;;; solar.el --- calendar functions for solar events
;; Copyright (C) 1992, 1993, 1995, 1997, 2001, 2002, 2003, 2004, 2005,
-;; 2006, 2007, 2008 Free Software Foundation, Inc.
+;; 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
;; Author: Edward M. Reingold <reingold@cs.uiuc.edu>
;; Denis B. Roegel <Denis.Roegel@loria.fr>
;; Maintainer: Glenn Morris <rgm@gnu.org>
;; Keywords: calendar
;; Human-Keywords: sunrise, sunset, equinox, solstice, calendar, diary, holidays
+;; Package: calendar
;; This file is part of GNU Emacs.
-;; GNU Emacs is free software; you can redistribute it and/or modify
+;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
-;; the Free Software Foundation; either version 3, or (at your option)
-;; any later version.
+;; the Free Software Foundation, either version 3 of the License, or
+;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
-;; along with GNU Emacs; see the file COPYING. If not, write to the
-;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
-;; Boston, MA 02110-1301, USA.
+;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;; Commentary:
-;; This collection of functions implements the features of calendar.el,
-;; diary.el, and holiday.el that deal with times of day, sunrise/sunset, and
-;; equinoxes/solstices.
+;; See calendar.el. This file implements features that deal with
+;; times of day, sunrise/sunset, and equinoxes/solstices.
;; Based on the ``Almanac for Computers 1984,'' prepared by the Nautical
;; Almanac Office, United States Naval Observatory, Washington, 1984, on
;; 2. Equinox/solstice times will be accurate to the minute for years
;; 1951--2050. For other years the times will be within +/- 1 minute.
-;; Technical details of all the calendrical calculations can be found in
-;; ``Calendrical Calculations: The Millennium Edition'' by Edward M. Reingold
-;; and Nachum Dershowitz, Cambridge University Press (2001).
-
;;; Code:
-(defvar displayed-month)
-(defvar displayed-year)
-
-(if (fboundp 'atan)
- (require 'lisp-float-type)
- (error "Solar calculations impossible since floating point is unavailable"))
-
+(require 'calendar)
(require 'cal-dst)
-(require 'cal-julian)
+;; calendar-astro-to-absolute and v versa are cal-autoloads.
+;;;(require 'cal-julian)
(defcustom calendar-time-display-form
(/ (aref calendar-latitude 1) 60.0)))
(if (numberp calendar-latitude)
(if (> calendar-latitude 0) "N" "S")
- (if (equal (aref calendar-latitude 2) 'north) "N" "S"))
+ (if (eq (aref calendar-latitude 2) 'north) "N" "S"))
(if (numberp calendar-longitude)
(abs calendar-longitude)
(+ (aref calendar-longitude 0)
(/ (aref calendar-longitude 1) 60.0)))
(if (numberp calendar-longitude)
(if (> calendar-longitude 0) "E" "W")
- (if (equal (aref calendar-longitude 2) 'east) "E" "W"))))
+ (if (eq (aref calendar-longitude 2) 'east) "E" "W"))))
"Expression evaluating to the name of the calendar location.
For example, \"New York City\". The default value is just the
variable `calendar-latitude' paired with the variable `calendar-longitude'.
:type 'number
:group 'calendar)
-(defcustom diary-sabbath-candles-minutes 18
- "Number of minutes before sunset for sabbath candle lighting."
- :group 'diary
- :type 'integer
- :version "21.1")
-
-
-;;; End of user options.
-
-
-(defvar solar-n-hemi-seasons
+(defcustom solar-n-hemi-seasons
'("Vernal Equinox" "Summer Solstice" "Autumnal Equinox" "Winter Solstice")
- "List of season changes for the northern hemisphere.")
+ "List of season changes for the northern hemisphere."
+ :type '(list
+ (string :tag "Vernal Equinox")
+ (string :tag "Summer Solstice")
+ (string :tag "Autumnal Equinox")
+ (string :tag "Winter Solstice"))
+ :group 'calendar)
-(defvar solar-s-hemi-seasons
+(defcustom solar-s-hemi-seasons
'("Autumnal Equinox" "Winter Solstice" "Vernal Equinox" "Summer Solstice")
- "List of season changes for the southern hemisphere.")
+ "List of season changes for the southern hemisphere."
+ :type '(list
+ (string :tag "Autumnal Equinox")
+ (string :tag "Winter Solstice")
+ (string :tag "Vernal Equinox")
+ (string :tag "Summer Solstice"))
+ :group 'calendar)
+
+;;; End of user options.
-(defvar solar-sidereal-time-greenwich-midnight
- nil
+(defvar solar-sidereal-time-greenwich-midnight nil
"Sidereal time at Greenwich at midnight (universal time).")
(defvar solar-northern-spring-or-summer-season nil
calendar-latitude
(let ((lat (+ (aref calendar-latitude 0)
(/ (aref calendar-latitude 1) 60.0))))
- (if (equal (aref calendar-latitude 2) 'north)
+ (if (eq (aref calendar-latitude 2) 'north)
lat
(- lat)))))
calendar-longitude
(let ((long (+ (aref calendar-longitude 0)
(/ (aref calendar-longitude 1) 60.0))))
- (if (equal (aref calendar-longitude 2) 'east)
+ (if (eq (aref calendar-longitude 2) 'east)
long
(- long)))))
+(defun solar-get-number (prompt)
+ "Return a number from the minibuffer, prompting with PROMPT.
+Returns nil if nothing was entered."
+ (let ((x (read-string prompt "")))
+ (unless (string-equal x "")
+ (string-to-number x))))
+
(defun solar-setup ()
"Prompt for `calendar-longitude', `calendar-latitude', `calendar-time-zone'."
(beep)
"Enter difference from Coordinated Universal Time (in minutes): ")
)))
-(defun solar-get-number (prompt)
- "Return a number from the minibuffer, prompting with PROMPT.
-Returns nil if nothing was entered."
- (let ((x (read-string prompt "")))
- (if (not (string-equal x ""))
- (string-to-number x))))
-
(defun solar-sin-degrees (x)
"Return sin of X degrees."
(sin (degrees-to-radians (mod x 360.0))))
(defun solar-arctan (x quad)
"Arctangent of X in quadrant QUAD."
