* @returns {Array} [ type, saros series index, #NO of series ]
*/
function saros(TT_JD, type) {
if (!type)
return saros(TT_JD, TYPE_SOLAR)
//
|| saros(TT_JD, TYPE_LUNAR);
var data = type === TYPE_SOLAR ? solar_saros_remainder
: lunar_saros_remainder, series, remainder = TT_JD
.mod(saros_days),
// get TT
index = data[0].search_sorted(remainder, data[1]), NOm1;
if (!index && remainder < data[0][0])
// 若是比最小的還小，則當作最後一個。
index = data[1].at(-1);
if (index && 0 <=
// NOm1: #NO - 1
(NOm1 = Math.round((TT_JD - index[1]) / saros_days))
&& MAX_SAROS_SERIES > NOm1) {
var series = [ type, index[0], NOm1 + 1 ],
// mean TT
TT = index[1] + NOm1 * saros_days;
// 2: 別差太多，最起碼應在2天內。
if (Math.abs(TT_JD - TT) < 2) {
series.TT = TT;
return series;
}
}
}
/**
* Get the JD of specified saros series and NO.
*
* @param {Natural}type
* type = 1: solar, 2: lunar
* @param {Natural}series
* saros series
* @param {Natural}[NO]
* NO of saros series
*
* @returns {Number}JD (UT) of specified saros series and NO
*/
function saros_JD(type, series, NO) {
series = (type === TYPE_SOLAR
//
? solar_saros : lunar_saros)[series];
if (isNaN(series))
return;
// JD: TT
var JD = series
+ (0 < NO && NO <= MAX_SAROS_SERIES ? (NO - 1) * saros_days : 0);
// JD: UT
JD = library_namespace.Julian_day.to_YMD(UT_of(JD));
// JD: UT
JD = lunar_phase([ JD[0], JD[1] ],
//
type === TYPE_SOLAR ? 0 : 2);
// TODO: 此處得到的是朔望時間，而非食甚時間。應進一步處理之。
return JD;
}
saros.JD = saros_JD;
_.saros = saros;
// TODO: metonic series
// https://en.wikipedia.org/wiki/Solar_eclipse_of_March_20,_2015#Metonic_series
// ------------------------------------------------------------------------------------------------------//
// LEA-406a, LEA-406b lunar model & periodic terms
/**
* 預設使用 type，'a' or 'b'。
*
* a 相當耗資源。當前 HORIZONS 已使用 DE-431 LE-431，與 LEA-406 及 ELP/MPP02 相差不小。何況 a, b
* 常僅差不到 10秒，因此似無必要使用 LEA-406a。
*/
LEA406.default_type = 'b';
var LEA406_name = 'LEA-406',
/**
* the mean longitude of the Moon referred to the moving ecliptic and mean
* equinox of date (Simon et al. 1994). (formula 9)
*
* Simon (1994): "Numerical expressions for precession formulae and mean
* elements for the Moon and the planets"
*
* (b.3) Mean elements referred to the mean ecliptic and equinox of date
* (P_1 = 5028″.8200/cy)
*
* But modified: t as 儒略千年數 Julian millennia since J2000.0.
*
* LEA406_V_coefficients in arcseconds.
*
* @inner
*/
LEA406_V_coefficients = [ 218.31664563 * DEGREES_TO_ARCSECONDS,
17325643723.0470, -527.90, 6.665, -0.5522 ];
/**
* Gets coordinates of lunar (geocentric dynamical ecliptic coordinates).
* Using full LEA-406a or LEA-406b model.<br />
* 計算月亮位置(地心瞬時黃道坐標)，採用完整的 LEA-406a, LEA-406b。
*
* Reference 資料來源/資料依據:<br />
* S. M. Kudryavtsev, Long-term harmonic development of lunar ephemeris,
* Astronomy & Astrophysics 471 (2007), pp. 1069-1075.
* http://www.eas.slu.edu/GGP/kudryavtsev/LEA-406.zip
* <q>This is 9–70 times better than the accuracy of the latest analytical theory of lunar motion ELP/MPP02, and the number of terms in the new development is less than that in ELP/MPP02.</q>
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.degrees: translate radians to degrees.<br />
* {Boolean}options.km: translate AU to km.<br />
* {String|Array}options.terms: request terms.<br />
* V: 地心黃經 in radians. ecliptic longitude reckoned along the
* moving ecliptic from the mean equinox of date<br />
* U: 地心黃緯 in radians. ecliptic latitude reckoned from the moving
* ecliptic<br />
* R: 地心距離 in AU. geocentric distance<br />
*
* @returns {Object} { V:longitude in radians, U:latitude in radians,
* R:distance in AU }
*
* @see http://www.gautschy.ch/~rita/archast/ephemeriden.html
* @see https://github.com/infinet/lunar-calendar/
*/
function LEA406(TT_JD, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = typeof options === 'string' ? {
terms : options
} : Object.create(null);
/**
* Julian millennia since J2000.0.<br />
* J2000.0 起算的儒略千年數.
*
* @type {Number}
*/
var τ = Julian_century(TT_JD) / 10,
// τ²
τ2 = τ * τ, terms = options.terms,
//
warn_term = !options.ignore_term,
/**
* spherical coordinates of its centre:
*
* r: 地心距離 in AU. (geocentric distance)
*
* V: 從曆元平春分點沿移動黃道(瞬時黃道?)的地心黃經 in radians. (ecliptic longitude reckoned
* along the moving ecliptic from the mean equinox of date)
*
* U: 移動黃道(瞬時黃道?)計算的地心黃緯 in radians. (ecliptic latitude reckoned from
* the moving ecliptic)
*/
coordinates = Object.create(null);
library_namespace.debug(
//
TT_JD + ': τ: ' + τ + ', τ²: ' + τ2, 3);
if (!Array.isArray(terms)) {
if (!terms || typeof terms !== 'string') {
terms = 'VUR';
// 有什麼就用什麼。
warn_term = false;
}
terms = terms.split('');
}
// Geocentric spherical coordinates of the Moon r, V, U are
// expanded to Poisson series of the form
terms.forEach(function(term) {
var type = options.type || LEA406.default_type,
//
subterms = LEA406_terms[term + type];
if (!subterms) {
// try another one.
type = type === 'a' ? 'b' : 'a';
subterms = LEA406_terms[term + type];
}
if (!subterms) {
if (warn_term)
library_namespace.error(
//
'LEA406: Invalid term name: [' + term
+ ']. You may need to load it first.');
return;
}
var sum = 0,
// R (formula 6),
// V (formula 7), U (formula 8)
operator = term === 'R' ? Math.cos : Math.sin;
subterms.forEach(function(T, index) {
// T = [ coefficients[4 in arcseconds],
// Amp0,Amp1,Phase1,Amp2,Phase2 ]
var ω = polynomial_value(T[0], τ);
// Amp 常為 0
if (T[1])
sum += T[1] * operator(ω);
if (T[2])
sum += T[2] * operator(ω + T[3]) * τ;
if (T[4])
sum += T[4] * operator(ω + T[5]) * τ2;
if (false && isNaN(sum)) {
console.error(T);
throw '內部錯誤 @ index ' + index + ': ' + T;
}
});
library_namespace.debug(
//
TT_JD + '.' + term + ': ' + sum, 3);
// Amp_to_integer: see convert_LEA406()
sum /= Amp_to_integer;
if (term === 'V')
sum += polynomial_value(LEA406_V_coefficients, τ);
// R is now km. e.g., 384399.
// V, U is now arcseconds.
if (term !== 'R')
// default: V, U in arcseconds → radians
sum *= ARCSECONDS_TO_RADIANS;
coordinates[term] = sum;
});
/**
* 2451545.5-64.183889/86400 ≈ 2451545.499257131
* <q>
{source: DE-0431LE-0431}
Date__(UT)__HR:MN:SC.fff Date_________JDUT CT-UT ObsEcLon ObsEcLat
2013-Jun-02 06:33:23.000 2456445.773182870 67.184868 359.9999798 3.8258600
2013-Jun-02 06:33:23.500 2456445.773188658 67.184868 0.0000545 3.8258553
</q>
* 360-359.9999798=0.0000202
* <code>2456445.773182870+(2456445.773188658-2456445.773182870)*202/(202+545)+67.184868/86400</code> ≈
* 2456445.7739620376 TT
*
* CeL.LEA406.default_type = 'a'; CeL.LEA406.load_terms('Va');
* CeL.LEA406.load_terms('Ua'); CeL.LEA406.load_terms('Ra');
* <code>CeL.find_root(function(TT){return CeL.normalize_radians(CeL.LEA406(TT).V,true);},2456445,2456446)</code> ≈
* 2456445.774202571 TT
*
* (.774202571-.7739620376)*86400≈20.78208575999696
*
* <code>CeL.find_root(function(TT){return CeL.normalize_radians(CeL.LEA406(TT,{FK5:false}).V,true);},2456445,2456446)</code> ≈
* 2456445.7742006825 TT
*
* (.7742006825-.7739620376)*86400≈20.618919359992915
*
* no FK5 較接近。但仍有誤差 20.6 s
*/
if (false && options.FK5 !== false) {
// τ: tmp
τ = dynamical_to_FK5({
L : coordinates.V,
B : coordinates.U
}, τ);
coordinates.V = τ.L;
coordinates.U = τ.B;
}
// 單位轉換。
if (options.degrees) {
// V, U in radians → degrees
if (coordinates.V)
coordinates.V /= DEGREES_TO_RADIANS;
if (coordinates.U)
coordinates.U /= DEGREES_TO_RADIANS;
}
// R is now km. e.g., 384399.
if (!options.km && coordinates.R)
// default: R in km → AU.
// 1000: 1 km = 1000 m
coordinates.R /= AU_TO_METERS / 1000;
return terms.length === 1
//
? coordinates[terms[0]] : coordinates;
}
_.LEA406 = LEA406;
/**
* LEA406_terms[Va,Ua,Ra;Vb,Ub,Rb] = {terms}
*
* @type {Object}
* @inner
*/
var LEA406_terms = Object.create(null);
/**
* 增加指定項目的計算數據，提供給模組內部函數使用。
*
* @param {String}term_name
* 項目名稱 (Va,Ua,Ra;Vb,Ub,Rb).
* @param {Array}terms
* 計算數據.
*/
function LEA406_add_terms(term_name, terms) {
// 初始化: 將 sin() 之引數全部轉成 radians。
terms.forEach(function(T) {
// T = [ coefficients[4 in arcseconds],
// Amp0,Amp1,Phase1,Amp2,Phase2 ]
T[0].forEach(function(coefficient, index) {
T[0][index] *= ARCSECONDS_TO_RADIANS;
});
// T[2–5] 可能為了節省大小，而為 undefined!
var i = 3;
T[i] = T[i] ? T[i] * ARCSECONDS_TO_RADIANS : 0;
i = 5;
T[i] = T[i] ? T[i] * ARCSECONDS_TO_RADIANS : 0;
});
// .reverse(): smallest terms first
LEA406_terms[term_name] = terms.reverse();
}
LEA406.add_terms = LEA406_add_terms;
/**
* 載入指定項目的計算數據後，執行 callback。提供給模組外部函數使用。
*
* @param {String}term_name
* 項目名稱 (V,U,R).
* @param {Function}callback
* callback.
*/
function LEA406_load_terms(term_name, callback) {
var type;
if (term_name.length === 2) {
type = term_name.charAt(1);
term_name = term_name.charAt(0);
} else
type = LEA406.default_type;
if ((term_name + type) in LEA406_terms) {
if (typeof callback === 'function')
callback();
return;
}
var name = LEA406_name + type + '-' + term_name;
library_namespace.run(library_namespace.get_module_path(module_name
//
+ library_namespace.env.path_separator + name), [ function() {
library_namespace.info(
// resources
'LEA406_load_terms: resource files of [' + name
//
+ '] loaded, ' + LEA406_terms[term_name + type].length
// Poisson series
+ ' terms.');
}, callback ]);
}
LEA406.load_terms = LEA406_load_terms;
/**
* 確定已經載入那些 terms。
*
* @param {String}[term_name]
* 項目名稱 (V,U,R).
*
* @returns {Array|String} 已載入 terms。
*/
function LEA406_loaded(term_name) {
if (!term_name)
return Object.keys(LEA406_terms);
// ab: LEA-406a, LEA-406b
var terms = [], types = 'ab'.split('');
types.forEach(function(type) {
if ((term_name + type) in LEA406_terms)
terms.push(type);
});
return terms.join('');
}
LEA406.loaded = LEA406_loaded;
/**
* 轉換 LEA-406 (LEA-406a, LEA-406b) file。
*
* need data.native, run @ node.js
*
* TODO: parse LEA-406 file
*
* @param {String}file_name
* source file name
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @since 2015/4/20
*/
function convert_LEA406(file_name, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var encoding = options.encoding || 'ascii',
//
floating = 9,
// 需要先設定 fs = require('fs');
// https://nodejs.org/api/fs.html
fs = require('fs');
fs.readFile(file_name, {
encoding : encoding
}, function(error, data) {
if (error)
throw error;
// parse LEA-406 file.
data = data.split(/\n/);
// Lines 1-8 give a short description of the data included
// to the file.
data.splice(0, 8);
var terms = [];
data
.forEach(function(line) {
if (!line)
return;
var fields = line.trim().replace(/(\d)-/g, '$1 -')
.split(/\s+/);
if (fields.length !== 21 || isNaN(fields[0]))
throw line;
var i = 15;
// 將 Amp 轉整數: Amp *= 1e7
// (表格中小數7位數)。
fields[i] = Math.round(fields[i] * Amp_to_integer);
i++;
fields[i] = Math.round(fields[i] * Amp_to_integer);
i++;
fields[i] = Math.round(fields[i] * Amp_to_integer);
i++;
// 轉整數以作無誤差加減。
fields[i] = Math.round(fields[i] * 1e12);
i++;
fields[i] = Math.round(fields[i] * 1e12);
i++;
fields[i] = Math.round(fields[i] * 1e12);
fields[19] -= fields[18];
fields[20] -= fields[18];
i = 18;
// φ: Phase1, Phase2 → in arcseconds
// φ: Phase 有12位數，*DEGREES_TO_ARCSECONDS 之後最多10位數
fields[i] = (fields[i]
// / 1e2 / 1e10 = / 1e12
* (DEGREES_TO_ARCSECONDS / 1e2) / 1e10).to_fixed(10);
i++;
fields[i] = (fields[i]
//
* (DEGREES_TO_ARCSECONDS / 1e2) / 1e10).to_fixed(10);
i++;
fields[i] = (fields[i]
//
* (DEGREES_TO_ARCSECONDS / 1e2) / 1e10).to_fixed(10);
var coefficients = [ fields[18], 0, 0, 0, 0 ];
if (false) {
coefficients.forEach(function(i, index) {
coefficients[index]
//
= new library_namespace.data.math.integer(0);
});
coefficients[0]
//
= new library_namespace.data.math.integer(
fields[18]);
coefficients[0].divide(1e12, 12);
}
terms.push([ coefficients,
// Amp0,Amp1,Phase1,Amp2,Phase2
fields[15], fields[16], fields[16] ? fields[19] : 0,
fields[17], fields[17] ? fields[20] : 0 ]);
i = 1;
for (var multiplier; i <= 14; i++)
if (multiplier = +fields[i])
convert_LEA406_arguments[i]
//
.forEach(function(a, index) {
// a 為整數，coefficients 小數位數最多即為[0]，6位數。
// coefficients[index]=(coefficients[index]+(a*multiplier).to_fixed(6)).to_fixed(6);
coefficients[index] += a * multiplier;
if (false) {
coefficients[index].add(
//
(new library_namespace.data.math
//
.integer(a)).multiply(multiplier));
}
if (false &&
//
!Number.isSafeInteger(coefficients[index]))
throw 'Out of range from: ' + fields
+ '\ncoefficients: '
+ coefficients;
});
coefficients.forEach(function(c, index) {
// coefficients[index]=c*DEGREES_TO_RADIANS;
// coefficients[index]=c.to_fixed(6);
coefficients[index] = c.to_fixed();
// coefficients[index]=coefficients[index].valueOf();
});
});
var name = options.name || LEA406_name,
//
new_line = '\n', prefix = '// auto-generated from '
//
+ name
// e.g., 'a' for LEA-406a.
+ (options.type || '') + new_line + library_namespace.Class + '.'
+ name.replace(/-/g, '') + '.add_terms(',
//
postfix = options.postfix || new_line + ');';
fs.writeFile(name + (options.type || '') + '-' + options.term
+ '.js', prefix
+ JSON.stringify(options.term + (options.type || ''))
+ ','
+ new_line
+ JSON.stringify(terms).replace(/,0/g, ',').replace(
/,+\]/g, ']').replace(/(\]\],)/g, '$1' + new_line)
// .replace(/(\],)/g,
// '$1' +
// new_line)
+ postfix, {
encoding : encoding
});
});
}
LEA406.convert = convert_LEA406;
// ------------------------------------------------------------------------------------------------------//
// lunar coordinates 月亮位置(坐標)
/**
* lunar coordinates, moon's coordinates 月亮位置(地心黃道坐標)計算。<br />
* get lunar angle, moon's angle. 僅將 LEA-406 修正地球章動 nutation。
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.degrees: translate radians to degrees.<br />
* {Boolean}options.km: translate AU to km.<br />
*
* @returns {Object} { V:longitude in radians, U:latitude in radians,
* R:distance in AU }
*/
function lunar_coordinates(TT_JD, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var coordinates = LEA406(TT_JD, 'FK5' in options ? {
FK5 : options.FK5
} : null);
if (('V' in coordinates) || ('U' in coordinates)) {
// var n = nutation(TT_JD);
if ('V' in coordinates) {
coordinates.λ = coordinates.V;
// V, U in radians
/**
* 修正經度 of 月亮光行時間 light-time correction (Moon's
* light-time)。忽略對緯度之影響。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 337. formula 49.1.<br />
* <q>the constant term of the effect of the light-time (-0″.70)</q>
*
* -0″.704:
* <q>formula in: G.M.Clemence, J.G.Porter, D.H.Sadler (1952): "Aberration in the lunar ephemeris", Astronomical Journal 57(5) (#1198) pp.46..47; but computed with the conventional value of 384400 km for the mean distance which gives a different rounding in the last digit.</q>
* http://en.wikipedia.org/wiki/New_moon
*
* @see http://blog.csdn.net/orbit/article/details/8223751
* @see http://en.wikipedia.org/wiki/Light-time_correction
* @see http://lifesci.net/pod/bbs/board.php?bo_table=B07&wr_id=52
*/
var light_time = -0.70 * ARCSECONDS_TO_RADIANS;
if (false)
(function() {
/**
* 錯誤的方法:
*
* @deprecated
*/
// coordinates.R in AU.
var r = coordinates.R * AU_TO_METERS
|| LUNAR_DISTANCE_M;
// 地球半徑。
r -= TERRA_RADIUS_M;
// 1000: 1 km = 1000 m (CELERITAS in m/s)
light_time = -r / CELERITAS * TURN_TO_DEGREES
/ ONE_DAY_SECONDS;
library_namespace.debug(
//
'月亮經度光行差 of JD' + TT_JD + ' ('
//
+ library_namespace.JD_to_Date(
//
UT_of(TT_JD)).format('CE') + '): '
+ format_degrees(light_time), 3);
});
// 經測試， LEA-406 似已修正月亮光行時、地球章動
// coordinates.λ += light_time;
/**
* 修正地球章動 nutation: LEA-406 基於 LE406，未包含 nutations, librations。
*
* @see http://www.projectpluto.com/jpl_eph.htm
*
* DE405 : Created May 1997; includes both nutations and
* librations. Referred to the International Celestial Reference
* Frame. Covers JED 2305424.50 (1599 DEC 09) to JED 2525008.50
* (2201 FEB 20)
*
* DE406 : Created May 1997; includes neither nutations nor
* librations. Referred to the International Celestial Reference
* Frame. Spans JED 0625360.5 (-3000 FEB 23) to 2816912.50
* (+3000 MAY 06)
*/
// 經測試， LEA-406 似已修正月亮光行時、地球章動
// coordinates.λ += n[0];
coordinates.λ = normalize_radians(coordinates.λ);
}
if ('U' in coordinates) {
coordinates.β = coordinates.U;
// V, U in radians.
// 修正地球章動 nutation。
// 經測試， LEA-406 似已修正月亮光行時、地球章動
// coordinates.β += n[1];
coordinates.β = normalize_radians(coordinates.β, true);
}
}
if ('R' in coordinates) {
coordinates.Δ = coordinates.R;
if (coordinates.β && coordinates.λ) {
get_horizontal(coordinates, TT_JD, options);
}
// 單位轉換。
if (options.km) {
// R in AU → km.
// 1000: 1 km = 1000 m
coordinates.R *= AU_TO_METERS / 1000;
coordinates.Δ *= AU_TO_METERS / 1000;
}
}
// 單位轉換。
if (options.degrees) {
// V, U in radians → degrees
if ('V' in coordinates) {
coordinates.V /= DEGREES_TO_RADIANS;
coordinates.λ /= DEGREES_TO_RADIANS;
}
if ('U' in coordinates) {
coordinates.U /= DEGREES_TO_RADIANS;
coordinates.β /= DEGREES_TO_RADIANS;
}
}
return coordinates;
}
_.lunar_coordinates = lunar_coordinates;
// lunar_phase_of_JD_cache[TT_JD] = degrees;
var lunar_phase_of_JD_cache = [];
/**
* get the longitudinal angle between the Moon and the Sun.<br />
* 計算 JD 時的月日視黃經差（月-日）。<br />
* 趨近 the elongation of Moon，但忽略緯度影響。
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Boolean}normalize_360
* 正規化成 0°–360°，而非 -180°–180°。
*
* @returns {Number}angle in degrees
*/
function lunar_phase_angle_of_JD(TT_JD, normalize_360) {
var degrees;
if (String(TT_JD) in lunar_phase_of_JD_cache)
degrees = lunar_phase_of_JD_cache[TT_JD];
else if (!isNaN(degrees =
// 可以忽略章動的影響。
lunar_coordinates(TT_JD).λ / DEGREES_TO_RADIANS
- solar_coordinates(TT_JD).apparent))
lunar_phase_of_JD_cache[TT_JD] = degrees;
if (!isNaN(degrees))
degrees = normalize_degrees(degrees, !normalize_360);
return degrees;
}
_.lunar_phase_angle_of_JD = lunar_phase_angle_of_JD;
/**
* 平朔望月長度 in days. 日月合朔週期。
*
* @type {Number}
*
* @see mean_lunar_phase_coefficients
*/
var mean_lunar_phase_days = 29.530588861,
/**
* 平月相的不變時間參數。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 349. Chapter 49 Phases of the Moon. formula 49.1.<br />
*
* @type {Array}
*
* @inner
*/
mean_lunar_phase_coefficients = [ 2451550.09766,
// 29.530588861 * k, but k = 1236.85 * T.
