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 of the License, or
  16 ;; (at your option) 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.  If not, see <http://www.gnu.org/licenses/>.
  25
  26 ;;; Commentary:
  27
  28 ;; See calendar.el.
  29
  30 ;; Based on ``Astronomical Formulae for Calculators,'' 3rd ed., by Jean Meeus,
  31 ;; Willmann-Bell, Inc., 1985 and ``Astronomical Algorithms'' by Jean Meeus,
  32 ;; Willmann-Bell, Inc., 1991.
  33 ;;
  34 ;; WARNING: The calculations will be accurate only to within a few minutes.
  35
  36 ;; The author would be delighted to have an astronomically more sophisticated
  37 ;; person rewrite the code for the lunar calculations in this file!
  38
  39 ;;; Code:
  40
  41 (require 'calendar)
  42 (require 'solar)
  43 (require 'cal-dst)
  44 ;; calendar-astro-to-absolute and v versa are cal-autoloads.
  45 ;;;(require 'cal-julian)
  46
  47 (defun lunar-phase (index)
  48   "Local date and time of lunar phase INDEX.
  49 Integer below INDEX/4 gives the lunation number, counting from Jan 1, 1900;
  50 remainder mod 4 gives the phase: 0 new moon, 1 first quarter, 2 full moon,
  51 3 last quarter."
  52   (let* ((phase (mod index 4))
  53          (index (/ index 4.0))
  54          (time (/ index 1236.85))
  55          (date (+ (calendar-absolute-from-gregorian '(1 0.5 1900))
  56                   0.75933
  57                   (* 29.53058868 index)
  58                   (* 0.0001178 time time)
  59                   (* -0.000000155 time time time)
  60                   (* 0.00033
  61                      (solar-sin-degrees (+ 166.56
  62                                            (* 132.87 time)
  63                                            (* -0.009173 time time))))))
  64          (sun-anomaly (mod
  65                        (+ 359.2242
  66                           (* 29.105356 index)
  67                           (* -0.0000333 time time)
  68                           (* -0.00000347 time time time))
  69                        360.0))
  70          (moon-anomaly (mod
  71                         (+ 306.0253
  72                            (* 385.81691806 index)
  73                            (* 0.0107306 time time)
  74                            (* 0.00001236 time time time))
  75                         360.0))
  76          (moon-lat (mod
  77                     (+ 21.2964
  78                        (* 390.67050646 index)
  79                        (* -0.0016528 time time)
  80                        (* -0.00000239 time time time))
  81                     360.0))
  82          (adjustment
  83           (if (memq phase '(0 2))
  84               (+ (* (- 0.1734 (* 0.000393 time))
  85                     (solar-sin-degrees sun-anomaly))
  86                  (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
  87                  (* -0.4068 (solar-sin-degrees moon-anomaly))
  88                  (* 0.0161 (solar-sin-degrees (* 2 moon-anomaly)))
  89                  (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
  90                  (* 0.0104 (solar-sin-degrees (* 2 moon-lat)))
  91                  (* -0.0051 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
  92                  (* -0.0074 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
  93                  (* 0.0004 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
  94                  (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
  95                  (* -0.0006 (solar-sin-degrees
  96                              (+ (* 2 moon-lat) moon-anomaly)))
  97                  (* 0.0010 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
  98                  (* 0.0005 (solar-sin-degrees
  99                             (+ (* 2 moon-anomaly) sun-anomaly))))
 100             (+ (* (- 0.1721 (* 0.0004 time))
 101                   (solar-sin-degrees sun-anomaly))
 102                (* 0.0021 (solar-sin-degrees (* 2 sun-anomaly)))
 103                (* -0.6280 (solar-sin-degrees moon-anomaly))
 104                (* 0.0089 (solar-sin-degrees (* 2 moon-anomaly)))
 105                (* -0.0004 (solar-sin-degrees (* 3 moon-anomaly)))
 106                (* 0.0079 (solar-sin-degrees (* 2 moon-lat)))
 107                (* -0.0119 (solar-sin-degrees (+ sun-anomaly moon-anomaly)))
 108                (* -0.0047 (solar-sin-degrees (- sun-anomaly moon-anomaly)))
 109                (* 0.0003 (solar-sin-degrees (+ (* 2 moon-lat) sun-anomaly)))
 110                (* -0.0004 (solar-sin-degrees (- (* 2 moon-lat) sun-anomaly)))
 111                (* -0.0006 (solar-sin-degrees (+ (* 2 moon-lat) moon-anomaly)))
 112                (* 0.0021 (solar-sin-degrees (- (* 2 moon-lat) moon-anomaly)))