(let ((deg (radians-to-degrees (atan x))))
- (cond ((equal quad 2) (+ deg 180))
- ((equal quad 3) (+ deg 180))
- ((equal quad 4) (+ deg 360))
- (t deg))))
+ (cond ((= quad 2) (+ deg 180))
+ ((= quad 3) (+ deg 180))
+ ((= quad 4) (+ deg 360))
+ (t deg))))
(defun solar-atn2 (x y)
"Arctangent of point X, Y."
(* (solar-sin-degrees obliquity)
(solar-sin-degrees longitude))))
-(defun solar-sunrise-and-sunset (time latitude longitude height)
- "Sunrise, sunset and length of day.
-Parameters are the midday TIME and the LATITUDE, LONGITUDE of the location.
+(defun solar-ecliptic-coordinates (time sunrise-flag)
+ "Return solar longitude, ecliptic inclination, equation of time, nutation.
+Values are for TIME in Julian centuries of Ephemeris Time since
+January 1st, 2000, at 12 ET. Longitude and inclination are in
+degrees, equation of time in hours, and nutation in seconds of longitude.
+If SUNRISE-FLAG is non-nil, only calculate longitude and inclination."
+ (let* ((l (+ 280.46645
+ (* 36000.76983 time)
+ (* 0.0003032 time time))) ; sun mean longitude
+ (ml (+ 218.3165
+ (* 481267.8813 time))) ; moon mean longitude
+ (m (+ 357.52910
+ (* 35999.05030 time)
+ (* -0.0001559 time time)
+ (* -0.00000048 time time time))) ; sun mean anomaly
+ (i (+ 23.43929111 (* -0.013004167 time)
+ (* -0.00000016389 time time)
+ (* 0.0000005036 time time time))) ; mean inclination
+ (c (+ (* (+ 1.914600
+ (* -0.004817 time)
+ (* -0.000014 time time))
+ (solar-sin-degrees m))
+ (* (+ 0.019993 (* -0.000101 time))
+ (solar-sin-degrees (* 2 m)))
+ (* 0.000290
+ (solar-sin-degrees (* 3 m))))) ; center equation
+ (L (+ l c)) ; total longitude
+ ;; Longitude of moon's ascending node on the ecliptic.
+ (omega (+ 125.04
+ (* -1934.136 time)))
+ ;; nut = nutation in longitude, measured in seconds of angle.
+ (nut (unless sunrise-flag
+ (+ (* -17.20 (solar-sin-degrees omega))
+ (* -1.32 (solar-sin-degrees (* 2 l)))
+ (* -0.23 (solar-sin-degrees (* 2 ml)))
+ (* 0.21 (solar-sin-degrees (* 2 omega))))))
+ (ecc (unless sunrise-flag ; eccentricity of earth's orbit
+ (+ 0.016708617
+ (* -0.000042037 time)
+ (* -0.0000001236 time time))))
+ (app (+ L ; apparent longitude of sun
+ -0.00569
+ (* -0.00478
+ (solar-sin-degrees omega))))
+ (y (unless sunrise-flag
+ (* (solar-tangent-degrees (/ i 2))
+ (solar-tangent-degrees (/ i 2)))))
+ ;; Equation of time, in hours.
+ (time-eq (unless sunrise-flag
+ (/ (* 12 (+ (* y (solar-sin-degrees (* 2 l)))
+ (* -2 ecc (solar-sin-degrees m))
+ (* 4 ecc y (solar-sin-degrees m)
+ (solar-cosine-degrees (* 2 l)))
+ (* -0.5 y y (solar-sin-degrees (* 4 l)))
+ (* -1.25 ecc ecc (solar-sin-degrees (* 2 m)))))
+ 3.1415926535))))
+ (list app i time-eq nut)))
+
+(defun solar-ephemeris-correction (year)
+ "Ephemeris time minus Universal Time during Gregorian YEAR.
+Result is in days. For the years 1800-1987, the maximum error is
+1.9 seconds. For the other years, the maximum error is about 30 seconds."
+ (cond ((and (<= 1988 year) (< year 2020))
+ (/ (+ year -2000 67.0) 60.0 60.0 24.0))
+ ((and (<= 1900 year) (< year 1988))
+ (let* ((theta (/ (- (calendar-astro-from-absolute
+ (calendar-absolute-from-gregorian
+ (list 7 1 year)))
+ (calendar-astro-from-absolute
+ (calendar-absolute-from-gregorian
+ '(1 1 1900))))
+ 36525.0))
+ (theta2 (* theta theta))
+ (theta3 (* theta2 theta))
+ (theta4 (* theta2 theta2))
+ (theta5 (* theta3 theta2)))
+ (+ -0.00002
+ (* 0.000297 theta)
+ (* 0.025184 theta2)
+ (* -0.181133 theta3)
+ (* 0.553040 theta4)
+ (* -0.861938 theta5)
+ (* 0.677066 theta3 theta3)
+ (* -0.212591 theta4 theta3))))
+ ((and (<= 1800 year) (< year 1900))
+ (let* ((theta (/ (- (calendar-astro-from-absolute
+ (calendar-absolute-from-gregorian
+ (list 7 1 year)))
+ (calendar-astro-from-absolute
+ (calendar-absolute-from-gregorian
+ '(1 1 1900))))
+ 36525.0))
+ (theta2 (* theta theta))
+ (theta3 (* theta2 theta))
+ (theta4 (* theta2 theta2))
+ (theta5 (* theta3 theta2)))
+ (+ -0.000009
+ (* 0.003844 theta)
+ (* 0.083563 theta2)
+ (* 0.865736 theta3)
+ (* 4.867575 theta4)
+ (* 15.845535 theta5)
+ (* 31.332267 theta3 theta3)
+ (* 38.291999 theta4 theta3)
+ (* 28.316289 theta4 theta4)
+ (* 11.636204 theta4 theta5)
+ (* 2.043794 theta5 theta5))))
+ ((and (<= 1620 year) (< year 1800))
+ (let ((x (/ (- year 1600) 10.0)))
+ (/ (+ (* 2.19167 x x) (* -40.675 x) 196.58333) 60.0 60.0 24.0)))
+ (t (let* ((tmp (- (calendar-astro-from-absolute
+ (calendar-absolute-from-gregorian
+ (list 1 1 year)))
+ 2382148))
+ (second (- (/ (* tmp tmp) 41048480.0) 15)))
+ (/ second 60.0 60.0 24.0)))))
+(defun solar-ephemeris-time (time)
+ "Ephemeris Time at moment TIME.