29.530588861 * 1236.85, 0.00015437, -0.000000150, 0.00000000073 ],
// Sun's mean anomaly at time JDE: 太陽平近點角： in radians
eclipse_coefficients_M = [ 2.5534, 29.10535670 * 1236.85, -0.0000014,
-0.00000011 ].map(degrees_to_radians),
// Moon's mean anomaly: (Mʹ, M′) 月亮的平近點角： in radians
eclipse_coefficients_Mm = [ 201.5643, 385.81693528 * 1236.85, 0.0107582,
0.00001238, -0.000000058 ].map(degrees_to_radians),
// Moon's argument of latitude: 月亮的緯度參數： in radians
eclipse_coefficients_F = [ 160.7108, 390.67050284 * 1236.85, -0.0016118,
-0.00000227, 0.000000011 ].map(degrees_to_radians),
// Longitude of the ascending node of the lunar orbit:
// 月亮軌道升交點經度： in radians
eclipse_coefficients_Ω = [ 124.7746, -1.56375588 * 1236.85, 0.0020672,
0.00000215 ].map(degrees_to_radians),
// p. 338. (47.6)
eclipse_coefficients_E = [ 1, -0.002516, -0.0000074 ],
// p. 380.
eclipse_coefficients_A1 =
//
[ 299.77, 0.107408 * 1236.85, -0.009173 ];
/**
* 平月相的時間，已修正了太陽光行差及月球光行時間。<br />
* The times of the mean phases of the Moon, already affected by the Sun's
* aberration and by the Moon's light-time
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 349. formula 49.1.<br />
*
* @param {Number}year_month
* 帶小數點的年數，例如1987.25表示1987年3月末。
* @param {Integer}phase
* 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.nearest: 取得最接近之月相時間。
*
* @returns {Number} Julian date (JD of 天文計算用時間 TT)
*
* @see https://github.com/soniakeys/meeus/blob/master/eclipse/eclipse.go
*/
function mean_lunar_phase(year_month, phase, options) {
phase /= 4;
if (Array.isArray(year_month))
year_month = year_month[0] + (year_month[1] - 1) / 12;
/**
* 12.36853:
* <q>DAYS_OF_JULIAN_CENTURY / 100 / 29.530588861 = 12.368530872148396</q>
*/
var k = (year_month - 2000) * 12.36853,
// 取 year_month 之後，第一個 phase。
// Any other value for k will give meaningless results
T = Math.floor(k) + phase;
if (options && options.nearest && T - k > .5)
// 取前一個。
k = T - 1;
else
// 取之後最接近的。
k = T;
// T是J2000.0起算的儒略世紀數，用下式可得到足夠的精度：
T = k / 1236.85;
var TT_JD = polynomial_value(mean_lunar_phase_coefficients, T);
if (!options || !options.eclipse
//
|| phase !== 0 && phase !== .5)
return TT_JD;
var
// Moon's argument of latitude: 月亮的緯度參數： in radians
F = normalize_radians(polynomial_value(eclipse_coefficients_F, T), true),
//
F_ = F / DEGREES_TO_RADIANS;
/**
* p. 380.
*
* If F differs from the nearest multiple of 180° by less than 13.9
* degrees, then there is certainly an eclipse; if the difference is
* larger than 21°.0, there is no eclipse; between these two values, the
* eclipse is uncertain at this stage and the case must be examined
* further.
*/
if (90 - Math.abs(90 - Math.abs(F_)) > 21.0)
return TT_JD;
var
// Sun's mean anomaly at time JDE: 太陽平近點角： in radians
M = polynomial_value(eclipse_coefficients_M, T),
// Moon's mean anomaly: (Mʹ, M′) 月亮的平近點角： in radians
Mm = polynomial_value(eclipse_coefficients_Mm, T),
// Longitude of the ascending node of the lunar orbit:
// 月亮軌道升交點經度： in radians
Ω = polynomial_value(eclipse_coefficients_Ω, T),
// p. 338. (47.6)
// 表中的這些項包含了了M(太陽平近點角)，它與地球公轉軌道的離心率有關，就目前而言離心率隨時間不斷減小。由於這個原因，振幅A實際上是個變數(並不是表中的常數)，角度中含M或-M時，還須乘上E，含2M或-2M時須乘以E的平方進行修正。E的運算式如下：
// The coefficient, not the argument of the sine or cosine,
// should be multiplied by E.
E = polynomial_value(eclipse_coefficients_E, T),
// p. 380.
F1 = F - 0.02665 * DEGREES_TO_RADIANS * Math.sin(Ω),
// p. 380.
A1 = polynomial_value(eclipse_coefficients_A1, T)
//
* DEGREES_TO_RADIANS;
// 取得最大食的時間(對於地球一般是日食)，使用(47.1)平會合時間加上以下修正(單位是天)。
var ΔJD = (phase === 0
// 日食
? -0.4075 * Math.sin(Mm) + 0.1721 * E * Math.sin(M)
// 月食
: -0.4065 * Math.sin(Mm) + 0.1727 * E * Math.sin(M))
// p. 380.
+ 0.0161 * Math.sin(2 * Mm) - 0.0097 * Math.sin(2 * F1) + 0.0073 * E
* Math.sin(Mm - M) - 0.0050 * E * Math.sin(Mm + M) - 0.0023
* Math.sin(Mm - 2 * F1) + 0.0021 * E * Math.sin(2 * M) + 0.0012
* Math.sin(Mm + 2 * F1) + 0.0006 * E * Math.sin(2 * Mm + M)
- 0.0004 * Math.sin(3 * Mm) - 0.0003 * E * Math.sin(M + 2 * F1)
+ 0.0003 * Math.sin(A1) - 0.0002 * E * Math.sin(M - 2 * F1)
- 0.0002 * E * Math.sin(2 * Mm - M) - 0.0002 * Math.sin(Ω);
// p. 381. 高精度的日月位置計算需要幾百個項才能得到。
var P = 0.2070 * E * Math.sin(M) + 0.0024 * E * Math.sin(2 * M)
- 0.0392 * Math.sin(Mm) + 0.0116 * Math.sin(2 * Mm) - 0.0073
* E * Math.sin(Mm + M) + 0.0067 * E * Math.sin(Mm - M) + 0.0118
* Math.sin(2 * F1),
// p. 381. 高精度的日月位置計算需要幾百個項才能得到。
Q = 5.2207 - 0.0048 * E * Math.cos(M) + 0.0020 * E * Math.cos(2 * M)
- 0.3299 * Math.cos(Mm) - 0.0060 * E * Math.cos(Mm + M)
+ 0.0041 * E * Math.cos(Mm - M),
// p. 381.
W = Math.abs(Math.cos(F1)),
// p. 381. Gamma
// 在日食情況下，γ表示月影軸到地心的最小距離，單位是地球赤道半徑。
// 在月食的情況下，γ表示月亮中心到地影軸的最小距離，單位是地球赤道半徑。γ是正還是負，取決於月亮中心經過地影軸的北邊或是南邊。
γ = (P * Math.cos(F1) + Q * Math.sin(F1)) * (1 - 0.0048 * W),
// p. 381.
u = 0.0059 + 0.0046 * E * Math.cos(M) - 0.0182 * Math.cos(Mm) + 0.0004
* Math.cos(2 * Mm) + -0.0005 * Math.cos(M + Mm),
//
abs_γ = Math.abs(γ),
// 計算日月食的特性值。
feature = {
/**
* 日月食食點出現在月亮軌道的升交點 ascending node / 降交點 descending node。
*
* If F is near 0° or 360°, the eclipse occurs near the Moon's
* ascending node. If F is near 180°, the eclipse takes place near
* the descending node of the Moon's orbit.
*/
node : Math.abs(F_) < 22 ? 'ascending' : 'descending',
γ : γ,
};
if (phase === 0) {
// 日食。地球的扁率是0.9972。
// the oblateness of the Earth it is 0.9972.
// 0.9972 may vary between 0.9970 and 0.9974 from one
// eclipse to another.
if (abs_γ < 0.9972) {
// 日食中心是：在地球表面上存在一條日食中央線，影軸在地表經過的那條線。
/**
* u表示月亮影錐在基平面上的半徑，單位也是地球半徑。基平面指：經過地心並且垂直月亮影軸的平面。半影錐在基平面上的半徑是u+0.5461
*
* The quantity u denotes the radius of the Moon's umbral cone
* in the fundamental plane, again in units of the Earth's
* equatorial radius. The radius of the penumbral cone in the
* fundamental plane is u + 0.5461.
*/
// 影錐半徑
feature.umbral_radius = u;
// 半影錐半徑
feature.penumbral_radius = u + 0.5461;
// 對於有中心的日食，食的類型由以下規則決定：
if (u < 0)
// 日全食
// magnitude > 1;
feature.type = 'total';
else if (u > 0.0047)
// 日環食
// magnitude < 1;
feature.type = 'annular';
else {
var ω = 0.00464 * Math.sqrt(1 - γ * γ);
if (u < ω)
// 日全環食 Hybrid, annular-total
feature.type = 'hybrid';
else
// 日環食
// magnitude < 1;
feature.type = 'annular';
}
} else if (abs_γ < 1.5433 + u) {
// 則沒有日食中心，是一個部分食。日偏食
feature.type = 'partial';
if (abs_γ < 1.0260) {
// 影錐的一部分可能觸及地表(在地球兩極地區)，而錐軸則沒有碰到地球。
} else {
// 沒有日食中心的全食或環食(因錐軸不經過地表，所以沒有中心)，是一個部分食。
}
// 在部分食的情況下，最大食發生在地表上距離影軸最近的那個點。在該點，食的程度(譯者注：大概指食分吧)是：
// p. 382. (54.2)
feature.magnitude = (1.5433 + u - abs_γ) / (0.5461 + 2 * u);
} else {
// 在地表上看不到日食。
// no eclipse is visible from the Earth's surface.
}
} else {
// 月食, parse === 2
var semiduration_c,
// penumbra 半影在月亮上的半徑，單位是地球直徑
ρ = 1.2848 + u,
// umbra 本影在月亮上的半徑，單位是地球直徑
σ = 0.7403 - u,
// p. 382. (54.4) 本影 umbral eclipses
magnitude = (1.0128 - u - abs_γ) / 0.5450;
if (magnitude >= 1) {
feature.type = 'total';
semiduration_c = 0.4678 - u;
} else if (magnitude > 0) {
feature.type = 'partial';
semiduration_c = 1.0128 - u;
} else {
// p. 382. (54.3) 半影 penumbral eclipses
magnitude = (1.5573 + u - abs_γ) / 0.545;
if (magnitude > 0) {
// 應注意，大部分半影月食(月亮僅進入地球半影)不能人眼分辨出來。
feature.type = 'penumbral';
semiduration_c = 1.5573 + u;
} else {
// 如食分為負值，說明沒有月食。
}
}
if (semiduration_c > 0) {
feature.magnitude = magnitude;
// 計算半持續時間，單位是分鐘：
feature.semiduration = 60 * Math.sqrt(
// semidurations of the partial and total phases
semiduration_c * semiduration_c - γ * γ)
/ (0.5458 + 0.0400 * Math.cos(Mm));
}
}
if (feature.type) {
feature.object = phase === 0 ? 'solar' : 'lunar';
// the time of maximum eclipse, 食甚時間.
feature.TT = TT_JD + ΔJD;
}
// assert: typeof new Number(TT_JD) === "object";
// Object.prototype.toString.call(new Number(TT_JD)) ===
// "[object Number]"
TT_JD = Object.assign(new Number(TT_JD), {
M : normalize_radians(M),
// M′
Mm : normalize_radians(Mm),
F : F,
Ω : normalize_radians(Ω),
E : E,
P : P
}, feature);
return TT_JD;
}
_.mean_lunar_phase = mean_lunar_phase;
/**
* 超過此角度則不會發生日蝕。
*
* Reference 資料來源/資料依據:<br />
* Explanatory Supplement to the Astronomical Ephemeris. Third impression
* 1974.<br />
* p. 215.<br />
*
* @type {Number} in radians
* @inner
*/
var solar_eclipse_limit = degrees_to_radians(1, 34, 46),
/**
* 超過此角度則不會發生月蝕。
*
* Reference 資料來源/資料依據:<br />
* Explanatory Supplement to the Astronomical Ephemeris. Third impression
* 1974.<br />
* p. 258.<br />
*
* @type {Number} in radians
* @inner
*/
lunar_eclipse_limit = degrees_to_radians(1, 26, 19);
/**
* the ellipticity of the Earth's spheroid. e^2 = 0.00669454 for 1968
* onwards<br />
*
* Reference 資料來源/資料依據:<br />
* Explanatory Supplement to the Astronomical Ephemeris. Third impression
* 1974.<br />
* p. 223.
*
* For Hayford's spheroid (flattening 1/297) the coefficient (1 -
* e^2)^(-1/2) is equal to 1.003378.
*
* @see https://en.wikipedia.org/wiki/Flattening
*/
var eccentricity_square
//
= (2 - TERRA_FLATTENING) * TERRA_FLATTENING,
// For 1968 onwards:
// Lunar Radius Constants (Penumbra)
Lunar_Radius_k1 = 0.272488,
// Lunar Radius Constants (Umbra)
Lunar_Radius_k2 = 0.272281;
/**
* 取得 TT_JD 時的 Besselian Elements 日月食資訊。<br />
* not yet done
*
* Reference 資料來源/資料依據:<br />
* Explanatory Supplement to the Astronomical Ephemeris. Third impression
* 1974.<br />
* p. 219.<br />
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Array}local [
* latitude (°), longitude (°), time zone (e.g., UTC+8: 8),
* elevation or geometric height (m) ]
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
*
* @returns {Object}Besselian Elements
*/
function Besselian_elements(TT_JD, local, options) {
// 前置處理。
if (!library_namespace.is_Object(options)) {
if (!options && library_namespace.is_Object(local)) {
options = local;
// 這邊預設採用 0,0 是為了計算 .π，但此法不見得理想!
local = options.local || [ 0, 0 ];
} else
options = Object.create(null);
}
var sun_coordinates = solar_coordinates(TT_JD, {
equatorial : true,
local : local
}), moon_coordinates = lunar_coordinates(TT_JD, {
equatorial : true,
local : local
});
// adapt p. 219.
if (false) {
if (options.get_diff)
return {};
moon_coordinates.α
//
= degrees_to_radians(328, 13, 44.29);
moon_coordinates.δ
//
= degrees_to_radians(-11, 53, 31.83);
sun_coordinates.α
//
= degrees_to_radians(328, 38, 50.42);
sun_coordinates.δ
//
= degrees_to_radians(-12, 42, 49.04);
moon_coordinates.π
//
= degrees_to_radians(0, 61, 5.814);
sun_coordinates.Δ = 0.9878805;
Lunar_Radius_k1 = Lunar_Radius_k2 = 0.272274;
sun_coordinates.LHA
//
= degrees_to_radians(296, 26, 22.3);
}
// p. 215.
/**
* β☾: the latitude of the Moon at the time of conjunction in longitude
*/
var βm = moon_coordinates.π - sun_coordinates.π
+ (semidiameter(moon_coordinates, MOON_NAME)
//
- semidiameter(sun_coordinates, SUN_NAME))
* ARCSECONDS_TO_RADIANS;
// TODO: test solar_eclipse_limit, lunar_eclipse_limit.
// p. 216.
var b = Math.sin(sun_coordinates.π) / Math.sin(moon_coordinates.π),
// cos(α☉)
cos_αs = Math.cos(sun_coordinates.α),
// cos(δ☉)
cos_δs = Math.cos(sun_coordinates.δ),
// cos(α☾)
cos_αm = Math.cos(moon_coordinates.α),
// cos(δ☾)
cos_δm = Math.cos(moon_coordinates.δ),
// sin(δ☾)
sin_δm = Math.sin(moon_coordinates.δ),
/**
* a and d designate the right ascension and declination of the point Z
* on the celestial sphere towards which the axis of the shadow is
* directed
*/
/** g*cos(d)*cos(a) */
g_cos_d_cos_a = cos_δs * cos_αs - b * cos_δm * cos_αm,
/** g*cos(d)*sin(a) */
g_cos_d_sin_a = cos_δs * Math.sin(sun_coordinates.α) - b * cos_δm
* Math.sin(moon_coordinates.α),
/** g*cos(d) */
g_cos_d = Math.sqrt(g_cos_d_cos_a * g_cos_d_cos_a + g_cos_d_sin_a
* g_cos_d_sin_a),
/** g*sin(d) */
g_sin_d = Math.sin(sun_coordinates.δ) - b * sin_δm,
/** g=G/R */
g = Math.sqrt(g_cos_d * g_cos_d + g_sin_d * g_sin_d),
sin_d = g_sin_d / g, cos_d = Math.sqrt(1 - sin_d * sin_d),
//
tan_a = g_cos_d_sin_a / g_cos_d_cos_a,
// a 與 α☉=sun_coordinates.α 有差距 (p. 219.)
a = Math.atan(tan_a),
// p. 217.
/** sin(π☾) */
sin_πm = Math.sin(moon_coordinates.π),
/** cos(α☾-a) */
cos_αmma = Math.cos(moon_coordinates.α - a),
// 月球於地球上之 rectangular coordinates (直角座標)投影。
// fundamental plane (基準平面)之 z 軸對準太陽。x 軸對準地球赤道。y 軸向北。
// [x,y,z] unit: Earth equatorial radius
x = cos_δm * Math.sin(moon_coordinates.α - a) / sin_πm,
//
y = (sin_δm * cos_d - cos_δm * sin_d * cos_αmma) / sin_πm;
var z = (sin_δm * sin_d + cos_δm * cos_d * cos_αmma) / sin_πm;
// var R = sun_coordinates.Δ;
var tmp = g * sun_coordinates.Δ;
// NG
if (false) {
sin_f1 = (Math.sin(sun_coordinates.semidiameter
* ARCSECONDS_TO_RADIANS) + Lunar_Radius_k1
* Math.sin(sun_coordinates.π))
/ tmp;
sin_f2 = (Math.sin(sun_coordinates.semidiameter
* ARCSECONDS_TO_RADIANS) - Lunar_Radius_k2
* Math.sin(sun_coordinates.π))
/ tmp;
}
/**
* The angles f1, f2 which the generators of the penumbral (subscript 1)
* and umbral (subscript 2)<br />
* For 1968 onwards:
*/
var sin_f1 = 0.004664018 / tmp,
//
sin_f2 = 0.004640792 / tmp,
/**
* p. 218.<br />
* distances of the vertices of the penumbral and umbral cones above the
* fundamental plane are thus, in units of the equatorial radius of the
* Earth:
*/
c1 = z + Lunar_Radius_k1 / sin_f1,
//
c2 = z - Lunar_Radius_k2 / sin_f2,
tan_f1 = sin_f1 / Math.sqrt(1 - sin_f1 * sin_f1),
//
tan_f2 = sin_f2 / Math.sqrt(1 - sin_f2 * sin_f2),
/**
* l1,l2: the radii of the penumbra and umbra on the fundamental plane
*/
l1 = c1 * tan_f1,
// p. 239.
// 0.5464: mean value of l1 - l2 adopted from 1963 onwards.
// l2 = c2 * tan_f2 || (l1 - 0.5464),
l2 = c2 * tan_f2;
if (false) {
console.log(format_radians(
//
normalize_radians(sun_coordinates.LHA)));
console.log(normalize_radians(sun_coordinates.LHA)
/ DEGREES_TO_RADIANS);
}
// p. 217.
// ephemeris hour angle = ephemeris sidereal time - a
// μ = Greenwich視恆星時"Apparent sidereal time" − 地心赤經a
var μ = GAST(TT_of(TT_JD, true), TT_JD) - a;
// console.log('μ=' + format_radians(normalize_radians(μ)));
if (options.get_diff)
return {
x : x,
y : y,
z : z,
c1 : c1,
c2 : c2,
l1 : l1,
l2 : l2,
μ : μ,
sin_d : sin_d
};
var elements_1_hour = Besselian_elements(TT_JD + 1 / ONE_DAY_HOURS,
local, {
get_diff : true
});
// console.log(elements_1_hour);
// p. 219.
var
// μ′, hourly variations
// μp/DEGREES_TO_RADIANS
μp = elements_1_hour.μ - μ,
// d′
dp = Math.asin(elements_1_hour.sin_d) - Math.asin(sin_d);
// console.log("μ′=" + μp + ", d′=" + dp);
var
// p. 220.
/**
* It is always sufficient to calculate them for the integral hour
* nearest conjunction
*/
ρ1 = Math.sqrt(1 - eccentricity_square * cos_d * cos_d),
//
ρ2 = Math.sqrt(1 - eccentricity_square * sin_d * sin_d);
var
// p. 220.
sin_d1 = sin_d / ρ1,
//
cos_d1 = Math.sqrt(1 - eccentricity_square) * cos_d / ρ1,
/** sin(d1-d2) */
sin_d1md2 = eccentricity_square * sin_d * cos_d / ρ1 / ρ2,
/** cos(d1-d2) */
cos_d1md2 = Math.sqrt(1 - eccentricity_square) / ρ1 / ρ2;
var
// x′
xp = elements_1_hour.x - x,
// y′
yp = elements_1_hour.y - y,
// z′
zp = elements_1_hour.z - z,
// c2′
c2p = elements_1_hour.c2 - c2;
// p. 223.
