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1 /*
2 * sunpos.c
3 * kirk johnson
4 * july 1993
5 *
6 * includes revisions from Frank T. Solensky, february 1999
7 *
8 * code for calculating the position on the earth's surface for which
9 * the sun is directly overhead (adapted from _practical astronomy
10 * with your calculator, third edition_, peter duffett-smith,
11 * cambridge university press, 1988.)
12 *
13 * Copyright (C) 1989, 1990, 1993-1995, 1999 Kirk Lauritz Johnson
14 *
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>
18 *
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
23 * documentation.
24 *
25 * Unisys Corporation holds worldwide patent rights on the Lempel Zev
26 * Welch (LZW) compression technique employed in the CompuServe GIF
27 * image file format as well as in other formats. Unisys has made it
28 * clear, however, that it does not require licensing or fees to be
29 * paid for freely distributed, non-commercial applications (such as
30 * xearth) that employ LZW/GIF technology. Those wishing further
31 * information about licensing the LZW patent should contact Unisys
32 * directly at (lzw_info@unisys.com) or by writing to
33 *
34 * Unisys Corporation
35 * Welch Licensing Department
36 * M/S-C1SW19
37 * P.O. Box 500
38 * Blue Bell, PA 19424
39 *
40 * The author makes no representations about the suitability of this
41 * software for any purpose. It is provided "as is" without express or
42 * implied warranty.
43 *
44 * THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
45 * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS,
46 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT
47 * OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
48 * LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
49 * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
50 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
51 */
52
53 #include "xearth.h"
54 #include "kljcpyrt.h"
55
56 #define TWOPI (2*M_PI)
57 #define DegsToRads(x) ((x)*(TWOPI/360))
58
59 /*
60 * the epoch upon which these astronomical calculations are based is
61 * 1990 january 0.0, 631065600 seconds since the beginning of the
62 * "unix epoch" (00:00:00 GMT, Jan. 1, 1970)
63 *
64 * given a number of seconds since the start of the unix epoch,
65 * DaysSinceEpoch() computes the number of days since the start of the
66 * astronomical epoch (1990 january 0.0)
67 */
68
69 #define EpochStart (631065600)
70 #define DaysSinceEpoch(secs) (((secs)-EpochStart)*(1.0/(24*3600)))
71
72 /*
73 * assuming the apparent orbit of the sun about the earth is circular,
74 * the rate at which the orbit progresses is given by RadsPerDay --
75 * TWOPI radians per orbit divided by 365.242191 days per year:
76 */
77
78 #define RadsPerDay (TWOPI/365.242191)
79
80 /*
81 * details of sun's apparent orbit at epoch 1990.0 (after
82 * duffett-smith, table 6, section 46)
83 *
84 * Epsilon_g (ecliptic longitude at epoch 1990.0) 279.403303 degrees
85 * OmegaBar_g (ecliptic longitude of perigee) 282.768422 degrees
86 * Eccentricity (eccentricity of orbit) 0.016713
87 */
88
89 #define Epsilon_g (DegsToRads(279.403303))
90 #define OmegaBar_g (DegsToRads(282.768422))
91 #define Eccentricity (0.016713)
92
93 /*
94 * MeanObliquity gives the mean obliquity of the earth's axis at epoch
95 * 1990.0 (computed as 23.440592 degrees according to the method given
96 * in duffett-smith, section 27)
97 */
98 #define MeanObliquity (23.440592*(TWOPI/360))
99
100 /*
101 * Lunar parameters, epoch January 0, 1990.0
102 */
103 #define MoonMeanLongitude DegsToRads(318.351648)
104 #define MoonMeanLongitudePerigee DegsToRads( 36.340410)
105 #define MoonMeanLongitudeNode DegsToRads(318.510107)
106 #define MoonInclination DegsToRads( 5.145396)
107
108 #define SideralMonth (27.3217)
109
110 /*
111 * Force an angular value into the range [-PI, +PI]
112 */
113 #define Normalize(x) \
114 do { \
115 if ((x) < -M_PI) \
116 do (x) += TWOPI; while ((x) < -M_PI); \
117 else if ((x) > M_PI) \
118 do (x) -= TWOPI; while ((x) > M_PI); \
119 } while (0)
120
121 static double solve_keplers_equation _P((double));
122 static double mean_sun _P((double));
123 static double sun_ecliptic_longitude _P((time_t));
124 static void ecliptic_to_equatorial _P((double, double, double *, double *));
125 static double julian_date _P((int, int, int));
126 static double GST _P((time_t));
127
128 /*
129 * solve Kepler's equation via Newton's method
130 * (after duffett-smith, section 47)
131 */
132 static double solve_keplers_equation(M)
133 double M;
134 {
135 double E;
136 double delta;
137
138 E = M;
139 while (1)
140 {
141 delta = E - Eccentricity*sin(E) - M;
142 if (fabs(delta) <= 1e-10) break;
143 E -= delta / (1 - Eccentricity*cos(E));
144 }
145
146 return E;
147 }
148
149
150 /*
151 * Calculate the position of the mean sun: where the sun would
152 * be if the earth's orbit were circular instead of ellipictal.