TIME is a pair with the first component being the number of Julian centuries
elapsed at 0 Universal Time, and the second component being the universal
time. For instance, the pair corresponding to November 28, 1995 at 16 UT is
\(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
-HEIGHT is the angle the center of the sun has over the horizon for the contact
-we are trying to find. For sunrise and sunset, it is usually -0.61 degrees,
-accounting for the edge of the sun being on the horizon.
+Result is in Julian centuries of ephemeris time."
+ (let* ((t0 (car time))
+ (ut (cadr time))
+ (t1 (+ t0 (/ (/ ut 24.0) 36525)))
+ (y (+ 2000 (* 100 t1)))
+ (dt (* 86400 (solar-ephemeris-correction (floor y)))))
+ (+ t1 (/ (/ dt 86400) 36525))))
-Coordinates are included because this function is called with latitude=1
-degrees to find out if polar regions have 24 hours of sun or only night."
- (let* ((rise-time (solar-moment -1 latitude longitude time height))
- (set-time (solar-moment 1 latitude longitude time height))
- (day-length))
- (if (not (and rise-time set-time))
- (if (or (and (> latitude 0)
- solar-northern-spring-or-summer-season)
- (and (< latitude 0)
- (not solar-northern-spring-or-summer-season)))
- (setq day-length 24)
- (setq day-length 0))
- (setq day-length (- set-time rise-time)))
- (list (if rise-time (+ rise-time (/ calendar-time-zone 60.0)) nil)
- (if set-time (+ set-time (/ calendar-time-zone 60.0)) nil)
- day-length)))
+(defun solar-equatorial-coordinates (time sunrise-flag)
+ "Right ascension (in hours) and declination (in degrees) of the sun at TIME.
+TIME is a pair with the first component being the number of
+Julian centuries elapsed at 0 Universal Time, and the second
+component being the universal time. For instance, the pair
+corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
+-0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT. SUNRISE-FLAG is passed
+to `solar-ecliptic-coordinates'."
+ (let ((ec (solar-ecliptic-coordinates (solar-ephemeris-time time)
+ sunrise-flag)))
+ (list (solar-right-ascension (car ec) (cadr ec))
+ (solar-declination (car ec) (cadr ec)))))
+
+(defun solar-horizontal-coordinates (time latitude longitude sunrise-flag)
+ "Azimuth and height of the sun at TIME, LATITUDE, and LONGITUDE.
+TIME is a pair with the first component being the number of
+Julian centuries elapsed at 0 Universal Time, and the second
+component being the universal time. For instance, the pair
+corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
+-0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT. SUNRISE-FLAG
+is passed to `solar-ecliptic-coordinates'. Azimuth and
+height (between -180 and 180) are both in degrees."
+ (let* ((ut (cadr time))
+ (ec (solar-equatorial-coordinates time sunrise-flag))
+ (st (+ solar-sidereal-time-greenwich-midnight
+ (* ut 1.00273790935)))
+ ;; Hour angle (in degrees).
+ (ah (- (* st 15) (* 15 (car ec)) (* -1 (calendar-longitude))))
+ (de (cadr ec))
+ (azimuth (solar-atn2 (- (* (solar-cosine-degrees ah)
+ (solar-sin-degrees latitude))
+ (* (solar-tangent-degrees de)
+ (solar-cosine-degrees latitude)))
+ (solar-sin-degrees ah)))
+ (height (solar-arcsin
+ (+ (* (solar-sin-degrees latitude) (solar-sin-degrees de))
+ (* (solar-cosine-degrees latitude)
+ (solar-cosine-degrees de)
+ (solar-cosine-degrees ah))))))
+ (if (> height 180) (setq height (- height 360)))
+ (list azimuth height)))
(defun solar-moment (direction latitude longitude time height)
"Sunrise/sunset at location.
(setq possible nil)) ; the sun never sets
(if possible utmoment)))
+(defun solar-sunrise-and-sunset (time latitude longitude height)
+ "Sunrise, sunset and length of day.
+Parameters are the midday TIME and the LATITUDE, LONGITUDE of the location.
+
+TIME is a pair with the first component being the number of Julian centuries
+elapsed at 0 Universal Time, and the second component being the universal
+time. For instance, the pair corresponding to November 28, 1995 at 16 UT is
+\(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
+Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
+
+HEIGHT is the angle the center of the sun has over the horizon for the contact
+we are trying to find. For sunrise and sunset, it is usually -0.61 degrees,
+accounting for the edge of the sun being on the horizon.
+
+Coordinates are included because this function is called with latitude=1
+degrees to find out if polar regions have 24 hours of sun or only night."
+ (let ((rise-time (solar-moment -1 latitude longitude time height))
+ (set-time (solar-moment 1 latitude longitude time height))
+ day-length)
+ (if (not (and rise-time set-time))
+ (if (or (and (> latitude 0)
+ solar-northern-spring-or-summer-season)
+ (and (< latitude 0)
+ (not solar-northern-spring-or-summer-season)))
+ (setq day-length 24)
+ (setq day-length 0))
+ (setq day-length (- set-time rise-time)))
+ (list (if rise-time (+ rise-time (/ calendar-time-zone 60.0)) nil)
+ (if set-time (+ set-time (/ calendar-time-zone 60.0)) nil)
+ day-length)))
+
(defun solar-time-string (time time-zone)
"Printable form for decimal fraction TIME in TIME-ZONE.
Format used is given by `calendar-time-display-form'."
(24-hours (format "%02d" 24-hours)))
(mapconcat 'eval calendar-time-display-form "")))
-
(defun solar-daylight (time)
"Printable form for TIME expressed in hours."
(format "%d:%02d"
(floor time)
(floor (* 60 (- time (floor time))))))
+(defun solar-julian-ut-centuries (date)
+ "Number of Julian centuries since 1 Jan, 2000 at noon UT for Gregorian DATE."
