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., 51 Franklin Street, Fifth Floor,
  24 ;; Boston, MA 02110-1301, 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 date)
  53 (defvar displayed-month)
  54 (defvar displayed-year)
  55
  56 (if (fboundp 'atan)
  57     (require 'lisp-float-type)
  58   (error "Lunar calculations impossible since floating point is unavailable"))
  59
  60 (require 'solar)
  61
  62 (defun lunar-phase-list (month year)
  63   "List of lunar phases for three months starting with Gregorian MONTH, YEAR."
  64   (let ((end-month month)
  65         (end-year year)
  66         (start-month month)
  67         (start-year year))
  68     (increment-calendar-month end-month end-year 3)
  69     (increment-calendar-month start-month start-year -1)
  70     (let* ((end-date (list (list end-month 1 end-year)))
  71            (start-date (list (list start-month
  72                                    (calendar-last-day-of-month
  73                                     start-month start-year)
  74                                    start-year)))
  75            (index (* 4
  76                      (truncate
  77                       (* 12.3685
  78                          (+ year
  79                             ( / (calendar-day-number (list month 1 year))
  80                                 366.0)
  81                             -1900)))))
  82            (new-moon (lunar-phase index))
  83            (list))
  84       (while (calendar-date-compare new-moon end-date)
  85         (if (calendar-date-compare start-date new-moon)
  86             (setq list (append list (list new-moon))))
  87         (setq index (1+ index))
  88         (setq new-moon (lunar-phase index)))
  89       list)))
  90
  91 (defun lunar-phase (index)
  92   "Local date and time of lunar phase INDEX.
  93 Integer below INDEX/4 gives the lunation number, counting from Jan 1, 1900;
  94 remainder mod 4 gives the phase: 0 new moon, 1 first quarter, 2 full moon,
  95 3 last quarter."
  96   (let* ((phase (mod index 4))
  97          (index (/ index 4.0))
  98          (time (/ index 1236.85))
  99          (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
 100                   0.75933
 101                   (* 29.53058868 index)
 102                   (* 0.0001178 time time)
 103                   (* -0.000000155 time time time)
 104                   (* 0.00033
 105                      (solar-sin-degrees (+ 166.56
 106                                            (* 132.87 time)
 107                                            (* -0.009173 time time))))))
 108          (sun-anomaly (mod
 109                        (+ 359.2242
 110                           (* 29.105356 index)
 111                           (* -0.0000333 time time)
 112                           (* -0.00000347 time time time))
 113                        360.0))
 114          (moon-anomaly (mod
 115                         (+ 306.0253
 116                            (* 385.81691806 index)
 117                            (* 0.0107306 time time)
 118                            (* 0.00001236 time time time))
 119                         360.0))
 120          (moon-lat (mod
 121                     (+ 21.2964
 122                        (* 390.67050646 index)
 123                        (* -0.0016528 time time)
 124                        (* -0.00000239 time time time))
 125                     360.0))
 126          (adjustment
 127           (if (memq phase '(0 2))
 128               (+ (* (- 0.1734 (* 0.000393 time))
 129                     (solar-sin-degrees sun-anomaly))
 130                  (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
 131                  (* -0.4068 (solar-sin-degrees moon-anomaly))
 132                  (* 0.0161 (solar-sin-degrees (* 2 moon-anomaly)))
 133                  (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
 134                  (* 0.0104 (solar-sin-degrees (* 2 moon-lat)))
 135                  (* -0.0051 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
 136                  (* -0.0074 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
 137                  (* 0.0004 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
 138                  (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
 139                  (* -0.0006 (solar-sin-degrees
 140                              (+ (* 2 moon-lat) moon-anomaly)))
 141                  (* 0.0010 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
 142                  (* 0.0005 (solar-sin-degrees
 143                             (+ (* 2 moon-anomaly) sun-anomaly))))
 144             (+ (* (- 0.1721 (* 0.0004 time))
 145                   (solar-sin-degrees sun-anomaly))