153 */
154
155 static double mean_sun (D)
156 double D; /* days since ephemeris epoch */
157 {
158 double N, M;
159
160 N = RadsPerDay * D;
161 N = fmod(N, TWOPI);
162 if (N < 0) N += TWOPI;
163
164 M = N + Epsilon_g - OmegaBar_g;
165 if (M < 0) M += TWOPI;
166 return M;
167 }
168
169 /*
170 * compute ecliptic longitude of sun (in radians)
171 * (after duffett-smith, section 47)
172 */
173 static double sun_ecliptic_longitude(ssue)
174 time_t ssue; /* seconds since unix epoch */
175 {
176 double D;
177 double M_sun, E;
178 double v;
179
180 D = DaysSinceEpoch(ssue);
181 M_sun = mean_sun(D);
182
183 E = solve_keplers_equation(M_sun);
184 v = 2 * atan(sqrt((1+Eccentricity)/(1-Eccentricity)) * tan(E/2));
185
186 return (v + OmegaBar_g);
187 }
188
189
190 /*
191 * convert from ecliptic to equatorial coordinates
192 * (after duffett-smith, section 27)
193 */
194 static void ecliptic_to_equatorial(lambda, beta, alpha, delta)
195 double lambda; /* ecliptic longitude */
196 double beta; /* ecliptic latitude */
197 double *alpha; /* (return) right ascension */
198 double *delta; /* (return) declination */
199 {
200 double sin_e, cos_e;
201
202 sin_e = sin(MeanObliquity);
203 cos_e = cos(MeanObliquity);
204
205 *alpha = atan2(sin(lambda)*cos_e - tan(beta)*sin_e, cos(lambda));
206 *delta = asin(sin(beta)*cos_e + cos(beta)*sin_e*sin(lambda));
207 }
208
209
210 /*
211 * computing julian dates (assuming gregorian calendar, thus this is
212 * only valid for dates of 1582 oct 15 or later)
213 * (after duffett-smith, section 4)
214 */
215 static double julian_date(y, m, d)
216 int y; /* year (e.g. 19xx) */
217 int m; /* month (jan=1, feb=2, ...) */
218 int d; /* day of month */
219 {
220 int A, B, C, D;
221 double JD;
222
223 /* lazy test to ensure gregorian calendar */
224 assert(y >= 1583);
225
226 if ((m == 1) || (m == 2))
227 {
228 y -= 1;
229 m += 12;
230 }
231
232 A = y / 100;
233 B = 2 - A + (A / 4);
234 C = 365.25 * y;
235 D = 30.6001 * (m + 1);
236
237 JD = B + C + D + d + 1720994.5;
238
239 return JD;
240 }
241
242
243 /*
244 * compute greenwich mean sidereal time (GST) corresponding to a given
245 * number of seconds since the unix epoch
246 * (after duffett-smith, section 12)
247 */
248 static double GST(ssue)
249 time_t ssue; /* seconds since unix epoch */
250 {
251 double JD;
252 double T, T0;
253 double UT;
254 struct tm *tm;
255
256 tm = gmtime(&ssue);
257
258 JD = julian_date(tm->tm_year+1900, tm->tm_mon+1, tm->tm_mday);
259 T = (JD - 2451545) / 36525;
260
261 T0 = ((T + 2.5862e-5) * T + 2400.051336) * T + 6.697374558;
262
263 T0 = fmod(T0, 24.0);
264 if (T0 < 0) T0 += 24;
265
266 UT = tm->tm_hour + (tm->tm_min + tm->tm_sec / 60.0) / 60.0;
267
268 T0 += UT * 1.002737909;
269 T0 = fmod(T0, 24.0);
270 if (T0 < 0) T0 += 24;
271
272 return T0;
273 }
274
275
276 /*
277 * given a particular time (expressed in seconds since the unix
278 * epoch), compute position on the earth (lat, lon) such that sun is
279 * directly overhead.
