1 ;;; lunar.el --- calendar functions for phases of the moon
3 ;; Copyright (C) 1992, 1993, 1995, 1997 Free Software Foundation, Inc.
5 ;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
7 ;; Human-Keywords: moon, lunar phases, calendar, diary
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is free software; you can redistribute it and/or modify
12 ;; it under the terms of the GNU General Public License as published by
13 ;; the Free Software Foundation; either version 2, or (at your option)
16 ;; GNU Emacs is distributed in the hope that it will be useful,
17 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
18 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 ;; GNU General Public License for more details.
21 ;; You should have received a copy of the GNU General Public License
22 ;; along with GNU Emacs; see the file COPYING. If not, write to the
23 ;; Free Software Foundation, Inc., 59 Temple Place - Suite 330,
24 ;; Boston, MA 02111-1307, USA.
28 ;; This collection of functions implements lunar phases for calendar.el and
31 ;; Based on ``Astronomical Formulae for Calculators,'' 3rd ed., by Jean Meeus,
32 ;; Willmann-Bell, Inc., 1985 and ``Astronomical Algorithms'' by Jean Meeus,
33 ;; Willmann-Bell, Inc., 1991.
35 ;; WARNING: The calculations will be accurate only to within a few minutes.
37 ;; The author would be delighted to have an astronomically more sophisticated
38 ;; person rewrite the code for the lunar calculations in this file!
40 ;; Technical details of all the calendrical calculations can be found in
41 ;; ``Calendrical Calculations'' by Nachum Dershowitz and Edward M. Reingold,
42 ;; Cambridge University Press (1997).
44 ;; Comments, corrections, and improvements should be sent to
45 ;; Edward M. Reingold Department of Computer Science
46 ;; (217) 333-6733 University of Illinois at Urbana-Champaign
47 ;; reingold@cs.uiuc.edu 1304 West Springfield Avenue
48 ;; Urbana, Illinois 61801
52 (defvar displayed-month
)
53 (defvar displayed-year
)
56 (require 'lisp-float-type
)
57 (error "Lunar calculations impossible since floating point is unavailable"))
61 (defun lunar-phase-list (month year
)
62 "List of lunar phases for three months starting with Gregorian MONTH, YEAR."
63 (let ((end-month month
)
67 (increment-calendar-month end-month end-year
3)
68 (increment-calendar-month start-month start-year -
1)
69 (let* ((end-date (list (list end-month
1 end-year
)))
70 (start-date (list (list start-month
71 (calendar-last-day-of-month
72 start-month start-year
)
78 ( / (calendar-day-number (list month
1 year
))
81 (new-moon (lunar-phase index
))
83 (while (calendar-date-compare new-moon end-date
)
84 (if (calendar-date-compare start-date new-moon
)
85 (setq list
(append list
(list new-moon
))))
86 (setq index
(1+ index
))
87 (setq new-moon
(lunar-phase index
)))
90 (defun lunar-phase (index)
91 "Local date and time of lunar phase INDEX.
