File: phase.c

package info (click to toggle)
xphoon 20000613%2B0-3
  • links: PTS, VCS
  • area: main
  • in suites: jessie, jessie-kfreebsd, stretch
  • size: 604 kB
  • ctags: 301
  • sloc: ansic: 2,013; makefile: 7; sh: 1
file content (458 lines) | stat: -rw-r--r-- 12,951 bytes parent folder | download | duplicates (3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
/* phase.c - routines to calculate the phase of the moon
**
** Adapted from "moontool.c" by John Walker, Release 2.0.
*/

#ifndef lint
static char rcsid[] =
    "@(#) $Header: phase.c,v 1.2 91/09/13 22:15:26 jef Exp $ (LBL)";
#endif

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "tws.h"

/* Astronomical constants. */

#define epoch	    2444238.5	   /* 1980 January 0.0 */

/* Constants defining the Sun's apparent orbit. */

#define elonge	    278.833540	   /* ecliptic longitude of the Sun
				        at epoch 1980.0 */
#define elongp	    282.596403	   /* ecliptic longitude of the Sun at
				        perigee */
#define eccent      0.016718       /* eccentricity of Earth's orbit */
#define sunsmax     1.495985e8     /* semi-major axis of Earth's orbit, km */
#define sunangsiz   0.533128       /* sun's angular size, degrees, at
				        semi-major axis distance */

/* Elements of the Moon's orbit, epoch 1980.0. */

#define mmlong      64.975464      /* moon's mean lonigitude at the epoch */
#define mmlongp     349.383063	   /* mean longitude of the perigee at the
				        epoch */
#define mlnode	    151.950429	   /* mean longitude of the node at the
				        epoch */
#define minc        5.145396       /* inclination of the Moon's orbit */
#define mecc        0.054900       /* eccentricity of the Moon's orbit */
#define mangsiz     0.5181         /* moon's angular size at distance a
				        from Earth */
#define msmax       384401.0       /* semi-major axis of Moon's orbit in km */
#define mparallax   0.9507	   /* parallax at distance a from Earth */
#define synmonth    29.53058868    /* synodic month (new Moon to new Moon) */
#define lunatbase   2423436.0      /* base date for E. W. Brown's numbered
				        series of lunations (1923 January 16) */

/* Properties of the Earth. */

#define earthrad    6378.16	   /* radius of Earth in kilometres */


#define PI 3.14159265358979323846  /* assume not near black hole nor in
				        Tennessee */

/* Handy mathematical functions. */

#define sgn(x) (((x) < 0) ? -1 : ((x) > 0 ? 1 : 0))	  /* extract sign */
#define abs(x) ((x) < 0 ? (-(x)) : (x)) 		  /* absolute val */
#define fixangle(a) ((a) - 360.0 * (floor((a) / 360.0)))  /* fix angle	  */
#define torad(d) ((d) * (PI / 180.0))			  /* deg->rad	  */
#define todeg(d) ((d) * (180.0 / PI))			  /* rad->deg	  */
#define dsin(x) (sin(torad((x))))			  /* sin from deg */
#define dcos(x) (cos(torad((x))))			  /* cos from deg */


/* jdate - convert internal GMT date and time to Julian day and fraction */

static long jdate(t)
struct tws *t;
{
	long c, m, y;

	y = t->tw_year + 1900;
	m = t->tw_mon + 1;
	if (m > 2)
	   m = m - 3;
	else {
	   m = m + 9;
	   --y;
	}
	c = y / 100L;		/* compute century */
	y -= 100L * c;
	return t->tw_mday + (c * 146097L) / 4 + (y * 1461L) / 4 +
	    (m * 153L + 2) / 5 + 1721119L;
}

/* jtime - convert internal date and time to astronomical Julian
**	     time (i.e. Julian date plus day fraction, expressed as
**	     a double)
*/

double jtime(t)
struct tws *t;
{
	int c;

	c = - t->tw_zone;
	if ( t->tw_flags & TW_DST )
		c += 60;

	return (jdate(t) - 0.5) + 
	   (t->tw_sec + 60 * (t->tw_min + c + 60 * t->tw_hour)) / 86400.0;
}