/**
* Central line of total or annular phase
*/
var central = {
ξ : x,
η : y,
η1 : y / ρ1
};
tmp = 1 - x * x - central.η1 * central.η1;
if (tmp >= 0) {
central.ζ1 = Math.sqrt(tmp);
// central.s = central.L2 / n;
central.ζ = ρ2 * (
//
central.ζ1 * cos_d1md2 - central.η1 * sin_d1md2);
// ξ′
central.ξp = μp * (-y * sin_d + central.ζ * cos_d);
// η′
central.ηp = μp * x * sin_d - dp * central.ζ;
tmp = xp - central.ξp;
central.n = Math.sqrt(tmp * tmp + (yp - central.ηp)
* (yp - central.ηp));
central.L1 = l1 - central.ζ * tan_f1;
central.L2 = l2 - central.ζ * tan_f2;
central.magnitude = (central.L1 - central.L2)
/ (central.L1 + central.L2);
central.s = Math.abs(central.L2) / central.n;
central.duration = central.s * 60 * 60 * 2;
// p. 223.
central.θ = Math
.atan(x, -central.η1 * sin_d1 + central.ζ1 * cos_d1);
central.λ = μ - central.θ;
central.longitude = from_ephemeris_longitude(central.λ, TT_JD);
// sin(φ1)
tmp = central.η1 * cos_d1 + central.ζ1 * sin_d1;
central.φ = format_radians(normalize_radians(tmp
//
/ Math.sqrt(1 - tmp * tmp) / Math.sqrt(1 - eccentricity_square),
true), 'decimal');
} else {
// 超過了地球的半徑，無日月蝕。
central.ζ2 = tmp;
}
if (options.get_central)
return central;
// p. 219.
// p. 223.
var
// θ is the local hour angle of the axis of shadow.
// θ = LHA = μ - ephemeris longitude λ*
// a 與 sun_coordinates.α 有差距，因此重算，不用 sun_coordinates.LHA。
θ = μ - to_ephemeris_longitude(local[1], TT_JD),
//
sin_θ = Math.sin(θ), cos_θ = Math.sqrt(1 - sin_θ * sin_θ);
// console.log('θ=' + format_radians(normalize_radians(θ)));
// p. 220.
/** the geodetic latitude of a point on the Earth's surface */
var φ = local[0] * DEGREES_TO_RADIANS, sin_φ = Math.sin(φ),
//
C = 1 / Math.sqrt(1 - eccentricity_square * sin_φ * sin_φ),
//
S = (1 - eccentricity_square) * C,
// p. 241.
H = (local[3] || 0) * 0.1567850e-6,
// φ′: geocentric latitude of φ
ρsin_φp = (S + H) * sin_φ, ρcos_φp = (C + H) * Math.cos(φ),
//
sin_φ1 = ρsin_φp / Math.sqrt(1 - eccentricity_square),
//
cos_φ1 = ρcos_φp;
// ((sin_φ1*sin_φ1+cos_φ1*cos_φ1)) should be 1
// p. 219.
// ephemeris longitude λ*, geocentric latitude φ′, at a distance
// ρ from the centre of the terrestrial spheroid
// [ξ,η,ζ] unit: Earth equatorial radius
var ξ = ρcos_φp * sin_θ,
//
η = ρsin_φp * cos_d - ρcos_φp * sin_d * cos_θ,
//
ζ = ρsin_φp * sin_d + ρcos_φp * cos_d * cos_θ;
var η1 = sin_φ1 * cos_d1 - cos_φ1 * sin_d1 * cos_θ,
//
ζ1 = sin_φ1 * sin_d1 + cos_φ1 * cos_d1 * cos_θ;
// p. 221.
// Auxiliary elements of an eclipse
/**
* Q: the position angle (measured eastwards from the north, i.e. from
* the y-axis towards the x-axis) of the axis from the observer
*/
var
/**
* At a height ζ above the fundamental plane the radius L of the shadow
* is given by: L = l - ζ * tan(f)
*/
// penumbra
L1 = l1 - ζ * tan_f1,
// umbra
L2 = l2 - ζ * tan_f2;
var
// p. 222.
l1p = elements_1_hour.l1 - l1,
//
l2p = elements_1_hour.l2 - l2,
// a1′
a1p = -l1p - μp * x * tan_f1 * cos_d,
// a2′
a2p = -l2p - μp * x * tan_f2 * cos_d,
// b′
bp = -yp + μp * x * sin_d,
// c1′
c1p = xp + μp * y * sin_d + μp * l1 * tan_f1 * cos_d,
// c2′
c2p = xp + μp * y * sin_d + μp * l2 * tan_f2 * cos_d,
// p. 224.
// ξ′= μp * (y*sin_d + ζ*cos_d)
ξp = μp * cos_φ1 * cos_θ,
// η′
ηp = μp * x * sin_d - dp * ζ,
// p. 223.
/** speed of the shadow relative to the observer */
n = Math.sqrt((xp - ξp) * (xp - ξp) + (yp - ηp) * (yp - ηp)),
/**
* semi-duration s of the total, or annular, phase on the central line
*/
s = Math.abs(L2) / n,
// duration: hour (semi-duration) to seconds
duration = s * 60 * 60 * 2,
// p. 224.
// tan Qo is required in example 9.7
tan_Q0 = (ηp - yp) / (xp - ξp);
// p. 224.
// Northern and southern limits of umbra and penumbra
function get_limit(southern, penumbra) {
var ap, cp, l, tan_f;
if (penumbra)
ap = a1p, cp = c1p, l = l1, tan_f = tan_f2;
else
// umbra
ap = a2p, cp = c2p, l = l2, tan_f = tan_f2;
/**
* p. 225.<br />
* If the latter is not available, as for example in the case of
* non-central eclipses, it is sufficient to set: _ζ = 0
*/
var _ζ = ζ || 0, cos_Q = 1;
var _ξ, last_ζ;
do {
// 高
var adjacent = bp - _ζ * dp - ap / cos_Q;
// 底邊
var opposite = cp - _ζ * μp * cos_d;
// 斜邊
var hypotenuse = Math.sqrt(adjacent * adjacent + opposite
* opposite);
// var Q = Math.atan2(bp, (cp - _ζ * μp * cos_d));
cos_Q = opposite / hypotenuse;
/**
* The sign of cos Q is positive for the northern limit of a
* total eclipse and the southern limit of an annular eclipse;
* it is negative for the southern limit of a total eclipse and
* the northern limit of an annular eclipse.
*/
if (southern ^ penumbra ^ (cos_Q < 0))
hypotenuse = -hypotenuse, cos_Q = -cos_Q;
var _L = l - _ζ * tan_f;
// var _ξ = x - _L * Math.sin(Q);
_ξ = x - _L * bp / hypotenuse;
var _η1 = (y - _L * cos_Q) / ρ1;
// warning: 對於northern penumbra，可能有 |_ξ|>=1 &&
// |_η1|>=1，表示不在範圍內?
var _ζ1 = Math.sqrt(1 - _ξ * _ξ - _η1 * _η1);
last_ζ = _ζ;
_ζ = ρ2 * (_ζ1 * cos_d1md2 - _η1 * sin_d1md2);
// console.log([ _ζ, _ζ - last_ζ ]);
} while (Math.abs(_ζ - last_ζ) > Number.EPSILON);
// p. 223.
var Q = Math.acos(cos_Q);
var sin_θ = _ξ / cos_φ1, θ = Math.asin(sin_θ);
// λ*: ephemeris longitude 星曆經度
var λ = μ - θ;
var _sin_φ1 = _η1 * cos_d1 + _ζ1 * sin_d1,
//
_cos_φ1 = (-_η1 * sin_d1 + _ζ1 * cos_d1) / Math.cos(θ),
//
φ = Math.atan(_sin_φ1 / _cos_φ1
/ Math.sqrt(1 - eccentricity_square));
return isNaN(φ) ? null : [
format_radians(normalize_radians(λ), 'decimal'),
format_radians(normalize_radians(φ, true), 'decimal') ];
}
var northern_limit = get_limit(),
//
southern_limit = get_limit(true);
var northern_penumbra_limit = get_limit(false, true);
var southern_penumbra_limit = get_limit(true, true);
// p. 228.
// Outline curves
var m = Math.sqrt(x * x + y * y),
// in radians
M = Math.atan(x / y),
//
QmM = Math.acos((m * m + l1 * l1 - 1) / 2 / l1 / m);
// p. 228.
// using the mean the same as get_limit()
// test for Q = 0°
var c_Q = 0,
//
c_ξ = x - L1 * Math.sin(c_Q),
//
c_η1 = (y - L1 * Math.cos(c_Q)) / ρ1,
// ξ^2
c_ξ2 = 1 - c_ξ * c_ξ - c_η1 * c_η1;
/**
* If the angle (Q - M) is imaginary, there are no end points to the
* curve, and the angle Q takes all values from 0° to 360°.
*/
var outline = [ format_radians(normalize_radians(M - QmM), 'decimal'),
format_radians(normalize_radians(M + QmM), 'decimal')
//
];
// console.log(c_ξ2 + ', [' + outline + ']');
if ((c_ξ2 > 0) ^ (outline[0] > outline[1]))
// swap.
outline = [ outline[1], outline[0] ];
// outline = [30,200]: 200°~360°, 0°~30°
// TODO: p. 229.
return {
βm : βm,
d : Math.asin(sin_d),
μ : μ,
θ : θ,
φ : φ,
l1 : l1,
l1p : l1p,
l2 : l2,
l2p : l2p,
central : central,
ζ : ζ,
c1 : c1,
c2 : c2,
L1 : L1,
L2 : L2,
// p. 246.
magnitude : (L1 - L2) / (L1 + L2),
// Central Duration
duration : duration,
x : x,
xp : xp,
y : y,
yp : yp,
z : z,
zp : zp,
tan_Q0 : tan_Q0,
// 4 items in degrees
northern_limit : northern_limit,
southern_limit : southern_limit,
northern_penumbra_limit : northern_penumbra_limit,
southern_penumbra_limit : southern_penumbra_limit,
// in degrees
outline : outline
};
}
_.Besselian_elements = Besselian_elements;
Besselian_elements.lunar = function(TT_JD, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var local = options.local || [ 0, 0 ];
var sun_coordinates = solar_coordinates(TT_JD, {
equatorial : true,
local : local
}), moon_coordinates = lunar_coordinates(TT_JD, {
equatorial : true,
local : local
});
// p. 258.
var a = sun_coordinates.α + TURN_TO_RADIANS / 2,
//
d = -sun_coordinates.δ,
// p. 260.
// Corrections to position of the Moon
// α☾
αm = moon_coordinates.α - 0.20 * ARCSECONDS_TO_RADIANS,
// δ☾
δm = moon_coordinates.δ - 0.46 * ARCSECONDS_TO_RADIANS;
var b = Math.sin(sun_coordinates.π) / Math.sin(moon_coordinates.π),
// cos(α☉)
cos_αs = Math.cos(a),
// cos(δ☉)
cos_δs = Math.cos(d),
// cos(α☾)
cos_αm = Math.cos(moon_coordinates.α),
// cos(δ☾)
cos_δm = Math.cos(moon_coordinates.δ),
// sin(δ☾)
sin_δm = Math.sin(moon_coordinates.δ),
/**
* a and d designate the right ascension and declination of the point Z
* on the celestial sphere towards which the axis of the shadow is
* directed
*/
/** g*cos(d)*cos(a) */
g_cos_d_cos_a = cos_δs * cos_αs - b * cos_δm * cos_αm,
/** g*cos(d)*sin(a) */
g_cos_d_sin_a = cos_δs * Math.sin(a) - b * cos_δm
* Math.sin(moon_coordinates.α),
/** g*cos(d) */
g_cos_d = Math.sqrt(g_cos_d_cos_a * g_cos_d_cos_a + g_cos_d_sin_a
* g_cos_d_sin_a),
/** g*sin(d) */
g_sin_d = Math.sin(d) - b * sin_δm,
/** g=G/R */
g = Math.sqrt(g_cos_d * g_cos_d + g_sin_d * g_sin_d),
sin_d = g_sin_d / g, cos_d = Math.sqrt(1 - sin_d * sin_d),
//
tan_a = g_cos_d_sin_a / g_cos_d_cos_a,
/** cos(α☾-a) */
cos_αmma = Math.cos(moon_coordinates.α - a),
//
x = cos_δm * Math.sin(moon_coordinates.α - a),
//
y = (sin_δm * cos_d - cos_δm * sin_d * cos_αmma);
if (options.get_diff)
return {
x : x,
y : y
};
var elements_1_hour = Besselian_elements.lunar(TT_JD + 1
/ ONE_DAY_HOURS, {
get_diff : true
});
var
// x′
xp = elements_1_hour.x - x,
// y′
yp = elements_1_hour.y - y;
/** n^2 */
var n2 = xp * xp + yp * yp,
//
n = Math.sqrt(n2),
//
t = -(x * xp + y * yp) / n2;
// the correction t to a starting time To to obtain the time of
// greatest obscuration is determined by solving:
var tmp = TT_JD + t / ONE_DAY_HOURS;
if (options.no_iterate && TT_JD !== tmp)
return Besselian_elements.lunar(tmp, options);
TT_JD = tmp;
var Δ = Math.abs(x * yp - y * xp) / n;
// p. 257.
/**
*
* Reference 資料來源/資料依據:<br />
* NASA - Enlargement of Earth's Shadows
*
* @see http://eclipse.gsfc.nasa.gov/LEcat5/shadow.html
*/
// 1.01 ≅ 1 + 1/85 - 1/594.
tmp = 1.01 * moon_coordinates.π + sun_coordinates.π;
/** s☉: semi-diameter of the Sun */
var ss = semidiameter(sun_coordinates, SUN_NAME)
* ARCSECONDS_TO_RADIANS,
/** s☾: semi-diameter of the Moon */
sm = semidiameter(moon_coordinates, MOON_NAME) * ARCSECONDS_TO_RADIANS,
// penumbral radius
f1 = tmp + ss,
// umbral radius
f2 = tmp - ss,
// angular distance (L) between the centres of the Moon and the
// shadow
// at beginning and end of the penumbral eclipse
L1 = f1 + sm,
// at beginning and end of the partial eclipse
L2 = f2 + sm,
// at beginning and end of the total eclipse
L3 = f2 - sm;
// p. 259.
/** Δ^2 */
var Δ2 = Δ * Δ, type,
// semi-duration in hours
semi_duration = [];
tmp = L1 * L1 - Δ2;
if (tmp < 0) {
// no eclipse
// return;
// ** DO NOT set type here!
} else {
semi_duration.push(Math.sqrt(tmp) / n);
tmp = L2 * L2 - Δ2;
if (tmp < 0)
// penumbral eclipse
type = 'penumbral';
else {
semi_duration.push(Math.sqrt(tmp) / n);
tmp = L3 * L3 - Δ2;
if (tmp < 0)
type = 'partial';
else {
semi_duration.push(Math.sqrt(tmp) / n);
type = 'total';
}
}
}
/** L^2 */
tmp = (x + xp * t) * (x + xp * t)
//
+ (y + yp * t) * (y + yp * t);
var L = Math.sqrt(tmp),
/** L^2 - Δ^2 */
L1mΔ2 = tmp - Δ2;
/**
* angular distance between the centres of the Moon and the shadow
*/
var m = Math.sqrt(x * x + y * y);
return {
TT : TT_JD,
semi_duration : semi_duration,
// f1 : normalize_radians(f1) / ARCSECONDS_TO_RADIANS,
// f2 : normalize_radians(f2) / ARCSECONDS_TO_RADIANS,
// L1 : normalize_radians(L1) / ARCSECONDS_TO_RADIANS,
// L2 : normalize_radians(L2) / ARCSECONDS_TO_RADIANS,
// L3 : normalize_radians(L3) / ARCSECONDS_TO_RADIANS,
// Δ : normalize_radians(Δ) / ARCSECONDS_TO_RADIANS,
type : type,
// The values of L, m, and s☉ should be those corresponding
// to the time of greatest obscuration.
magnitude : (L2 - m) / 2 / sm,
penumbral_magnitude : (L1 - m) / 2 / sm,
/**
* The latitudes (φ) and ephemeris longitudes (λ*) of the places
* that have the Moon in the zenith at given times
*/
latitude : format_radians(normalize_radians(moon_coordinates.δ,
true), 'decimal'),
// ephemeris sidereal time - α☾
longitude : from_ephemeris_longitude(
GAST(TT_of(TT_JD, true), TT_JD) - moon_coordinates.α, TT_JD)
};
};
/**
* 取得 TT_JD 時的日月食資訊。
*
* 中國古代天象記錄總表 http://chungfamily.woweb.net/zbxe/board_013/6819
* http://mdonchan.web.fc2.com/siryou/toita/jissoku-1.htm
*
* @param {Number}TT_JD
* Julian date (JD of 天文計算用時間 TT)
* @param {Integer}phase
* 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
*
* @returns {Object}日月食資訊。
*/
function eclipse_JD(TT_JD, phase, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
if (!options.eclipse)
options = Object.assign({
eclipse : true
}, options);
var year_month = options.year ? TT_JD
: Julian_century(TT_JD) * 100 + 2000;
/**
* 日月食資訊。
*
* @type {Object}
*/
var eclipse_data
//
= mean_lunar_phase(year_month, phase, options);
if (eclipse_data.type) {
eclipse_data.name
// gettext_config:{"id":"total-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"annular-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"hybrid-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"partial-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"total-lunar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"partial-lunar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"penumbral-lunar-eclipse","mark_type":"combination_message_id"}
= eclipse_data.type + ' ' + eclipse_data.object + ' eclipse';
eclipse_data.Δlongitude
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
= lunar_coordinates(eclipse_data.TT).β
//
/ DEGREES_TO_RADIANS;
eclipse_data.saros = saros(eclipse_data.TT,
// push saros series
phase === 0 ? TYPE_SOLAR : TYPE_LUNAR);
} else
eclipse_data = undefined;
if (eclipse_data && eclipse_data.saros)
return eclipse_data;
// ------------------------------------------------------------
if (!options.elements) {
var saros_data = saros(TT_JD,
// push saros series
phase === 0 ? TYPE_SOLAR : TYPE_LUNAR);
// 若是有 saros 就當作可能有日月食。
return saros_data && {
TT : TT_JD,
object : phase === 0 ? 'solar' : 'lunar',
// gettext_config:{"id":"solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"lunar-eclipse","mark_type":"combination_message_id"}
name : (phase === 0 ? 'solar' : 'lunar') + ' eclipse',
Δlongitude :
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
lunar_coordinates(TT_JD).β
//
/ DEGREES_TO_RADIANS,
saros : saros_data
};
}
// ------------------------------------------------------------
// 下面運算頗耗時間。
if (phase !== 0) {
eclipse_data = Besselian_elements.lunar(TT_JD)
if (!eclipse_data.type)
return;
var TT = eclipse_data.TT,
//
saros_data = saros(TT,
// push saros series
phase === 0 ? TYPE_SOLAR : TYPE_LUNAR);
return Object.assign(eclipse_data, {
TT : TT,
object : phase === 0 ? 'solar' : 'lunar',
// gettext_config:{"id":"total-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"annular-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"hybrid-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"partial-solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"total-lunar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"partial-lunar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"penumbral-lunar-eclipse","mark_type":"combination_message_id"}
name : eclipse_data.type + ' '
+ (phase === 0 ? 'solar' : 'lunar') + ' eclipse',
Δlongitude :
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
lunar_coordinates(TT).β
//
/ DEGREES_TO_RADIANS,
saros : saros_data
});
}
var get_magnitude = function(TT_JD) {
var data = Besselian_elements(TT_JD, {
get_central : true
}), magnitude = data.magnitude;
if (isNaN(magnitude))
// 9: 隨便給，夠大就好。
// assert: -magnitude < 5 < 9 - data.ζ2
return 9 - data.ζ2;
return [ -magnitude, {
data : data
} ];
};
if (get_magnitude(TT)[0] > 5)
// 連正中都無值。
return;
// using Besselian Elements
// Explanatory Supplement to the Astronomical Ephemeris. Third
// impression 1974.
// p. 211. ECLIPSES AND TRANSITS
// 朔的時間點日月黃經差為0，距離最大食分應在五分左右，十分內？
var range = Math.abs(options.range) || .2,
//
min_TT = TT_JD - range, max_TT = TT_JD + range;
if (false) {
while (isNaN(get_magnitude(min_TT)[0]))
min_TT += 0.001;
while (isNaN(get_magnitude(max_TT)[0]))
max_TT -= 0.001;
}
// 發生此日月食，時甚時之實際 TT in JD.
var TT = library_namespace.find_minima(
//
get_magnitude, min_TT, max_TT);
if (TT.y > 5)
return;
var saros_data = saros(TT,
// push saros series
phase === 0 ? TYPE_SOLAR : TYPE_LUNAR);
return Object.assign(TT.data, {
TT : TT,
object : phase === 0 ? 'solar' : 'lunar',
// gettext_config:{"id":"solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"lunar-eclipse","mark_type":"combination_message_id"}
name : (phase === 0 ? 'solar' : 'lunar') + ' eclipse',
Δlongitude :
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
lunar_coordinates(TT).β
//
/ DEGREES_TO_RADIANS,
saros : saros_data
});
// ------------------------------------------------------------
// 以下方法無依據。這樣的條件也有可能過疏過密？
var
/**
* eclipse conjunction 黃經衝 or 合(有相同的黃經)時之日月角距離 (in arcseconds)。
*
* TT.y≈Math.sqrt((TT.s.λ-TT.l.λ)*(TT.s.λ-TT.l.λ)+(TT.s.β-TT.l.β)*(TT.s.β-TT.l.β))
*
* @type {Number} in arcseconds
*/
distance = TT.y / ARCSECONDS_TO_RADIANS,
/**
* 日面的地心視半徑 (in arcseconds)。Geocentric semi-diameter of the Sun.
