1 ;;; lunar.el --- calendar functions for phases of the moon
3 ;; Copyright (C) 1992, 1993, 1995, 1997, 2001, 2002, 2003, 2004, 2005,
4 ;; 2006, 2007, 2008 Free Software Foundation, Inc.
6 ;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
7 ;; Maintainer: Glenn Morris <rgm@gnu.org>
9 ;; Human-Keywords: moon, lunar phases, calendar, diary
11 ;; This file is part of GNU Emacs.
13 ;; GNU Emacs is free software; you can redistribute it and/or modify
14 ;; it under the terms of the GNU General Public License as published by
15 ;; the Free Software Foundation; either version 3, or (at your option)
18 ;; GNU Emacs is distributed in the hope that it will be useful,
19 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
20 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 ;; GNU General Public License for more details.
23 ;; You should have received a copy of the GNU General Public License
24 ;; along with GNU Emacs; see the file COPYING. If not, write to the
25 ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
26 ;; Boston, MA 02110-1301, USA.
32 ;; Based on ``Astronomical Formulae for Calculators,'' 3rd ed., by Jean Meeus,
33 ;; Willmann-Bell, Inc., 1985 and ``Astronomical Algorithms'' by Jean Meeus,
34 ;; Willmann-Bell, Inc., 1991.
36 ;; WARNING: The calculations will be accurate only to within a few minutes.
38 ;; The author would be delighted to have an astronomically more sophisticated
39 ;; person rewrite the code for the lunar calculations in this file!
46 ;; calendar-absolute-from-astro and v versa are cal-autoloads.
47 ;;;(require 'cal-julian)
49 (defun lunar-phase (index)
50 "Local date and time of lunar phase INDEX.
51 Integer below INDEX/4 gives the lunation number, counting from Jan 1, 1900;
52 remainder mod 4 gives the phase: 0 new moon, 1 first quarter, 2 full moon,
54 (let* ((phase (mod index 4))
56 (time (/ index 1236.85))
57 (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
60 (* 0.0001178 time time)
61 (* -0.000000155 time time time)
63 (solar-sin-degrees (+ 166.56
65 (* -0.009173 time time))))))
69 (* -0.0000333 time time)
70 (* -0.00000347 time time time))
74 (* 385.81691806 index)
75 (* 0.0107306 time time)
76 (* 0.00001236 time time time))
80 (* 390.67050646 index)
81 (* -0.0016528 time time)
82 (* -0.00000239 time time time))
85 (if (memq phase '(0 2))
86 (+ (* (- 0.1734 (* 0.000393 time))
87 (solar-sin-degrees sun-anomaly))
88 (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
89 (* -0.4068 (solar-sin-degrees moon-anomaly))
90 (* 0.0161 (solar-sin-degrees (* 2 moon-anomaly)))
91 (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
92 (* 0.0104 (solar-sin-degrees (* 2 moon-lat)))
93 (* -0.0051 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
94 (* -0.0074 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
95 (* 0.0004 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
96 (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
97 (* -0.0006 (solar-sin-degrees
98 (+ (* 2 moon-lat) moon-anomaly)))
99 (* 0.0010 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
100 (* 0.0005 (solar-sin-degrees
101 (+ (* 2 moon-anomaly) sun-anomaly))))
102 (+ (* (- 0.1721 (* 0.0004 time))
103 (solar-sin-degrees sun-anomaly))
104 (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
105 (* -0.6280 (solar-sin-degrees moon-anomaly))
106 (* 0.0089 (solar-sin-degrees (* 2 moon-anomaly)))
107 (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
108 (* 0.0079 (solar-sin-degrees (* 2 moon-lat)))
109 (* -0.0119 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
110 (* -0.0047 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
111 (* 0.0003 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
112 (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
113 (* -0.0006 (solar-sin-degrees (+ (* 2 moon-lat) moon-anomaly)))
114 (* 0.0021 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
115 (* 0.0003 (solar-sin-degrees
116 (+ (* 2 moon-anomaly) sun-anomaly)))
117 (* 0.0004 (solar-sin-degrees
118 (- sun-anomaly (* 2 moon-anomaly))))
119 (* -0.0003 (solar-sin-degrees
120 (+ (* 2 sun-anomaly) moon-anomaly))))))
122 (* -0.0004 (solar-cosine-degrees
124 (* 0.0003 (solar-cosine-degrees
126 (adjustment (cond ((= phase 1) (+ adjustment adj))
127 ((= phase 2) (- adjustment adj))
129 (date (+ date adjustment))
130 (date (+ date (/ (- calendar-time-zone
131 (solar-ephemeris-correction
132 (extract-calendar-year
133 (calendar-gregorian-from-absolute
136 (time (* 24 (- date (truncate date))))
137 (date (calendar-gregorian-from-absolute (truncate date)))
138 (adj (dst-adjust-time date time)))
139 (list (car adj) (apply 'solar-time-string (cdr adj)) phase)))
141 (defun lunar-phase-list (month year)
142 "List of lunar phases for three months starting with Gregorian MONTH, YEAR."