/* jyear - convert Julian date to year, month, day, which are
**	     returned via integer pointers to integers
*/

static void jyear(td, yy, mm, dd)
double td;
int *yy, *mm, *dd;
{
	double j, d, y, m;

	td += 0.5;		   /* astronomical to civil */
	j = floor(td);
	j = j - 1721119.0;
	y = floor(((4 * j) - 1) / 146097.0);
	j = (j * 4.0) - (1.0 + (146097.0 * y));
	d = floor(j / 4.0);
	j = floor(((4.0 * d) + 3.0) / 1461.0);
	d = ((4.0 * d) + 3.0) - (1461.0 * j);
	d = floor((d + 4.0) / 4.0);
	m = floor(((5.0 * d) - 3) / 153.0);
	d = (5.0 * d) - (3.0 + (153.0 * m));
	d = floor((d + 5.0) / 5.0);
	y = (100.0 * y) + j;
	if (m < 10.0)
	   m = m + 3;
	else {
	   m = m - 9;
	   y = y + 1;
	}
	*yy = y;
	*mm = m;
	*dd = d;
}

/* meanphase - calculates mean phase of the Moon for a given base date
**               and desired phase:
**		     0.0   New Moon
**		     0.25  First quarter
**		     0.5   Full moon
**		     0.75  Last quarter
**		 Beware!!!  This routine returns meaningless
**               results for any other phase arguments.  Don't
**		 attempt to generalise it without understanding
**		 that the motion of the moon is far more complicated
**		 that this calculation reveals.
*/

static double meanphase(sdate, phase, usek)
double sdate, phase;
double *usek;
{
	int yy, mm, dd;
	double k, t, t2, t3, nt1;

	jyear(sdate, &yy, &mm, &dd);

	k = (yy + ((mm - 1) * (1.0 / 12.0)) - 1900) * 12.3685;

	/* Time in Julian centuries from 1900 January 0.5. */
	t = (sdate - 2415020.0) / 36525;
	t2 = t * t;		   /* square for frequent use */
	t3 = t2 * t;		   /* cube for frequent use */

	*usek = k = floor(k) + phase;
	nt1 = 2415020.75933 + synmonth * k
	      + 0.0001178 * t2
	      - 0.000000155 * t3
	      + 0.00033 * dsin(166.56 + 132.87 * t - 0.009173 * t2);

	return nt1;
}

/* truephase - given a K value used to determine the mean phase of the
**               new moon, and a phase selector (0.0, 0.25, 0.5, 0.75),
**               obtain the true, corrected phase time
*/

static double truephase(k, phase)
double k, phase;
{
	double t, t2, t3, pt, m, mprime, f;
	int apcor = 0;

	k += phase;		   /* add phase to new moon time */
	t = k / 1236.85;	   /* time in Julian centuries from
				        1900 January 0.5 */
	t2 = t * t;		   /* square for frequent use */
	t3 = t2 * t;		   /* cube for frequent use */
	pt = 2415020.75933	   /* mean time of phase */
	     + synmonth * k
	     + 0.0001178 * t2
	     - 0.000000155 * t3
	     + 0.00033 * dsin(166.56 + 132.87 * t - 0.009173 * t2);

        m = 359.2242               /* Sun's mean anomaly */
	    + 29.10535608 * k
	    - 0.0000333 * t2
	    - 0.00000347 * t3;
        mprime = 306.0253          /* Moon's mean anomaly */
	    + 385.81691806 * k
	    + 0.0107306 * t2
	    + 0.00001236 * t3;
        f = 21.2964                /* Moon's argument of latitude */
	    + 390.67050646 * k
	    - 0.0016528 * t2
	    - 0.00000239 * t3;
	if ((phase < 0.01) || (abs(phase - 0.5) < 0.01)) {

