lisp/calendar/lunar.el

   1 ;;; lunar.el --- calendar functions for phases of the moon.
   2
   3 ;; Copyright (C) 1992, 1993, 1995, 1997 Free Software Foundation, Inc.
   4
   5 ;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
   6 ;; Keywords: calendar
   7 ;; Human-Keywords: moon, lunar phases, calendar, diary
   8
   9 ;; This file is part of GNU Emacs.
  10
  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)
  14 ;; any later version.
  15
  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.
  20
  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.
  25
  26 ;;; Commentary:
  27
  28 ;; This collection of functions implements lunar phases for calendar.el and
  29 ;; diary.el.
  30
  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.
  34 ;;
  35 ;; WARNING: The calculations will be accurate only to within a few minutes.
  36
  37 ;; The author would be delighted to have an astronomically more sophisticated
  38 ;; person rewrite the code for the lunar calculations in this file!
  39
  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).
  43
  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
  49
  50 ;;; Code:
  51
  52 (if (fboundp 'atan)
  53     (require 'lisp-float-type)
  54   (error "Lunar calculations impossible since floating point is unavailable."))
  55
  56 (require 'solar)
  57
  58 (defun lunar-phase-list (month year)
  59   "List of lunar phases for three months starting with Gregorian MONTH, YEAR."
  60   (let ((end-month month)
  61         (end-year year)
  62         (start-month month)
  63         (start-year year))
  64     (increment-calendar-month end-month end-year 3)
  65     (increment-calendar-month start-month start-year -1)
  66     (let* ((end-date (list (list end-month 1 end-year)))
  67            (start-date (list (list start-month
  68                                    (calendar-last-day-of-month
  69                                     start-month start-year)
  70                                    start-year)))
  71            (index (* 4
  72                      (truncate
  73                       (* 12.3685
  74                          (+ year
  75                             ( / (calendar-day-number (list month 1 year))
  76                                 366.0)
  77                             -1900)))))
  78            (new-moon (lunar-phase index))
  79            (list))
  80       (while (calendar-date-compare new-moon end-date)
  81         (if (calendar-date-compare start-date new-moon)
  82             (setq list (append list (list new-moon))))
  83         (setq index (1+ index))
  84         (setq new-moon (lunar-phase index)))
  85       list)))
  86
  87 (defun lunar-phase (index)
  88   "Local date and time of lunar phase INDEX.
  89 Integer below INDEX/4 gives the lunation number, counting from Jan 1, 1900;
  90 remainder mod 4 gives the phase: 0 new moon, 1 first quarter, 2 full moon,
  91 3 last quarter."
  92   (let* ((phase (mod index 4))
  93          (index (/ index 4.0))
  94          (time (/ index 1236.85))
  95          (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
  96                   0.75933
  97                   (* 29.53058868 index)
  98                   (* 0.0001178 time time)
  99                   (* -0.000000155 time time time)
 100                   (* 0.00033
 101                      (solar-sin-degrees (+ 166.56
 102                                            (* 132.87 time)
 103                                            (* -0.009173 time time))))))
 104          (sun-anomaly (mod
 105                        (+ 359.2242
 106                           (* 29.105356 index)
 107                           (* -0.0000333 time time)
 108                           (* -0.00000347 time time time))
 109                        360.0))
 110          (moon-anomaly (mod
 111                         (+ 306.0253
 112                            (* 385.81691806 index)
 113                            (* 0.0107306 time time)
 114                            (* 0.00001236 time time time))
 115                         360.0))
 116          (moon-lat (mod
 117                     (+ 21.2964
 118                        (* 390.67050646 index)
 119                        (* -0.0016528 time time)
 120                        (* -0.00000239 time time time))
 121                     360.0))
 122          (adjustment
 123           (if (memq phase '(0 2))
 124               (+ (* (- 0.1734 (* 0.000393 time))
 125                     (solar-sin-degrees sun-anomaly))
 126                  (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
 127                  (* -0.4068 (solar-sin-degrees moon-anomaly))
 128                  (* 0.0161 (solar-sin-degrees (* 2 moon-anomaly)))
 129                  (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
 130                  (* 0.0104 (solar-sin-degrees (* 2 moon-lat)))
 131                  (* -0.0051 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
