doctor/rappaurio-sae501_502
1
0
Fork 0
mirror of https://scm.univ-tours.fr/22107988t/rappaurio-sae501_502.git synced 2025-08-29 08:35:58 +02:00
Code Issues Packages Projects Releases Wiki Activity
Files
361112699ce955116de49e11081016fc0fef6f58
rappaurio-sae501_502/app/node_modules/cejs/application/astronomy.js
22107988t 361112699c permet l'ajout des frameworks et des routes
2023-09-25 09:41:55 +02:00

7923 lines
261 KiB
JavaScript
Raw Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

/**
* @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_
);
}
Reference in New Issue View Git Blame Copy Permalink