lisp/calendar/lunar.el

   1 ;;; lunar.el --- calendar functions for phases of the moon
   2
   3 ;; Copyright (C) 1992, 1993, 1995, 1997, 2001, 2002, 2003, 2004, 2005,
   4 ;;   2006, 2007, 2008  Free Software Foundation, Inc.
   5
   6 ;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
   7 ;; Maintainer: Glenn Morris <rgm@gnu.org>
   8 ;; Keywords: calendar
   9 ;; Human-Keywords: moon, lunar phases, calendar, diary
  10
  11 ;; This file is part of GNU Emacs.
  12
  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)
  16 ;; any later version.
  17
  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.
  22
  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.
  27
  28 ;;; Commentary:
  29
  30 ;; This collection of functions implements lunar phases for calendar.el and
  31 ;; diary.el.
  32
  33 ;; Based on ``Astronomical Formulae for Calculators,'' 3rd ed., by Jean Meeus,
  34 ;; Willmann-Bell, Inc., 1985 and ``Astronomical Algorithms'' by Jean Meeus,
  35 ;; Willmann-Bell, Inc., 1991.
  36 ;;
  37 ;; WARNING: The calculations will be accurate only to within a few minutes.
  38
  39 ;; The author would be delighted to have an astronomically more sophisticated
  40 ;; person rewrite the code for the lunar calculations in this file!
  41
  42 ;; Technical details of all the calendrical calculations can be found in
  43 ;; ``Calendrical Calculations: The Millennium Edition'' by Edward M. Reingold
  44 ;; and Nachum Dershowitz, Cambridge University Press (2001).
  45
  46 ;;; Code:
  47
  48 (defvar date)
  49 (defvar displayed-month)
  50 (defvar displayed-year)
  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 ;;;###cal-autoload
 188 (defun calendar-phases-of-moon ()
 189   "Create a buffer with the lunar phases for the current calendar window."
 190   (interactive)
 191   (message "Computing phases of the moon...")
 192   (let ((m1 displayed-month)
 193         (y1 displayed-year)
 194         (m2 displayed-month)
 195         (y2 displayed-year))
 196     (increment-calendar-month m1 y1 -1)
 197     (increment-calendar-month m2 y2 1)
 198     (set-buffer (get-buffer-create lunar-phases-buffer))
 199     (setq buffer-read-only nil)
 200     (calendar-set-mode-line
 201      (if (= y1 y2)
 202          (format "Phases of the Moon from %s to %s, %d%%-"
 203                  (calendar-month-name m1) (calendar-month-name m2) y2)
 204        (format "Phases of the Moon from %s, %d to %s, %d%%-"
 205                (calendar-month-name m1) y1 (calendar-month-name m2) y2)))
 206     (erase-buffer)
 207     (insert
 208      (mapconcat
 209       (lambda (x)
 210          (let ((date (car x))
 211                (time (car (cdr x)))
 212                (phase (car (cdr (cdr x)))))
 213            (concat (calendar-date-string date)
 214                    ": "
 215                    (lunar-phase-name phase)
 216                    " "
 217                    time)))
 218       (lunar-phase-list m1 y1) "\n"))
 219     (goto-char (point-min))
 220     (set-buffer-modified-p nil)
 221     (setq buffer-read-only t)
 222     (display-buffer lunar-phases-buffer)
 223     (message "Computing phases of the moon...done")))
 224
 225 ;;;###autoload
 226 (defun phases-of-moon (&optional arg)
 227   "Display the quarters of the moon for last month, this month, and next month.
 228 If called with an optional prefix argument ARG, prompts for month and year.
 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 ;;;###diary-autoload
 240 (defun diary-phases-of-moon (&optional mark)
 241 "Moon phases diary entry.
 242 An optional parameter MARK specifies a face or single-character string to
 243 use when highlighting the day in the calendar."