280 */
281 void sun_position(ssue, lat, lon)
282 time_t ssue; /* seconds since unix epoch */
283 double *lat; /* (return) latitude */
284 double *lon; /* (return) longitude */
285 {
286 double lambda;
287 double alpha, delta;
288 double tmp;
289
290 lambda = sun_ecliptic_longitude(ssue);
291 ecliptic_to_equatorial(lambda, 0.0, &alpha, &delta);
292
293 tmp = alpha - (TWOPI/24)*GST(ssue);
294 Normalize(tmp);
295 *lon = tmp * (360/TWOPI);
296 *lat = delta * (360/TWOPI);
297 }
298
299
300 /*
301 * given a particular time (expressed in seconds since the unix
302 * epoch), compute position on the earth (lat, lon) such that the
303 * moon is directly overhead.
304 *
305 * Based on duffett-smith **2nd ed** section 61; combines some steps
306 * into single expressions to reduce the number of extra variables.
307 */
308 void moon_position(ssue, lat, lon)
309 time_t ssue; /* seconds since unix epoch */
310 double *lat; /* (return) latitude */
311 double *lon; /* (return) longitude */
312 {
313 double lambda, beta;
314 double D, L, Ms, Mm, N, Ev, Ae, Ec, alpha, delta;
315
316 D = DaysSinceEpoch(ssue);
317 lambda = sun_ecliptic_longitude(ssue);
318 Ms = mean_sun(D);
319
320 L = fmod(D/SideralMonth, 1.0)*TWOPI + MoonMeanLongitude;
321 Normalize(L);
322 Mm = L - DegsToRads(0.1114041*D) - MoonMeanLongitudePerigee;
323 Normalize(Mm);
324 N = MoonMeanLongitudeNode - DegsToRads(0.0529539*D);
325 Normalize(N);
326 Ev = DegsToRads(1.2739) * sin(2.0*(L-lambda)-Mm);
327 Ae = DegsToRads(0.1858) * sin(Ms);
328 Mm += Ev - Ae - DegsToRads(0.37)*sin(Ms);
329 Ec = DegsToRads(6.2886) * sin(Mm);
330 L += Ev + Ec - Ae + DegsToRads(0.214) * sin(2.0*Mm);
331 L += DegsToRads(0.6583) * sin(2.0*(L-lambda));
332 N -= DegsToRads(0.16) * sin(Ms);
333
334 L -= N;
335 lambda =(fabs(cos(L)) < 1e-12) ?
336 (N + sin(L) * cos(MoonInclination) * M_PI/2) :
337 (N + atan2(sin(L) * cos(MoonInclination), cos(L)));
338 Normalize(lambda);
339 beta = asin(sin(L) * sin(MoonInclination));
340 ecliptic_to_equatorial(lambda, beta, &alpha, &delta);
341 alpha -= (TWOPI/24)*GST(ssue);
342 Normalize(alpha);
343 *lon = alpha * (360/TWOPI);
344 *lat = delta * (360/TWOPI);
345 }