*
* @type {Number} in arcseconds
*/
sun_radius = semidiameter(TT.s, SUN_NAME),
/**
* 月面的地心視半徑 (in arcseconds)。
*
* @type {Number} in arcseconds
*/
moon_radius = semidiameter(TT.l, MOON_NAME),
/**
* 食甚食分 magnitude 角距離 (in arcseconds)。
*
* @type {Number} in arcseconds
*/
magnitude = sun_radius + moon_radius - distance;
// ((magnitude < 0))在魯隱公1年4月1日(-722/4/14)會漏掉!!
if (false && magnitude < 0 && !saros_data)
// 無遮掩??
return;
// β☾
var βm = TT.l.π - TT.s.π + (moon_radius - sun_radius)
* ARCSECONDS_TO_RADIANS;
if (βm > phase === 0 ? solar_eclipse_limit : lunar_eclipse_limit)
return;
magnitude /= phase === 0 ? sun_radius : moon_radius;
eclipse_data = {
TT : TT,
object : phase === 0 ? 'solar' : 'lunar',
// gettext_config:{"id":"solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"lunar-eclipse","mark_type":"combination_message_id"}
name : (phase === 0 ? 'solar' : 'lunar') + ' eclipse',
Δlongitude :
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
lunar_coordinates(TT).β
//
/ DEGREES_TO_RADIANS,
saros : saros_data
};
if (magnitude > 0)
eclipse_data.magnitude = magnitude;
return eclipse_data;
// ------------------------------------------------------------
// old
/**
* local (地面某點) 觀測者緯度 latitude (度)。
*
* @type {Number}
*/
var latitude =
//
Array.isArray(options.local) ? options.local[0]
//
: options.latitude || 45,
// 朔的時間點日月黃經差為0，距離最大食分應在五分左右，十分內？
/**
* 計算月亮(月心)的緯度→與黃道距離(度)。
*
* @type {Number}
*/
d = lunar_coordinates(TT).β / DEGREES_TO_RADIANS,
// 計算月面視半徑 (度)。
/**
* 月面的地心視半徑 (度)。
*
* TODO: use (coordinates.Δ * AU_TO_METERS) instead of LUNAR_DISTANCE_M
*
* @type {Number}
*/
r = Math.asin(LUNAR_RADIUS_M / LUNAR_DISTANCE_M)
// → 以觀測者為中心的座標中看到的月亮視半徑
* (1 + Math.sin(latitude * DEGREES_TO_RADIANS)
//
* TERRA_RADIUS_M / LUNAR_DISTANCE_M)
// → 度
/ DEGREES_TO_RADIANS,
/**
* calculate range (度)
*
* 初始值: 日面的地心視半徑 (度)。 Geocentric semi-diameter of the Sun
*
* @type {Number}
*/
range = SOLAR_RADIUS_RADIANS / DEGREES_TO_RADIANS;
if (phase === 2) {
// 日食: 計算日面視半徑 (度)。
// TODO: Besselian elements
} else {
// assert: phase === 2
// 月食: 計算地球本影之半徑, Earth's umbra radius.
/**
*
* Reference 資料來源/資料依據:<br />
* NASA - Enlargement of Earth's Shadows
*
* @see http://eclipse.gsfc.nasa.gov/LEcat5/shadow.html
*/
/**
* Equatorial horizontal parallax of the Sun, and 1.01 ≅ 1 + 1/85 -
* 1/594. 太陽赤道地平視差 (度)
*
* Astronomical Almanac 2011:<br />
* Solar parallax, pi_odot:<br />
* sin^-1(a_e/A) = 8.794143″
*
* @type {Number}
*
* @see https://en.wikipedia.org/wiki/Parallax#Solar_parallax
*/
var Solar_parallax
// 1: distance in AU
= 8.794143 / DEGREES_TO_ARCSECONDS / 1,
/**
* Equatorial horizontal parallax of the Moon 月球赤道地平視差 (度)
*
* @type {Number}
*
* @see http://farside.ph.utexas.edu/Books/Syntaxis/Almagest/node42.html
*/
Lunar_parallax = 41 / DEGREES_TO_ARCSECONDS;
// http://eclipse.gsfc.nasa.gov/LEcat5/shadow.html
range = 1.01 * Lunar_parallax + Solar_parallax
// Geocentric semi-diameter of the Sun
// 日面的地心視半徑 (度)。
- range;
// range: umbral radius 地球本影半徑
}
if (eclipse_data = Math.abs(d) < range + r) {
eclipse_data = {
TT : TT,
object : phase === 0 ? 'solar' : 'lunar',
// gettext_config:{"id":"solar-eclipse","mark_type":"combination_message_id"}
// gettext_config:{"id":"lunar-eclipse","mark_type":"combination_message_id"}
name : (phase === 0 ? 'solar' : 'lunar') + ' eclipse',
Δlongitude :
// eclipse conjunction 黃經衝 or 合(有相同的黃經)時之月黃緯
lunar_coordinates(TT_JD).β
//
/ DEGREES_TO_RADIANS,
saros : saros(TT_JD,
// push saros series
phase === 0 ? TYPE_SOLAR : TYPE_LUNAR)
};
}
// return maybe has eclipse.
return eclipse_data;
}
_.eclipse_JD = eclipse_JD;
/**
* get JD of lunar phase. Using full LEA-406a or LEA-406b model.
* 計算特定月相之時間精準值。可用來計算月相、日月合朔(黑月/新月)、弦、望(滿月，衝)、月食、月齡。
*
* @deprecated using accurate_lunar_phase()
*
* @param {Number}year_month
* 帶小數點的年數，例如1987.25表示1987年3月末。
* @param {Integer}phase
* 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Number} Julian date (JD of 天文計算用時間 TT)
*
* @see http://koyomi8.com/sub/sunmoon_long.htm
* @see http://eco.mtk.nao.ac.jp/cgi-bin/koyomi/cande/phenom_phase.cgi
* @see http://homepage3.nifty.com/ayumi_ho/moon1.htm
* @see http://www2s.biglobe.ne.jp/~yoss/moon/moon.html
*
* @deprecated
*/
function deprecated_accurate_lunar_phase
//
(year_month, phase, options) {
var up_degrees, low_degrees,
// 內插法(線性插值)上下限。
up_JD, low_JD,
// 目標角度。
degrees = phase * 90,
// 利用平月相的時間，以取得內插法初始近似值。
TT_JD = mean_lunar_phase(year_month, phase, options),
// 計算月日視黃經差。
angle = // options
//
// && typeof options.angle === 'function' ? options.angle :
//
degrees < 90 ? function(_JD) {
// window.lunar_count = (window.lunar_count || 0) + 1;
var d = lunar_phase_angle_of_JD(_JD || TT_JD, true);
if (d > TURN_TO_DEGREES - 90)
d -= TURN_TO_DEGREES;
return d;
} : function(_JD) {
return lunar_phase_angle_of_JD(_JD || TT_JD, true);
},
// 誤差常於2°之內。
result_degrees = angle();
// / 12: 月日視黃經差每日必於 12°–13°之內。
// 因此每度耗時必小於 1/12 日。此處取最大值。
if (degrees < result_degrees) {
// 將 TT_JD 作為上限。
up_JD = TT_JD, up_degrees = result_degrees;
// 以 result 反推出一個<b>一定</b>小於目標 TT_JD 之下限。
low_JD = TT_JD - (result_degrees - degrees) / 12;
low_degrees = angle(low_JD);
} else {
// 將 TT_JD 作為下限。
low_JD = TT_JD, low_degrees = result_degrees;
// 以 result 反推出一個<b>一定</b>大於目標 TT_JD 之上限。
up_JD = TT_JD - (result_degrees - degrees) / 12;
up_degrees = angle(up_JD);
}
library_namespace.debug(
//
'初始值: year ' + year_month + ', phase ' + phase
//
+ ' (' + degrees + '°): JD' + TT_JD + ' ('
//
+ library_namespace.JD_to_Date(UT_of(TT_JD)).format('CE') + '), '
+ format_degrees(result_degrees) + '; JD: ' + low_JD + '–'
+ up_JD, 2);
// 內插法 main loop
while (low_JD < up_JD) {
// 估值
TT_JD = low_JD + (up_JD - low_JD)
//
* (degrees - low_degrees) / (up_degrees - low_degrees);
result_degrees = angle();
if (result_degrees < degrees) {
if (low_JD === TT_JD) {
// 已經得到相當好的效果。
break;
// 也可以改變另一項。但效果通常不大，反而浪費時間。
up_JD = (low_JD + up_JD) / 2;
up_degrees = angle(up_JD);
} else {
low_JD = TT_JD;
low_degrees = result_degrees;
}
} else if (result_degrees > degrees) {
if (up_JD === TT_JD) {
// 已經得到相當好的效果。
break;
// 也可以改變另一項。但效果通常不大，反而浪費時間。
low_JD = (low_JD + up_JD) / 2;
low_degrees = angle(low_JD);
} else {
up_JD = TT_JD;
up_degrees = result_degrees;
}
} else
break;
}
library_namespace.debug('JD' + TT_JD + ' ('
//
+ library_namespace.JD_to_Date(UT_of(TT_JD)).format('CE')
//
+ '): ' + format_degrees(angle(TT_JD)), 2);
// apply ΔT: TT → UT.
return options && options.UT ? UT_of(TT_JD) : TT_JD;
}
/**
* get JD of lunar phase. Using full LEA-406a or LEA-406b model.
* 計算特定月相之時間精準值。可用來計算月相、日月合朔(黑月/新月)、弦、望(滿月，衝)、月食、月齡。
*
* @param {Number}year_month
* 帶小數點的年數，例如1987.25表示1987年3月末。
* @param {Integer}phase
* 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
* @param {Object}[options]
* 附加參數/設定特殊功能與選項
*
* @returns {Number} Julian date (JD of 天文計算用時間 TT)
*
* @see http://koyomi8.com/sub/sunmoon_long.htm
* @see http://eco.mtk.nao.ac.jp/cgi-bin/koyomi/cande/phenom_phase.cgi
* @see http://homepage3.nifty.com/ayumi_ho/moon1.htm
* @see http://www2s.biglobe.ne.jp/~yoss/moon/moon.html
*/
function accurate_lunar_phase
//
(year_month, phase, options) {
var
// 目標角度。
degrees = phase * 90,
// 利用平月相的時間，以取得內插法初始近似值。
TT_JD = mean_lunar_phase(year_month, phase, options),
// 計算月日視黃經差。
angle = // options
//
// && typeof options.angle === 'function' ? options.angle :
//
degrees < 90 ? function(TT_JD) {
// window.lunar_count = (window.lunar_count || 0) + 1;
var d = lunar_phase_angle_of_JD(TT_JD, true);
if (d > TURN_TO_DEGREES - 90)
d -= TURN_TO_DEGREES;
return d;
} : function(TT_JD) {
return lunar_phase_angle_of_JD(TT_JD, true);
},
// 誤差常於2°之內。
result_degrees = angle(TT_JD);
TT_JD = library_namespace.find_root(
'count' in options ? function(TT_JD) {
options.count++;
return angle(TT_JD);
} : angle,
// / 12: 月日視黃經差每日必於 12°–13°之內。
// 因此每度耗時必小於 1/12 日。此處取最大值。
TT_JD - (result_degrees - degrees) / 12, TT_JD, degrees, {
y1 : result_degrees
});
library_namespace.debug(
//
'JD' + TT_JD + ' ('
//
+ library_namespace.JD_to_Date(UT_of(TT_JD)).format('CE')
//
+ '): ' + format_degrees(angle(TT_JD)), 2);
// apply ΔT: TT → UT.
return options && options.UT ? UT_of(TT_JD) : TT_JD;
}
// phase: 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
// lunar_phase_cache[year][phase:0–3] = [JD of 日常生活時間 UT, JD, ...]
var lunar_phase_cache = [];
/**
* get JD of lunar phases. 取得整年之月相。
*
* 注意: 中曆2057年9月朔日 為 2057/9/28 UTC+8，與 香港天文台 (
* http://www.weather.gov.hk/gts/time/conversionc.htm )、兩千年中西曆轉換 (
* http://sinocal.sinica.edu.tw/ ) 不相同。<br />
* According to HORIZONS (DE-431), it's about 9/28 19:54 (月亮追過太陽) or 9/29
* 00:08 (視角度差最小).
*
* 中曆2089年8月朔日 為 2089/9/4 UTC+8，與 兩千年中西曆轉換 不相同。<br />
* 中曆2097年7月朔日 為 2097/8/7 UTC+8，與 兩千年中西曆轉換 不相同。<br />
* 2000–2100 不合者如上。
*
* @param {Number}year
* 年數
* @param {Integer}phase
* 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.mean: 是否採用平月相。 false: 採用精準值。<br />
* {Integer}options.duration: 取得年數<br />
* {Boolean}options.to_Date: return Date<br />
* {String|Object}options.format: 將 Date 轉成特定 format
*
* @returns {Array} [ Julian date (JD of 日常生活時間 UT), JD, ... ]
*/
function lunar_phase(year, phase, options) {
if (year === (year | 0)) {
if (options === true)
options = 1;
if (options > 0 && (options === options | 0))
// 取得整年之月相。
options = {
duration : options
};
}
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var operator, UT_JD;
if (typeof options.mean === 'boolean')
operator = options.mean ? mean_lunar_phase : accurate_lunar_phase;
// whole year
// options.duration = 1
// 2 years:
// options.duration = 2
if (!options.duration) {
UT_JD = UT_of((operator || accurate_lunar_phase)(year, phase,
options));
return UT_JD;
}
var phase_JD = [];
year |= 0;
phase |= 0;
for (var phase_data,
//
end = year + options.duration; year < end; year++) {
// using cache.
phase_data = lunar_phase_cache[year];
if (!phase_data)
// 初始化。
lunar_phase_cache[year] = phase_data = [];
if (phase_data = phase_data[phase])
// has cache. using clone.
phase_data = phase_data.slice();
else {
phase_data = [];
for (var year_month = year, date, hours;;
// 0.08: 1 / 12 = .08333333333333
year_month = Julian_century(TT_of(UT_JD)) * 100 + 2000
// year_month 加此值以跳到下一個月。
+ mean_lunar_phase_days / (DAYS_OF_JULIAN_CENTURY / 100)) {
UT_JD = UT_of((operator || mean_lunar_phase)(year_month,
phase, options));
date = library_namespace.JD_to_Date(UT_JD);
if (!operator
// auto: 在特別可能有問題的時候採用精準值。
&& ((hours = date.getHours()) < 2 || hours > 21)) {
UT_JD = UT_of(accurate_lunar_phase(year_month, phase,
options));
date = library_namespace.JD_to_Date(UT_JD);
}
date = date.getFullYear();
if (date === year)
phase_data.push(UT_JD);
else if (date - year === 1) {
phase_data.end = UT_JD;
// 已經算到次年了。
break;
}
}
if (options.mean === false)
lunar_phase_cache[year][phase]
// using clone.
= phase_data.slice();
}
if (options.to_Date)
phase_data.forEach(function(UT_JD, index) {
UT_JD = library_namespace.JD_to_Date(UT_JD);
if (options.format)
UT_JD = UT_JD.format(options.format);
phase_data[index] = UT_JD;
});
phase_JD.push(phase_data);
}
return options.duration === 1 ? phase_JD[0] : phase_JD;
}
_.lunar_phase = lunar_phase;
/**
* get lunar phase of JD. 取得 JD 之月相。
*
* @param {Number}UT_JD
* Julian date of local midnight (00:00) (JD of 日常生活時間 UT)
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.time: 取得月相時，亦取得時刻。<br />
* {Boolean|String}options.晦: 顯示晦。<br />
* {Boolean}options.index: 顯示 index 而非名稱。<br />
* {Boolean}options.TT: date is TT instead of UT.
*
* @returns {Number} phase: 0:朔0°, 1:上弦90°, 2:望180°, 3:下弦270°
*/
function lunar_phase_of_JD(UT_JD, options) {
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var TT_JD;
if (options.TT)
UT_JD = UT_of(TT_JD = UT_JD);
else
TT_JD = TT_of(UT_JD);
// 隔日子夜0時剛開始之月相。
// 90: TURN_TO_DEGREES / 4相 = 360 / 4
var _phase = lunar_phase_angle_of_JD(TT_JD + 1) / 90;
if (isNaN(_phase)) {
library_namespace.debug('資料還沒載入。', 2);
return;
}
var phase = Math.floor(_phase);
// 假如變換剛好落在隔日子夜0時剛開始(這機率應該極低)，則今日還是應該算前一個。
// 因為月相長度大於日長度，此即表示今天還沒變換月相。
if (phase !== _phase
// 檢查今天子夜0時與明日子夜0時是否有改變月相。
&& phase !== (_phase = Math.floor(lunar_phase_angle_of_JD(TT_JD) / 90))) {
// UT_JD, UT_JD+1 有不同月相，表示這天中改變了月相。
// phase: −2–1
if (phase < 0)
phase += 4;
// phase: 0–3
var phase_shown = options.index ? phase : LUNAR_PHASE_NAME[phase];
if (options.time || options.eclipse) {
// 發生此月相之實際 TT in JD.
var TT = accurate_lunar_phase(
Julian_century(TT_JD) * 100 + 2000, phase, {
JD : TT_JD,
// eclipse : true,
nearest : true
});
phase_shown = [ phase_shown, UT_of(TT) ];
/**
* @see
*
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 380. chapter 54
*
* If F differs from the nearest multiple of 180° by less than
* 13.9 degrees, then there is certainly an eclipse; ifthe
* difference is larger than 21°, there is no eclipse;
*
* Use can be made of the following rule: there is no eclipse if
* |sin F| > 0.36.
*/
if (options.eclipse
// 0:朔才可能日食, 2:望才可能月食
&& (phase === 0 || phase === 2)) {
/**
* 日月食資訊。
*
* @type {Object}
*/
var eclipse_data
//
= eclipse_JD(TT, phase, options);
if (eclipse_data) {
// 遮到了。
phase_shown.push(eclipse_data);
}
}
}
// [ phase type index, UT (JD), eclipse_data ]
return phase_shown;
}
if (options.晦 && phase === -1 && 0 ===
// +2: 晦日午夜之2天之後(之午夜)恰好過朔。phase: -1 → -1 → 0
Math.floor(lunar_phase_angle_of_JD(TT_JD + 2) / 90))
return options.晦 === true ? '晦' : options.晦;
}
_.lunar_phase_of_JD = lunar_phase_of_JD;
// ------------------------------------------------------------------------------------------------------//
// 制曆/排曆/排陰陽曆譜
// 中國傳統曆法是一種陰陽合曆，以月相定月份，以太陽定年周期。
// TODO: 孫郁興 中國各朝曆法及其基數變遷: 沈括提出以「十二氣」為一年的曆法，十二氣曆
/**
* normalize minute offset.
*
* @param {Number}minute_offset
* time-zone offset from UTC in minutes.<br />
* e.g., UTC+8: 8 * 60 = 480
*
* @returns {Number} normalized minute offset
*/
function normalize_minute_offset(minute_offset) {
return isNaN(minute_offset) ? default_offset : minute_offset;
}
/**
* JD (UT) to local midnight (00:00).
*
* @param {Number}UT_JD
* Julian date (JD of 日常生活時間 UT)
* @param {Number}[minute_offset]
* time-zone offset from UTC in minutes.<br />
* e.g., UTC+8: 8 * 60 = +480. default: UTC+0.
* @param {Boolean}[get_local_Date]
* 轉成當地之 Date
*
* @returns {Number|Date}
*/
function midnight_of(UT_JD, minute_offset, get_local_Date) {
// -day_offset: to local (UT_JD+.5). 此時把 local 當作 UTC+0.
