;;; lunar.el --- calendar functions for phases of the moon.
-;; Copyright (C) 1992, 1993 Free Software Foundation, Inc.
+;; Copyright (C) 1992, 1993, 1995 Free Software Foundation, Inc.
;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
;; Keywords: calendar
;; diary.el.
;; Based on ``Astronomical Formulae for Calculators,'' 3rd ed., by Jean Meeus,
-;; Willmann-Bell, Inc., 1985.
+;; Willmann-Bell, Inc., 1985 and ``Astronomical Algorithms'' by Jean Meeus,
+;; Willmann-Bell, Inc., 1991.
;;
;; WARNING: The calculations will be accurate only to within a few minutes.
60.0 24.0)))
(time (* 24 (- date (truncate date))))
(date (calendar-gregorian-from-absolute (truncate date)))
- (adj (solar-adj-time-for-dst date time)))
+ (adj (dst-adjust-time date time)))
(list (car adj) (apply 'solar-time-string (cdr adj)) phase)))
(defun lunar-phase-name (phase)
(concat (lunar-phase-name (car (cdr (cdr phase)))) " "
(car (cdr phase))))))
+
+;; For the Chinese calendar the calculations for the new moon need to be more
+;; accurate than those above, so we use more terms in the approximation.
+
+(defun lunar-new-moon-time (k)
+ "Astronomical (Julian) day number of K th new moon."
+ (let* ((T (/ k 1236.85))
+ (T2 (* T T))
+ (T3 (* T T T))
+ (T4 (* T2 T2))
+ (JDE (+ 2451550.09765
+ (* 29.530588853 k)
+ (* 0.0001337 T2)
+ (* -0.000000150 T3)
+ (* 0.00000000073 T4)))
+ (E (- 1 (* 0.002516 T) (* 0.0000074 T2)))
+ (sun-anomaly (+ 2.5534
+ (* 29.10535669 k)
+ (* -0.0000218 T2)
+ (* -0.00000011 T3)))
+ (moon-anomaly (+ 201.5643
+ (* 385.81693528 k)
+ (* 0.0107438 T2)
+ (* 0.00001239 T3)
+ (* -0.000000058 T4)))
+ (moon-argument (+ 160.7108
+ (* 390.67050274 k)
+ (* -0.0016341 T2)
+ (* -0.00000227 T3)
+ (* 0.000000011 T4)))
+ (omega (+ 124.7746
+ (* -1.56375580 k)
+ (* 0.0020691 T2)
+ (* 0.00000215 T3)))
+ (A1 (+ 299.77 (* 0.107408 k) (* -0.009173 T2)))
+ (A2 (+ 251.88 (* 0.016321 k)))
+ (A3 (+ 251.83 (* 26.641886 k)))
+ (A4 (+ 349.42 (* 36.412478 k)))
+ (A5 (+ 84.66 (* 18.206239 k)))
+ (A6 (+ 141.74 (* 53.303771 k)))
+ (A7 (+ 207.14 (* 2.453732 k)))
+ (A8 (+ 154.84 (* 7.306860 k)))
+ (A9 (+ 34.52 (* 27.261239 k)))
+ (A10 (+ 207.19 (* 0.121824 k)))
+ (A11 (+ 291.34 (* 1.844379 k)))
+ (A12 (+ 161.72 (* 24.198154 k)))
+ (A13 (+ 239.56 (* 25.513099 k)))
+ (A14 (+ 331.55 (* 3.592518 k)))
+ (correction
+ (+ (* -0.40720 (solar-sin-degrees moon-anomaly))
+ (* 0.17241 E (solar-sin-degrees sun-anomaly))
+ (* 0.01608 (solar-sin-degrees (* 2 moon-anomaly)))
+ (* 0.01039 (solar-sin-degrees (* 2 moon-argument)))
+ (* 0.00739 E (solar-sin-degrees (- moon-anomaly sun-anomaly)))
+ (* -0.00514 E (solar-sin-degrees (+ moon-anomaly sun-anomaly)))
+ (* 0.00208 E E (solar-sin-degrees (* 2 sun-anomaly)))
+ (* -0.00111 (solar-sin-degrees
+ (- moon-anomaly (* 2 moon-argument))))
+ (* -0.00057 (solar-sin-degrees
+ (+ moon-anomaly (* 2 moon-argument))))
+ (* 0.00056 E (solar-sin-degrees
+ (+ (* 2 moon-anomaly) sun-anomaly)))
+ (* -0.00042 (solar-sin-degrees (* 3 moon-anomaly)))
+ (* 0.00042 E (solar-sin-degrees