+ (/ (- (calendar-absolute-from-gregorian date)
+ (calendar-absolute-from-gregorian '(1 1.5 2000)))
+ 36525.0))
+
+(defun solar-date-to-et (date ut)
+ "Ephemeris Time at Gregorian DATE at Universal Time UT (in hours).
+Expressed in Julian centuries of Ephemeris Time."
+ (solar-ephemeris-time (list (solar-julian-ut-centuries date) ut)))
+
+(defun solar-time-equation (date ut)
+ "Equation of time expressed in hours at Gregorian DATE at Universal time UT."
+ (nth 2 (solar-ecliptic-coordinates (solar-date-to-et date ut) nil)))
+
(defun solar-exact-local-noon (date)
"Date and Universal Time of local noon at *local date* DATE.
The date may be different from the one asked for, but it will be the right
(calendar-absolute-from-gregorian nd)))
(list nd ut)))
-(defun solar-sunrise-sunset (date)
- "List of *local* times of sunrise, sunset, and daylight on Gregorian DATE.
-Corresponding value is nil if there is no sunrise/sunset."
- ;; First, get the exact moment of local noon.
- (let* ((exact-local-noon (solar-exact-local-noon date))
- ;; Get the time from the 2000 epoch.
+(defun solar-sidereal-time (t0)
+ "Sidereal time (in hours) in Greenwich at T0 Julian centuries.
+T0 must correspond to 0 hours UT."
+ (let* ((mean-sid-time (+ 6.6973746
+ (* 2400.051337 t0)
+ (* 0.0000258622 t0 t0)
+ (* -0.0000000017222 t0 t0 t0)))
+ (et (solar-ephemeris-time (list t0 0.0)))
+ (nut-i (solar-ecliptic-coordinates et nil))
+ (nut (nth 3 nut-i)) ; nutation
+ (i (cadr nut-i))) ; inclination
+ (mod (+ (mod (+ mean-sid-time
+ (/ (/ (* nut (solar-cosine-degrees i)) 15) 3600)) 24.0)
+ 24.0)
+ 24.0)))
+
+(defun solar-sunrise-sunset (date)
+ "List of *local* times of sunrise, sunset, and daylight on Gregorian DATE.
+Corresponding value is nil if there is no sunrise/sunset."
+ ;; First, get the exact moment of local noon.
+ (let* ((exact-local-noon (solar-exact-local-noon date))
+ ;; Get the time from the 2000 epoch.
(t0 (solar-julian-ut-centuries (car exact-local-noon)))
;; Store the sidereal time at Greenwich at midnight of UT time.
;; Find if summer or winter slightly above the equator.
(list t0 (cadr exact-local-noon))
(calendar-latitude)
(calendar-longitude) -0.61)))
- (rise (car rise-set))
- (adj-rise (if rise (dst-adjust-time date rise)))
- (set (cadr rise-set)) ; FIXME ?
- (adj-set (if set (dst-adjust-time date set)))
+ (rise-time (car rise-set))
+ (adj-rise (if rise-time (dst-adjust-time date rise-time)))
+ (set-time (cadr rise-set))
+ (adj-set (if set-time (dst-adjust-time date set-time)))
(length (nth 2 rise-set)))
(list
- (and rise (calendar-date-equal date (car adj-rise)) (cdr adj-rise))
- (and set (calendar-date-equal date (car adj-set)) (cdr adj-set))
+ (and rise-time (calendar-date-equal date (car adj-rise)) (cdr adj-rise))
+ (and set-time (calendar-date-equal date (car adj-set)) (cdr adj-set))
(solar-daylight length))))
-(defun solar-sunrise-sunset-string (date)
- "String of *local* times of sunrise, sunset, and daylight on Gregorian DATE."
+(defun solar-sunrise-sunset-string (date &optional nolocation)
+ "String of *local* times of sunrise, sunset, and daylight on Gregorian DATE.
+Optional NOLOCATION non-nil means do not print the location."
(let ((l (solar-sunrise-sunset date)))
(format
- "%s, %s at %s (%s hours daylight)"
+ "%s, %s%s (%s hours daylight)"
(if (car l)
(concat "Sunrise " (apply 'solar-time-string (car l)))
"No sunrise")
(if (cadr l)
(concat "sunset " (apply 'solar-time-string (cadr l)))
"no sunset")
- (eval calendar-location-name)
+ (if nolocation ""
+ (format " at %s" (eval calendar-location-name)))
(nth 2 l))))
-(defun solar-julian-ut-centuries (date)
- "Number of Julian centuries since 1 Jan, 2000 at noon UT for Gregorian DATE."
- (/ (- (calendar-absolute-from-gregorian date)
- (calendar-absolute-from-gregorian '(1 1.5 2000)))
- 36525.0))
-
-(defun solar-ephemeris-time (time)
- "Ephemeris Time at moment TIME.
-TIME is a pair with the first component being the number of Julian centuries
-elapsed at 0 Universal Time, and the second component being the universal
-time. For instance, the pair corresponding to November 28, 1995 at 16 UT is
-\(-0.040945 16), -0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT.
-
-Result is in Julian centuries of ephemeris time."
- (let* ((t0 (car time))
- (ut (cadr time))
- (t1 (+ t0 (/ (/ ut 24.0) 36525)))
- (y (+ 2000 (* 100 t1)))
- (dt (* 86400 (solar-ephemeris-correction (floor y)))))
- (+ t1 (/ (/ dt 86400) 36525))))
-
-(defun solar-date-next-longitude (d l)
- "First time after day D when solar longitude is a multiple of L degrees.
-D is a Julian day number. L must be an integer divisor of 360.
-The result is for `calendar-location-name', and is in local time
-\(including any daylight saving rules) expressed in astronomical (Julian)
-day numbers. 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' are used to interpret local time."
- (let* ((long)
- (start d)
- (start-long (solar-longitude d))
- (next (mod (* l (1+ (floor (/ start-long l)))) 360))
- (end (+ d (* (/ l 360.0) 400)))
- (end-long (solar-longitude end)))
- (while ; bisection search for nearest minute
- (< 0.00001 (- end start))
- ;; start <= d < end
- ;; start-long <= next < end-long when next != 0
- ;; when next = 0, we look for the discontinuity (start-long is near 360
- ;; and end-long is small (less than l).