// Math.floor(): reset to local midnight, 00:00
// +day_offset: recover to UTC
var day_offset = (minute_offset | 0) / (ONE_DAY_HOURS * 60) - .5;
UT_JD = Math.floor(UT_JD + day_offset) - day_offset;
if (get_local_Date) {
UT_JD = library_namespace.JD_to_Date(
//
UT_JD + (minute_offset - default_offset) / (60 * ONE_DAY_HOURS));
// 歸零用。
var ms = UT_JD.getMilliseconds();
// 歸零。
if (ms)
UT_JD.setMilliseconds(Math.round(ms / 500) * 500);
}
return UT_JD;
}
_.midnight_of = midnight_of;
/**
* 冬至序 = 18
*
* @type {Integer}
*/
var 冬至序 = SOLAR_TERMS_NAME.indexOf('冬至');
/**
* 取得整年之月首朔日/月齡。
*
* 注意：若中氣發生於朔時刻之前、朔日當日子夜後，如清世祖順治2年閏6月1日，此中氣會被算做發生於當日，而非前一個月之晦日；因此閏月基本上會被排在上一個月而非本月。
*
* @param {Integer}CE_year
* 公元年數
* @param {Number}minute_offset
* time-zone offset from UTC in minutes.<br />
* e.g., UTC+8: 8 * 60 = 480
*
* @returns {Array} 年朔日 = [ [ Julian date (JD of 日常生活時間 UT), JD, ...], 冬至所在月 ]
*/
function 子月序(CE_year, minute_offset) {
minute_offset = normalize_minute_offset(minute_offset);
// 冬至所在月為十一月，之後為十二月、正月、二月……復至十一月。
var 冬至 = solar_term_JD(CE_year, 冬至序),
// 取得整年之朔日。依現行農曆曆法，每年以朔分月（朔日為每月初一）。
年朔日 = lunar_phase(CE_year, 0, {
duration : 1,
mean : false
})
// 魯僖公五年正月壬子朔旦冬至
.map(function(UT_JD) {
// 日月合朔時間 → 朔日0時
return midnight_of(UT_JD, minute_offset);
});
年朔日.冬至 = 冬至;
var index = 年朔日.search_sorted(冬至, true);
// assert: 冬至 >= 年朔日[index];
return [ 年朔日, index ];
}
/**
* 取得歲首(建正/年始)為建子之整年月首朔日/月齡。
*
* @param {Integer}年
* 基本上與公元年數同步。 e.g., 2000: 1999/12/8–2000/11/25
* @param {Number}minute_offset
* time-zone offset from UTC in minutes.<br />
* e.g., UTC+8: 8 * 60 = 480
*
* @returns {Array} 年朔日 = [ {Number}朔日JD, 朔日JD, ... ]
*/
function 建子朔日(年, minute_offset) {
minute_offset = normalize_minute_offset(minute_offset);
var 朔日 = 子月序(年 - 1, minute_offset),
//
次年朔日 = 子月序(年, minute_offset);
朔日[0].splice(0, 朔日[1]);
朔日 = 朔日[0].concat(次年朔日[0].slice(0, 次年朔日[1]));
朔日.end = 次年朔日[0][次年朔日[1]];
if (朔日.length === 13) {
// 確定/找閏月。
// 若兩冬至間有13個月（否則應有12個月），則置閏於冬至後第一個沒中氣的月，月序與前一個月相同（閏月在幾月後面，就稱閏幾月）。
var 中氣, 中氣序 = 冬至序 + 2, 閏 = 1, year = 年 - 1;
for (; 中氣序 !== 冬至序; 中氣序 += 2) {
if (中氣序 === SOLAR_TERMS_NAME.length)
year++, 中氣序 -= SOLAR_TERMS_NAME.length;
中氣 = solar_term_JD(year, 中氣序);
朔日[SOLAR_TERMS_NAME[中氣序]] = 中氣;
if (中氣 >= 朔日[閏]
// 測中氣序: 朔日[閏]: 沒中氣的月
&& 中氣 >= 朔日[++閏]) {
閏--;
// CeL.JD_to_Date(1727046.1666666667).format('CE')
// CeL.JD_to_Date(1727076.9971438504).format('CE')
library_namespace.debug('沒中氣的月: 朔日[' + 閏 + '] = ' + 朔日[閏]
+ ', 中氣 ' + 中氣, 3);
break;
}
}
朔日.閏 = 閏;
} else if (朔日.length !== 12)
library_namespace.error(年 + '年有' + 朔日.length + '個月!');
// [ {Number}朔日JD, 朔日JD, ... ].閏 = {Boolean};
return 朔日;
}
/**
* 年朔日 = 朔日_cache[ 年 + '/' + minute_offset ]<br /> = [ {Number}朔日JD, 朔日JD,
* ... ]<br />
* e.g., [ 1727075.1666666667, 1727104.1666666667, ... ]
*
* 年朔日.閏 = {Boolean};
*
* @inner
*/
var 朔日_cache = [];
/**
* clone 曆數
*
* @param {String}index
* cache index
* @param {Object}options
* options
* @param {Array}[朔日]
* 本初年朔日曆數
*
* @returns {Array} 年朔日曆數
*
* @inner
*/
function clone_朔日(index, options, 朔日) {
library_namespace.debug('Get cache index [' + index
+ '] (年 /歲首/minute_offset)');
if (朔日)
朔日_cache[index] = 朔日;
else if (!(朔日 = 朔日_cache[index]))
return;
if (options.月名 && !朔日.月名)
朔日.月名 = 定朔.月名(朔日);
var clone = 朔日.slice();
clone.end = 朔日.end;
if (options.月名)
// 添加月名
clone.月名 = 朔日.月名.slice();
if (朔日.閏)
clone.閏 = 朔日.閏;
return clone;
}
/**
* 以定氣定朔法排曆，編排中國傳統曆法（陰陽曆），取得整年月首朔日/月齡。
*
* @param {Integer}年
* 基本上與公元年數同步。 e.g., 2000: 1999/12/8–2000/11/25
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Number}options.minute_offset: time-zone offset from UTC in
* minutes.<br />
* e.g., UTC+8: 8 * 60 = 480<br />
* {String|Integer}options.歲首: 年始之地支/地支序(0:子)<br />
* {Integer}options.year_offset: 年數將自動加上此 offset。<br />
* {Boolean}options.月名: 順便加上 .月名 = [ 月名 ]
*
* @returns {Array} 年朔日 = [ {Number}朔日JD, 朔日JD, ... ]
*/
function 定朔(年, options) {
if (!LEA406_loaded('V'))
// 尚未載入指定天體/行星的計算數據。而採用低精度之誤差過大，不能用。
return;
// 前置處理。
if (!library_namespace.is_Object(options))
options = Object.create(null);
var 歲首 = options.歲首,
//
minute_offset = options.minute_offset;
if (library_namespace.is_Date(年)) {
if (isNaN(minute_offset))
minute_offset = 年[
// see data.date.era
library_namespace.era.MINUTE_OFFSET_KEY];
年 = Math.round(年.getFullYear() + 年.getMonth() / 12);
}
minute_offset = normalize_minute_offset(minute_offset);
if (!isNaN(options.year_offset))
年 += options.year_offset;
if (isNaN(歲首) && NOT_FOUND ===
//
(歲首 = library_namespace.BRANCH_LIST.indexOf(歲首))) {
if (定朔.歲首 && isNaN(定朔.歲首)) {
定朔.歲首 = library_namespace.BRANCH_LIST.indexOf(定朔.歲首);
if (定朔.歲首 === NOT_FOUND) {
library_namespace.warn('定朔: Invalid 歲首');
定朔.歲首 = undefined;
}
}
歲首 = 定朔.歲首;
}
// 至此已確定: 年, 歲首, minute_offset.
var cache_index = 年 + '/' + 歲首 + '/' + minute_offset,
//
朔日 = clone_朔日(cache_index, options);
if (朔日)
return 朔日;
朔日 = 建子朔日(年, minute_offset);
if (歲首 === 0)
return clone_朔日(cache_index, options, 朔日);
var 閏 = 朔日.閏 - 歲首;
library_namespace.debug('歲首 ' + 歲首 + ', ' + 朔日.閏 + ', 閏=' + 閏, 3);
// 此處已清掉(朔日.閏)
朔日 = 朔日.slice(閏 <= 0 ? 歲首 + 1 : 歲首);
if (閏 > 0)
朔日.閏 = 閏;
var 次年朔日 = 建子朔日(年 + 1, minute_offset);
library_namespace.debug('次年 ' + 歲首 + ', ' + 次年朔日.閏, 3);
閏 = 次年朔日.閏;
var index = 閏 <= 歲首 ? 歲首 + 1 : 歲首,
//
end = 次年朔日[index];
library_namespace.debug(
//
'end[' + index + ']=' + 次年朔日[index], 3);
次年朔日 = 次年朔日.slice(0, index);
if (閏 <= 歲首)
if (朔日.閏)
// 這將造成無法阻絕一年內可能有兩閏月，以及一年僅有11個月的可能。
library_namespace.error(年 + '年有兩個閏月!!');
else
朔日.閏 = 閏 + 朔日.length;
閏 = 朔日.閏;
library_namespace.debug('閏=' + 閏, 3);
// 此處會清掉(朔日.閏)
朔日 = 朔日.concat(次年朔日);
朔日.end = end;
if (閏)
朔日.閏 = 閏;
return clone_朔日(cache_index, options, 朔日);
}
// default 預設歲首為建寅
// 正謂年始，朔謂月初，言王者得政，示從我始，改故用新，隨寅、丑、子所建也。周子，殷丑，夏寅，是改正也；周夜半，殷雞鳴夏平旦，是易朔也。
定朔.歲首 = '寅';
定朔.月名 = function(年朔日) {
var 閏 = 年朔日.閏, 月序 = 0;
library_namespace.debug('閏=' + 閏, 3);
return 年朔日.map(function(朔, index) {
return index === 閏 ? '閏' + 月序 : ++月序;
});
};
_.定朔 = 定朔;
/**
* 取得指定日期之夏曆。
*
* @param {Date}date
* 指定日期。
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
*
* @returns {Array} [ 年, 月, 日 ]
*/
function 夏曆(date, options) {
if (!LEA406_loaded('V'))
// 採用低精度之誤差過大，不能用。
return;
var JDN = library_namespace.Julian_day(date),
//
年朔日 = {
月名 : true
};
options = options ? Object.assign(年朔日, options) : 年朔日;
options.year_offset |= 0;
年朔日 = 定朔(date, options);
if (JDN < 年朔日[0]) {
// date 實際上在上一年。
options.year_offset--;
年朔日 = 定朔(date, options);
} else if (JDN >= 年朔日.end) {
// date 實際上在下一年。
options.year_offset++;
年朔日 = 定朔(date, options);
}
var index = 年朔日.search_sorted(JDN, true);
// [ 年, 月, 日 ]
return [ date.getFullYear() + options.year_offset, 年朔日.月名[index],
1 + JDN - 年朔日[index] | 0 ];
}
_.夏曆 = 夏曆;
// ------------------------------------------------------------------------------------------------------//
// 天體的升、中天、降
/**
* 計算天體的升（出:星面頂之緯度負→正）、上中天（該天體正經過當地子午圈，但與緯度最高點的位置當有些微差別）、降（沒:星面底之緯度正→負）時刻。
* 天体の出没 e.g., 日出正午日落,太陽升降。 約有兩三分的精準度?
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* Chapter 15 Rising, Transit, and Setting
*
* @param {Array}local
* the observer's geographic location [ latitude (°), longitude
* (°), time zone (e.g., UTC+8: 8), elevation or geometric height
* (m) ]<br />
* 觀測者 [ 緯度（北半球為正,南半球為負）, 經度（從Greenwich向東為正，西為負）, 時區,
* 海拔標高(觀測者距海平面的高度) ]
* @param {Number}JDN
* UT JDN
* @param {Number}type
* 0:lower culmination, 1:rise, 2:upper culmination, 3:set
* @param {String}object
* 天體 (e.g., planets 行星).
* @param {Boolean}force
* 即使預期應出現升降的時段，天體卻一直處於地平之同一側（同在地平線上或下），依然嘗試估算；取得即使不是當天，但符合的時點。
*
* @returns {Number}UT JD
*
* @see https://en.wikipedia.org/wiki/Sunrise_equation
* https://en.wikipedia.org/wiki/Culmination
* http://www.zhihu.com/question/23423763
* http://www.astronomy.com.cn/bbs/thread-157520-1-1.html<br />
* 于Paul Schlyter的1992年的sunriset函数
* http://www.spectralcalc.com/solar_calculator/solar_position.php
*/
function rise_set(local, JDN, type, object, force) {
if (!object)
object = SUN_NAME;
if (type) {
if (typeof type !== 'number' && !isNaN(type))
type = +type;
} else if (!type && type !== 0)
// get [ 0下中天, 1升, 2上中天, 3降 ]
type = [ 0, 1, 2, 3 ];
if (Array.isArray(type)) {
return type.map(function(type) {
return rise_set(local, JDN, type, object, force);
});
}
function angle(TT_JD) {
coordinates = get_coordinates(TT_JD, {
local : local,
object : object
});
var angle = type % 2 === 1 || type > 3 ? coordinates.Alt + Δ
// 上中天: LHA: 2π → 應為0
// 下中天: LHA: 應為π
: normalize_radians(coordinates.LHA + Δ, true);
// 常需演算十數次。
if (false)
console.log(TT_JD + ' ('
//
+ library_namespace.JD_to_Date(TT_JD).format('CE') + ' TT): '
+ angle);
return angle;
}
var Δ, get_coordinates, coordinates,
// 自動判別時區。
zone = get_time_zone(local);
// UT_JD: local 當地之 0:0
var UT_JD = JDN - .5 - zone / ONE_DAY_HOURS,
// hour 上下限
hour0, hour1;
// TODO: 考慮 dip of the horizon (地平俯角, 海岸視高差)
// @see
// https://en.wikipedia.org/wiki/Horizon#Effect_of_atmospheric_refraction
// http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/altitudes.html
if (object === SUN_NAME) {
Δ = SOLAR_RADIUS_RADIANS;
get_coordinates = solar_coordinates;
} else {
get_coordinates = object === MOON_NAME ? lunar_coordinates
: object_coordinates;
coordinates = get_coordinates(TT_of(UT_JD), {
local : local,
object : object
});
// UT_JD 與上一個上中天之距離 (in days, 0~1)。
Δ = normalize_radians(coordinates.LHA) / TURN_TO_RADIANS;
// 決定要使用的下中天。
// 確認最靠近 UT_JD 的下中天。
if (Δ < .5) {
// 正常情況:下中天 在本日上半天。
} else {
// 下中天 在前一日下半天。
// TODO: 本日 0:0 後首個下中天。
// UT_JD += 1;
// 取前一個下中天。
}
UT_JD += .5 - Δ;
Δ = object === MOON_NAME
// http://aa.usno.navy.mil/faq/docs/RST_defs.php
// Moon's apparent radius varies from 15 to 17 arcminutes
// and its horizontal parallax varies from 54 to 61
// arcminutes.
? Math.atan(LUNAR_RADIUS_M / AU_TO_METERS / coordinates.Δ)
// 其他天體之 apparent radius 當作0。
: 0;
}
// Δ: 天體之 apparent radius (in radians)
switch (type) {
case 0:
// 下中天
hour0 = -2;
hour1 = 2;
Δ = -TURN_TO_RADIANS / 2;
break;
case 2:
// 上中天, 過中天
hour0 = ONE_DAY_HOURS / 2 - 2;
hour1 = ONE_DAY_HOURS / 2 + 2;
Δ = 0;
break;
case 1:
// 升
// http://tamweb.tam.gov.tw/v3/tw/content.asp?mtype=c2&idx=1255
// 夏至並非一年中日出最早、日落最晚之時
hour0 = 0;
hour1 = ONE_DAY_HOURS / 2;
break;
case 3:
// 降
hour0 = ONE_DAY_HOURS / 2;
hour1 = ONE_DAY_HOURS;
break;
// civil twilight, nautical twilight, astronomical twilight
case 4:
case 5:
case 6:
hour0 = 0;
hour1 = ONE_DAY_HOURS / 2;
Δ = (7 - type) * 6 * DEGREES_TO_RADIANS;
break;
case 7:
case 8:
case 9:
hour0 = ONE_DAY_HOURS / 2;
hour1 = ONE_DAY_HOURS;
Δ = (type - 6) * 6 * DEGREES_TO_RADIANS;
break;
default:
throw new Error('rise_set: Invalid type: [' + type + ']');
}
/**
* 天文/航海/民用曙暮光(晨起天亮/晚上天黑)時刻。
* http://aa.usno.navy.mil/faq/docs/RST_defs.php
* <q>Civil twilight is defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 6 degrees below the horizon.</q>
* <br />
* <q>Nautical twilight is defined to begin in the morning, and to end in the evening, when the center of the sun is geometrically 12 degrees below the horizon.</q>
* <br />
* <q>Astronomical twilight is defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 18 degrees below the horizon.</q>
* <br />
*/
// 檢測分布
if (false)
for (var m = 0; m < 4 * 60; m++)
angle(TT_of(UT_JD + hour0 / ONE_DAY_HOURS + m / ONE_DAY_HOURS
/ 60));
UT_JD = UT_of(library_namespace.find_root(angle, TT_of(UT_JD + hour0
/ ONE_DAY_HOURS), TT_of(UT_JD + hour1 / ONE_DAY_HOURS), 0,
// 即使預期應出現升降的時段，天體卻一直處於地平之同一側(同在地平線上或下)，依然嘗試估算。
force ? null : {
start_OK : function(y0, y1) {
// console.log([ y0, y1 ]);
return Math.sign(y0) !== Math.sign(y1);
}
}));
// 出沒方位角。
coordinates.Az;
// 過中天仰角。
coordinates.Alt;
return UT_JD;
}
_.rise_set = rise_set;
/**
* name of type rise_set() gets.<br />
* <q>下中天,升,上中天,降</q>
*
* @type {Array}
*/
rise_set.type_name = [
// gettext_config:{"id":"lower-culmination"}
"lower culmination",
// gettext_config:{"id":"sunrise","mark_type":"combination_message_id"}
// gettext_config:{"id":"moonrise","mark_type":"combination_message_id"}
"rise",
// gettext_config:{"id":"upper-culmination"}
"upper culmination",
// gettext_config:{"id":"sunset","mark_type":"combination_message_id"}
// gettext_config:{"id":"moonset","mark_type":"combination_message_id"}
"set" ];
'astronomical,nautical,civil'.split(',')
//
.forEach(function(twilight, index) {
// gettext_config:{"id":"astronomical-twilight-begin","mark_type":"combination_message_id"}
// gettext_config:{"id":"nautical-twilight-begin","mark_type":"combination_message_id"}
// gettext_config:{"id":"civil-twilight-begin","mark_type":"combination_message_id"}
rise_set.type_name[4 + index] = twilight + ' twilight begin';
// gettext_config:{"id":"astronomical-twilight-end","mark_type":"combination_message_id"}
// gettext_config:{"id":"nautical-twilight-end","mark_type":"combination_message_id"}
// gettext_config:{"id":"civil-twilight-end","mark_type":"combination_message_id"}
rise_set.type_name[9 - index] = twilight + ' twilight end';
});
// ------------------------------------------------------------------------------------------------------//
// coordinates 統合 API
/**
* 太陽名稱。
*
* @type {String}
*/
var SUN_NAME = 'sun'.toLowerCase(),
/**
* 月亮名稱。
*
* @type {String}
*/
MOON_NAME = 'moon'.toLowerCase();
/**
* 天體位置統合 API。
*
* @param {String}object
* 天體名稱 (planets 行星).
* @param {Nunber|String|Date}date
* UT (or TT).
* @param {Array}local
* the observer's geographic location [ latitude (°), longitude
* (°), time zone (e.g., UTC+8: 8), elevation or geometric height
* (m) ]<br />
* 觀測者 [ 緯度（北半球為正,南半球為負）, 經度（從Greenwich向東為正，西為負）, 時區,
* 海拔標高(觀測者距海平面的高度) ]
* @param {Object}[options]
* 附加參數/設定特殊功能與選項:<br />
* {Boolean}options.TT: date is TT instead of UT.
*
* @constructor
*/
function Coordinates(object, date, local, options) {
// object name
this.object = object = Coordinates.normalize_object(object);
// 先行載入必須的 terms。
// 對 sun, moon 特別處理。
if (object === MOON_NAME) {
if (!LEA406_loaded('V'))
LEA406_load_terms('V');
if (!LEA406_loaded('U'))
LEA406_load_terms('U');
if (local && !LEA406_loaded('R'))
LEA406_load_terms('R');
} else if (object !== SUN_NAME) {
object = VSOP87.object_name(object);
if (!(object in VSOP87_terms))
VSOP87_load_terms(object);
}
object = VSOP87.object_name(solar_terms_object);
if (!(object in VSOP87_terms))
VSOP87_load_terms(object);
// use google map longitude latitude picker
if (local)
this.local = local;
// 紀錄時間。
this.JD = Number.isFinite(date) ? date : library_namespace.Julian_day
.JD(date);
if (options && options.TT)
this.UT = UT_of(this.TT = this.JD);
else
this.TT = TT_of(this.UT = this.JD);
}
_.celestial_coordinates = Coordinates;
Coordinates.object_alias = {
solar : SUN_NAME,
lunar : MOON_NAME
};
// normalize object name
Coordinates.normalize_object = function(name) {
name = name.toLowerCase();
if (name in Coordinates.object_alias)
name = Coordinates.object_alias[name];
return name;
};
/**
* 設定 coordinates。
*
* @param {String}type
* one of DSGETH
* @param {Object}coordinates
* coordinates get through get_horizontal()
*
* @returns {Object}coordinates
*
* @inner
*/
function set_coordinates(type, coordinates) {
// reset property to cache.
Object.defineProperty(this, type, {
value : coordinates
});
return coordinates;
}
/**
* 一次把 E地心赤道, T站心赤道, H站心地平 全部設定完。
*
* @param {Object}coordinates
* coordinates get through get_horizontal()
*
* @inner
*/
function set_horizontal_coordinates(coordinates) {
this.s('E', [ normalize_radians(coordinates.α),
//
normalize_radians(coordinates.δ, true), coordinates.Δ ]);
this.s('H', coordinates.Az ? [ normalize_radians(coordinates.Az),
normalize_radians(coordinates.Alt, true) ]
// 站心地平座標 .Az, .Alt 比較可能未設定。
: undefined);
// the equatorial horizontal parallax of the body in radians.
// 天體的赤道地平視差.