	   /* Corrections for New and Full Moon. */

	   pt +=     (0.1734 - 0.000393 * t) * dsin(m)
		    + 0.0021 * dsin(2 * m)
		    - 0.4068 * dsin(mprime)
		    + 0.0161 * dsin(2 * mprime)
		    - 0.0004 * dsin(3 * mprime)
		    + 0.0104 * dsin(2 * f)
		    - 0.0051 * dsin(m + mprime)
		    - 0.0074 * dsin(m - mprime)
		    + 0.0004 * dsin(2 * f + m)
		    - 0.0004 * dsin(2 * f - m)
		    - 0.0006 * dsin(2 * f + mprime)
		    + 0.0010 * dsin(2 * f - mprime)
		    + 0.0005 * dsin(m + 2 * mprime);
	   apcor = 1;
	} else if ((abs(phase - 0.25) < 0.01 || (abs(phase - 0.75) < 0.01))) {
	   pt +=     (0.1721 - 0.0004 * t) * dsin(m)
		    + 0.0021 * dsin(2 * m)
		    - 0.6280 * dsin(mprime)
		    + 0.0089 * dsin(2 * mprime)
		    - 0.0004 * dsin(3 * mprime)
		    + 0.0079 * dsin(2 * f)
		    - 0.0119 * dsin(m + mprime)
		    - 0.0047 * dsin(m - mprime)
		    + 0.0003 * dsin(2 * f + m)
		    - 0.0004 * dsin(2 * f - m)
		    - 0.0006 * dsin(2 * f + mprime)
		    + 0.0021 * dsin(2 * f - mprime)
		    + 0.0003 * dsin(m + 2 * mprime)
		    + 0.0004 * dsin(m - 2 * mprime)
		    - 0.0003 * dsin(2 * m + mprime);
	   if (phase < 0.5)
	      /* First quarter correction. */
	      pt += 0.0028 - 0.0004 * dcos(m) + 0.0003 * dcos(mprime);
	   else
	      /* Last quarter correction. */
	      pt += -0.0028 + 0.0004 * dcos(m) - 0.0003 * dcos(mprime);
	   apcor = 1;
	}
	if (!apcor) {
           (void) fprintf(
		   stderr, "truephase() called with invalid phase selector.\n");
	   exit(1);
	}
	return pt;
}

/* phasehunt5 - find time of phases of the moon which surround the current
**                date.  Five phases are found, starting and ending with the
**                new moons which bound the current lunation
*/

void phasehunt5(sdate, phases)
double sdate;
double phases[5];
{
	double adate, k1, k2, nt1, nt2;

	adate = sdate - 45;
	nt1 = meanphase(adate, 0.0, &k1);
	for ( ; ; ) {
	   adate += synmonth;
	   nt2 = meanphase(adate, 0.0, &k2);
	   if (nt1 <= sdate && nt2 > sdate)
	      break;
	   nt1 = nt2;
	   k1 = k2;
	}
	phases[0] = truephase(k1, 0.0);
	phases[1] = truephase(k1, 0.25);
	phases[2] = truephase(k1, 0.5);
	phases[3] = truephase(k1, 0.75);
	phases[4] = truephase(k2, 0.0);
}


/* phasehunt2 - find time of phases of the moon which surround the current
**                date.  Two phases are found.
*/

void phasehunt2(sdate, phases, which)
double sdate;
double phases[2];
double which[2];
{
	double adate, k1, k2, nt1, nt2;

	adate = sdate - 45;
	nt1 = meanphase(adate, 0.0, &k1);
	for ( ; ; ) {
	   adate += synmonth;
	   nt2 = meanphase(adate, 0.0, &k2);
	   if (nt1 <= sdate && nt2 > sdate)
	      break;
	   nt1 = nt2;
	   k1 = k2;
	}
	phases[0] = truephase(k1, 0.0);
	which[0] = 0.0;
	phases[1] = truephase(k1, 0.25);
	which[1] = 0.25;
	if ( phases[1] <= sdate ) {
	   phases[0] = phases[1];
	   which[0] = which[1];
	   phases[1] = truephase(k1, 0.5);
	   which[1] = 0.5;
	   if ( phases[1] <= sdate ) {
	      phases[0] = phases[1];
	      which[0] = which[1];
	      phases[1] = truephase(k1, 0.75);
	      which[1] = 0.75;
	      if ( phases[1] <= sdate ) {
		 phases[0] = phases[1];
		 which[0] = which[1];
		 phases[1] = truephase(k2, 0.0);
		 which[1] = 0.0;
	      }
	   }
	}
}


/* kepler - solve the equation of Kepler */

static double kepler(m, ecc)
double m, ecc;
{
	double e, delta;
#define EPSILON 1E-6

	e = m = torad(m);
	do {
	   delta = e - ecc * sin(e) - m;
	   e -= delta / (1 - ecc * cos(e));
	} while (abs(delta) > EPSILON);
	return e;
}