 146                (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
 147                (* -0.6280 (solar-sin-degrees moon-anomaly))
 148                (* 0.0089 (solar-sin-degrees (* 2 moon-anomaly)))
 149                (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
 150                (* 0.0079 (solar-sin-degrees (* 2 moon-lat)))
 151                (* -0.0119 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
 152                (* -0.0047 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
 153                (* 0.0003 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
 154                (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
 155                (* -0.0006 (solar-sin-degrees (+ (* 2 moon-lat) moon-anomaly)))
 156                (* 0.0021 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
 157                (* 0.0003 (solar-sin-degrees
 158                           (+ (* 2 moon-anomaly) sun-anomaly)))
 159                (* 0.0004 (solar-sin-degrees
 160                           (- sun-anomaly (* 2 moon-anomaly))))
 161                (* -0.0003 (solar-sin-degrees
 162                           (+ (* 2 sun-anomaly) moon-anomaly))))))
 163          (adj (+ 0.0028
 164                  (* -0.0004 (solar-cosine-degrees
 165                              sun-anomaly))
 166                  (* 0.0003 (solar-cosine-degrees
 167                             moon-anomaly))))
 168          (adjustment (cond ((= phase 1) (+ adjustment adj))
 169                            ((= phase 2) (- adjustment adj))
 170                            (t adjustment)))
 171          (date (+ date adjustment))
 172          (date (+ date (/ (- calendar-time-zone
 173                              (solar-ephemeris-correction
 174                               (extract-calendar-year
 175                                (calendar-gregorian-from-absolute
 176                                 (truncate date)))))
 177                           60.0 24.0)))
 178          (time (* 24 (- date (truncate date))))
 179          (date (calendar-gregorian-from-absolute (truncate date)))
 180          (adj (dst-adjust-time date time)))
 181     (list (car adj) (apply 'solar-time-string (cdr adj)) phase)))
 182
 183 (defun lunar-phase-name (phase)
 184   "Name of lunar PHASE.
 185 0 = new moon, 1 = first quarter, 2 = full moon, 3 = last quarter."
 186   (cond ((= 0 phase) "New Moon")
 187         ((= 1 phase) "First Quarter Moon")
 188         ((= 2 phase) "Full Moon")
 189         ((= 3 phase) "Last Quarter Moon")))
 190
 191 (defun calendar-phases-of-moon ()
 192   "Create a buffer with the lunar phases for the current calendar window."
 193   (interactive)
 194   (message "Computing phases of the moon...")
 195   (let ((m1 displayed-month)
 196         (y1 displayed-year)
 197         (m2 displayed-month)
 198         (y2 displayed-year))
 199     (increment-calendar-month m1 y1 -1)
 200     (increment-calendar-month m2 y2 1)
 201     (set-buffer (get-buffer-create lunar-phases-buffer))
 202     (setq buffer-read-only nil)
 203     (calendar-set-mode-line
 204      (if (= y1 y2)
 205          (format "Phases of the Moon from %s to %s, %d%%-"
 206                  (calendar-month-name m1) (calendar-month-name m2) y2)
 207        (format "Phases of the Moon from %s, %d to %s, %d%%-"
 208                (calendar-month-name m1) y1 (calendar-month-name m2) y2)))
 209     (erase-buffer)
 210     (insert
 211      (mapconcat
 212       '(lambda (x)
 213          (let ((date (car x))
 214                (time (car (cdr x)))
 215                (phase (car (cdr (cdr x)))))
 216            (concat (calendar-date-string date)
 217                    ": "
 218                    (lunar-phase-name phase)
 219                    " "
 220                    time)))
 221       (lunar-phase-list m1 y1) "\n"))
 222     (goto-char (point-min))
 223     (set-buffer-modified-p nil)
 224     (setq buffer-read-only t)
 225     (display-buffer lunar-phases-buffer)
 226     (message "Computing phases of the moon...done")))
 227
 228 ;;;###autoload
 229 (defun phases-of-moon (&optional arg)
 230   "Display the quarters of the moon for last month, this month, and next month.
 231 If called with an optional prefix argument, prompts for month and year.
 232
 233 This function is suitable for execution in a .emacs file."
 234   (interactive "P")
 235   (save-excursion
 236     (let* ((date (if arg
 237                      (calendar-read-date t)
 238                    (calendar-current-date)))
 239            (displayed-month (extract-calendar-month date))
 240            (displayed-year (extract-calendar-year date)))
 241       (calendar-phases-of-moon))))
 242
 243 (defun diary-phases-of-moon (&optional mark)
 244 "Moon phases diary entry.