92 Integer below INDEX/4 gives the lunation number, counting from Jan 1, 1900;
93 remainder mod 4 gives the phase: 0 new moon, 1 first quarter, 2 full moon,
95 (let* ((phase (mod index
4))
97 (time (/ index
1236.85))
98 (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
100 (* 29.53058868 index
)
101 (* 0.0001178 time time
)
102 (* -
0.000000155 time time time
)
104 (solar-sin-degrees (+ 166.56
106 (* -
0.009173 time time
))))))
110 (* -
0.0000333 time time
)
111 (* -
0.00000347 time time time
))
115 (* 385.81691806 index
)
116 (* 0.0107306 time time
)
117 (* 0.00001236 time time time
))
121 (* 390.67050646 index
)
122 (* -
0.0016528 time time
)
123 (* -
0.00000239 time time time
))
126 (if (memq phase
'(0 2))
127 (+ (* (- 0.1734 (* 0.000393 time
))
128 (solar-sin-degrees sun-anomaly
))
129 (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly
)))
130 (* -
0.4068 (solar-sin-degrees moon-anomaly
))
131 (* 0.0161 (solar-sin-degrees (* 2 moon-anomaly
)))
132 (* -
0.0004 (solar-sin-degrees (* 3 moon-anomaly
)))
133 (* 0.0104 (solar-sin-degrees (* 2 moon-lat
)))
134 (* -
0.0051 (solar-sin-degrees (+ sun-anomaly moon-anomaly
)))
135 (* -
0.0074 (solar-sin-degrees (- sun-anomaly moon-anomaly
)))
136 (* 0.0004 (solar-sin-degrees (+ (* 2 moon-lat
) sun-anomaly
)))
137 (* -
0.0004 (solar-sin-degrees (- (* 2 moon-lat
) sun-anomaly
)))
138 (* -
0.0006 (solar-sin-degrees
139 (+ (* 2 moon-lat
) moon-anomaly
)))
140 (* 0.0010 (solar-sin-degrees (- (* 2 moon-lat
) moon-anomaly
)))
141 (* 0.0005 (solar-sin-degrees
142 (+ (* 2 moon-anomaly
) sun-anomaly
))))
143 (+ (* (- 0.1721 (* 0.0004 time
))
144 (solar-sin-degrees sun-anomaly
))
145 (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly
)))
146 (* -
0.6280 (solar-sin-degrees moon-anomaly
))
147 (* 0.0089 (solar-sin-degrees (* 2 moon-anomaly
)))
148 (* -
0.0004 (solar-sin-degrees (* 3 moon-anomaly
)))
149 (* 0.0079 (solar-sin-degrees (* 2 moon-lat
)))
150 (* -
0.0119 (solar-sin-degrees (+ sun-anomaly moon-anomaly
)))
151 (* -
0.0047 (solar-sin-degrees (- sun-anomaly moon-anomaly
)))
152 (* 0.0003 (solar-sin-degrees (+ (* 2 moon-lat
) sun-anomaly
)))
153 (* -
0.0004 (solar-sin-degrees (- (* 2 moon-lat
) sun-anomaly
)))
154 (* -
0.0006 (solar-sin-degrees (+ (* 2 moon-lat
) moon-anomaly
)))
155 (* 0.0021 (solar-sin-degrees (- (* 2 moon-lat
) moon-anomaly
)))
156 (* 0.0003 (solar-sin-degrees
157 (+ (* 2 moon-anomaly
) sun-anomaly
)))
158 (* 0.0004 (solar-sin-degrees
159 (- sun-anomaly
(* 2 moon-anomaly
))))
160 (* -
0.0003 (solar-sin-degrees
161 (+ (* 2 sun-anomaly
) moon-anomaly
))))))
163 (* -
0.0004 (solar-cosine-degrees
165 (* 0.0003 (solar-cosine-degrees
167 (adjustment (cond ((= phase
1) (+ adjustment adj
))
168 ((= phase
2) (- adjustment adj
))
170 (date (+ date adjustment
))
171 (date (+ date
(/ (- calendar-time-zone
172 (solar-ephemeris-correction
173 (extract-calendar-year
174 (calendar-gregorian-from-absolute
177 (time (* 24 (- date
(truncate date
))))
178 (date (calendar-gregorian-from-absolute (truncate date
)))
179 (adj (dst-adjust-time date time
)))
180 (list (car adj
) (apply 'solar-time-string
(cdr adj
)) phase
)))
182 (defun lunar-phase-name (phase)
183 "Name of lunar PHASE.
184 0 = new moon, 1 = first quarter, 2 = full moon, 3 = last quarter."
185 (cond ((= 0 phase
) "New Moon")
186 ((= 1 phase
) "First Quarter Moon")
187 ((= 2 phase
) "Full Moon")
188 ((= 3 phase
) "Last Quarter Moon")))
190 (defun calendar-phases-of-moon ()
191 "Create a buffer with the lunar phases for the current calendar window."
193 (message "Computing phases of the moon...")
