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: The Millennium Edition'' by Edward M. Reingold
  42 ;; and Nachum Dershowitz, Cambridge University Press (2001).
  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 (defvar displayed-month)
  53 (defvar displayed-year)
  54
  55 (if (fboundp 'atan)
  56     (require 'lisp-float-type)
  57   (error "Lunar calculations impossible since floating point is unavailable"))
  58
  59 (require 'solar)
  60
  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)
  64         (end-year year)
  65         (start-month month)
  66         (start-year year))
  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)
  73                                    start-year)))
  74            (index (* 4
  75                      (truncate
  76                       (* 12.3685
  77                          (+ year
  78                             ( / (calendar-day-number (list month 1 year))
  79                                 366.0)
  80                             -1900)))))
  81            (new-moon (lunar-phase index))
  82            (list))
  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)))
  88       list)))
  89
  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,
  94 3 last quarter."
  95   (let* ((phase (mod index 4))
  96          (index (/ index 4.0))
  97          (time (/ index 1236.85))
  98          (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
  99                   0.75933
 100                   (* 29.53058868 index)
 101                   (* 0.0001178 time time)
 102                   (* -0.000000155 time time time)
 103                   (* 0.00033
 104                      (solar-sin-degrees (+ 166.56
 105                                            (* 132.87 time)
 106                                            (* -0.009173 time time))))))
 107          (sun-anomaly (mod
 108                        (+ 359.2242
 109                           (* 29.105356 index)
 110                           (* -0.0000333 time time)
 111                           (* -0.00000347 time time time))
 112                        360.0))
 113          (moon-anomaly (mod
 114                         (+ 306.0253
 115                            (* 385.81691806 index)
 116                            (* 0.0107306 time time)
 117                            (* 0.00001236 time time time))
 118                         360.0))
 119          (moon-lat (mod
 120                     (+ 21.2964
 121                        (* 390.67050646 index)
 122                        (* -0.0016528 time time)
 123                        (* -0.00000239 time time time))
 124                     360.0))
 125          (adjustment
 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))))))
 162          (adj (+ 0.0028
 163                  (* -0.0004 (solar-cosine-degrees
 164                              sun-anomaly))
 165                  (* 0.0003 (solar-cosine-degrees
 166                             moon-anomaly))))
 167          (adjustment (cond ((= phase 1) (+ adjustment adj))
 168                            ((= phase 2) (- adjustment adj))
 169                            (t adjustment)))
 170          (date (+ date adjustment))
 171          (date (+ date (/ (- calendar-time-zone
 172                              (solar-ephemeris-correction
 173                               (extract-calendar-year
 174                                (calendar-gregorian-from-absolute
 175                                 (truncate date)))))
 176                           60.0 24.0)))
 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)))
 181
 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")))
 189
 190 (defun calendar-phases-of-moon ()
 191   "Create a buffer with the lunar phases for the current calendar window."
 192   (interactive)
 193   (message "Computing phases of the moon...")
 194   (let ((m1 displayed-month)
 195         (y1 displayed-year)
 196         (m2 displayed-month)
 197         (y2 displayed-year))
 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
 203      (if (= y1 y2)
 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)))
 208     (erase-buffer)
 209     (insert
 210      (mapconcat
 211       '(lambda (x)
 212          (let ((date (car x))
 213                (time (car (cdr x)))
 214                (phase (car (cdr (cdr x)))))
 215            (concat (calendar-date-string date)
 216                    ": "
 217                    (lunar-phase-name phase)
 218                    " "
 219                    time)))
 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")))
 226
 227 ;;;###autoload
 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.
 231
 232 This function is suitable for execution in a .emacs file."
 233   (interactive "P")
 234   (save-excursion
 235     (let* ((date (if arg
 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))))
 241
 242 (defun diary-phases-of-moon (&optional mark)
 243 "Moon phases diary entry.
 244
 245 An optional parameter MARK specifies a face or single-character string to
 246 use when highlighting the day in the calendar."
 247   (let* ((index (* 4
 248                    (truncate
 249                     (* 12.3685
 250                        (+ (extract-calendar-year date)
 251                           ( / (calendar-day-number date)
 252                               366.0)
 253                           -1900)))))
 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)))))))
 261
 262
 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.
 265
 266 (defun lunar-new-moon-time (k)
 267   "Astronomical (Julian) day number of K th new moon."
 268   (let* ((T (/ k 1236.85))
 269          (T2 (* T T))
 270          (T3 (* T T T))
 271          (T4 (* T2 T2))
 272          (JDE (+ 2451550.09765
 273                  (* 29.530588853 k)
 274                  (* 0.0001337 T2)
 275                  (* -0.000000150 T3)
 276                  (* 0.00000000073 T4)))
 277          (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
 278          (sun-anomaly (+ 2.5534
 279                          (* 29.10535669 k)
 280                          (* -0.0000218 T2)
 281                          (* -0.00000011 T3)))
 282          (moon-anomaly (+ 201.5643
 283                           (* 385.81693528 k)
 284                           (* 0.0107438 T2)
 285                           (* 0.00001239 T3)
 286                           (* -0.000000058 T4)))
 287          (moon-argument (+ 160.7108
 288                            (* 390.67050274 k)
 289                            (* -0.0016341 T2)
 290                            (* -0.00000227 T3)
 291                            (* 0.000000011 T4)))
 292          (omega (+ 124.7746
 293                    (* -1.56375580 k)
 294                    (* 0.0020691 T2)
 295                    (* 0.00000215 T3)))
 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)))
 310          (correction
 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)))))
 350          (additional
 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)))
 366     (+ newJDE
 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))))
 372
 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.
 376
 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
 381 calendar-time-zone."
 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)))
 388     (while (< date d)
 389       (setq k (1+ 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))))))
 398
 399 (provide 'lunar)
 400
 401 ;;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
 402 ;;; lunar.el ends here