// CeL.format_radians(coordinates.π)
if (coordinates.π)
this.π = coordinates.π;
// LHA: local hour angle (in radians) 本地地心時角。
if (coordinates.LHA)
this.LHA = coordinates.LHA;
// elongation Ψ of the planet, its angular distance to the Sun
// https://en.wikipedia.org/wiki/Elongation_%28astronomy%29
// 行星的距角，即地心看行星與太陽的角距離。
if (coordinates.Ψ)
this.elongation = coordinates.Ψ;
// semi-diameter (in arcseconds). 天體的中心視半徑。
this.semidiameter = semidiameter(coordinates, this.object);
this.s('T', (coordinates = coordinates.T) ? [
normalize_radians(coordinates[0]),
normalize_radians(coordinates[1], true) ]
// coordinates.T 可能未設定。
: undefined);
}
/**
* @inner
*/
function get_dimension(coordinates, type) {
if (type.includes('longitude'))
return coordinates[0];
if (type.includes('latitude'))
return coordinates[1];
return coordinates;
}
/**
* 取得指定類型之座標。
*
* @param {String}type
* 指定類型/symbols
*
* @returns {Object|Number}座標
*
* @see https://en.wikipedia.org/wiki/Celestial_coordinate_system#Coordinate_systems
*/
function get_coordinates(type) {
if (typeof type === 'string' && type.includes(','))
type = type.split(/,+/);
if (Array.isArray(type))
return type.map(get_coordinates.bind(this));
type = String(type).toLowerCase().split(/[\s\-]+/).join(' ');
if (type.includes('λ'))
return this.G[0];
if (type.includes('β'))
return this.G[1];
if (type.includes('distance'))
return this.G[2];
if (type.includes('α'))
return this.E[0];
// 注意: 'Δ'.toLowerCase() === 'δ'
if (type.includes('δ'))
return this.E[1];
// Azimuth, Altitude
if (type.includes('az'))
return this.H && this.H[0];
if (type.includes('alt'))
return this.H && this.H[1];
if (type.includes('dynamic'))
return get_dimension(this.D, type);
// after detect dynamical
if (type.includes('heliocentric'))
return get_dimension(this.S, type);
if (type.includes('horizontal'))
return get_dimension(this.H, type);
// after detect horizontal
if (type.includes('topocentric'))
return get_dimension(this.T, type);
// after detect heliocentric, topocentric
if (type.includes('equatorial'))
return get_dimension(this.E, type);
// after detect equatorial
if (type.includes('geocentric') || type.includes('ecliptic'))
return get_dimension(this.G, type);
// TODO: rectangular
if ((type[0] in this)
//
&& typeof this[type[0]] !== 'function')
return this[type[0]];
// 只輸入經緯度時，預設當作 G地心視黃道: 地心視黃經/地心視黃緯
type = get_dimension(this.G, type);
if (typeof type === 'number')
return type;
}
Object.defineProperties(Coordinates.prototype, {
s : {
enumerable : false,
value : set_coordinates
},
sh : {
enumerable : false,
value : set_horizontal_coordinates
},
c : {
value : get_coordinates
}
});
// ----------------------------------------------------------------------------
// 計算順序:
// @see
// https://github.com/kanasimi/IAU-SOFA/blob/master/doc/sofa_ast_c.pdf
// :: VSOP87 進入點→
// 日心黃道: D日心瞬時黃道 by VSOP87
// (太陽: 日心黃道: FK5) (FK5 2選1)
// (天體/行星: S日心視黃道:修正光行時及光行差) (修正光行時及光行差 2選1)
// 地心直角黃道座標 = 天體S日心視黃道 - 地球S日心視黃道
// G地心視黃道: 球座標
// :: LEA406 進入點: 計算月亮位置(地心瞬時黃道坐標)
// (天體/行星: G地心視黃道: FK5? why here?) (FK5 2選1)
// (G地心視黃道: 修正月亮光行時及太陽光行差) (修正光行時及光行差 2選1)
// G地心視黃道: 修正地球章動 nutation。
//
// E地心赤道座標:
// topocentric(本地站心)(T站心赤道): 修正恆星時/經緯度/時角, 行星視差
// H站心地平座標: 修正大氣折射
// D日心瞬時黃道 heliocentric dynamical ecliptic coordinate system
// [ longitude 黃經(radians), latitude 黃緯(radians), distance 距離(AU) ]
Coordinates.D = function() {
var coordinates;
if (this.object === MOON_NAME) {
// LEA406 計算月亮位置(地心瞬時黃道坐標)
coordinates = LEA406(this.TT, {
FK5 : false
});
coordinates = [
normalize_radians(coordinates.V + TURN_TO_RADIANS / 2),
normalize_radians(-coordinates.B, true), coordinates.R ];
} else if (this.object === SUN_NAME)
// 日心瞬時黃道以太陽為中心。
coordinates = [ 0, 0, 0 ];
else {
var tmp_c = object_coordinates(this.TT, this.object, {
equatorial : true,
local : this.local,
elongation : true
});
// S日心視黃道 heliocentric ecliptic coordinate system
coordinates = tmp_c.S;
this.s('S', [ normalize_radians(coordinates.L),
normalize_radians(coordinates.B, true), coordinates.R ]);
coordinates = tmp_c;
this.s('G', [ normalize_radians(coordinates.λ),
normalize_radians(coordinates.β, true), coordinates.Δ ]);
this.sh(coordinates);
// D日心瞬時黃道 heliocentric dynamical ecliptic coordinate system
coordinates = tmp_c.D;
coordinates
//
= [ normalize_radians(coordinates.L),
normalize_radians(coordinates.B, true), coordinates.R ];
}
return this.s('D', coordinates);
};
// S日心視黃道 heliocentric ecliptic coordinate system
// [ longitude 黃經(radians), latitude 黃緯(radians), distance 距離(AU) ]
Coordinates.S = function() {
var coordinates;
if (this.object === MOON_NAME) {
coordinates = this.G;
coordinates = dynamical_to_FK5({
L : coordinates[0],
B : coordinates[1]
}, Julian_century(this.TT) / 10);
coordinates = [ coordinates.L, coordinates.B, this.G[2] ];
} else if (this.object === SUN_NAME)
// 日心黃道以太陽為中心。
coordinates = [ 0, 0, 0 ];
else {
return this.D && this.S;
}
return this.s('S', coordinates);
};
// G地心視黃道 geocentric solar ecliptic coordinate system
// [ longitude λ黃經(radians), latitude β黃緯(radians), distance 距離(AU)
// ]
Coordinates.G = function() {
var coordinates;
if (this.object === MOON_NAME) {
coordinates = lunar_coordinates(this.TT, {
equatorial : true,
local : this.local,
elongation : true
});
this.sh(coordinates);
coordinates
//
= [ coordinates.λ, coordinates.β, coordinates.Δ ];
} else if (this.object === SUN_NAME) {
coordinates = solar_coordinates(this.TT, {
equatorial : true,
local : this.local,
elongation : true
});
this.sh(coordinates);
// coordinates.apparent or use coordinates.L
coordinates = [ coordinates.apparent * DEGREES_TO_RADIANS,
coordinates.β, coordinates.Δ ];
} else {
return this.D && this.G;
}
return this.s('G', coordinates);
};
// E地心赤道 geocentric equatorial coordinate system
// [ right ascension α赤經(radians), declination δ赤緯(radians),
// distance 距離(AU) ]
Coordinates.E = function() {
// eval
return this.G && this.E;
};
// T站心赤道 topocentric equatorial coordinate system
// [ right ascension α赤經(radians), declination δ赤緯(radians) ]
Coordinates.T = function() {
// eval
return this.G && this.T;
};
// H站心地平 topocentric horizontal coordinate system
// [ Azimuth (Az) 方位角又稱地平經度, Altitude (Alt) 高度角或仰角又稱地平緯度 ]
Coordinates.H = function() {
// eval
return this.G && this.H;
};
// D日心瞬時黃道 heliocentric dynamical ecliptic coordinate system
// S日心視黃道 heliocentric ecliptic coordinate system
// G地心視黃道 geocentric solar ecliptic coordinate system
// E地心赤道 geocentric equatorial coordinate system
// T站心赤道 topocentric equatorial coordinate system
// H站心地平 topocentric horizontal coordinate system
'DSGETH'.split('').forEach(function(type) {
if (Object.defineProperty[library_namespace.env.not_native_keyword])
// e.g., IE8
return;
// type: to [ radians, radians, AU ]
Object.defineProperty(Coordinates.prototype, type, {
enumerable : true,
get : Coordinates[type]
});
// type + 'd': to [ degrees, degrees, meters ]
Object.defineProperty(Coordinates.prototype, type + 'd', {
enumerable : true,
get : function() {
var c = [ this[type][0] / DEGREES_TO_RADIANS,
//
this[type][1] / DEGREES_TO_RADIANS ];
if (this[type].length > 2)
c.push(this[type][2] * AU_TO_METERS);
this.s(type + 'd', c);
return c;
}
});
});
// 天球坐標系統
// Celestial coordinate system
// https://en.wikipedia.org/wiki/Celestial_coordinate_system
// International Celestial Reference System
// 國際天體參考系統（ICRS）原點在太陽系重心
// 中心/質量中心 center point (origin)
// https://en.wikipedia.org/wiki/Centre_%28geometry%29
// H 日心 heliocentric
// G 地心 geocentric, Earth-centered
// T 本地站心,觀測中心座標系,視心 topocentric, local, observer's
// 基礎平面/基面 fundamental plane of reference
// https://en.wikipedia.org/wiki/Fundamental_plane_%28spherical_coordinates%29
// https://en.wikipedia.org/wiki/Plane_of_reference
// https://en.wikipedia.org/wiki/Celestial_coordinate_system#Coordinate_systems
// D 瞬時黃道 dynamical ecliptic
// S 黃道 ecliptic, solar
// E 赤道 equatorial, celestial equator
// H 地平 horizontal, observer's horizon
//
// G 銀道坐標系，又作銀道座標系 galactic
// SG 超星系坐標系統 Supergalactic
// position, seen position
// https://en.wikipedia.org/wiki/Apparent_place
// A 視 apparent
// T 真 true
// coordinates
// S 球 spherical
// e.g., 日心黃道直角座標系
// R 直角正交 rectangular, cartesian (three-dimensional), orthogonality
// 維度 dimension
// https://en.wikipedia.org/wiki/Dimension
// https://en.wikipedia.org/wiki/Geographic_coordinate_system
// L 經度 longitude
// B 緯度 latitude
// R 距離 radius or elevation
//
// X →x
// Y ↑y
// Z ↗z
// ----------------------------------------------------------------------------------------------------------------------------------------------//
/**
* 計算月亮近地點 perigee 和遠地點 apogee 的修正量。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 355. Chapter 50 Perigee and apogee of the Moon<br />
*
* @param {Array}coefficients
* 修正量係數。
* @param {Array}c2
* 修正量係數2: [ D, M, F, T ]
* @param {Number}starts
* 初始值
* @param {Boolean}parallax
* is parallax
*
* @returns {Number}月亮近地點 perigee 和遠地點 apogee 的值。
*
* @inner
*/
function lunar_perigee_apogee_Δ
//
(coefficients, c2, starts, parallax) {
return coefficients.reduce(function(Δ, c) {
// 三角函數係數, T之係數.
var tc = 0, Tc = c[3];
if (c[0])
// D
tc += c[0] * c2[0];
if (c[1])
// M
tc += c[1] * c2[1];
if (c[2])
// F
tc += c[2] * c2[2];
if (c[4])
Tc += c[4] * c2[3];
return Δ + Tc * (parallax ? Math.cos(tc) : Math.sin(tc));
}, starts);
}
/**
* 月亮的近地點 perigee 和遠地點 apogee。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 355. Chapter 50 Perigee and apogee of the Moon<br />
*
* @param {Number}year_month
* 帶小數點的年數，例如1987.25表示1987年3月末。
* @param {Boolean}apogee
* get apogee 遠地點
*
* @returns {Array}[ TT in JD, 距離 in km, Moon's Equatorial Horizontal
* Parallax in radians ]
*
* @see https://github.com/helixcn/skycalc/blob/master/src/AAMoonPerigeeApogee.cpp
*/
function lunar_perigee_apogee(year_month, apogee) {
// Mean time of perigee or apogee.
// k是整數對應近點，增加0.5則是遠點。其它k值無意義。
// 當k=0時，對應1999年12月22日的近點。
/**
* 1999.971:
* <q>1999 + (2451534.6698 - CeL.Julian_day.from_YMD(1999, 1, 1, 'CE')) / (DAYS_OF_JULIAN_CENTURY / 100) = 1999.9710329911014363</q>
* 26.511:
* <q>DAYS_OF_JULIAN_CENTURY / 100 / 27.55454989 * 2 = 13.25552409522593 * 2 = 26.51104819045186</q>
*/
var k = (year_month - 1999.971) * 26.511;
k = apogee ? Math.round((k - 1) / 2) + .5 : Math.round(k / 2);
// T is the time in Julian centuries since the epoch 2000.0.
var T = k / 1325.55,
// 修正量係數2
c2 = [ polynomial_value(lunar_perigee_apogee_D, T),
polynomial_value(lunar_perigee_apogee_M, T),
polynomial_value(lunar_perigee_apogee_F, T), T ],
// the time of the mean perigee or apogee
// 計算近點或遠點時刻
// 與ELP-2000/82理論的精準結果比較，最大誤差如下：
// 時間的誤差：近地點31分，遠地點3分
// 視差的誤差：近地點0″.124，遠地點0″.051
// 相應的距離誤差分別是：12km和6km
TT_JD = lunar_perigee_apogee_Δ(apogee ? apogee_coefficients_JD
: perigee_coefficients_JD, c2, polynomial_value(
lunar_perigee_apogee_T, T)),
// The corresponding value of the Moon's equatorial horizontal
// Moon's Equatorial Horizontal Parallax 月亮赤道地平視差修正量 in radians
parallax = lunar_perigee_apogee_Δ(apogee ? apogee_coefficients_parallax
: perigee_coefficients_parallax, c2, 0, true)
* ARCSECONDS_TO_RADIANS;
if (false)
console.log('→ starts ' + TT_JD + ' ('
+ library_namespace.JD_to_Date(TT_JD).format('CE') + '): '
+ LEA406(TT_JD, {
km : true
}).R);
// CeL.LEA406.load_terms('R');
// find_minima() 會因輸入而有秒單位的誤差偏移。
TT_JD = library_namespace.find_minima(function(TT_JD) {
var distance = LEA406(TT_JD, {
km : true
}).R;
if (false)
console.log(TT_JD + ' ('
//
+ library_namespace.JD_to_Date(TT_JD).format('CE') + '): '
+ distance);
// find_minima: 求取局部極小值
return apogee ? -distance : distance;
},
// (31+1)/60/24≈1/45
TT_JD - 1 / 45, TT_JD + 1 / 45);
if (apogee)
TT_JD[1] = -TT_JD[1];
TT_JD.push(parallax);
// [ TT in JD, 距離 in km, 月亮赤道地平視差修正量 in radians ]
return TT_JD;
}
_.lunar_perigee_apogee = lunar_perigee_apogee;
// ----------------------------------------------------------------------------------------------------------------------------------------------//
/**
* data section: 以下為計算用天文數據。
*/
// ------------------------------------------------------------------------------------------------------//
// terms for ΔT
/**
* terms for function ΔT()
*
* Reference 資料來源/資料依據:<br />
* <a href="http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html"
* accessdate="2015/3/26 20:8">NASA - Polynomial Expressions for Delta T</a><br />
* <a href="http://www.staff.science.uu.nl/~gent0113/deltat/deltat_old.htm"
* accessdate="2015/3/26 20:7">Delta T: Pre-Telescopic Era</a>
*
* @inner
*/
var ΔT_year_start = [ 2150, 2050, 2005, 1986, 1961, 1941, 1920, 1900, 1860,
1800, 1700, 1600, 500, -500 ],
// http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html
// All values of ΔT based on Morrison and Stephenson [2004]
// assume a value for the Moon's secular acceleration of -26
// arcsec/cy².
ΔT_year_base = [ 1820, 1820, 2000, 2000, 1975, 1950, 1920, 1900, 1860,
1800, 1700, 1600, 1000, 0 ],
// 為統合、方便計算，在演算方法上作了小幅變動。
ΔT_coefficients = [
[ -20, 0, 32 ],
[ -205.724, 56.28, 32 ],
[ 62.92, 32.217, 55.89 ],
[ 63.86, 33.45, -603.74, 1727.5, 65181.4, 237359.9 ],
[ 45.45, 106.7, -10000 / 260, -1000000 / 718 ],
[ 29.07, 40.7, -10000 / 233, 1000000 / 2547 ],
[ 21.20, 84.493, -761.00, 2093.6 ],
[ -2.79, 149.4119, -598.939, 6196.6, -19700 ],
[ 7.62, 57.37, -2517.54, 16806.68, -44736.24, 10000000000 / 233174 ],
[ 13.72, -33.2447, 68.612, 4111.6, -37436, 121272, -169900, 87500 ],
[ 8.83, 16.03, -59.285, 133.36, -100000000 / 1174000 ],
[ 120, -98.08, -153.2, 1000000 / 7129 ],
[ 1574.2, -556.01, 71.23472, 0.319781, -0.8503463, -0.005050998,
0.0083572073 ],
[ 10583.6, -1014.41, 33.78311, -5.952053, -0.1798452, 0.022174192,
0.0090316521 ] ];
// ------------------------------------------------------------------------------------------------------//
// terms for obliquity 轉軸傾角
/**
* IAU2006 obliquity coefficients.<br />
* terms for function mean_obliquity_IAU2006()
*
* Reference 資料來源/資料依據:
* https://github.com/kanasimi/IAU-SOFA/blob/master/src/obl06.c
*
* @inner
*/
var IAU2006_obliquity_coefficients = [
// Astronomical Almanac 2011:
// Mean obliquity of the ecliptic, epsilon_0:
// epsilon_J2000.0 = 84381.406″ ± 0.001″
84381.406, -46.836769, -0.0001831, 0.00200340, -0.000000576, -0.0000000434 ];
/**
* terms for function equinox()
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 章動及黃赤交角.
*
* @inner
*/
var Laskar_obliquity_coefficients = [
// ε = 23° 26′ 21.448″ - 4680.93″ T - 1.55″ T²
// + 1999.25″ T³ - 51.38″ T⁴ - 249.67″ T⁵
// - 39.05″ T⁶ + 7.12″ T⁷ + 27.87″ T⁸ + 5.79″ T⁹ + 2.45″ T¹⁰
23 * 60 * 60 + 26 * 60 + 21.448, -4680.93, -1.55, 1999.25, -51.38, -249.67,
-39.05, 7.12, 27.87, 5.79, 2.45 ];
Laskar_obliquity_coefficients.forEach(function(v, index) {
Laskar_obliquity_coefficients[index] = v / DEGREES_TO_ARCSECONDS;
});
// ------------------------------------------------------------------------------------------------------//
// terms for precession
var
/**
* terms for function ecliptic_precession()
*
* Reference 資料來源/資料依據:<br />
* Kai Tang (2015). A long time span relativistic precession model of the
* Earth.<br />
* Table B.1 The Periodic Terms in PA, QA.
*
* @inner
*/
唐凯_ecliptic_precession_terms = [ [ -3720, 1260, -1290, -3698, 68975 ],
[ 657, -2585, 2508, 736, 235535 ],
[ -2068, -302, 288, -2056, 72488 ],
[ -855, -570, 548, -838, 192342 ], [ 438, 338, -334, 435, 49178 ],
[ 309, 255, -225, 289, 67341 ], [ 217, 322, -191, 5, 424863 ],
[ 168, -313, 288, 183, 65723 ], [ -278, 130, -112, -294, 173673 ],
[ -278, -79, 89, -285, 75817 ], [ -77, 258, -157, -194, 255871 ],
[ -24, 124, -106, -33, 64138 ], [ 29, 3, -91, 187, 496536 ],
[ -135, -153, 176, -151, 70820 ], [ -85, 124, -257, 187, 1080090 ],
[ 153, -276, 395, -117, 1309223 ], [ 14, -12, 77, -94, 663722 ],
[ 55, -11, 46, 20, 214239 ], [ 81, 39, -41, 92, 77777 ],
[ -55, -16, 19, -61, 80440 ], [ 6, -88, -50, 206, 367386 ],
[ -22, 107, 16, -189, 321366 ], [ 5, -130, 24, 141, 284995 ],
[ 11, -28, 8, 27, 164405 ], [ 15, 19, -19, 19, 83199 ] ],
/**
* terms for function precession()
*
* Reference 資料來源/資料依據:<br />
* Kai Tang (2015). A long time span relativistic precession model of the
* Earth.<br />
* Table B.2 The Periodic Terms in pA, εA.
*
* @inner
*/
唐凯_precession_terms = [ [ -6653, -2199, 739, -2217, 40938 ],
[ -3349, 541, -175, -1126, 39803 ],
[ 1526, -1218, 376, 469, 53789 ], [ 227, 874, -313, 84, 28832 ],
[ -370, 256, -91, -129, 29639 ], [ 518, -353, 110, 174, 41557 ],
[ 324, 542, -174, 107, 42171 ], [ -482, 200, -72, -158, 38875 ],
[ -46, -201, 63, -17, 42847 ], [ -140, -45, 16, -50, 30127 ],
[ -224, 404, -143, -69, 40316 ], [ 181, -98, 38, 55, 38379 ],
[ -121, 59, -24, -35, 37783 ], [ -9, -73, 27, -6, 28550 ],
[ 35, -42, 15, 13, 27300 ], [ 63, -35, 15, 16, 37225 ],
[ 56, -64, 15, 12, 20459 ], [ 18, -77, 18, 3, 20151 ],
[ -8, 41, -9, -13, 170984 ], [ 51, 9, -2, 16, 29197 ],
[ 3425, -2525, , , 1309223 ], [ -2951, 1938, , , 991814 ],
[ 2117, -704, , , 716770 ], [ 877, -993, , , 416787 ],
[ -805, 226, , , 554293 ], [ -710, -52, , , 371201 ],
[ 448, -33, , , 324763 ], [ -217, 111, , , 122237 ],
[ 224, -55, , , 94370 ], [ -228, 37, , , 287695 ] ];
唐凯_ecliptic_precession_terms
// 原數值: [ [ 5540″, -1.98e-4″ ], [ -1608″, -2.06e-4 ] ]
// 已轉成適用於 Julian century 使用。
.init = [ [ 5540, -0.0198 ], [ -1608, -0.0206 ] ];
唐凯_ecliptic_precession_terms.forEach(function(term) {
// 100: 轉成適用於 Julian century 使用。
// Julian year (the time reckoned from J2000.0 in years)
// → Julian century
term[4] = 100 * TURN_TO_RADIANS / term[4];
});
唐凯_precession_terms
// 原數值: [ [ 6221″, 50″.44766 ], [ 83953″, -8.9e-5″ ] ]
// 已轉成適用於 Julian century 使用。
.init = [ [ 6221, 5044.766 ], [ 83953, -0.0089 ] ];
唐凯_precession_terms.forEach(function(term) {
// 100: 轉成適用於 Julian century 使用。
// Julian year (the time reckoned from J2000.0 in years)
// → Julian century
term[4] = 100 * TURN_TO_RADIANS / term[4];
});
// ------------------------------------------------------------------------------------------------------//
// 章動 nutation
var IAU2000B_nutation_offset_Δψ = -0.135,
//
IAU2000B_nutation_offset_Δε = 0.388;
(function() {
var d = TURN_TO_RADIANS / ONE_DAY_SECONDS / 1e3;
IAU2000B_nutation_offset_Δψ *= d;
IAU2000B_nutation_offset_Δε *= d;
})();
/**
* terms for function nutation()
*
* Reference 資料來源/資料依據:<br />
* Nutation, IAU 2000B model.
* https://github.com/kanasimi/IAU-SOFA/blob/master/src/nut00b.c
*
* @see http://www.neoprogrammics.com/nutations/nutations_1980_2000b/index.php
*
* @inner
*/
var IAU2000B_nutation_parameters = [
// el: Mean anomaly of the Moon. 月亮平近點角
[ 485868.249036, 1717915923.2178
// , 31.8792, 0.051635, -0.00024470
],
// elp(el'): Mean anomaly of the Sun. 太陽平近點角
[ 1287104.79305, 129596581.0481
// , -0.5532, 0.000136, -0.00001149
],
// f: Mean argument of the latitude of the Moon. 月亮平升交角距
[ 335779.526232, 1739527262.8478
// , -12.7512, -0.001037, 0.00000417
],
// d: Mean elongation of the Moon from the Sun. 日月平角距
[ 1072260.70369, 1602961601.2090
// , -6.3706, 0.006593, -0.00003169
],
// om(Ω): Mean longitude of the ascending node of the Moon.