 244   (let* ((index (* 4
 245                    (truncate
 246                     (* 12.3685
 247                        (+ (extract-calendar-year date)
 248                           ( / (calendar-day-number date)
 249                               366.0)
 250                           -1900)))))
 251          (phase (lunar-phase index)))
 252     (while (calendar-date-compare phase (list date))
 253       (setq index (1+ index))
 254       (setq phase (lunar-phase index)))
 255     (if (calendar-date-equal (car phase) date)
 256         (cons mark (concat (lunar-phase-name (car (cdr (cdr phase)))) " "
 257                 (car (cdr phase)))))))
 258
 259 ;;  For the Chinese calendar the calculations for the new moon need to be more
 260 ;;  accurate than those above, so we use more terms in the approximation.
 261 (defun lunar-new-moon-time (k)
 262   "Astronomical (Julian) day number of K th new moon."
 263   (let* ((T (/ k 1236.85))
 264          (T2 (* T T))
 265          (T3 (* T T T))
 266          (T4 (* T2 T2))
 267          (JDE (+ 2451550.09765
 268                  (* 29.530588853 k)
 269                  (* 0.0001337 T2)
 270                  (* -0.000000150 T3)
 271                  (* 0.00000000073 T4)))
 272          (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
 273          (sun-anomaly (+ 2.5534
 274                          (* 29.10535669 k)
 275                          (* -0.0000218 T2)
 276                          (* -0.00000011 T3)))
 277          (moon-anomaly (+ 201.5643
 278                           (* 385.81693528 k)
 279                           (* 0.0107438 T2)
 280                           (* 0.00001239 T3)
 281                           (* -0.000000058 T4)))
 282          (moon-argument (+ 160.7108
 283                            (* 390.67050274 k)
 284                            (* -0.0016341 T2)
 285                            (* -0.00000227 T3)
 286                            (* 0.000000011 T4)))
 287          (omega (+ 124.7746
 288                    (* -1.56375580 k)
 289                    (* 0.0020691 T2)
 290                    (* 0.00000215 T3)))
 291          (A1  (+ 299.77 (*  0.107408 k) (* -0.009173 T2)))
 292          (A2  (+ 251.88 (*  0.016321 k)))
 293          (A3  (+ 251.83 (* 26.641886 k)))
 294          (A4  (+ 349.42 (* 36.412478 k)))
 295          (A5  (+  84.66 (* 18.206239 k)))
 296          (A6  (+ 141.74 (* 53.303771 k)))
 297          (A7  (+ 207.14 (*  2.453732 k)))
 298          (A8  (+ 154.84 (*  7.306860 k)))
 299          (A9  (+  34.52 (* 27.261239 k)))
 300          (A10 (+ 207.19 (*  0.121824 k)))
 301          (A11 (+ 291.34 (*  1.844379 k)))
 302          (A12 (+ 161.72 (* 24.198154 k)))
 303          (A13 (+ 239.56 (* 25.513099 k)))
 304          (A14 (+ 331.55 (*  3.592518 k)))
 305          (correction
 306             (+ (* -0.40720   (solar-sin-degrees moon-anomaly))
 307                (*  0.17241 E (solar-sin-degrees sun-anomaly))
 308                (*  0.01608   (solar-sin-degrees (* 2 moon-anomaly)))
 309                (*  0.01039   (solar-sin-degrees (* 2 moon-argument)))
 310                (*  0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
 311                (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
 312                (*  0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
 313                (* -0.00111   (solar-sin-degrees
 314                                (- moon-anomaly (* 2 moon-argument))))
 315                (* -0.00057   (solar-sin-degrees
 316                                (+ moon-anomaly (* 2 moon-argument))))
 317                (*  0.00056 E (solar-sin-degrees
 318                                (+ (* 2 moon-anomaly) sun-anomaly)))
 319                (* -0.00042   (solar-sin-degrees (* 3 moon-anomaly)))
 320                (*  0.00042 E (solar-sin-degrees
 321                                (+ sun-anomaly (* 2 moon-argument))))
 322                (*  0.00038 E (solar-sin-degrees
 323                                (- sun-anomaly (* 2 moon-argument))))