- (setq d (/ (+ start end) 2.0)
- long (solar-longitude d))
- (if (or (and (not (zerop next)) (< long next))
- (and (zerop next) (< l long)))
- (setq start d
- start-long long)
- (setq end d
- end-long long)))
- (/ (+ start end) 2.0)))
-
-(defun solar-horizontal-coordinates (time latitude longitude sunrise-flag)
- "Azimuth and height of the sun at TIME, LATITUDE, and LONGITUDE.
-TIME is a pair with the first component being the number of
-Julian centuries elapsed at 0 Universal Time, and the second
-component being the universal time. For instance, the pair
-corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
--0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT. SUNRISE-FLAG
-is passed to `solar-ecliptic-coordinates'. Azimuth and
-height (between -180 and 180) are both in degrees."
- (let* ((ut (cadr time))
- (ec (solar-equatorial-coordinates time sunrise-flag))
- (st (+ solar-sidereal-time-greenwich-midnight
- (* ut 1.00273790935)))
- ;; Hour angle (in degrees).
- (ah (- (* st 15) (* 15 (car ec)) (* -1 (calendar-longitude))))
- (de (cadr ec))
- (azimuth (solar-atn2 (- (* (solar-cosine-degrees ah)
- (solar-sin-degrees latitude))
- (* (solar-tangent-degrees de)
- (solar-cosine-degrees latitude)))
- (solar-sin-degrees ah)))
- (height (solar-arcsin
- (+ (* (solar-sin-degrees latitude) (solar-sin-degrees de))
- (* (solar-cosine-degrees latitude)
- (solar-cosine-degrees de)
- (solar-cosine-degrees ah))))))
- (if (> height 180) (setq height (- height 360)))
- (list azimuth height)))
-
-(defun solar-equatorial-coordinates (time sunrise-flag)
- "Right ascension (in hours) and declination (in degrees) of the sun at TIME.
-TIME is a pair with the first component being the number of
-Julian centuries elapsed at 0 Universal Time, and the second
-component being the universal time. For instance, the pair
-corresponding to November 28, 1995 at 16 UT is (-0.040945 16),
--0.040945 being the number of Julian centuries elapsed between
-Jan 1, 2000 at 12 UT and November 28, 1995 at 0 UT. SUNRISE-FLAG is passed
-to `solar-ecliptic-coordinates'."
- (let* ((tm (solar-ephemeris-time time))
- (ec (solar-ecliptic-coordinates tm sunrise-flag)))
- (list (solar-right-ascension (car ec) (car (cdr ec)))
- (solar-declination (car ec) (car (cdr ec))))))
-
-(defun solar-ecliptic-coordinates (time sunrise-flag)
- "Return solar longitude, ecliptic inclination, equation of time, nutation.
-Values are for TIME in Julian centuries of Ephemeris Time since
-January 1st, 2000, at 12 ET. Longitude and inclination are in
-degrees, equation of time in hours, and nutation in seconds of longitude.
-If SUNRISE-FLAG is non-nil, only calculate longitude and inclination."
- (let* ((l (+ 280.46645
- (* 36000.76983 time)
- (* 0.0003032 time time))) ; sun mean longitude
- (ml (+ 218.3165
- (* 481267.8813 time))) ; moon mean longitude
- (m (+ 357.52910
- (* 35999.05030 time)
- (* -0.0001559 time time)
- (* -0.00000048 time time time))) ; sun mean anomaly
- (i (+ 23.43929111 (* -0.013004167 time)
- (* -0.00000016389 time time)
- (* 0.0000005036 time time time))) ; mean inclination
- (c (+ (* (+ 1.914600
- (* -0.004817 time)
- (* -0.000014 time time))
- (solar-sin-degrees m))
- (* (+ 0.019993 (* -0.000101 time))
- (solar-sin-degrees (* 2 m)))
- (* 0.000290
- (solar-sin-degrees (* 3 m))))) ; center equation
- (L (+ l c)) ; total longitude
- ;; Longitude of moon's ascending node on the ecliptic.
- (omega (+ 125.04
- (* -1934.136 time)))
- ;; nut = nutation in longitude, measured in seconds of angle.
- (nut (unless sunrise-flag
- (+ (* -17.20 (solar-sin-degrees omega))
- (* -1.32 (solar-sin-degrees (* 2 l)))
- (* -0.23 (solar-sin-degrees (* 2 ml)))
- (* 0.21 (solar-sin-degrees (* 2 omega))))))
- (ecc (unless sunrise-flag ; eccentricity of earth's orbit
- (+ 0.016708617
- (* -0.000042037 time)
- (* -0.0000001236 time time))))
- (app (+ L ; apparent longitude of sun
- -0.00569
- (* -0.00478
- (solar-sin-degrees omega))))
- (y (unless sunrise-flag
- (* (solar-tangent-degrees (/ i 2))
- (solar-tangent-degrees (/ i 2)))))
- ;; Equation of time, in hours.
- (time-eq (unless sunrise-flag
- (/ (* 12 (+ (* y (solar-sin-degrees (* 2 l)))
- (* -2 ecc (solar-sin-degrees m))
- (* 4 ecc y (solar-sin-degrees m)
- (solar-cosine-degrees (* 2 l)))
- (* -0.5 y y (solar-sin-degrees (* 4 l)))
- (* -1.25 ecc ecc (solar-sin-degrees (* 2 m)))))
- 3.1415926535))))
- (list app i time-eq nut)))
-
(defconst solar-data-list
'((403406 4.721964 1.621043)
(195207 5.937458 62830.348067)
`calendar-daylight-savings-starts-time', `calendar-daylight-savings-ends',
`calendar-daylight-savings-ends-time', `calendar-daylight-time-offset', and
`calendar-time-zone' are used to interpret local time."
- (let* ((a-d (calendar-absolute-from-astro d))
+ (let* ((a-d (calendar-astro-to-absolute d))
;; Get Universal Time.
(date (calendar-astro-from-absolute
(- a-d
(/ calendar-time-zone 60.0 24.0))))
;; Get Ephemeris Time.