// 月亮升交點平黃經
[ 450160.398036, -6962890.5431
// , 7.4722, 0.007702, -0.00005939
] ],
// 0–4: coefficients of l,l',F,D,Om
// int nl,nlp,nf,nd,nom;
// 5–7: longitude sin, t*sin, cos coefficients
// double ps,pst,pc;
// 8–10: obliquity cos, t*cos, sin coefficients
// double ps,pst,pc;
IAU2000B_nutation_terms = [
/* 1-10 */
[ 0, 0, 0, 0, 1, -172064161, -174666, 33386,
// Astronomical Almanac 2011:
// Constant of nutation at epoch J2000.0:
// N = 9.2052331″
92052331, 9086, 15377 ],
[ 0, 0, 2, -2, 2, -13170906, -1675, -13696, 5730336, -3015, -4587 ],
[ 0, 0, 2, 0, 2,
//
-2276413, -234, 2796, 978459, -485, 1374 ],
[ 0, 0, 0, 0, 2, 2074554, 207, -698, -897492, 470, -291 ],
[ 0, 1, 0, 0, 0,
//
1475877, -3633, 11817, 73871, -184, -1924 ], [ 0, 1, 2, -2, 2,
//
-516821, 1226, -524, 224386, -677, -174 ],
[ 1, 0, 0, 0, 0, 711159, 73, -872, -6750, 0, 358 ],
[ 0, 0, 2, 0, 1, -387298, -367, 380, 200728, 18, 318 ],
[ 1, 0, 2, 0, 2, -301461, -36, 816, 129025, -63, 367 ],
[ 0, -1, 2, -2, 2, 215829, -494, 111, -95929, 299, 132 ],
/* 11-20 */
[ 0, 0, 2, -2, 1, 128227, 137, 181, -68982, -9, 39 ],
[ -1, 0, 2, 0, 2, 123457, 11, 19, -53311, 32, -4 ],
[ -1, 0, 0, 2, 0, 156994, 10, -168, -1235, 0, 82 ],
[ 1, 0, 0, 0, 1, 63110, 63, 27, -33228, 0, -9 ],
[ -1, 0, 0, 0, 1, -57976, -63, -189, 31429, 0, -75 ],
[ -1, 0, 2, 2, 2, -59641, -11, 149, 25543, -11, 66 ],
[ 1, 0, 2, 0, 1, -51613, -42, 129, 26366, 0, 78 ],
[ -2, 0, 2, 0, 1, 45893, 50, 31, -24236, -10, 20 ],
[ 0, 0, 0, 2, 0, 63384, 11, -150, -1220, 0, 29 ],
[ 0, 0, 2, 2, 2, -38571, -1, 158, 16452, -11, 68 ],
/* 21-30 */
[ 0, -2, 2, -2, 2, 32481, 0, 0, -13870, 0, 0 ],
[ -2, 0, 0, 2, 0, -47722, 0, -18, 477, 0, -25 ],
[ 2, 0, 2, 0, 2, -31046, -1, 131, 13238, -11, 59 ],
[ 1, 0, 2, -2, 2, 28593, 0, -1, -12338, 10, -3 ],
[ -1, 0, 2, 0, 1, 20441, 21, 10, -10758, 0, -3 ],
[ 2, 0, 0, 0, 0, 29243, 0, -74, -609, 0, 13 ],
[ 0, 0, 2, 0, 0, 25887, 0, -66, -550, 0, 11 ],
[ 0, 1, 0, 0, 1, -14053, -25, 79, 8551, -2, -45 ],
[ -1, 0, 0, 2, 1, 15164, 10, 11, -8001, 0, -1 ],
[ 0, 2, 2, -2, 2, -15794, 72, -16, 6850, -42, -5 ],
/* 31-40 */
[ 0, 0, -2, 2, 0, 21783, 0, 13, -167, 0, 13 ],
[ 1, 0, 0, -2, 1, -12873, -10, -37, 6953, 0, -14 ],
[ 0, -1, 0, 0, 1, -12654, 11, 63, 6415, 0, 26 ],
[ -1, 0, 2, 2, 1, -10204, 0, 25, 5222, 0, 15 ],
[ 0, 2, 0, 0, 0, 16707, -85, -10, 168, -1, 10 ],
[ 1, 0, 2, 2, 2, -7691, 0, 44, 3268, 0, 19 ],
[ -2, 0, 2, 0, 0, -11024, 0, -14, 104, 0, 2 ],
[ 0, 1, 2, 0, 2, 7566, -21, -11, -3250, 0, -5 ],
[ 0, 0, 2, 2, 1, -6637, -11, 25, 3353, 0, 14 ],
[ 0, -1, 2, 0, 2, -7141, 21, 8, 3070, 0, 4 ],
/* 41-50 */
[ 0, 0, 0, 2, 1, -6302, -11, 2, 3272, 0, 4 ],
[ 1, 0, 2, -2, 1, 5800, 10, 2, -3045, 0, -1 ],
[ 2, 0, 2, -2, 2, 6443, 0, -7, -2768, 0, -4 ],
[ -2, 0, 0, 2, 1, -5774, -11, -15, 3041, 0, -5 ],
[ 2, 0, 2, 0, 1, -5350, 0, 21, 2695, 0, 12 ],
[ 0, -1, 2, -2, 1, -4752, -11, -3, 2719, 0, -3 ],
[ 0, 0, 0, -2, 1, -4940, -11, -21, 2720, 0, -9 ],
[ -1, -1, 0, 2, 0, 7350, 0, -8, -51, 0, 4 ],
[ 2, 0, 0, -2, 1, 4065, 0, 6, -2206, 0, 1 ],
[ 1, 0, 0, 2, 0, 6579, 0, -24, -199, 0, 2 ],
/* 51-60 */
[ 0, 1, 2, -2, 1, 3579, 0, 5, -1900, 0, 1 ],
[ 1, -1, 0, 0, 0, 4725, 0, -6, -41, 0, 3 ],
[ -2, 0, 2, 0, 2, -3075, 0, -2, 1313, 0, -1 ],
[ 3, 0, 2, 0, 2, -2904, 0, 15, 1233, 0, 7 ],
[ 0, -1, 0, 2, 0, 4348, 0, -10, -81, 0, 2 ],
[ 1, -1, 2, 0, 2, -2878, 0, 8, 1232, 0, 4 ],
[ 0, 0, 0, 1, 0, -4230, 0, 5, -20, 0, -2 ],
[ -1, -1, 2, 2, 2, -2819, 0, 7, 1207, 0, 3 ],
[ -1, 0, 2, 0, 0, -4056, 0, 5, 40, 0, -2 ],
[ 0, -1, 2, 2, 2, -2647, 0, 11, 1129, 0, 5 ],
/* 61-70 */
[ -2, 0, 0, 0, 1, -2294, 0, -10, 1266, 0, -4 ],
[ 1, 1, 2, 0, 2, 2481, 0, -7, -1062, 0, -3 ],
[ 2, 0, 0, 0, 1, 2179, 0, -2, -1129, 0, -2 ],
[ -1, 1, 0, 1, 0, 3276, 0, 1, -9, 0, 0 ],
[ 1, 1, 0, 0, 0, -3389, 0, 5, 35, 0, -2 ],
[ 1, 0, 2, 0, 0, 3339, 0, -13, -107, 0, 1 ],
[ -1, 0, 2, -2, 1, -1987, 0, -6, 1073, 0, -2 ],
[ 1, 0, 0, 0, 2, -1981, 0, 0, 854, 0, 0 ],
[ -1, 0, 0, 1, 0, 4026, 0, -353, -553, 0, -139 ],
[ 0, 0, 2, 1, 2, 1660, 0, -5, -710, 0, -2 ],
/* 71-77 */
[ -1, 0, 2, 4, 2, -1521, 0, 9, 647, 0, 4 ],
[ -1, 1, 0, 1, 1, 1314, 0, 0, -700, 0, 0 ],
[ 0, -2, 2, -2, 1, -1283, 0, 0, 672, 0, 0 ],
[ 1, 0, 2, 2, 1, -1331, 0, 8, 663, 0, 4 ],
[ -2, 0, 2, 2, 2, 1383, 0, -2, -594, 0, -2 ],
[ -1, 0, 0, 0, 2, 1405, 0, 4, -610, 0, 2 ],
[ 1, 1, 2, -2, 2, 1290, 0, 0, -556, 0, 0 ] ];
/**
* terms for function nutation()
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* table 22.A.<br />
*
* @see https://github.com/kanasimi/IAU-SOFA/blob/master/src/nut80.c
*
* @inner
*/
// IAU1980_nutation_parameters 單位是度。
var IAU1980_nutation_parameters = [
// 平距角(日月對地心的角距離)：
// D = 297.85036 + 445267.111480*T - 0.0019142*T² +
// T³/189474
[ 297.85036, 445267.111480, -0.0019142, 1 / 189474 ],
// 太陽（地球）平近點角：
// M = 357.52772 + 35999.050340*T - 0.0001603*T² -
// T³/300000
[ 357.52772, 35999.050340, -0.0001603, -1 / 300000 ],
// 月球平近點角：
// M′= 134.96298 + 477198.867398*T + 0.0086972*T² +
// T³/56250
[ 134.96298, 477198.867398, 0.0086972, 1 / 56250 ],
// 月球緯度參數：
// F = 93.27191 + 483202.017538*T - 0.0036825*T² +
// T³/327270
[ 93.27191, 483202.017538, -0.0036825, 1 / 327270 ],
// 黃道與月球平軌道升交點黃經，從Date黃道平分點開始測量：
// Ω= 125.04452 - 1934.136261*T + 0.0020708*T² +
// T³/450000
[ 125.04452, -1934.136261, 0.0020708, 1 / 450000 ] ],
// 這些項來自 IAU 1980 章動理論，忽略了係數小於0″.0003的項。
// https://github.com/kanasimi/IAU-SOFA/blob/master/src/nut80.c
IAU1980_nutation_terms = [ [ 0, 0, 0, 0, 1, -171996, -1742, 92025, 89 ],
[ -2, 0, 0, 2, 2, -13187, -16, 5736, -31 ],
[ 0, 0, 0, 2, 2, -2274, -2, 977, -5 ],
[ 0, 0, 0, 0, 2, 2062, 2, -895, 5 ],
[ 0, 1, 0, 0, 0, 1426, -34, 54, -1 ],
[ 0, 0, 1, 0, 0, 712, 1, -7, 0 ],
[ -2, 1, 0, 2, 2, -517, 12, 224, -6 ],
[ 0, 0, 0, 2, 1, -386, -4, 200, 0 ],
[ 0, 0, 1, 2, 2, -301, 0, 129, -1 ],
[ -2, -1, 0, 2, 2, 217, -5, -95, 3 ],
[ -2, 0, 1, 0, 0, -158, 0, 0, 0 ],
[ -2, 0, 0, 2, 1, 129, 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, 1, -33, 0 ],
[ 2, 0, -1, 2, 2, -59, 0, 26, 0 ],
[ 0, 0, -1, 0, 1, -58, -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, -1, 0, 0 ],
[ 2, 0, -1, 0, 1, 16, 0, -8, 0 ], [ -2, 2, 0, 2, 2, -16, 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 ] ];
// ------------------------------------------------------------------------------------------------------//
// Sun's aberration. 太陽地心黃經光行差修正量。
/**
* constant term of Sun's aberration
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 167–168. chapter 太陽位置計算.
*
* If needed with respect to the mean equinox of the date instead of to a
* fixed reference frame, the constant term 3548.193 should be replaced by
* 3548.330. 如果Δλ須是在Date黃道中的，則應把常數項3548.193換為3548.330
*
* The ICRF is a fixed reference frame. The FK5 based on fixed reference
* frame of J2000.0?
*
* @see http://blog.csdn.net/songgz/article/details/2680144<br />
* 通過數以千計的恆星位置，反推出春風點在天球上的位置，我們常說的FK5天球坐標系統就與它有關。
* @see https://en.wikipedia.org/wiki/Barycentric_celestial_reference_system<br />
* The orientation of the BCRS/ICRS axes also align within 0.02
* arcsecond of the Earth's mean equator and equinox for the Fifth
* Fundamental Catalog (FK5) J2000.0 epoch.
* @see http://aa.usno.navy.mil/faq/docs/ICRS_doc.php<br />
* The orientation of the ICRS axes is consistent with the equator and
* equinox of J2000.0 represented by the FK5, within the errors of the
* latter.
*
* @inner
*/
var sun_aberration_variation_constant = 3548.193,
/**
* coefficients of Sun's aberration
*
* Σ : Σ ([0] * sin ( [1] + [2] τ) )
*
* daily variation = sun_aberration_variation_constant + Σ(variation[0]) +
* Σ(variation[1])*τ + Σ(variation[2])*τ² + Σ(variation[3])*τ³
*
* τ的係數為359993.7、719987或1079981的週期項，與地球離心率相關。<br />
* τ的係數為4452671、9224660或4092677的週期項，與月球運動相關。<br />
* τ的係數為450369、225184、315560或675553的週期項，與金星攝動相關。<br />
* τ的係數為329645、659289、或299296的週期項，與火星攝動相關。
*
* @inner
*/
sun_aberration_variation = [
// τ⁰
[ [ 118.568, 87.5287, 359993.7286 ],
[ 2.476, 85.0561, 719987.4571 ],
[ 1.376, 27.8502, 4452671.1152 ],
[ 0.119, 73.1375, 450368.8564 ],
[ 0.114, 337.2264, 329644.6718 ],
[ 0.086, 222.5400, 659289.3436 ],
[ 0.078, 162.8136, 9224659.7915 ],
[ 0.054, 82.5823, 1079981.1857 ],
[ 0.052, 171.5189, 225184.4282 ],
[ 0.034, 30.3214, 4092677.3866 ],
[ 0.033, 119.8105, 337181.4711 ],
[ 0.023, 247.5418, 299295.6151 ],
[ 0.023, 325.1526, 315559.5560 ],
[ 0.021, 155.1241, 675553.2846 ] ],
// τ¹
[ [ 7.311, 333.4515, 359993.7286 ],
[ 0.305, 330.9814, 719987.4571 ],
[ 0.010, 328.5170, 1079981.1857 ] ],
// τ²
[ [ 0.309, 241.4518, 359993.7286 ],
[ 0.021, 205.0482, 719987.4571 ],
[ 0.004, 297.8610, 4452671.1152 ] ],
// τ³
[ [ 0.010, 154.7066, 359993.7286 ] ] ];
sun_aberration_variation.forEach(function(term) {
term.forEach(function(sub_term) {
sub_term[1] *= DEGREES_TO_RADIANS;
sub_term[2] *= DEGREES_TO_RADIANS;
});
});
// ------------------------------------------------------------------------------------------------------//
/**
* terms for function equinox()
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* chapter 分點和至點.<br />
*
* @inner
*/
// for years -1000 to 1000
var equinox_terms_before_1000 = [
// March equinox, 春分點時刻
[ 1721139.29189, 365242.13740, 0.06134, 0.00111, -0.00071 ],
// June Solstice, 夏至點時刻
[ 1721233.25401, 365241.72562, -0.05323, 0.00907, 0.00025 ],
// September equinox, 秋分點時刻
[ 1721325.70455, 365242.49558, -0.11677, -0.00297, 0.00074 ],
// December Solstice, 冬至點時刻
[ 1721414.39987, 365242.88257, -0.00769, -0.00933, -0.00006 ] ],
// for years 1000 to 3000
equinox_terms_after_1000 = [
// March equinox, 春分點時刻
[ 2451623.80984, 365242.37404, 0.05169, -0.00411, -0.00057 ],
// June Solstice, 夏至點時刻
[ 2451716.56767, 365241.62603, 0.00325, 0.00888, -0.00030 ],
// September equinox, 秋分點時刻
[ 2451810.21715, 365242.01767, -0.11575, 0.00337, 0.00078 ],
// December Solstice, 冬至點時刻
[ 2451900.05952, 365242.74049, -0.06223, -0.00823, 0.00032 ] ],
// 週期項
equinox_periodic_terms = [
//
[ 485, 324.96, 1934.136 ], [ 203, 337.23, 32964.467 ],
[ 199, 342.08, 20.186 ], [ 182, 27.85, 445267.112 ],
[ 156, 73.14, 45036.886 ], [ 136, 171.52, 22518.443 ],
[ 77, 222.54, 65928.934 ], [ 74, 296.72, 3034.906 ],
[ 70, 243.58, 9037.513 ], [ 58, 119.81, 33718.147 ],
[ 52, 297.17, 150.678 ], [ 50, 21.02, 2281.226 ],
[ 45, 247.54, 29929.562 ], [ 44, 325.15, 31555.956 ],
[ 29, 60.93, 4443.417 ], [ 18, 155.12, 67555.328 ],
[ 17, 288.79, 4562.452 ], [ 16, 198.04, 62894.029 ],
[ 14, 199.76, 31436.921 ], [ 12, 95.39, 14577.848 ],
[ 12, 287.11, 31931.756 ], [ 12, 320.81, 34777.259 ],
[ 9, 227.73, 1222.114 ], [ 8, 15.45, 16859.074 ] ];
// 把能先做的做一做，加快運算速度。
equinox_periodic_terms.forEach(function(terms) {
terms[1] *= DEGREES_TO_RADIANS;
terms[2] *= DEGREES_TO_RADIANS;
});
// ------------------------------------------------------------------------------------------------------//
// VSOP87 半解析（semi-analytic）理論 periodic terms
/**
* 這邊僅擷取行星 Earth 地球數值，以計算二十四節氣 (solar terms)。
*
* VSOP87_terms.earth[L黃經/B黃緯/R距離] = [L0:[[A,B,C],[A,B,C]]];
*
* simplified VSOP87 by Jean Meeus.
* 從VSOP87中取出一些主要項(詳見附錄II)，利用它計算得到的太陽位置在-2000到6000年範圍內精度是1"。<br />
* 誤差 365.25*24*60*60/360/60/60 = 24.35秒鐘。相當於半分鐘。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* Appendix III 附表3.<br />
* http://forums.parallax.com/showthread.php/154838-Azimuth-angle-conversion-from-east-to-west
*
* @see http://www.neoprogrammics.com/vsop87/source_code_generator_tool/
* VSOP87B日心黃道球面坐標 Heliocentric LBR - J2000
* @see ftp://ftp.imcce.fr/pub/ephem/planets/vsop87/VSOP87B.ear
*/
VSOP87_terms.earth = {
multiplier : 1e-8,
// 行星 Earth 地球: 日心黃經
L : [
[ [ 175347046.0, 0, 0 ], [ 3341656.0, 4.6692568, 6283.07585 ],
[ 34894.0, 4.6261, 12566.1517 ],
[ 3497.0, 2.7441, 5753.3849 ],
[ 3418.0, 2.8289, 3.5231 ],
[ 3136.0, 3.6277, 77713.7715 ],
[ 2676.0, 4.4181, 7860.4194 ],
[ 2343.0, 6.1352, 3930.2097 ],
[ 1324.0, 0.7425, 11506.7698 ],
[ 1273.0, 2.0371, 529.691 ],
[ 1199.0, 1.1096, 1577.3435 ],
[ 990, 5.233, 5884.927 ], [ 902, 2.045, 26.298 ],
[ 857, 3.508, 398.149 ], [ 780, 1.179, 5223.694 ],
[ 753, 2.533, 5507.553 ], [ 505, 4.583, 18849.228 ],
[ 492, 4.205, 775.523 ], [ 357, 2.92, 0.067 ],
[ 317, 5.849, 11790.629 ], [ 284, 1.899, 796.298 ],
[ 271, 0.315, 10977.079 ], [ 243, 0.345, 5486.778 ],
[ 206, 4.806, 2544.314 ], [ 205, 1.869, 5573.143 ],
[ 202, 2.458, 6069.777 ], [ 156, 0.833, 213.299 ],
[ 132, 3.411, 2942.463 ], [ 126, 1.083, 20.775 ],
[ 115, 0.645, 0.98 ], [ 103, 0.636, 4694.003 ],
[ 102, 0.976, 15720.839 ], [ 102, 4.267, 7.114 ],
[ 99, 6.21, 2146.17 ], [ 98, 0.68, 155.42 ],
[ 86, 5.98, 161000.69 ], [ 85, 1.3, 6275.96 ],
[ 85, 3.67, 71430.7 ], [ 80, 1.81, 17260.15 ],
[ 79, 3.04, 12036.46 ], [ 75, 1.76, 5088.63 ],
[ 74, 3.5, 3154.69 ], [ 74, 4.68, 801.82 ],
[ 70, 0.83, 9437.76 ], [ 62, 3.98, 8827.39 ],
[ 61, 1.82, 7084.9 ], [ 57, 2.78, 6286.6 ],
[ 56, 4.39, 14143.5 ], [ 56, 3.47, 6279.55 ],
[ 52, 0.19, 12139.55 ], [ 52, 1.33, 1748.02 ],
[ 51, 0.28, 5856.48 ], [ 49, 0.49, 1194.45 ],
[ 41, 5.37, 8429.24 ], [ 41, 2.4, 19651.05 ],
[ 39, 6.17, 10447.39 ], [ 37, 6.04, 10213.29 ],
[ 37, 2.57, 1059.38 ], [ 36, 1.71, 2352.87 ],
[ 36, 1.78, 6812.77 ], [ 33, 0.59, 17789.85 ],
[ 30, 0.44, 83996.85 ], [ 30, 2.74, 1349.87 ],
[ 25, 3.16, 4690.48 ] ],
[ [ 628331966747.0, 0, 0 ], [ 206059.0, 2.678235, 6283.07585 ],
[ 4303.0, 2.6351, 12566.1517 ], [ 425.0, 1.59, 3.523 ],
[ 119.0, 5.796, 26.298 ], [ 109.0, 2.966, 1577.344 ],
[ 93, 2.59, 18849.23 ], [ 72, 1.14, 529.69 ],
[ 68, 1.87, 398.15 ], [ 67, 4.41, 5507.55 ],
[ 59, 2.89, 5223.69 ], [ 56, 2.17, 155.42 ],
[ 45, 0.4, 796.3 ], [ 36, 0.47, 775.52 ],
[ 29, 2.65, 7.11 ], [ 21, 5.34, 0.98 ],
[ 19, 1.85, 5486.78 ], [ 19, 4.97, 213.3 ],
[ 17, 2.99, 6275.96 ], [ 16, 0.03, 2544.31 ],
[ 16, 1.43, 2146.17 ], [ 15, 1.21, 10977.08 ],
[ 12, 2.83, 1748.02 ], [ 12, 3.26, 5088.63 ],
[ 12, 5.27, 1194.45 ], [ 12, 2.08, 4694 ],
[ 11, 0.77, 553.57 ], [ 10, 1.3, 6286.6 ],
[ 10, 4.24, 1349.87 ], [ 9, 2.7, 242.73 ],
[ 9, 5.64, 951.72 ], [ 8, 5.3, 2352.87 ],
[ 6, 2.65, 9437.76 ], [ 6, 4.67, 4690.48 ] ],
[ [ 52919.0, 0, 0 ], [ 8720.0, 1.0721, 6283.0758 ],
[ 309.0, 0.867, 12566.152 ], [ 27, 0.05, 3.52 ],
[ 16, 5.19, 26.3 ], [ 16, 3.68, 155.42 ],
[ 10, 0.76, 18849.23 ], [ 9, 2.06, 77713.77 ],
[ 7, 0.83, 775.52 ], [ 5, 4.66, 1577.34 ],
[ 4, 1.03, 7.11 ], [ 4, 3.44, 5573.14 ],
[ 3, 5.14, 796.3 ], [ 3, 6.05, 5507.55 ],
[ 3, 1.19, 242.73 ], [ 3, 6.12, 529.69 ],
[ 3, 0.31, 398.15 ], [ 3, 2.28, 553.57 ],
[ 2, 4.38, 5223.69 ], [ 2, 3.75, 0.98 ] ],
[ [ 289.0, 5.844, 6283.076 ], [ 35, 0, 0 ],
[ 17, 5.49, 12566.15 ], [ 3, 5.2, 155.42 ],
[ 1, 4.72, 3.52 ], [ 1, 5.3, 18849.23 ],
[ 1, 5.97, 242.73 ] ],
[ [ 114.0, 3.142, 0 ], [ 8, 4.13, 6283.08 ],
[ 1, 3.84, 12566.15 ] ], [ [ 1, 3.14, 0 ] ] ],
// 行星 Earth 地球: 日心黃緯
B : [
[ [ 280, 3.199, 84334.662 ], [ 102, 5.422, 5507.553 ],
[ 80, 3.88, 5223.69 ], [ 44, 3.7, 2352.87 ],
[ 32, 4, 1577.34 ] ],
[ [ 9, 3.9, 5507.55 ], [ 6, 1.73, 5223.69 ] ] ],
// 行星 Earth 地球: 行星到太陽的距離, 日地距離, 位置向量（又稱向徑或徑矢 radius vector）
// https://zh.wikipedia.org/wiki/%E4%BD%8D%E7%BD%AE%E5%90%91%E9%87%8F
R : [
[ [ 100013989.0, 0, 0 ], [ 1670700.0, 3.0984635, 6283.07585 ],
[ 13956.0, 3.05525, 12566.1517 ],
[ 3084.0, 5.1985, 77713.7715 ],
[ 1628.0, 1.1739, 5753.3849 ],
[ 1576.0, 2.8469, 7860.4194 ],
[ 925.0, 5.453, 11506.77 ], [ 542.0, 4.564, 3930.21 ],
[ 472.0, 3.661, 5884.927 ], [ 346.0, 0.964, 5507.553 ],
[ 329.0, 5.9, 5223.694 ], [ 307.0, 0.299, 5573.143 ],
[ 243.0, 4.273, 11790.629 ],
[ 212.0, 5.847, 1577.344 ],
[ 186.0, 5.022, 10977.079 ],
[ 175.0, 3.012, 18849.228 ],
[ 110.0, 5.055, 5486.778 ], [ 98, 0.89, 6069.78 ],
[ 86, 5.69, 15720.84 ], [ 86, 1.27, 161000.69 ],
[ 65, 0.27, 17260.15 ], [ 63, 0.92, 529.69 ],
[ 57, 2.01, 83996.85 ], [ 56, 5.24, 71430.7 ],
[ 49, 3.25, 2544.31 ], [ 47, 2.58, 775.52 ],
[ 45, 5.54, 9437.76 ], [ 43, 6.01, 6275.96 ],
[ 39, 5.36, 4694 ], [ 38, 2.39, 8827.39 ],
[ 37, 0.83, 19651.05 ], [ 37, 4.9, 12139.55 ],
[ 36, 1.67, 12036.46 ], [ 35, 1.84, 2942.46 ],
[ 33, 0.24, 7084.9 ], [ 32, 0.18, 5088.63 ],
[ 32, 1.78, 398.15 ], [ 28, 1.21, 6286.6 ],
[ 28, 1.9, 6279.55 ], [ 26, 4.59, 10447.39 ] ],
[ [ 103019.0, 1.10749, 6283.07585 ],
[ 1721.0, 1.0644, 12566.1517 ], [ 702.0, 3.142, 0 ],
[ 32, 1.02, 18849.23 ], [ 31, 2.84, 5507.55 ],
[ 25, 1.32, 5223.69 ], [ 18, 1.42, 1577.34 ],
[ 10, 5.91, 10977.08 ], [ 9, 1.42, 6275.96 ],
[ 9, 0.27, 5486.78 ] ],
[ [ 4359.0, 5.7846, 6283.0758 ], [ 124.0, 5.579, 12566.152 ],
[ 12, 3.14, 0 ], [ 9, 3.63, 77713.77 ],
[ 6, 1.87, 5573.14 ], [ 3, 5.47, 18849.23 ] ],
[ [ 145.0, 4.273, 6283.076 ], [ 7, 3.92, 12566.15 ] ],
[ [ 4, 2.56, 6283.08 ] ] ]
};
// ------------------------------------------------------------------------------------------------------//
/**
* convert_LEA406 使用之行星數據。
*
* mean longitudes of major planets.