143 (let* ((end-month month)
148 (increment-calendar-month end-month end-year 3)
149 (list (list end-month 1 end-year))))
151 (increment-calendar-month start-month start-year -1)
152 (list (list start-month
153 (calendar-last-day-of-month
154 start-month start-year)
156 (index (* 4 (truncate
159 ( / (calendar-day-number (list month 1 year))
162 (new-moon (lunar-phase index))
164 (while (calendar-date-compare new-moon end-date)
165 (if (calendar-date-compare start-date new-moon)
166 (setq list (append list (list new-moon))))
167 (setq index (1+ index)
168 new-moon (lunar-phase index)))
171 (defun lunar-phase-name (phase)
172 "Name of lunar PHASE.
173 0 = new moon, 1 = first quarter, 2 = full moon, 3 = last quarter."
174 (cond ((= 0 phase) "New Moon")
175 ((= 1 phase) "First Quarter Moon")
176 ((= 2 phase) "Full Moon")
177 ((= 3 phase) "Last Quarter Moon")))
179 (defvar displayed-month) ; from generate-calendar
180 (defvar displayed-year)
183 (defun calendar-phases-of-moon ()
184 "Create a buffer with the lunar phases for the current calendar window."
186 (message "Computing phases of the moon...")
187 (let ((m1 displayed-month)
191 (increment-calendar-month m1 y1 -1)
192 (increment-calendar-month m2 y2 1)
193 (calendar-in-read-only-buffer lunar-phases-buffer
194 (calendar-set-mode-line
196 (format "Phases of the Moon from %s to %s, %d%%-"
197 (calendar-month-name m1) (calendar-month-name m2) y2)
198 (format "Phases of the Moon from %s, %d to %s, %d%%-"
199 (calendar-month-name m1) y1 (calendar-month-name m2) y2)))
206 (concat (calendar-date-string date)
208 (lunar-phase-name phase)
211 (lunar-phase-list m1 y1) "\n")))
212 (message "Computing phases of the moon...done")))
215 (defun phases-of-moon (&optional arg)
216 "Display the quarters of the moon for last month, this month, and next month.
217 If called with an optional prefix argument ARG, prompts for month and year.
218 This function is suitable for execution in a .emacs file."
221 (let* ((date (if arg (calendar-read-date t)
222 (calendar-current-date)))
223 (displayed-month (extract-calendar-month date))
224 (displayed-year (extract-calendar-year date)))
225 (calendar-phases-of-moon))))
229 ;; To be called from list-sexp-diary-entries, where DATE is bound.
232 (defun diary-phases-of-moon (&optional mark)
233 "Moon phases diary entry.
234 An optional parameter MARK specifies a face or single-character string to
235 use when highlighting the day in the calendar."
239 (+ (extract-calendar-year date)
240 ( / (calendar-day-number date)
243 (phase (lunar-phase index)))
244 (while (calendar-date-compare phase (list date))
245 (setq index (1+ index)
246 phase (lunar-phase index)))
247 (if (calendar-date-equal (car phase) date)
248 (cons mark (concat (lunar-phase-name (nth 2 phase)) " "
251 ;; For the Chinese calendar the calculations for the new moon need to be more
252 ;; accurate than those above, so we use more terms in the approximation.
253 (defun lunar-new-moon-time (k)
254 "Astronomical (Julian) day number of K th new moon."