 245
 246 An optional parameter MARK specifies a face or single-character string to
 247 use when highlighting the day in the calendar."
 248   (let* ((index (* 4
 249                    (truncate
 250                     (* 12.3685
 251                        (+ (extract-calendar-year date)
 252                           ( / (calendar-day-number date)
 253                               366.0)
 254                           -1900)))))
 255          (phase (lunar-phase index)))
 256     (while (calendar-date-compare phase (list date))
 257       (setq index (1+ index))
 258       (setq phase (lunar-phase index)))
 259     (if (calendar-date-equal (car phase) date)
 260         (cons mark (concat (lunar-phase-name (car (cdr (cdr phase)))) " "
 261                 (car (cdr phase)))))))
 262
 263
 264 ;;  For the Chinese calendar the calculations for the new moon need to be more
 265 ;;  accurate than those above, so we use more terms in the approximation.
 266
 267 (defun lunar-new-moon-time (k)
 268   "Astronomical (Julian) day number of K th new moon."
 269   (let* ((T (/ k 1236.85))
 270          (T2 (* T T))
 271          (T3 (* T T T))
 272          (T4 (* T2 T2))
 273          (JDE (+ 2451550.09765
 274                  (* 29.530588853 k)
 275                  (* 0.0001337 T2)
 276                  (* -0.000000150 T3)
 277                  (* 0.00000000073 T4)))
 278          (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
 279          (sun-anomaly (+ 2.5534
 280                          (* 29.10535669 k)
 281                          (* -0.0000218 T2)
 282                          (* -0.00000011 T3)))
 283          (moon-anomaly (+ 201.5643
 284                           (* 385.81693528 k)
 285                           (* 0.0107438 T2)
 286                           (* 0.00001239 T3)
 287                           (* -0.000000058 T4)))
 288          (moon-argument (+ 160.7108
 289                            (* 390.67050274 k)
 290                            (* -0.0016341 T2)
 291                            (* -0.00000227 T3)
 292                            (* 0.000000011 T4)))
 293          (omega (+ 124.7746
 294                    (* -1.56375580 k)
 295                    (* 0.0020691 T2)
 296                    (* 0.00000215 T3)))
 297          (A1  (+ 299.77 (*  0.107408 k) (* -0.009173 T2)))
 298          (A2  (+ 251.88 (*  0.016321 k)))
 299          (A3  (+ 251.83 (* 26.641886 k)))
 300          (A4  (+ 349.42 (* 36.412478 k)))
 301          (A5  (+  84.66 (* 18.206239 k)))
 302          (A6  (+ 141.74 (* 53.303771 k)))
 303          (A7  (+ 207.14 (*  2.453732 k)))
 304          (A8  (+ 154.84 (*  7.306860 k)))
 305          (A9  (+  34.52 (* 27.261239 k)))
 306          (A10 (+ 207.19 (*  0.121824 k)))
 307          (A11 (+ 291.34 (*  1.844379 k)))
 308          (A12 (+ 161.72 (* 24.198154 k)))
 309          (A13 (+ 239.56 (* 25.513099 k)))
 310          (A14 (+ 331.55 (*  3.592518 k)))
 311          (correction
 312             (+ (* -0.40720   (solar-sin-degrees moon-anomaly))
 313                (*  0.17241 E (solar-sin-degrees sun-anomaly))
 314                (*  0.01608   (solar-sin-degrees (* 2 moon-anomaly)))
 315                (*  0.01039   (solar-sin-degrees (* 2 moon-argument)))
 316                (*  0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
 317                (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
 318                (*  0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
 319                (* -0.00111   (solar-sin-degrees
 320                                (- moon-anomaly (* 2 moon-argument))))
 321                (* -0.00057   (solar-sin-degrees
 322                                (+ moon-anomaly (* 2 moon-argument))))
 323                (*  0.00056 E (solar-sin-degrees
 324                                (+ (* 2 moon-anomaly) sun-anomaly)))
 325                (* -0.00042   (solar-sin-degrees (* 3 moon-anomaly)))
 326                (*  0.00042 E (solar-sin-degrees
 327                                (+ sun-anomaly (* 2 moon-argument))))
 328                (*  0.00038 E (solar-sin-degrees