 113                (* 0.0003 (solar-sin-degrees
 114                           (+ (* 2 moon-anomaly) sun-anomaly)))
 115                (* 0.0004 (solar-sin-degrees
 116                           (- sun-anomaly (* 2 moon-anomaly))))
 117                (* -0.0003 (solar-sin-degrees
 118                            (+ (* 2 sun-anomaly) moon-anomaly))))))
 119          (adj (+ 0.0028
 120                  (* -0.0004 (solar-cosine-degrees
 121                              sun-anomaly))
 122                  (* 0.0003 (solar-cosine-degrees
 123                             moon-anomaly))))
 124          (adjustment (cond ((= phase 1) (+ adjustment adj))
 125                            ((= phase 2) (- adjustment adj))
 126                            (t adjustment)))
 127          (date (+ date adjustment))
 128          (date (+ date (/ (- calendar-time-zone
 129                              (solar-ephemeris-correction
 130                               (calendar-extract-year
 131                                (calendar-gregorian-from-absolute
 132                                 (truncate date)))))
 133                           60.0 24.0)))
 134          (time (* 24 (- date (truncate date))))
 135          (date (calendar-gregorian-from-absolute (truncate date)))
 136          (adj (dst-adjust-time date time)))
 137     (list (car adj) (apply 'solar-time-string (cdr adj)) phase)))
 138
 139 (defun lunar-phase-list (month year)
 140   "List of lunar phases for three months starting with Gregorian MONTH, YEAR."
 141   (let* ((end-month month)
 142          (end-year year)
 143          (start-month month)
 144          (start-year year)
 145          (end-date (progn
 146                      (calendar-increment-month end-month end-year 3)
 147                      (list (list end-month 1 end-year))))
 148          (start-date (progn
 149                        (calendar-increment-month start-month start-year -1)
 150                        (list (list start-month
 151                                    (calendar-last-day-of-month
 152                                     start-month start-year)
 153                                    start-year))))
 154          (index (* 4 (truncate
 155                       (* 12.3685
 156                          (+ year
 157                             ( / (calendar-day-number (list month 1 year))
 158                                 366.0)
 159                             -1900)))))
 160          (new-moon (lunar-phase index))
 161          list)
 162     (while (calendar-date-compare new-moon end-date)
 163       (if (calendar-date-compare start-date new-moon)
 164           (setq list (append list (list new-moon))))
 165       (setq index (1+ index)
 166             new-moon (lunar-phase index)))
 167     list))
 168
 169 (defun lunar-phase-name (phase)
 170   "Name of lunar PHASE.
 171 0 = new moon, 1 = first quarter, 2 = full moon, 3 = last quarter."
 172   (cond ((= 0 phase) "New Moon")
 173         ((= 1 phase) "First Quarter Moon")
 174         ((= 2 phase) "Full Moon")
 175         ((= 3 phase) "Last Quarter Moon")))
 176
 177 (defvar displayed-month)                ; from calendar-generate
 178 (defvar displayed-year)
 179
 180 ;;;###cal-autoload
 181 (defun calendar-phases-of-moon ()
 182   "Create a buffer with the lunar phases for the current calendar window."
 183   (interactive)
 184   (message "Computing phases of the moon...")
 185   (let ((m1 displayed-month)
 186         (y1 displayed-year)
 187         (m2 displayed-month)
 188         (y2 displayed-year))
 189     (calendar-increment-month m1 y1 -1)
 190     (calendar-increment-month m2 y2 1)
 191     (calendar-in-read-only-buffer lunar-phases-buffer
 192       (calendar-set-mode-line
 193        (if (= y1 y2)
 194            (format "Phases of the Moon from %s to %s, %d%%-"
 195                    (calendar-month-name m1) (calendar-month-name m2) y2)
 196          (format "Phases of the Moon from %s, %d to %s, %d%%-"
 197                  (calendar-month-name m1) y1 (calendar-month-name m2) y2)))
 198       (insert
 199        (mapconcat
 200         (lambda (x)
 201           (let ((date (car x))
 202                 (time (cadr x))
 203                 (phase (nth 2 x)))
 204             (concat (calendar-date-string date)
 205                     ": "
 206                     (lunar-phase-name phase)
 207                     " "
 208                     time)))
 209         (lunar-phase-list m1 y1) "\n")))
 210     (message "Computing phases of the moon...done")))
 211
 212 ;; FIXME ?
 213 ;;;###autoload
 214 (defun phases-of-moon (&optional arg)
 215   "Display the quarters of the moon for last month, this month, and next month.