 132                  (* -0.0074 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
 133                  (* 0.0004 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
 134                  (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
 135                  (* -0.0006 (solar-sin-degrees
 136                              (+ (* 2 moon-lat) moon-anomaly)))
 137                  (* 0.0010 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
 138                  (* 0.0005 (solar-sin-degrees
 139                             (+ (* 2 moon-anomaly) sun-anomaly))))
 140             (+ (* (- 0.1721 (* 0.0004 time))
 141                   (solar-sin-degrees sun-anomaly))
 142                (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
 143                (* -0.6280 (solar-sin-degrees moon-anomaly))
 144                (* 0.0089 (solar-sin-degrees (* 2 moon-anomaly)))
 145                (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
 146                (* 0.0079 (solar-sin-degrees (* 2 moon-lat)))
 147                (* -0.0119 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
 148                (* -0.0047 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
 149                (* 0.0003 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
 150                (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
 151                (* -0.0006 (solar-sin-degrees (+ (* 2 moon-lat) moon-anomaly)))
 152                (* 0.0021 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
 153                (* 0.0003 (solar-sin-degrees
 154                           (+ (* 2 moon-anomaly) sun-anomaly)))
 155                (* 0.0004 (solar-sin-degrees
 156                           (- sun-anomaly (* 2 moon-anomaly))))
 157                (* -0.0003 (solar-sin-degrees
 158                           (+ (* 2 sun-anomaly) moon-anomaly))))))
 159          (adj (+ 0.0028
 160                  (* -0.0004 (solar-cosine-degrees
 161                              sun-anomaly))
 162                  (* 0.0003 (solar-cosine-degrees
 163                             moon-anomaly))))
 164          (adjustment (cond ((= phase 1) (+ adjustment adj))
 165                            ((= phase 2) (- adjustment adj))
 166                            (t adjustment)))
 167          (date (+ date adjustment))
 168          (date (+ date (/ (- calendar-time-zone
 169                              (solar-ephemeris-correction
 170                               (extract-calendar-year
 171                                (calendar-gregorian-from-absolute
 172                                 (truncate date)))))
 173                           60.0 24.0)))
 174          (time (* 24 (- date (truncate date))))
 175          (date (calendar-gregorian-from-absolute (truncate date)))
 176          (adj (dst-adjust-time date time)))
 177     (list (car adj) (apply 'solar-time-string (cdr adj)) phase)))
 178
 179 (defun lunar-phase-name (phase)
 180   "Name of lunar PHASE.
 181 0 = new moon, 1 = first quarter, 2 = full moon, 3 = last quarter."
 182   (cond ((= 0 phase) "New Moon")
 183         ((= 1 phase) "First Quarter Moon")
 184         ((= 2 phase) "Full Moon")
 185         ((= 3 phase) "Last Quarter Moon")))
 186
 187 (defun calendar-phases-of-moon ()
 188   "Create a buffer with the lunar phases for the current calendar window."
 189   (interactive)
 190   (message "Computing phases of the moon...")
 191   (let ((m1 displayed-month)
 192         (y1 displayed-year)
 193         (m2 displayed-month)
 194         (y2 displayed-year))
 195     (increment-calendar-month m1 y1 -1)
 196     (increment-calendar-month m2 y2 1)
 197     (set-buffer (get-buffer-create lunar-phases-buffer))
 198     (setq buffer-read-only nil)
 199     (calendar-set-mode-line
 200      (if (= y1 y2)
 201          (format "Phases of the Moon from %s to %s, %d%%-"
 202                  (calendar-month-name m1) (calendar-month-name m2) y2)
 203        (format "Phases of the Moon from %s, %d to %s, %d%%-"
 204                (calendar-month-name m1) y1 (calendar-month-name m2) y2)))
 205     (erase-buffer)
 206     (insert
 207      (mapconcat
 208       '(lambda (x)
 209          (let ((date (car x))
 210                (time (car (cdr x)))
 211                (phase (car (cdr (cdr x)))))
 212            (concat (calendar-date-string date)
 213                    ": "
 214                    (lunar-phase-name phase)
 215                    " "
 216                    time)))
 217       (lunar-phase-list m1 y1) "\n"))
 218     (goto-char (point-min))
 219     (set-buffer-modified-p nil)
 220     (setq buffer-read-only t)
 221     (display-buffer lunar-phases-buffer)
 222     (message "Computing phases of the moon...done")))
 223
 224 ;;;###autoload
 225 (defun phases-of-moon (&optional arg)
 226   "Display the quarters of the moon for last month, this month, and next month.