/* phase - calculate phase of moon as a fraction:
**
**	The argument is the time for which the phase is requested,
**	expressed as a Julian date and fraction.  Returns the terminator
**	phase angle as a percentage of a full circle (i.e., 0 to 1),
**	and stores into pointer arguments the illuminated fraction of
**      the Moon's disc, the Moon's age in days and fraction, the
**	distance of the Moon from the centre of the Earth, and the
**	angular diameter subtended by the Moon as seen by an observer
**	at the centre of the Earth.
*/

double phase(pdate, pphase, mage, dist, angdia, sudist, suangdia)
double pdate;
double *pphase; 		   /* illuminated fraction */
double *mage;			   /* age of moon in days */
double *dist;			   /* distance in kilometres */
double *angdia; 		   /* angular diameter in degrees */
double *sudist; 		   /* distance to Sun */
double *suangdia;                  /* sun's angular diameter */
{

	double Day, N, M, Ec, Lambdasun, ml, MM, Ev, Ae, A3, MmP,
	       mEc, A4, lP, V, lPP,
	       MoonAge, MoonPhase,
	       MoonDist, MoonDFrac, MoonAng,
	       F, SunDist, SunAng;

        /* Calculation of the Sun's position. */

	Day = pdate - epoch;			/* date within epoch */
	N = fixangle((360 / 365.2422) * Day);	/* mean anomaly of the Sun */
	M = fixangle(N + elonge - elongp);  /* convert from perigee
					         co-ordinates to epoch 1980.0 */
	Ec = kepler(M, eccent);			/* solve equation of Kepler */
	Ec = sqrt((1 + eccent) / (1 - eccent)) * tan(Ec / 2);
	Ec = 2 * todeg(atan(Ec));		/* true anomaly */
        Lambdasun = fixangle(Ec + elongp);	/* Sun's geocentric ecliptic
					             longitude */
	/* Orbital distance factor. */
	F = ((1 + eccent * cos(torad(Ec))) / (1 - eccent * eccent));
	SunDist = sunsmax / F;			/* distance to Sun in km */
        SunAng = F * sunangsiz;		/* Sun's angular size in degrees */


        /* Calculation of the Moon's position. */

        /* Moon's mean longitude. */
	ml = fixangle(13.1763966 * Day + mmlong);

        /* Moon's mean anomaly. */
	MM = fixangle(ml - 0.1114041 * Day - mmlongp);

	/* Evection. */
	Ev = 1.2739 * sin(torad(2 * (ml - Lambdasun) - MM));

	/* Annual equation. */
	Ae = 0.1858 * sin(torad(M));

	/* Correction term. */
	A3 = 0.37 * sin(torad(M));

	/* Corrected anomaly. */
	MmP = MM + Ev - Ae - A3;

	/* Correction for the equation of the centre. */
	mEc = 6.2886 * sin(torad(MmP));

	/* Another correction term. */
	A4 = 0.214 * sin(torad(2 * MmP));

	/* Corrected longitude. */
	lP = ml + Ev + mEc - Ae + A4;

	/* Variation. */
	V = 0.6583 * sin(torad(2 * (lP - Lambdasun)));

	/* True longitude. */
	lPP = lP + V;

	/* Calculation of the phase of the Moon. */

	/* Age of the Moon in degrees. */
	MoonAge = lPP - Lambdasun;

	/* Phase of the Moon. */
	MoonPhase = (1 - cos(torad(MoonAge))) / 2;

	/* Calculate distance of moon from the centre of the Earth. */

	MoonDist = (msmax * (1 - mecc * mecc)) /
	   (1 + mecc * cos(torad(MmP + mEc)));

        /* Calculate Moon's angular diameter. */

	MoonDFrac = MoonDist / msmax;
	MoonAng = mangsiz / MoonDFrac;

	*pphase = MoonPhase;
	*mage = synmonth * (fixangle(MoonAge) / 360.0);
	*dist = MoonDist;
	*angdia = MoonAng;
	*sudist = SunDist;
	*suangdia = SunAng;
	return torad(fixangle(MoonAge));
}