(date (+ date (solar-ephemeris-correction
- (extract-calendar-year
+ (calendar-extract-year
(calendar-gregorian-from-absolute
(floor
- (calendar-absolute-from-astro
+ (calendar-astro-to-absolute
date)))))))
(U (/ (- date 2451545) 3652500))
(longitude
(mapcar (lambda (x)
(* (car x)
(sin (mod
- (+ (car (cdr x))
- (* (car (cdr (cdr x))) U))
- (* 2 pi)))))
+ (+ (cadr x)
+ (* (nth 2 x) U))
+ (* 2 float-pi)))))
solar-data-list)))))
(aberration
(* 0.0000001 (- (* 17 (cos (+ 3.10 (* 62830.14 U)))) 973)))
- (A1 (mod (+ 2.18 (* U (+ -3375.70 (* 0.36 U)))) (* 2 pi)))
- (A2 (mod (+ 3.51 (* U (+ 125666.39 (* 0.10 U)))) (* 2 pi)))
+ (A1 (mod (+ 2.18 (* U (+ -3375.70 (* 0.36 U)))) (* 2 float-pi)))
+ (A2 (mod (+ 3.51 (* U (+ 125666.39 (* 0.10 U)))) (* 2 float-pi)))
(nutation (* -0.0000001 (+ (* 834 (sin A1)) (* 64 (sin A2))))))
(mod (radians-to-degrees (+ longitude aberration nutation)) 360.0)))
-(defun solar-ephemeris-correction (year)
- "Ephemeris time minus Universal Time during Gregorian YEAR.
-Result is in days. For the years 1800-1987, the maximum error is
-1.9 seconds. For the other years, the maximum error is about 30 seconds."
- (cond ((and (<= 1988 year) (< year 2020))
- (/ (+ year -2000 67.0) 60.0 60.0 24.0))
- ((and (<= 1900 year) (< year 1988))
- (let* ((theta (/ (- (calendar-astro-from-absolute
- (calendar-absolute-from-gregorian
- (list 7 1 year)))
- (calendar-astro-from-absolute
- (calendar-absolute-from-gregorian
- '(1 1 1900))))
- 36525.0))
- (theta2 (* theta theta))
- (theta3 (* theta2 theta))
- (theta4 (* theta2 theta2))
- (theta5 (* theta3 theta2)))
- (+ -0.00002
- (* 0.000297 theta)
- (* 0.025184 theta2)
- (* -0.181133 theta3)
- (* 0.553040 theta4)
- (* -0.861938 theta5)
- (* 0.677066 theta3 theta3)
- (* -0.212591 theta4 theta3))))
- ((and (<= 1800 year) (< year 1900))
- (let* ((theta (/ (- (calendar-astro-from-absolute
- (calendar-absolute-from-gregorian
- (list 7 1 year)))
- (calendar-astro-from-absolute
- (calendar-absolute-from-gregorian
- '(1 1 1900))))
- 36525.0))
- (theta2 (* theta theta))
- (theta3 (* theta2 theta))
- (theta4 (* theta2 theta2))
- (theta5 (* theta3 theta2)))
- (+ -0.000009
- (* 0.003844 theta)
- (* 0.083563 theta2)
- (* 0.865736 theta3)
- (* 4.867575 theta4)
- (* 15.845535 theta5)
- (* 31.332267 theta3 theta3)
- (* 38.291999 theta4 theta3)
- (* 28.316289 theta4 theta4)
- (* 11.636204 theta4 theta5)
- (* 2.043794 theta5 theta5))))
- ((and (<= 1620 year) (< year 1800))
- (let ((x (/ (- year 1600) 10.0)))
- (/ (+ (* 2.19167 x x) (* -40.675 x) 196.58333) 60.0 60.0 24.0)))
- (t (let* ((tmp (- (calendar-astro-from-absolute
- (calendar-absolute-from-gregorian
- (list 1 1 year)))
- 2382148))
- (second (- (/ (* tmp tmp) 41048480.0) 15)))
- (/ second 60.0 60.0 24.0)))))
-
-(defun solar-sidereal-time (t0)
- "Sidereal time (in hours) in Greenwich at T0 Julian centuries.
-T0 must correspond to 0 hours UT."
- (let* ((mean-sid-time (+ 6.6973746
- (* 2400.051337 t0)
- (* 0.0000258622 t0 t0)
- (* -0.0000000017222 t0 t0 t0)))
- (et (solar-ephemeris-time (list t0 0.0)))
- (nut-i (solar-ecliptic-coordinates et nil))
- (nut (nth 3 nut-i)) ; nutation
- (i (cadr nut-i))) ; inclination
- (mod (+ (mod (+ mean-sid-time
- (/ (/ (* nut (solar-cosine-degrees i)) 15) 3600)) 24.0)
- 24.0)
- 24.0)))
-
-(defun solar-time-equation (date ut)
- "Equation of time expressed in hours at Gregorian DATE at Universal time UT."
- (nth 2 (solar-ecliptic-coordinates (solar-date-to-et date ut) nil)))
-
-(defun solar-date-to-et (date ut)
- "Ephemeris Time at Gregorian DATE at Universal Time UT (in hours).
-Expressed in Julian centuries of Ephemeris Time."
- (solar-ephemeris-time (list (solar-julian-ut-centuries date) ut)))
+(defun solar-date-next-longitude (d l)
+ "First time after day D when solar longitude is a multiple of L degrees.
+D is a Julian day number. L must be an integer divisor of 360.
+The result is for `calendar-location-name', and is in local time
+\(including any daylight saving rules) expressed in astronomical (Julian)
+day numbers. 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' are used to interpret local time."
+ (let* ((long)
+ (start d)
+ (start-long (solar-longitude d))
+ (next (mod (* l (1+ (floor (/ start-long l)))) 360))
+ (end (+ d (* (/ l 360.0) 400)))
+ (end-long (solar-longitude end)))
+ (while ; bisection search for nearest minute
+ (< 0.00001 (- end start))
+ ;; start <= d < end
+ ;; start-long <= next < end-long when next != 0
+ ;; when next = 0, we look for the discontinuity (start-long is near 360
+ ;; and end-long is small (less than l).