 329                                (- sun-anomaly (* 2 moon-argument))))
 330                (* -0.00024 E (solar-sin-degrees
 331                                (- (* 2 moon-anomaly) sun-anomaly)))
 332                (* -0.00017   (solar-sin-degrees omega))
 333                (* -0.00007   (solar-sin-degrees
 334                                (+ moon-anomaly (* 2 sun-anomaly))))
 335                (*  0.00004   (solar-sin-degrees
 336                                (- (* 2 moon-anomaly) (* 2 moon-argument))))
 337                (*  0.00004   (solar-sin-degrees (* 3 sun-anomaly)))
 338                (*  0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 339                                                    (* -2 moon-argument))))
 340                (*  0.00003   (solar-sin-degrees
 341                                (+ (* 2 moon-anomaly) (* 2 moon-argument))))
 342                (* -0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 343                                                    (* 2 moon-argument))))
 344                (*  0.00003   (solar-sin-degrees (- moon-anomaly sun-anomaly
 345                                                    (* -2 moon-argument))))
 346                (* -0.00002   (solar-sin-degrees (- moon-anomaly sun-anomaly
 347                                                    (* 2 moon-argument))))
 348                (* -0.00002   (solar-sin-degrees
 349                                (+ (* 3 moon-anomaly) sun-anomaly)))
 350                (*  0.00002   (solar-sin-degrees (* 4 moon-anomaly)))))
 351          (additional
 352             (+ (* 0.000325 (solar-sin-degrees A1))
 353                (* 0.000165 (solar-sin-degrees A2))
 354                (* 0.000164 (solar-sin-degrees A3))
 355                (* 0.000126 (solar-sin-degrees A4))
 356                (* 0.000110 (solar-sin-degrees A5))
 357                (* 0.000062 (solar-sin-degrees A6))
 358                (* 0.000060 (solar-sin-degrees A7))
 359                (* 0.000056 (solar-sin-degrees A8))
 360                (* 0.000047 (solar-sin-degrees A9))
 361                (* 0.000042 (solar-sin-degrees A10))
 362                (* 0.000040 (solar-sin-degrees A11))
 363                (* 0.000037 (solar-sin-degrees A12))
 364                (* 0.000035 (solar-sin-degrees A13))
 365                (* 0.000023 (solar-sin-degrees A14))))
 366          (newJDE (+ JDE correction additional)))
 367     (+ newJDE
 368        (- (solar-ephemeris-correction
 369            (extract-calendar-year
 370             (calendar-gregorian-from-absolute
 371              (floor (calendar-absolute-from-astro newJDE))))))
 372        (/ calendar-time-zone 60.0 24.0))))
 373
 374 (defun lunar-new-moon-on-or-after (d)
 375   "Astronomical (Julian) day number of first new moon on or after astronomical
 376 \(Julian) day number d.  The fractional part is the time of day.
 377
 378 The date and time are local time, including any daylight savings rules,
 379 as governed by the values of calendar-daylight-savings-starts,
 380 calendar-daylight-savings-starts-time, calendar-daylight-savings-ends,
 381 calendar-daylight-savings-ends-time, calendar-daylight-time-offset, and
 382 calendar-time-zone."
 383   (let* ((date (calendar-gregorian-from-absolute
 384                 (floor (calendar-absolute-from-astro d))))
 385          (year (+ (extract-calendar-year date)
 386                   (/ (calendar-day-number date) 365.25)))
 387          (k (floor (* (- year 2000.0) 12.3685)))
 388          (date (lunar-new-moon-time k)))
 389     (while (< date d)
 390       (setq k (1+ k))
 391       (setq date (lunar-new-moon-time k)))
 392     (let* ((a-date (calendar-absolute-from-astro date))
 393            (time (* 24 (- a-date (truncate a-date))))
 394            (date (calendar-gregorian-from-absolute (truncate a-date)))
 395            (adj (dst-adjust-time date time)))
 396       (calendar-astro-from-absolute
 397        (+ (calendar-absolute-from-gregorian (car adj))
 398           (/ (car (cdr adj)) 24.0))))))
 399
 400 (provide 'lunar)
 401
 402 ;;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
 403 ;;; lunar.el ends here