255 (let* ((T (/ k 1236.85))
259 (JDE (+ 2451550.09765
263 (* 0.00000000073 T4)))
264 (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
265 (sun-anomaly (+ 2.5534
269 (moon-anomaly (+ 201.5643
273 (* -0.000000058 T4)))
274 (moon-argument (+ 160.7108
283 (A1 (+ 299.77 (* 0.107408 k) (* -0.009173 T2)))
284 (A2 (+ 251.88 (* 0.016321 k)))
285 (A3 (+ 251.83 (* 26.641886 k)))
286 (A4 (+ 349.42 (* 36.412478 k)))
287 (A5 (+ 84.66 (* 18.206239 k)))
288 (A6 (+ 141.74 (* 53.303771 k)))
289 (A7 (+ 207.14 (* 2.453732 k)))
290 (A8 (+ 154.84 (* 7.306860 k)))
291 (A9 (+ 34.52 (* 27.261239 k)))
292 (A10 (+ 207.19 (* 0.121824 k)))
293 (A11 (+ 291.34 (* 1.844379 k)))
294 (A12 (+ 161.72 (* 24.198154 k)))
295 (A13 (+ 239.56 (* 25.513099 k)))
296 (A14 (+ 331.55 (* 3.592518 k)))
298 (+ (* -0.40720 (solar-sin-degrees moon-anomaly))
299 (* 0.17241 E (solar-sin-degrees sun-anomaly))
300 (* 0.01608 (solar-sin-degrees (* 2 moon-anomaly)))
301 (* 0.01039 (solar-sin-degrees (* 2 moon-argument)))
302 (* 0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
303 (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
304 (* 0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
305 (* -0.00111 (solar-sin-degrees
306 (- moon-anomaly (* 2 moon-argument))))
307 (* -0.00057 (solar-sin-degrees
308 (+ moon-anomaly (* 2 moon-argument))))
309 (* 0.00056 E (solar-sin-degrees
310 (+ (* 2 moon-anomaly) sun-anomaly)))
311 (* -0.00042 (solar-sin-degrees (* 3 moon-anomaly)))
312 (* 0.00042 E (solar-sin-degrees
313 (+ sun-anomaly (* 2 moon-argument))))
314 (* 0.00038 E (solar-sin-degrees
315 (- sun-anomaly (* 2 moon-argument))))
316 (* -0.00024 E (solar-sin-degrees
317 (- (* 2 moon-anomaly) sun-anomaly)))
318 (* -0.00017 (solar-sin-degrees omega))
319 (* -0.00007 (solar-sin-degrees
320 (+ moon-anomaly (* 2 sun-anomaly))))
321 (* 0.00004 (solar-sin-degrees
322 (- (* 2 moon-anomaly) (* 2 moon-argument))))
323 (* 0.00004 (solar-sin-degrees (* 3 sun-anomaly)))
324 (* 0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
325 (* -2 moon-argument))))
326 (* 0.00003 (solar-sin-degrees
327 (+ (* 2 moon-anomaly) (* 2 moon-argument))))
328 (* -0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
329 (* 2 moon-argument))))
330 (* 0.00003 (solar-sin-degrees (- moon-anomaly sun-anomaly
331 (* -2 moon-argument))))
332 (* -0.00002 (solar-sin-degrees (- moon-anomaly sun-anomaly
333 (* 2 moon-argument))))
334 (* -0.00002 (solar-sin-degrees
335 (+ (* 3 moon-anomaly) sun-anomaly)))
336 (* 0.00002 (solar-sin-degrees (* 4 moon-anomaly)))))
338 (+ (* 0.000325 (solar-sin-degrees A1))
339 (* 0.000165 (solar-sin-degrees A2))
340 (* 0.000164 (solar-sin-degrees A3))
341 (* 0.000126 (solar-sin-degrees A4))
342 (* 0.000110 (solar-sin-degrees A5))
343 (* 0.000062 (solar-sin-degrees A6))
344 (* 0.000060 (solar-sin-degrees A7))
345 (* 0.000056 (solar-sin-degrees A8))
346 (* 0.000047 (solar-sin-degrees A9))
347 (* 0.000042 (solar-sin-degrees A10))
348 (* 0.000040 (solar-sin-degrees A11))
349 (* 0.000037 (solar-sin-degrees A12))
350 (* 0.000035 (solar-sin-degrees A13))
351 (* 0.000023 (solar-sin-degrees A14))))
352 (newJDE (+ JDE correction additional)))
354 (- (solar-ephemeris-correction
355 (extract-calendar-year
356 (calendar-gregorian-from-absolute
357 (floor (calendar-absolute-from-astro newJDE))))))
358 (/ calendar-time-zone 60.0 24.0))))
360 (defun lunar-new-moon-on-or-after (d)
361 "Julian day number of first new moon on or after Julian day number D.
362 The fractional part is the time of day.
364 The date and time are local time, including any daylight saving rules,
365 as governed by the values of `calendar-daylight-savings-starts',
366 `calendar-daylight-savings-starts-time', `calendar-daylight-savings-ends',
367 `calendar-daylight-savings-ends-time', `calendar-daylight-time-offset', and
368 `calendar-time-zone'."
369 (let* ((date (calendar-gregorian-from-absolute
370 (floor (calendar-absolute-from-astro d))))
371 (year (+ (extract-calendar-year date)
372 (/ (calendar-day-number date) 365.25)))
373 (k (floor (* (- year 2000.0) 12.3685)))
374 (date (lunar-new-moon-time k))
378 date (lunar-new-moon-time k)))
379 (calendar-absolute-from-astro date)))
380 (time (* 24 (- a-date (truncate a-date))))
381 (date (calendar-gregorian-from-absolute (truncate a-date)))
382 (adj (dst-adjust-time date time)))
383 (calendar-astro-from-absolute
384 (+ (calendar-absolute-from-gregorian (car adj))
385 (/ (cadr adj) 24.0)))))
389 ;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
390 ;;; lunar.el ends here