*/
var convert_LEA406_arguments
// @see ReadMe_Eng.pdf, from build_LEA406.txt
// all in arcseconds.
= [
// [0]: 為配合 fields.
null, [ 485868.249036, 17179159232.178, 3187.92, 51.635, -2.447 ],
//
[ 1287104.793048, 1295965810.481, -55.32, 0.136, -0.1149 ],
//
[ 335779.526232, 17395272628.478, -1275.12, -1.037, 0.0417 ],
//
[ 1072260.703692, 16029616012.09, -637.06, 6.593, -0.3169 ],
//
[ 450160.398036, -69679193.631, 636.02, 7.625, -0.3586 ],
//
[ 908103.259872, 5381016286.88982, -1.92789, 0.00639, 0 ],
//
[ 655127.28306, 2106641364.33548, 0.59381, -0.00627, 0 ],
//
[ 361679.244588, 1295977422.83429, -2.04411, -0.00523, 0 ],
//
[ 1279558.798488, 689050774.93988, 0.94264, -0.01043, 0 ],
//
[ 123665.467464, 109256603.77991, -30.60378, 0.05706, 0.04667 ],
//
[ 180278.79948, 43996098.55732, 75.61614, -0.16618, -0.11484 ],
//
[ 1130598.018396, 15424811.93933, -1.75083, 0.02156, 0 ],
//
[ 1095655.195728, 7865503.20744, 0.21103, -0.00895, 0 ],
//
[ 0, 50288.2, 111.2022, 0.0773, -0.2353 ] ],
// 將 Amp 轉整數: Amp *= 1e7 (表格中小數7位數)。
Amp_to_integer = 1e7;
// ------------------------------------------------------------------------------------------------------//
/**
* 初始化 Saros Series data.
*
* @param {Array}saros_starts
* Solar/Lunar Eclipses Saros Series start TT, MUST > 1.5
* @param {Integer}offset
* offset of saros index
* @param {Array}saros_starts_TT
* Array to put Solar/Lunar Eclipses Saros Series start TT.
* saros_starts_TT[1] = start TT of series 1
*
* @returns {Array} [ remainder, saros_index ];
*
* @inner
*/
function create_saros_index(saros_starts, offset, saros_starts_TT) {
var saros_data = [];
saros_starts.forEach(function(TT, index) {
saros_starts_TT[index += offset] = TT;
// -1.5: 確保查詢時一定大於底限。因此需要壓低底限。
saros_data.push([ (TT - 1.5) % saros_days, [ index, TT ] ]);
});
saros_data.sort(function(a, b) {
return a[0] - b[0];
});
// console.log(saros_data);
var remainder = [], saros_index = [];
saros_data.forEach(function(data) {
remainder.push(data[0]);
saros_index.push(data[1]);
});
if (false) {
var min_gap = Infinity;
remainder.forEach(function(r, index) {
if (index > 0 && min_gap > r - remainder[index - 1])
min_gap = r - remainder[index - 1];
});
console.log('min gap: ' + min_gap);
// min gap ≈ 27.7707
}
return [ remainder, saros_index ];
}
/**
* 沙羅週期 The saros is a period of approximately 223 synodic months
*
* Reference 資料來源/資料依據:<br />
* wikipedia: 6585.3211 , SEsaros.html: 6585.3223
*
* 奇數的數字表示發生在接近昇交點的日食，偶數的數字表示發生在接近降交點的日食；但在月食這種數字的搭配是相反的。沙羅序列的編號是以最大食出現，也就是最接近交點的時間來排列的。
*
* 任何時間都有大約40個不同的沙羅序列在進行中。 以2008年為例，共有39個日食的沙羅序列在進行中，而月食則有41個序列在進行中。
*
* @see https://en.wikipedia.org/wiki/Saros_%28astronomy%29
* @see http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html
*/
var saros_days = 6585.3211,
// Solar/Lunar Eclipses Saros Series start TT
// solar_saros[1]: The start TT of Solar Eclipses Saros Series 1
solar_saros = [], lunar_saros = [],
// remainder[0] 為依 saros_days, sort 過的 remainder.
// remainder[1] 為 [ 所指向的 saros series index, start JDN (TT) ]
//
// http://eclipse.gsfc.nasa.gov/SEsaros/SEperiodtab4.html
// http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros0-180.html
// http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros000.html
solar_saros_remainder = create_saros_index([ 524207, 541365, 571692,
562508, 579666, 609994, 534956, 538943, 575856, 573257, 590415,
620743, 624729, 641887, 672215, 676201, 693358, 723686, 727672,
744830, 775158, 779144, 783132, 820045, 810860, 748994, 792493,
789893, 787295, 824208, 834780, 838767, 869095, 886252, 890239,
927152, 937723, 941710, 978624, 989195, 993182, 1023511, 1034082,
972215, 1061812, 1006530, 997346, 1021089, 1038246, 1042232,
1065975, 1089717, 1093704, 1117447, 1141189, 1145176, 1168919,
1192661, 1196648, 1220391, 1244133, 1234949, 1265278, 1282434,
1207396, 1217969, 1254882, 1252283, 1262856, 1293183, 1297170,
1314327, 1344655, 1348641, 1365799, 1396127, 1400113, 1417271,
1447599, 1445000, 1462158, 1492486, 1456960, 1421435, 1471519,
1455749, 1466321, 1496649, 1500635, 1511208, 1548121, 1552107,
1562680, 1599593, 1603579, 1614151, 1644480, 1655051, 1659038,
1695951, 1693352, 1631485, 1727667, 1672385, 1663201, 1693530,
1710686, 1714673, 1738416, 1755573, 1766145, 1789888, 1807045,
1817617, 1841360, 1858517, 1862503, 1892832, 1903403, 1887634,
1924548, 1921949, 1873252, 1890410, 1914152, 1918139, 1935297,
1959039, 1963025, 1986768, 2010511, 2014497, 2031655, 2061983,
2065969, 2083127, 2113455, 2104270, 2108257, 2151756, 2083303,
2080705, 2124204, 2121604, 2132177, 2162505, 2166491, 2177063,
2207391, 2217963, 2228535, 2258863, 2269435, 2273422, 2310335,
2314321, 2311723, 2355222, 2319696, 2284170, 2314499, 2325070,
2329057, 2352800, 2369957, 2380529, 2404272, 2421429, 2425415,
2455744, 2472901, 2476887, 2500630, 2517787, 2515188, 2545517,
2556088, 2487636, 2504794, 2535122, 2525937, 2543095, 2573423,
2577409, 2594567, 2624895, 2628881, 2646039, 2669781, 2673767,
2690925, 2721253, 2718654, 2729227, 2759554, 2704272, 2695089,
2738588, 2729403, 2739975, 2770303, 2774289, 2784862, 2815190 ],
-13, solar_saros),
// http://eclipse.gsfc.nasa.gov/LEsaros/LEperiodtab3.html
// http://eclipse.gsfc.nasa.gov/LEsaros/LEsaroscat.html
// https://en.wikipedia.org/wiki/List_of_Saros_series_for_lunar_eclipses
// http://eclipse.gsfc.nasa.gov/LEcat5/LE-1999--1900.html
lunar_saros_remainder = create_saros_index([ 534086, 544657, 542059,
585557, 582958, 507921, 538249, 555406, 552807, 576550, 600292,
604279, 628022, 645179, 655751, 679494, 703236, 707223, 730966,
754708, 752109, 782438, 799594, 783825, 754885, 824725, 762858,
773431, 810344, 807744, 824902, 855230, 859216, 876374, 906702,
910688, 927846, 958174, 962160, 979318, 1009646, 1007047, 1017619,
1054532, 979494, 976896, 1020395, 1017795, 1028368, 1058696,
1062682, 1073254, 1110168, 1114154, 1131312, 1161640, 1165626,
1176198, 1213112, 1217098, 1221085, 1257998, 1255399, 1186947,
1283129, 1227846, 1225248, 1255576, 1272733, 1276720, 1307048,
1317620, 1328192, 1358520, 1375677, 1379664, 1409992, 1420563,
1424550, 1461464, 1465450, 1436510, 1493180, 1457654, 1435299,
1452457, 1476199, 1480185, 1503929, 1527671, 1531657, 1548815,
1579143, 1583129, 1600287, 1624029, 1628016, 1651759, 1675501,
1672902, 1683475, 1713802, 1645350, 1649337, 1686250, 1683651,
1694223, 1731137, 1735123, 1745695, 1776023, 1786595, 1797167,
1827495, 1838067, 1848639, 1878967, 1882953, 1880355, 1923854,
1881742, 1852802, 1889716, 1893702, 1897689, 1928017, 1938589,
1942576, 1972904, 1990060, 1994047, 2024376, 2034947, 2045519,
2075848, 2086419, 2083821, 2120734, 2124720, 2062853, 2086597,
2103753, 2094569, 2118312, 2142055, 2146041, 2169784, 2186941,
2197513, 2214671, 2238413, 2242399, 2266143, 2289885, 2287286,
2311029, 2334771, 2292660, 2276891, 2326975, 2304620, 2308607,
2345521, 2349507, 2360079, 2390407, 2394393, 2411551, 2441879,
2445865, 2456438, 2486766, 2490752, 2501324, 2538237, 2529053,
2473772, 2563368, 2508086, 2505487, 2542401, 2546387, 2556959,
2587288, 2597859, 2601846, 2632174, 2649331, 2653318, 2683646,
2694218, 2698204, 2728533, 2739104, 2683823, 2740493, 2724723,
2708953, 2732696, 2749853, 2753840, 2777583, 2801325, 2805311 ],
-20, lunar_saros);
// ------------------------------------------------------------------------------------------------------//
// all 1325.55: T = k / 1325.55
// the time of the mean perigee or apogee
// 計算平近點或遠點時刻
var lunar_perigee_apogee_T = [ 2451534.6698, 27.55454989 * 1325.55,
-0.0006691, -0.000001098, 0.0000000052 ],
// Moon's mean elongation at time JDE:
// T 時刻的月亮平距角：
lunar_perigee_apogee_D = [ 171.9179, 335.9106046 * 1325.55, 0.0100383,
-0.00001156, 0.000000055 ].map(degrees_to_radians),
// Sun's mean anomaly:
// 太陽平近點角：
lunar_perigee_apogee_M = [ 347.3477, 27.1577721 * 1325.55, -0.0008130,
-0.0008130 ].map(degrees_to_radians),
// Moon's argument of latitude:
// 月亮緯度參數：
lunar_perigee_apogee_F = [ 316.6109, +364.5287911 * 1325.55, -0.0125053,
-0.0000148 ].map(degrees_to_radians),
/**
* 月亮的近地點 perigee 和遠地點 apogee 之 coefficients 數據 for function
* lunar_perigee_apogee()。
*
* Reference 資料來源/資料依據:<br />
* Jean Meeus, Astronomical Algorithms, 2nd Edition. 《天文算法》2版<br />
* p. 355. Chapter 50 Perigee and apogee of the Moon<br />
*
* @see https://github.com/helixcn/skycalc/blob/master/src/AAMoonPerigeeApogee.cpp
*/
perigee_coefficients_JD = [
// 近地點 JD 修正量係數。
[ 2, , , -1.6769 ], [ 4, , , .4589 ], [ 6, , , -.1856 ], [ 8, , , .0883 ],
[ 2, -1, , -.0773, .00019 ], [ , 1, , .0502, -.00013 ],
[ 10, , , -.0460 ], [ 4, -1, , .0422, -.00011 ],
[ 6, -1, , -.0256 ], [ 12, , , .0253 ], [ 1, , , .0237 ],
[ 8, -1, , .0162 ], [ 14, , , -.0145 ], [ , , 2, .0129 ],
[ 3, , , -.0112 ], [ 10, -1, , -.0104 ], [ 16, , , .0086 ],
[ 12, -1, , .0069 ], [ 5, , , .0066 ], [ 2, , 2, -.0053 ],
[ 18, , , -.0052 ], [ 14, -1, , -.0046 ], [ 7, , , -.0041 ],
[ 2, 1, , .0040 ], [ 20, , , .0032 ], [ 1, 1, , -.0032 ],
[ 16, -1, , .0031 ], [ 4, 1, , -.0029 ], [ 9, , , .0027 ],
[ 4, , 2, .0027 ], [ 2, -2, , -.0027 ], [ 4, -2, , .0024 ],
[ 6, -2, , -.0021 ], [ 22, , , -.0021 ], [ 18, -1, , -.0021 ],
[ 6, 1, , .0019 ], [ 11, , , -.0018 ], [ 8, 1, , -.0014 ],
[ 4, , -2, -.0014 ], [ 6, , 2, -.0014 ], [ 3, 1, , .0014 ],
[ 5, 1, , -.0014 ], [ 13, , , .0013 ], [ 20, -1, , .0013 ],
[ 3, 2, , .0011 ], [ 4, -2, 2, -.0011 ], [ 1, 2, , -.0010 ],
[ 22, -1, , -.0009 ], [ , , 4, -.0008 ], [ 6, , -2, .0008 ],
[ 2, 1, -2, .0008 ], [ , 2, , .0007 ], [ , -1, 2, .0007 ],
[ 2, , 4, .0007 ], [ , -2, 2, -.0006 ], [ 2, 2, -2, -.0006 ],
[ 24, , , .0006 ], [ 4, , -4, .0005 ], [ 2, 2, , .0005 ],
[ 1, -1, , -.0004 ] ],
//
perigee_coefficients_parallax = [
// 近地點赤道地平視差修正量係數。
[ , , , 3629.215 ], [ 2, , , 63.224 ], [ 4, , , -6.990 ],
[ 2, -1, , 2.834, -.0071 ], [ 6, , , 1.927 ], [ 1, , , -1.263 ],
[ 8, , , -.702 ], [ , 1, , .696, -.0017 ], [ , , 2, -.690 ],
[ 4, -1, , -.629, .0016 ], [ 2, , -2, -.392 ], [ 10, , , .297 ],
[ 6, -1, , .260 ], [ 3, , , .201 ], [ 2, 1, , -.161 ],
[ 1, 1, , .157 ], [ 12, , , -.138 ], [ 8, -1, , -.127 ],
[ 2, , 2, .104 ], [ 2, -2, , .104 ], [ 5, , , -.079 ],
[ 14, , , .068 ], [ 10, -1, , .067 ], [ 4, 1, , .054 ],
[ 12, -1, , -.038 ], [ 4, -2, , -.038 ], [ 7, , , .037 ],
[ 4, , 2, -.037 ], [ 16, , , -.035 ], [ 3, 1, , -.030 ],
[ 1, -1, , .029 ], [ 6, 1, , -.025 ], [ , 2, , .023 ],
[ 14, -1, , .023 ], [ 2, 2, , -.023 ], [ 6, -2, , .022 ],
[ 2, -1, -2, -.021 ], [ 9, , , -.020 ], [ 18, , , .019 ],
[ 6, , 2, .017 ], [ , -1, 2, .014 ], [ 16, -1, , -.014 ],
[ 4, , -2, .013 ], [ 8, 1, , .012 ], [ 11, , , .011 ],
[ 5, 1, , .010 ], [ 20, , , -.010 ] ],
//
apogee_coefficients_JD = [
// 遠地點 JD 修正量係數。
[ 2, , , .4392 ], [ 4, , , .0684 ], [ , 1, , .0456, -.00011 ],
[ 2, -1, , .0426, -.00011 ], [ , , 2, .0212 ], [ 1, , , -.0189 ],
[ 6, , , .0144 ], [ 4, -1, , .0113 ], [ 2, , 2, .0047 ],
[ 1, 1, , .0036 ], [ 8, , , .0035 ], [ 6, -1, , .0034 ],
[ 2, , -2, -.0034 ], [ 2, -2, , .0022 ], [ 3, , , -.0017 ],
[ 4, , 2, .0013 ], [ 8, -1, , .0011 ], [ 4, -2, , .0010 ],
[ 10, , , .0009 ], [ 3, 1, , .0007 ], [ , 2, , .0006 ],
[ 2, 1, , .0005 ], [ 2, 2, , .0005 ], [ 6, , 2, .0004 ],
[ 6, -2, , .0004 ], [ 10, -1, , .0004 ], [ 5, , , -.0004 ],
[ 4, , -2, -.0004 ], [ , 1, 2, .0003 ], [ 12, , , .0003 ],
[ 2, -1, 2, .0003 ], [ 1, -1, , -.0003 ] ],
//
apogee_coefficients_parallax = [
// 遠地點赤道地平視差修正量係數。
[ , , , 3245.251 ], [ 2, , , -9.147 ], [ 1, , , -.841 ], [ , , 2, .697 ],
[ , 1, , -.656, .0016 ], [ 4, , , .355 ], [ 2, -1, , .159 ],
[ 1, 1, , .127 ], [ 4, -1, , .065 ], [ 6, , , .052 ],
[ 2, 1, , .043 ], [ 2, , 2, .031 ], [ 2, , -2, -.023 ],
[ 2, -2, , .022 ], [ 2, 2, , .019 ], [ , 2, , -.016 ],
[ 6, -1, , .014 ], [ 8, , , .010 ] ];
// ---------------------------------------------------------------------------------------------------------------------------------------//
// export.
// ---------------------------------------
return (_// JSDT:_module_
);
}
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