194 (let ((m1 displayed-month
)
198 (increment-calendar-month m1 y1 -
1)
199 (increment-calendar-month m2 y2
1)
200 (set-buffer (get-buffer-create lunar-phases-buffer
))
201 (setq buffer-read-only nil
)
202 (calendar-set-mode-line
204 (format "Phases of the Moon from %s to %s, %d%%-"
205 (calendar-month-name m1
) (calendar-month-name m2
) y2
)
206 (format "Phases of the Moon from %s, %d to %s, %d%%-"
207 (calendar-month-name m1
) y1
(calendar-month-name m2
) y2
)))
214 (phase (car (cdr (cdr x
)))))
215 (concat (calendar-date-string date
)
217 (lunar-phase-name phase
)
220 (lunar-phase-list m1 y1
) "\n"))
221 (goto-char (point-min))
222 (set-buffer-modified-p nil
)
223 (setq buffer-read-only t
)
224 (display-buffer lunar-phases-buffer
)
225 (message "Computing phases of the moon...done")))
228 (defun phases-of-moon (&optional arg
)
229 "Display the quarters of the moon for last month, this month, and next month.
230 If called with an optional prefix argument, prompts for month and year.
232 This function is suitable for execution in a .emacs file."
236 (calendar-read-date t
)
237 (calendar-current-date)))
238 (displayed-month (extract-calendar-month date
))
239 (displayed-year (extract-calendar-year date
)))
240 (calendar-phases-of-moon))))
242 (defun diary-phases-of-moon (&optional mark
)
243 "Moon phases diary entry.
245 An optional parameter MARK specifies a face or single-character string to
246 use when highlighting the day in the calendar."
250 (+ (extract-calendar-year date
)
251 ( / (calendar-day-number date
)
254 (phase (lunar-phase index
)))
255 (while (calendar-date-compare phase
(list date
))
256 (setq index
(1+ index
))
257 (setq phase
(lunar-phase index
)))
258 (if (calendar-date-equal (car phase
) date
)
259 (cons mark
(concat (lunar-phase-name (car (cdr (cdr phase
)))) " "
260 (car (cdr phase
)))))))
263 ;; For the Chinese calendar the calculations for the new moon need to be more
264 ;; accurate than those above, so we use more terms in the approximation.
266 (defun lunar-new-moon-time (k)
267 "Astronomical (Julian) day number of K th new moon."
268 (let* ((T (/ k
1236.85))
272 (JDE (+ 2451550.09765
276 (* 0.00000000073 T4
)))
277 (E (- 1 (* 0.002516 T
) (* 0.0000074 T2
)))
278 (sun-anomaly (+ 2.5534
282 (moon-anomaly (+ 201.5643
286 (* -
0.000000058 T4
)))
287 (moon-argument (+ 160.7108
296 (A1 (+ 299.77 (* 0.107408 k
) (* -
0.009173 T2
)))
297 (A2 (+ 251.88 (* 0.016321 k
)))
298 (A3 (+ 251.83 (* 26.641886 k
)))
299 (A4 (+ 349.42 (* 36.412478 k
)))
300 (A5 (+ 84.66 (* 18.206239 k
)))
301 (A6 (+ 141.74 (* 53.303771 k
)))
302 (A7 (+ 207.14 (* 2.453732 k
)))
303 (A8 (+ 154.84 (* 7.306860 k
)))
304 (A9 (+ 34.52 (* 27.261239 k
)))
305 (A10 (+ 207.19 (* 0.121824 k
)))
306 (A11 (+ 291.34 (* 1.844379 k
)))
307 (A12 (+ 161.72 (* 24.198154 k
)))
308 (A13 (+ 239.56 (* 25.513099 k
)))
309 (A14 (+ 331.55 (* 3.592518 k
)))
311 (+ (* -
0.40720 (solar-sin-degrees moon-anomaly
))
312 (* 0.17241 E
(solar-sin-degrees sun-anomaly
))
313 (* 0.01608 (solar-sin-degrees (* 2 moon-anomaly
)))
314 (* 0.01039 (solar-sin-degrees (* 2 moon-argument
)))
315 (* 0.00739 E
(solar-sin-degrees (- moon-anomaly sun-anomaly
)))
316 (* -
0.00514 E
(solar-sin-degrees (+ moon-anomaly sun-anomaly
)))
317 (* 0.00208 E E
(solar-sin-degrees (* 2 sun-anomaly
)))
318 (* -
0.00111 (solar-sin-degrees
319 (- moon-anomaly
(* 2 moon-argument