+ (setq d (/ (+ start end) 2.0)
+ long (solar-longitude d))
+ (if (or (and (not (zerop next)) (< long next))
+ (and (zerop next) (< l long)))
+ (setq start d
+ start-long long)
+ (setq end d
+ end-long long)))
+ (/ (+ start end) 2.0)))
+;; FIXME but there already is solar-sunrise-sunset.
;;;###autoload
(defun sunrise-sunset (&optional arg)
"Local time of sunrise and sunset for today. Accurate to a few seconds.
(/ (aref calendar-latitude 1) 60.0)))
(if (numberp calendar-latitude)
(if (> calendar-latitude 0) "N" "S")
- (if (equal (aref calendar-latitude 2) 'north) "N" "S"))
+ (if (eq (aref calendar-latitude 2) 'north) "N" "S"))
(if (numberp calendar-longitude)
(abs calendar-longitude)
(+ (aref calendar-longitude 0)
(/ (aref calendar-longitude 1) 60.0)))
(if (numberp calendar-longitude)
(if (> calendar-longitude 0) "E" "W")
- (if (equal (aref calendar-longitude 2) 'east)
+ (if (eq (aref calendar-longitude 2) 'east)
"E" "W"))))))
(calendar-standard-time-zone-name
(if (< arg 16) calendar-standard-time-zone-name
- (cond ((= calendar-time-zone 0) "UTC")
+ (cond ((zerop calendar-time-zone) "UTC")
((< calendar-time-zone 0)
(format "UTC%dmin" calendar-time-zone))
(t (format "UTC+%dmin" calendar-time-zone)))))
contents of temp window."))))))
;;;###cal-autoload
-(defun calendar-sunrise-sunset ()
+(defun calendar-sunrise-sunset (&optional event)
"Local time of sunrise and sunset for date under cursor.
Accurate to a few seconds."
- (interactive)
+ (interactive (list last-nonmenu-event))
(or (and calendar-latitude calendar-longitude calendar-time-zone)
(solar-setup))
- (let ((date (calendar-cursor-to-date t)))
+ (let ((date (calendar-cursor-to-date t event)))
(message "%s: %s"
(calendar-date-string date t t)
(solar-sunrise-sunset-string date))))
+;;;###cal-autoload
+(defun calendar-sunrise-sunset-month (&optional event)
+ "Local time of sunrise and sunset for month under cursor or at EVENT."
+ (interactive (list last-nonmenu-event))
+ (or (and calendar-latitude calendar-longitude calendar-time-zone)
+ (solar-setup))
+ (let* ((date (calendar-cursor-to-date t event))
+ (month (car date))
+ (year (nth 2 date))
+ (last (calendar-last-day-of-month month year))
+ (title (format "Sunrise/sunset times for %s %d at %s"
+ (calendar-month-name month) year
+ (eval calendar-location-name))))
+ (calendar-in-read-only-buffer solar-sunrises-buffer
+ (calendar-set-mode-line title)
+ (insert title ":\n\n")
+ (dotimes (i last)
+ (setq date (list month (1+ i) year))
+ (insert (format "%s %2d: " (calendar-month-name month t) (1+ i))
+ (solar-sunrise-sunset-string date t) "\n")))))
+
(defvar date)
-;; To be called from list-sexp-diary-entries, where DATE is bound.
+;; To be called from diary-list-sexp-entries, where DATE is bound.
;;;###diary-autoload
(defun diary-sunrise-sunset ()
"Local time of sunrise and sunset as a diary entry.
(solar-setup))
(solar-sunrise-sunset-string date))
-;; To be called from list-sexp-diary-entries, where DATE is bound.
-;;;###diary-autoload
-(defun diary-sabbath-candles (&optional mark)
- "Local time of candle lighting diary entry--applies if date is a Friday.
-No diary entry if there is no sunset on that date.
-
-An optional parameter MARK specifies a face or single-character string to
-use when highlighting the day in the calendar."
- (or (and calendar-latitude calendar-longitude calendar-time-zone)
- (solar-setup))
- (if (= (% (calendar-absolute-from-gregorian date) 7) 5) ; Friday
- (let* ((sunset (cadr (solar-sunrise-sunset date)))
- (light (if sunset
- (cons (- (car sunset)
- (/ diary-sabbath-candles-minutes 60.0))
- (cdr sunset)))))
- (if sunset
- (cons mark
- (format "%s Sabbath candle lighting"
- (apply 'solar-time-string light)))))))
-
;; From Meeus, 1991, page 167.
(defconst solar-seasons-data
'((485 324.96 1934.136)
(defun solar-mean-equinoxes/solstices (k year)
"Julian day of mean equinox/solstice K for YEAR.
K=0, spring equinox; K=1, summer solstice; K=2, fall equinox; K=3, winter
-solstice. These formulas are only to be used between 1000 BC and 3000 AD."
+solstice. These formulae are only to be used between 1000 BC and 3000 AD."
