6 * code for calculating the position on the earth's surface for which
7 * the sun is directly overhead (adapted from _practical astronomy
8 * with your calculator, third edition_, peter duffett-smith,
9 * cambridge university press, 1988.)
13 * Copyright (C) 1989, 1990, 1993, 1994, 1995 Kirk Lauritz Johnson
15 * Parts of the source code (as marked) are:
16 * Copyright (C) 1989, 1990, 1991 by Jim Frost
17 * Copyright (C) 1992 by Jamie Zawinski <jwz@lucid.com>
19 * Permission to use, copy, modify and freely distribute xearth for
20 * non-commercial and not-for-profit purposes is hereby granted
21 * without fee, provided that both the above copyright notice and this
22 * permission notice appear in all copies and in supporting
25 * The author makes no representations about the suitability of this
26 * software for any purpose. It is provided "as is" without express or
29 * THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
30 * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS,
31 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT
32 * OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
33 * LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
34 * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
35 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
38 * (Log is kept at end of this file)
47 #include "../constants.h"
52 * the epoch upon which these astronomical calculations are based is
53 * 1990 january 0.0, 631065600 seconds since the beginning of the
54 * "unix epoch" (00:00:00 GMT, Jan. 1, 1970)
56 * given a number of seconds since the start of the unix epoch,
57 * DaysSinceEpoch() computes the number of days since the start of the
58 * astronomical epoch (1990 january 0.0)
61 #define EpochStart (631065600)
62 #define DaysSinceEpoch(secs) (((secs)-EpochStart)*(1.0/(24*3600)))
65 * assuming the apparent orbit of the sun about the earth is circular,
66 * the rate at which the orbit progresses is given by RadsPerDay --
67 * FG_2PI radians per orbit divided by 365.242191 days per year:
70 #define RadsPerDay (FG_2PI/365.242191)
73 * details of sun's apparent orbit at epoch 1990.0 (after
74 * duffett-smith, table 6, section 46)
76 * Epsilon_g (ecliptic longitude at epoch 1990.0) 279.403303 degrees
77 * OmegaBar_g (ecliptic longitude of perigee) 282.768422 degrees
78 * Eccentricity (eccentricity of orbit) 0.016713
81 #define Epsilon_g (279.403303*(FG_2PI/360))
82 #define OmegaBar_g (282.768422*(FG_2PI/360))
83 #define Eccentricity (0.016713)
86 * MeanObliquity gives the mean obliquity of the earth's axis at epoch
87 * 1990.0 (computed as 23.440592 degrees according to the method given
88 * in duffett-smith, section 27)
90 #define MeanObliquity (23.440592*(FG_2PI/360))
92 static double solve_keplers_equation(double);
93 static double sun_ecliptic_longitude(time_t);
94 static void ecliptic_to_equatorial(double, double, double *, double *);
95 static double julian_date(int, int, int);
96 static double GST(time_t);
99 * solve Kepler's equation via Newton's method
100 * (after duffett-smith, section 47)
102 static double solve_keplers_equation(double M) {
108 delta = E - Eccentricity*sin(E) - M;
109 if (fabs(delta) <= 1e-10) break;
110 E -= delta / (1 - Eccentricity*cos(E));
117 /* compute ecliptic longitude of sun (in radians) (after
118 * duffett-smith, section 47) */
120 static double sun_ecliptic_longitude(time_t ssue) {
121 /* time_t ssue; seconds since unix epoch */
126 D = DaysSinceEpoch(ssue);
130 if (N < 0) N += FG_2PI;
132 M_sun = N + Epsilon_g - OmegaBar_g;
133 if (M_sun < 0) M_sun += FG_2PI;
135 E = solve_keplers_equation(M_sun);
136 v = 2 * atan(sqrt((1+Eccentricity)/(1-Eccentricity)) * tan(E/2));
138 return (v + OmegaBar_g);
142 /* convert from ecliptic to equatorial coordinates (after
143 * duffett-smith, section 27) */
145 static void ecliptic_to_equatorial(double lambda, double beta,
146 double *alpha, double *delta) {
147 /* double lambda; ecliptic longitude */
148 /* double beta; ecliptic latitude */
149 /* double *alpha; (return) right ascension */
150 /* double *delta; (return) declination */
154 sin_e = sin(MeanObliquity);
155 cos_e = cos(MeanObliquity);
157 *alpha = atan2(sin(lambda)*cos_e - tan(beta)*sin_e, cos(lambda));
158 *delta = asin(sin(beta)*cos_e + cos(beta)*sin_e*sin(lambda));
162 /* computing julian dates (assuming gregorian calendar, thus this is
163 * only valid for dates of 1582 oct 15 or later) (after duffett-smith,
166 static double julian_date(int y, int m, int d) {
167 /* int y; year (e.g. 19xx) */
168 /* int m; month (jan=1, feb=2, ...) */
169 /* int d; day of month */
174 /* lazy test to ensure gregorian calendar */
176 printf("WHOOPS! Julian dates only valid for 1582 oct 15 or later\n");
179 if ((m == 1) || (m == 2)) {
187 D = 30.6001 * (m + 1);
189 JD = B + C + D + d + 1720994.5;
195 /* compute greenwich mean sidereal time (GST) corresponding to a given
196 * number of seconds since the unix epoch (after duffett-smith,
198 static double GST(time_t ssue) {
199 /* time_t ssue; seconds since unix epoch */
208 JD = julian_date(tm->tm_year+1900, tm->tm_mon+1, tm->tm_mday);
209 T = (JD - 2451545) / 36525;
211 T0 = ((T + 2.5862e-5) * T + 2400.051336) * T + 6.697374558;
214 if (T0 < 0) T0 += 24;
216 UT = tm->tm_hour + (tm->tm_min + tm->tm_sec / 60.0) / 60.0;
218 T0 += UT * 1.002737909;
220 if (T0 < 0) T0 += 24;
226 /* given a particular time (expressed in seconds since the unix
227 * epoch), compute position on the earth (lat, lon) such that sun is
228 * directly overhead. (lat, lon are reported in radians */
230 void fgSunPosition(time_t ssue, double *lon, double *lat) {
231 /* time_t ssue; seconds since unix epoch */
232 /* double *lat; (return) latitude */
233 /* double *lon; (return) longitude */
239 lambda = sun_ecliptic_longitude(ssue);
240 ecliptic_to_equatorial(lambda, 0.0, &alpha, &delta);
242 tmp = alpha - (FG_2PI/24)*GST(ssue);
245 while (tmp < -FG_PI);
246 } else if (tmp > FG_PI) {
248 while (tmp < -FG_PI);
257 /* Revision 1.1 1997/08/01 15:27:56 curt