))))
320 (* -
0.00057 (solar-sin-degrees
321 (+ moon-anomaly
(* 2 moon-argument
))))
322 (* 0.00056 E
(solar-sin-degrees
323 (+ (* 2 moon-anomaly
) sun-anomaly
)))
324 (* -
0.00042 (solar-sin-degrees (* 3 moon-anomaly
)))
325 (* 0.00042 E
(solar-sin-degrees
326 (+ sun-anomaly
(* 2 moon-argument
))))
327 (* 0.00038 E
(solar-sin-degrees
328 (- sun-anomaly
(* 2 moon-argument
))))
329 (* -
0.00024 E
(solar-sin-degrees
330 (- (* 2 moon-anomaly
) sun-anomaly
)))
331 (* -
0.00017 (solar-sin-degrees omega
))
332 (* -
0.00007 (solar-sin-degrees
333 (+ moon-anomaly
(* 2 sun-anomaly
))))
334 (* 0.00004 (solar-sin-degrees
335 (- (* 2 moon-anomaly
) (* 2 moon-argument
))))
336 (* 0.00004 (solar-sin-degrees (* 3 sun-anomaly
)))
337 (* 0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
338 (* -
2 moon-argument
))))
339 (* 0.00003 (solar-sin-degrees
340 (+ (* 2 moon-anomaly
) (* 2 moon-argument
))))
341 (* -
0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
342 (* 2 moon-argument
))))
343 (* 0.00003 (solar-sin-degrees (- moon-anomaly sun-anomaly
344 (* -
2 moon-argument
))))
345 (* -
0.00002 (solar-sin-degrees (- moon-anomaly sun-anomaly
346 (* 2 moon-argument
))))
347 (* -
0.00002 (solar-sin-degrees
348 (+ (* 3 moon-anomaly
) sun-anomaly
)))
349 (* 0.00002 (solar-sin-degrees (* 4 moon-anomaly
)))))
351 (+ (* 0.000325 (solar-sin-degrees A1
))
352 (* 0.000165 (solar-sin-degrees A2
))
353 (* 0.000164 (solar-sin-degrees A3
))
354 (* 0.000126 (solar-sin-degrees A4
))
355 (* 0.000110 (solar-sin-degrees A5
))
356 (* 0.000062 (solar-sin-degrees A6
))
357 (* 0.000060 (solar-sin-degrees A7
))
358 (* 0.000056 (solar-sin-degrees A8
))
359 (* 0.000047 (solar-sin-degrees A9
))
360 (* 0.000042 (solar-sin-degrees A10
))
361 (* 0.000040 (solar-sin-degrees A11
))
362 (* 0.000037 (solar-sin-degrees A12
))
363 (* 0.000035 (solar-sin-degrees A13
))
364 (* 0.000023 (solar-sin-degrees A14
))))
365 (newJDE (+ JDE correction additional
)))
367 (- (solar-ephemeris-correction
368 (extract-calendar-year
369 (calendar-gregorian-from-absolute
370 (floor (calendar-absolute-from-astro newJDE
))))))
371 (/ calendar-time-zone
60.0 24.0))))
373 (defun lunar-new-moon-on-or-after (d)
374 "Astronomical (Julian) day number of first new moon on or after astronomical
375 \(Julian) day number d. The fractional part is the time of day.
377 The date and time are local time, including any daylight savings rules,
378 as governed by the values of calendar-daylight-savings-starts,
379 calendar-daylight-savings-starts-time, calendar-daylight-savings-ends,
380 calendar-daylight-savings-ends-time, calendar-daylight-time-offset, and
382 (let* ((date (calendar-gregorian-from-absolute
383 (floor (calendar-absolute-from-astro d
))))
384 (year (+ (extract-calendar-year date
)
385 (/ (calendar-day-number date
) 365.25)))
386 (k (floor (* (- year
2000.0) 12.3685)))
387 (date (lunar-new-moon-time k
)))
390 (setq date
(lunar-new-moon-time k
)))
391 (let* ((a-date (calendar-absolute-from-astro date
))
392 (time (* 24 (- a-date
(truncate a-date
))))
393 (date (calendar-gregorian-from-absolute (truncate a-date
)))
394 (adj (dst-adjust-time date time
)))
395 (calendar-astro-from-absolute
396 (+ (calendar-absolute-from-gregorian (car adj
))
397 (/ (car (cdr adj
)) 24.0))))))
401 ;;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
402 ;;; lunar.el ends here