 216 If called with an optional prefix argument ARG, prompts for month and year.
 217 This function is suitable for execution in a .emacs file."
 218   (interactive "P")
 219   (save-excursion
 220     (let* ((date (if arg (calendar-read-date t)
 221                    (calendar-current-date)))
 222            (displayed-month (calendar-extract-month date))
 223            (displayed-year (calendar-extract-year date)))
 224       (calendar-phases-of-moon))))
 225
 226 (defvar date)
 227
 228 ;; To be called from diary-list-sexp-entries, where DATE is bound.
 229
 230 ;;;###diary-autoload
 231 (defun diary-phases-of-moon (&optional mark)
 232   "Moon phases diary entry.
 233 An optional parameter MARK specifies a face or single-character string to
 234 use when highlighting the day in the calendar."
 235   (let* ((index (* 4
 236                    (truncate
 237                     (* 12.3685
 238                        (+ (calendar-extract-year date)
 239                           ( / (calendar-day-number date)
 240                               366.0)
 241                           -1900)))))
 242          (phase (lunar-phase index)))
 243     (while (calendar-date-compare phase (list date))
 244       (setq index (1+ index)
 245             phase (lunar-phase index)))
 246     (if (calendar-date-equal (car phase) date)
 247         (cons mark (concat (lunar-phase-name (nth 2 phase)) " "
 248                            (cadr phase))))))
 249
 250 ;; For the Chinese calendar the calculations for the new moon need to be more
 251 ;; accurate than those above, so we use more terms in the approximation.
 252 (defun lunar-new-moon-time (k)
 253   "Astronomical (Julian) day number of K th new moon."
 254   (let* ((T (/ k 1236.85))
 255          (T2 (* T T))
 256          (T3 (* T T T))
 257          (T4 (* T2 T2))
 258          (JDE (+ 2451550.09765
 259                  (* 29.530588853 k)
 260                  (* 0.0001337 T2)
 261                  (* -0.000000150 T3)
 262                  (* 0.00000000073 T4)))
 263          (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
 264          (sun-anomaly (+ 2.5534
 265                          (* 29.10535669 k)
 266                          (* -0.0000218 T2)
 267                          (* -0.00000011 T3)))
 268          (moon-anomaly (+ 201.5643
 269                           (* 385.81693528 k)
 270                           (* 0.0107438 T2)
 271                           (* 0.00001239 T3)
 272                           (* -0.000000058 T4)))
 273          (moon-argument (+ 160.7108
 274                            (* 390.67050274 k)
 275                            (* -0.0016341 T2)
 276                            (* -0.00000227 T3)
 277                            (* 0.000000011 T4)))
 278          (omega (+ 124.7746
 279                    (* -1.56375580 k)
 280                    (* 0.0020691 T2)
 281                    (* 0.00000215 T3)))
 282          (A1  (+ 299.77 (*  0.107408 k) (* -0.009173 T2)))
 283          (A2  (+ 251.88 (*  0.016321 k)))
 284          (A3  (+ 251.83 (* 26.641886 k)))
 285          (A4  (+ 349.42 (* 36.412478 k)))
 286          (A5  (+  84.66 (* 18.206239 k)))
 287          (A6  (+ 141.74 (* 53.303771 k)))
 288          (A7  (+ 207.14 (*  2.453732 k)))
 289          (A8  (+ 154.84 (*  7.306860 k)))
 290          (A9  (+  34.52 (* 27.261239 k)))
 291          (A10 (+ 207.19 (*  0.121824 k)))
 292          (A11 (+ 291.34 (*  1.844379 k)))
 293          (A12 (+ 161.72 (* 24.198154 k)))
 294          (A13 (+ 239.56 (* 25.513099 k)))
 295          (A14 (+ 331.55 (*  3.592518 k)))
 296          (correction
 297           (+ (* -0.40720   (solar-sin-degrees moon-anomaly))
 298              (*  0.17241 E (solar-sin-degrees sun-anomaly))
 299              (*  0.01608   (solar-sin-degrees (* 2 moon-anomaly)))
 300              (*  0.01039   (solar-sin-degrees (* 2 moon-argument)))
 301              (*  0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
 302              (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
 303              (*  0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
 304              (* -0.00111   (solar-sin-degrees
 305                             (- moon-anomaly (* 2 moon-argument))))
 306              (* -0.00057   (solar-sin-degrees
 307                             (+ moon-anomaly (* 2 moon-argument))))
 308              (*  0.00056 E (solar-sin-degrees