(let ((y (/ year 1000.0))
(z (/ (- year 2000) 1000.0)))
(if (< year 1000) ; actually between -1000 and 1000
- (cond ((equal k 0) (+ 1721139.29189
- (* 365242.13740 y)
- (* 0.06134 y y)
- (* 0.00111 y y y)
- (* -0.00071 y y y y)))
- ((equal k 1) (+ 1721233.25401
- (* 365241.72562 y)
- (* -0.05323 y y)
- (* 0.00907 y y y)
- (* 0.00025 y y y y)))
- ((equal k 2) (+ 1721325.70455
- (* 365242.49558 y)
- (* -0.11677 y y)
- (* -0.00297 y y y)
- (* 0.00074 y y y y)))
- ((equal k 3) (+ 1721414.39987
- (* 365242.88257 y)
- (* -0.00769 y y)
- (* -0.00933 y y y)
- (* -0.00006 y y y y))))
+ (cond ((= k 0) (+ 1721139.29189
+ (* 365242.13740 y)
+ (* 0.06134 y y)
+ (* 0.00111 y y y)
+ (* -0.00071 y y y y)))
+ ((= k 1) (+ 1721233.25401
+ (* 365241.72562 y)
+ (* -0.05323 y y)
+ (* 0.00907 y y y)
+ (* 0.00025 y y y y)))
+ ((= k 2) (+ 1721325.70455
+ (* 365242.49558 y)
+ (* -0.11677 y y)
+ (* -0.00297 y y y)
+ (* 0.00074 y y y y)))
+ ((= k 3) (+ 1721414.39987
+ (* 365242.88257 y)
+ (* -0.00769 y y)
+ (* -0.00933 y y y)
+ (* -0.00006 y y y y))))
; actually between 1000 and 3000
- (cond ((equal k 0) (+ 2451623.80984
- (* 365242.37404 z)
- (* 0.05169 z z)
- (* -0.00411 z z z)
- (* -0.00057 z z z z)))
- ((equal k 1) (+ 2451716.56767
- (* 365241.62603 z)
- (* 0.00325 z z)
- (* 0.00888 z z z)
- (* -0.00030 z z z z)))
- ((equal k 2) (+ 2451810.21715
- (* 365242.01767 z)
- (* -0.11575 z z)
- (* 0.00337 z z z)
- (* 0.00078 z z z z)))
- ((equal k 3) (+ 2451900.05952
- (* 365242.74049 z)
- (* -0.06223 z z)
- (* -0.00823 z z z)
- (* 0.00032 z z z z)))))))
+ (cond ((= k 0) (+ 2451623.80984
+ (* 365242.37404 z)
+ (* 0.05169 z z)
+ (* -0.00411 z z z)
+ (* -0.00057 z z z z)))
+ ((= k 1) (+ 2451716.56767
+ (* 365241.62603 z)
+ (* 0.00325 z z)
+ (* 0.00888 z z z)
+ (* -0.00030 z z z z)))
+ ((= k 2) (+ 2451810.21715
+ (* 365242.01767 z)
+ (* -0.11575 z z)
+ (* 0.00337 z z z)
+ (* 0.00078 z z z z)))
+ ((= k 3) (+ 2451900.05952
+ (* 365242.74049 z)
+ (* -0.06223 z z)
+ (* -0.00823 z z z)
+ (* 0.00032 z z z z)))))))
+
+(defvar displayed-month) ; from calendar-generate
+(defvar displayed-year)
;;;###holiday-autoload
(defun solar-equinoxes-solstices ()
"Local date and time of equinoxes and solstices, if visible in the calendar.
Requires floating point."
- (let ((m displayed-month)
- (y displayed-year))
- (increment-calendar-month m y (cond ((= 1 (% m 3)) -1)
- ((= 2 (% m 3)) 1)
- (t 0)))
- (let* ((calendar-standard-time-zone-name
- (if calendar-time-zone calendar-standard-time-zone-name "UTC"))
- (calendar-daylight-savings-starts
- (if calendar-time-zone calendar-daylight-savings-starts))
- (calendar-daylight-savings-ends
- (if calendar-time-zone calendar-daylight-savings-ends))
- (calendar-time-zone (if calendar-time-zone calendar-time-zone 0))
- (k (1- (/ m 3)))
- (d0 (solar-equinoxes/solstices k y))
- (d1 (list (car d0) (floor (car (cdr d0))) (car (cdr (cdr d0)))))
- (h0 (* 24 (- (car (cdr d0)) (floor (car (cdr d0))))))
- (adj (dst-adjust-time d1 h0))
- (d (list (caar adj)
- (+ (car (cdar adj))
- (/ (cadr adj) 24.0))
- (cadr (cdar adj))))
- ;; The following is nearly as accurate, but not quite:
- ;; (d0 (solar-date-next-longitude
- ;; (calendar-astro-from-absolute
- ;; (calendar-absolute-from-gregorian
- ;; (list (+ 3 (* k 3)) 15 y)))
- ;; 90))
- ;; (abs-day (calendar-absolute-from-astro d)))
- (abs-day (calendar-absolute-from-gregorian d)))
- (list
- (list (calendar-gregorian-from-absolute (floor abs-day))
- (format "%s %s"
- (nth k (if (and calendar-latitude
- (< (calendar-latitude) 0))
- solar-s-hemi-seasons
- solar-n-hemi-seasons))
- (solar-time-string
- (* 24 (- abs-day (floor abs-day)))
- (if (dst-in-effect abs-day)
- calendar-daylight-time-zone-name
- calendar-standard-time-zone-name))))))))
+ (let* ((m displayed-month)
+ (y displayed-year)
+ (calendar-standard-time-zone-name
+ (if calendar-time-zone calendar-standard-time-zone-name "UTC"))
+ (calendar-daylight-savings-starts
+ (if calendar-time-zone calendar-daylight-savings-starts))
+ (calendar-daylight-savings-ends
+ (if calendar-time-zone calendar-daylight-savings-ends))
+ (calendar-time-zone (if calendar-time-zone calendar-time-zone 0))
+ (k (progn
+ (calendar-increment-month m y (cond ((= 1 (% m 3)) -1)
+ ((= 2 (% m 3)) 1)
+ (t 0)))
+ (1- (/ m 3))))
+ (d0 (solar-equinoxes/solstices k y))
+ (d1 (list (car d0) (floor (cadr d0)) (nth 2 d0)))
+ (h0 (* 24 (- (cadr d0) (floor (cadr d0)))))
+ (adj (dst-adjust-time d1 h0))
+ (d (list (caar adj)
+ (+ (car (cdar adj))
+ (/ (cadr adj) 24.0))
+ (cadr (cdar adj))))
+ ;; The following is nearly as accurate, but not quite:
+ ;; (d0 (solar-date-next-longitude
+ ;; (calendar-astro-from-absolute
+ ;; (calendar-absolute-from-gregorian
+ ;; (list (+ 3 (* k 3)) 15 y)))
+ ;; 90))
+ ;; (abs-day (calendar-astro-to-absolute d)))
+ (abs-day (calendar-absolute-from-gregorian d)))
+ (list
+ (list (calendar-gregorian-from-absolute (floor abs-day))
+ (format "%s %s"
+ (nth k (if (and calendar-latitude
+ (< (calendar-latitude) 0))
+ solar-s-hemi-seasons
+ solar-n-hemi-seasons))
+ (solar-time-string
+ (* 24 (- abs-day (floor abs-day)))
+ (if (dst-in-effect abs-day)
+ calendar-daylight-time-zone-name
+ calendar-standard-time-zone-name)))))))
(provide 'solar)