+ (+ sun-anomaly (* 2 moon-argument))))
+ (* 0.00038 E (solar-sin-degrees
+ (- sun-anomaly (* 2 moon-argument))))
+ (* -0.00024 E (solar-sin-degrees
+ (- (* 2 moon-anomaly) sun-anomaly)))
+ (* -0.00017 (solar-sin-degrees omega))
+ (* -0.00007 (solar-sin-degrees
+ (+ moon-anomaly (* 2 sun-anomaly))))
+ (* 0.00004 (solar-sin-degrees
+ (- (* 2 moon-anomaly) (* 2 moon-argument))))
+ (* 0.00004 (solar-sin-degrees (* 3 sun-anomaly)))
+ (* 0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
+ (* -2 moon-argument))))
+ (* 0.00003 (solar-sin-degrees
+ (+ (* 2 moon-anomaly) (* 2 moon-argument))))
+ (* -0.00003 (solar-sin-degrees (+ moon-anomaly sun-anomaly
+ (* 2 moon-argument))))
+ (* 0.00003 (solar-sin-degrees (- moon-anomaly sun-anomaly
+ (* -2 moon-argument))))
+ (* -0.00002 (solar-sin-degrees (- moon-anomaly sun-anomaly
+ (* 2 moon-argument))))
+ (* -0.00002 (solar-sin-degrees
+ (+ (* 3 moon-anomaly) sun-anomaly)))
+ (* 0.00002 (solar-sin-degrees (* 4 moon-anomaly)))))
+ (additional
+ (+ (* 0.000325 (solar-sin-degrees A1))
+ (* 0.000165 (solar-sin-degrees A2))
+ (* 0.000164 (solar-sin-degrees A3))
+ (* 0.000126 (solar-sin-degrees A4))
+ (* 0.000110 (solar-sin-degrees A5))
+ (* 0.000062 (solar-sin-degrees A6))
+ (* 0.000060 (solar-sin-degrees A7))
+ (* 0.000056 (solar-sin-degrees A8))
+ (* 0.000047 (solar-sin-degrees A9))
+ (* 0.000042 (solar-sin-degrees A10))
+ (* 0.000040 (solar-sin-degrees A11))
+ (* 0.000037 (solar-sin-degrees A12))
+ (* 0.000035 (solar-sin-degrees A13))
+ (* 0.000023 (solar-sin-degrees A14))))
+ (newJDE (+ JDE correction additional)))
+ (+ newJDE
+ (- (solar-ephemeris-correction
+ (extract-calendar-year
+ (calendar-gregorian-from-absolute
+ (floor (calendar-absolute-from-astro newJDE))))))
+ (/ calendar-time-zone 60.0 24.0))))
+
+(defun lunar-new-moon-on-or-after (d)
+ "Astronomical (Julian) day number of first new moon on or after astronomical
+(Julian) day number d. The fractional part is the time of day.
+
+The date and time are local time, including any daylight savings rules,
+as governed by the values of calendar-daylight-savings-starts,
+calendar-daylight-savings-starts-time, calendar-daylight-savings-ends,
+calendar-daylight-savings-ends-time, calendar-daylight-time-offset, and
+calendar-time-zone."
+ (let* ((date (calendar-gregorian-from-absolute
+ (floor (calendar-absolute-from-astro d))))
+ (year (+ (extract-calendar-year date)
+ (/ (calendar-day-number date) 365.25)))
+ (k (floor (* (- year 2000.0) 12.3685)))
+ (date (lunar-new-moon-time k)))
+ (while (< date d)
+ (setq k (1+ k))
+ (setq date (lunar-new-moon-time k)))
+ (let* ((a-date (calendar-absolute-from-astro date))
+ (time (* 24 (- a-date (truncate a-date))))
+ (date (calendar-gregorian-from-absolute (truncate a-date)))
+ (adj (dst-adjust-time date time)))
+ (calendar-astro-from-absolute
+ (+ (calendar-absolute-from-gregorian (car adj))
+ (/ (car (cdr adj)) 24.0))))))
+
(provide 'lunar)
;;; lunar.el ends here
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