 309                             (+ (* 2 moon-anomaly) sun-anomaly)))
 310              (* -0.00042   (solar-sin-degrees (* 3 moon-anomaly)))
 311              (*  0.00042 E (solar-sin-degrees
 312                             (+ sun-anomaly (* 2 moon-argument))))
 313              (*  0.00038 E (solar-sin-degrees
 314                             (- sun-anomaly (* 2 moon-argument))))
 315              (* -0.00024 E (solar-sin-degrees
 316                             (- (* 2 moon-anomaly) sun-anomaly)))
 317              (* -0.00017   (solar-sin-degrees omega))
 318              (* -0.00007   (solar-sin-degrees
 319                             (+ moon-anomaly (* 2 sun-anomaly))))
 320              (*  0.00004   (solar-sin-degrees
 321                             (- (* 2 moon-anomaly) (* 2 moon-argument))))
 322              (*  0.00004   (solar-sin-degrees (* 3 sun-anomaly)))
 323              (*  0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 324                                                  (* -2 moon-argument))))
 325              (*  0.00003   (solar-sin-degrees
 326                             (+ (* 2 moon-anomaly) (* 2 moon-argument))))
 327              (* -0.00003   (solar-sin-degrees (+ moon-anomaly sun-anomaly
 328                                                  (* 2 moon-argument))))
 329              (*  0.00003   (solar-sin-degrees (- moon-anomaly sun-anomaly
 330                                                  (* -2 moon-argument))))
 331              (* -0.00002   (solar-sin-degrees (- moon-anomaly sun-anomaly
 332                                                  (* 2 moon-argument))))
 333              (* -0.00002   (solar-sin-degrees
 334                             (+ (* 3 moon-anomaly) sun-anomaly)))
 335              (*  0.00002   (solar-sin-degrees (* 4 moon-anomaly)))))
 336          (additional
 337           (+ (* 0.000325 (solar-sin-degrees A1))
 338              (* 0.000165 (solar-sin-degrees A2))
 339              (* 0.000164 (solar-sin-degrees A3))
 340              (* 0.000126 (solar-sin-degrees A4))
 341              (* 0.000110 (solar-sin-degrees A5))
 342              (* 0.000062 (solar-sin-degrees A6))
 343              (* 0.000060 (solar-sin-degrees A7))
 344              (* 0.000056 (solar-sin-degrees A8))
 345              (* 0.000047 (solar-sin-degrees A9))
 346              (* 0.000042 (solar-sin-degrees A10))
 347              (* 0.000040 (solar-sin-degrees A11))
 348              (* 0.000037 (solar-sin-degrees A12))
 349              (* 0.000035 (solar-sin-degrees A13))
 350              (* 0.000023 (solar-sin-degrees A14))))
 351          (newJDE (+ JDE correction additional)))
 352     (+ newJDE
 353        (- (solar-ephemeris-correction
 354            (calendar-extract-year
 355             (calendar-gregorian-from-absolute
 356              (floor (calendar-astro-to-absolute newJDE))))))
 357        (/ calendar-time-zone 60.0 24.0))))
 358
 359 (defun lunar-new-moon-on-or-after (d)
 360   "Julian day number of first new moon on or after Julian day number D.
 361 The fractional part is the time of day.
 362
 363 The date and time are local time, including any daylight saving rules,
 364 as governed by the values of `calendar-daylight-savings-starts',
 365 `calendar-daylight-savings-starts-time', `calendar-daylight-savings-ends',
 366 `calendar-daylight-savings-ends-time', `calendar-daylight-time-offset', and
 367 `calendar-time-zone'."
 368   (let* ((date (calendar-gregorian-from-absolute
 369                 (floor (calendar-astro-to-absolute d))))
 370          (year (+ (calendar-extract-year date)
 371                   (/ (calendar-day-number date) 365.25)))
 372          (k (floor (* (- year 2000.0) 12.3685)))
 373          (date (lunar-new-moon-time k))
 374          (a-date (progn
 375                    (while (< date d)
 376                      (setq k (1+ k)
 377                            date (lunar-new-moon-time k)))
 378                    (calendar-astro-to-absolute date)))
 379          (time (* 24 (- a-date (truncate a-date))))
 380          (date (calendar-gregorian-from-absolute (truncate a-date)))
 381          (adj (dst-adjust-time date time)))
 382     (calendar-astro-from-absolute
 383      (+ (calendar-absolute-from-gregorian (car adj))
 384         (/ (cadr adj) 24.0)))))
 385
 386 (provide 'lunar)
 387
 388 ;; arch-tag: 72f0b8a4-7bcc-4a1b-b67a-ff53c4a1d222
 389 ;;; lunar.el ends here