 227 If called with an optional prefix argument, prompts for month and year.
 228
 229 This function is suitable for execution in a .emacs file."
 230   (interactive "P")
 231   (save-excursion
 232     (let* ((date (if arg
 233                      (calendar-read-date t)
 234                    (calendar-current-date)))
 235            (displayed-month (extract-calendar-month date))
 236            (displayed-year (extract-calendar-year date)))
 237       (calendar-phases-of-moon))))
 238
 239 (defun diary-phases-of-moon ()
 240   "Moon phases diary entry."
 241   (let* ((index (* 4
 242                    (truncate
 243                     (* 12.3685
 244                        (+ (extract-calendar-year date)
 245                           ( / (calendar-day-number date)
 246                               366.0)
 247                           -1900)))))
 248          (phase (lunar-phase index)))
 249     (while (calendar-date-compare phase (list date))
 250       (setq index (1+ index))
 251       (setq phase (lunar-phase index)))
 252     (if (calendar-date-equal (car phase) date)
 253         (concat (lunar-phase-name (car (cdr (cdr phase)))) " "
 254                 (car (cdr phase))))))
 255
 256
 257 ;;  For the Chinese calendar the calculations for the new moon need to be more
 258 ;;  accurate than those above, so we use more terms in the approximation.
 259
 260 (defun lunar-new-moon-time (k)
 261   "Astronomical (Julian) day number of K th new moon."
 262   (let* ((T (/ k 1236.85))
 263          (T2 (* T T))
 264          (T3 (* T T T))
 265          (T4 (* T2 T2))
 266          (JDE (+ 2451550.09765
 267                  (* 29.530588853 k)
 268                  (* 0.0001337 T2)
 269                  (* -0.000000150 T3)
 270                  (* 0.00000000073 T4)))
 271          (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
 272          (sun-anomaly (+ 2.5534
 273                          (* 29.10535669 k)
 274                          (* -0.0000218 T2)
 275                          (* -0.00000011 T3)))
 276          (moon-anomaly (+ 201.5643
 277                           (* 385.81693528 k)
 278                           (* 0.0107438 T2)
 279                           (* 0.00001239 T3)
 280                           (* -0.000000058 T4)))
 281          (moon-argument (+ 160.7108
 282                            (* 390.67050274 k)
 283                            (* -0.0016341 T2)
 284                            (* -0.00000227 T3)
 285                            (* 0.000000011 T4)))
 286          (omega (+ 124.7746
 287                    (* -1.56375580 k)
 288                    (* 0.0020691 T2)
 289                    (* 0.00000215 T3)))
 290          (A1  (+ 299.77 (*  0.107408 k) (* -0.009173 T2)))
 291          (A2  (+ 251.88 (*  0.016321 k)))
 292          (A3  (+ 251.83 (* 26.641886 k)))
 293          (A4  (+ 349.42 (* 36.412478 k)))
 294          (A5  (+  84.66 (* 18.206239 k)))
 295          (A6  (+ 141.74 (* 53.303771 k)))
 296          (A7  (+ 207.14 (*  2.453732 k)))
 297          (A8  (+ 154.84 (*  7.306860 k)))
 298          (A9  (+  34.52 (* 27.261239 k)))
 299          (A10 (+ 207.19 (*  0.121824 k)))
 300          (A11 (+ 291.34 (*  1.844379 k)))
 301          (A12 (+ 161.72 (* 24.198154 k)))
 302          (A13 (+ 239.56 (* 25.513099 k)))
 303          (A14 (+ 331.55 (*  3.592518 k)))
 304          (correction
 305             (+ (* -0.40720   (solar-sin-degrees moon-anomaly))
 306                (*  0.17241 E (solar-sin-degrees sun-anomaly))
 307                (*  0.01608   (solar-sin-degrees (* 2 moon-anomaly)))
 308                (*  0.01039   (solar-sin-degrees (* 2 moon-argument)))
 309                (*  0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
 310                (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
 311                (*  0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
 312                (* -0.00111   (solar-sin-degrees
 313                                (- moon-anomaly (* 2 moon-argument))))
 314                (* -0.00057   (solar-sin-degrees
 315                                (+ moon-anomaly (* 2 moon-argument))))
 316                (*  0.00056 E (solar-sin-degrees
 317                                (+ (* 2 moon-anomaly) sun-anomaly)))