 324                (* -0.00024 E (solar-sin-degrees
 325                                (- (* 2 moon-anomaly) sun-anomaly)))
 326                (* -0.00017   (solar-sin-degrees omega))
 327                (* -0.00007   (solar-sin-degrees
 328                                (+ moon-anomaly (* 2 sun-anomaly))))
 329                (*  0.00004   (solar-sin-degrees
 330                                (- (* 2 moon-anomaly) (* 2 moon-argument))))
 331                (*  0.00004   (solar-sin-degrees (* 3 sun-anomaly)))
 332                (*  0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 333                                                    (* -2 moon-argument))))
 334                (*  0.00003   (solar-sin-degrees
 335                                (+ (* 2 moon-anomaly) (* 2 moon-argument))))
 336                (* -0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 337                                                    (* 2 moon-argument))))
 338                (*  0.00003   (solar-sin-degrees (- moon-anomaly sun-anomaly
 339                                                    (* -2 moon-argument))))
 340                (* -0.00002   (solar-sin-degrees (- moon-anomaly sun-anomaly
 341                                                    (* 2 moon-argument))))
 342                (* -0.00002   (solar-sin-degrees
 343                                (+ (* 3 moon-anomaly) sun-anomaly)))
 344                (*  0.00002   (solar-sin-degrees (* 4 moon-anomaly)))))
 345          (additional
 346             (+ (* 0.000325 (solar-sin-degrees A1))
 347                (* 0.000165 (solar-sin-degrees A2))
 348                (* 0.000164 (solar-sin-degrees A3))
 349                (* 0.000126 (solar-sin-degrees A4))
 350                (* 0.000110 (solar-sin-degrees A5))
 351                (* 0.000062 (solar-sin-degrees A6))
 352                (* 0.000060 (solar-sin-degrees A7))
 353                (* 0.000056 (solar-sin-degrees A8))
 354                (* 0.000047 (solar-sin-degrees A9))
 355                (* 0.000042 (solar-sin-degrees A10))
 356                (* 0.000040 (solar-sin-degrees A11))
 357                (* 0.000037 (solar-sin-degrees A12))
 358                (* 0.000035 (solar-sin-degrees A13))
 359                (* 0.000023 (solar-sin-degrees A14))))
 360          (newJDE (+ JDE correction additional)))
 361     (+ newJDE
 362        (- (solar-ephemeris-correction
 363            (extract-calendar-year
 364             (calendar-gregorian-from-absolute
 365              (floor (calendar-absolute-from-astro newJDE))))))
 366        (/ calendar-time-zone 60.0 24.0))))
 367
 368 (defun lunar-new-moon-on-or-after (d)
 369   "Julian day number of first new moon on or after Julian day number D.
 370 The fractional part is the time of day.
 371
 372 The date and time are local time, including any daylight saving rules,
 373 as governed by the values of calendar-daylight-savings-starts,
 374 calendar-daylight-savings-starts-time, calendar-daylight-savings-ends,
 375 calendar-daylight-savings-ends-time, calendar-daylight-time-offset, and
 376 calendar-time-zone."
 377   (let* ((date (calendar-gregorian-from-absolute
 378                 (floor (calendar-absolute-from-astro d))))
 379          (year (+ (extract-calendar-year date)
 380                   (/ (calendar-day-number date) 365.25)))
 381          (k (floor (* (- year 2000.0) 12.3685)))
 382          (date (lunar-new-moon-time k)))
 383     (while (< date d)
 384       (setq k (1+ k))
 385       (setq date (lunar-new-moon-time k)))
 386     (let* ((a-date (calendar-absolute-from-astro date))
 387            (time (* 24 (- a-date (truncate a-date))))
 388            (date (calendar-gregorian-from-absolute (truncate a-date)))
 389            (adj (dst-adjust-time date time)))
 390       (calendar-astro-from-absolute
 391        (+ (calendar-absolute-from-gregorian (car adj))
 392           (/ (car (cdr adj)) 24.0))))))
 393
 394 (provide 'lunar)
 395
 396 ;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
 397 ;;; lunar.el ends here