 318                (* -0.00042   (solar-sin-degrees (* 3 moon-anomaly)))
 319                (*  0.00042 E (solar-sin-degrees
 320                                (+ sun-anomaly (* 2 moon-argument))))
 321                (*  0.00038 E (solar-sin-degrees
 322                                (- sun-anomaly (* 2 moon-argument))))
 323                (* -0.00024 E (solar-sin-degrees
 324                                (- (* 2 moon-anomaly) sun-anomaly)))
 325                (* -0.00017   (solar-sin-degrees omega))
 326                (* -0.00007   (solar-sin-degrees
 327                                (+ moon-anomaly (* 2 sun-anomaly))))
 328                (*  0.00004   (solar-sin-degrees
 329                                (- (* 2 moon-anomaly) (* 2 moon-argument))))
 330                (*  0.00004   (solar-sin-degrees (* 3 sun-anomaly)))
 331                (*  0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 332                                                    (* -2 moon-argument))))
 333                (*  0.00003   (solar-sin-degrees
 334                                (+ (* 2 moon-anomaly) (* 2 moon-argument))))
 335                (* -0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 336                                                    (* 2 moon-argument))))
 337                (*  0.00003   (solar-sin-degrees (- moon-anomaly sun-anomaly
 338                                                    (* -2 moon-argument))))
 339                (* -0.00002   (solar-sin-degrees (- moon-anomaly sun-anomaly
 340                                                    (* 2 moon-argument))))
 341                (* -0.00002   (solar-sin-degrees
 342                                (+ (* 3 moon-anomaly) sun-anomaly)))
 343                (*  0.00002   (solar-sin-degrees (* 4 moon-anomaly)))))
 344          (additional
 345             (+ (* 0.000325 (solar-sin-degrees A1))
 346                (* 0.000165 (solar-sin-degrees A2))
 347                (* 0.000164 (solar-sin-degrees A3))
 348                (* 0.000126 (solar-sin-degrees A4))
 349                (* 0.000110 (solar-sin-degrees A5))
 350                (* 0.000062 (solar-sin-degrees A6))
 351                (* 0.000060 (solar-sin-degrees A7))
 352                (* 0.000056 (solar-sin-degrees A8))
 353                (* 0.000047 (solar-sin-degrees A9))
 354                (* 0.000042 (solar-sin-degrees A10))
 355                (* 0.000040 (solar-sin-degrees A11))
 356                (* 0.000037 (solar-sin-degrees A12))
 357                (* 0.000035 (solar-sin-degrees A13))
 358                (* 0.000023 (solar-sin-degrees A14))))
 359          (newJDE (+ JDE correction additional)))
 360     (+ newJDE
 361        (- (solar-ephemeris-correction
 362            (extract-calendar-year
 363             (calendar-gregorian-from-absolute
 364              (floor (calendar-absolute-from-astro newJDE))))))
 365        (/ calendar-time-zone 60.0 24.0))))
 366
 367 (defun lunar-new-moon-on-or-after (d)
 368   "Astronomical (Julian) day number of first new moon on or after astronomical
 369 \(Julian) day number d.  The fractional part is the time of day.
 370
 371 The date and time are local time, including any daylight savings rules,
 372 as governed by the values of calendar-daylight-savings-starts,
 373 calendar-daylight-savings-starts-time, calendar-daylight-savings-ends,
 374 calendar-daylight-savings-ends-time, calendar-daylight-time-offset, and
 375 calendar-time-zone."
 376   (let* ((date (calendar-gregorian-from-absolute
 377                 (floor (calendar-absolute-from-astro d))))
 378          (year (+ (extract-calendar-year date)
 379                   (/ (calendar-day-number date) 365.25)))
 380          (k (floor (* (- year 2000.0) 12.3685)))
 381          (date (lunar-new-moon-time k)))
 382     (while (< date d)
 383       (setq k (1+ k))
 384       (setq date (lunar-new-moon-time k)))
 385     (let* ((a-date (calendar-absolute-from-astro date))
 386            (time (* 24 (- a-date (truncate a-date))))
 387            (date (calendar-gregorian-from-absolute (truncate a-date)))
 388            (adj (dst-adjust-time date time)))
 389       (calendar-astro-from-absolute
 390        (+ (calendar-absolute-from-gregorian (car adj))
 391           (/ (car (cdr adj)) 24.0))))))
 392
 393 (provide 'lunar)
 394
 395 ;;; lunar.el ends here