1 #include "astro.h"
2 
3 double k1, k2, k3, k4;
4 double mnom, msun, noded, dmoon;
5 
6 void
7 moon(void)
8 {
9 	Moontab *mp;
10 	double dlong, lsun, psun;
11 	double eccm, eccs, chp, cpe;
12 	double v0, t0, m0, j0;
13 	double arg1, arg2, arg3, arg4, arg5, arg6, arg7;
14 	double arg8, arg9, arg10;
15 	double dgamma, k5, k6;
16 	double lterms, sterms, cterms, nterms, pterms, spterms;
17 	double gamma1, gamma2, gamma3, arglat;
18 	double xmp, ymp, zmp;
19 	double obl2;
20 
21 /*
22  *	the fundamental elements - all referred to the epoch of
23  *	Jan 0.5, 1900 and to the mean equinox of date.
24  */
25 
26 	dlong = 270.434164 + 13.1763965268*eday - .001133*capt2
27 		 + 2.e-6*capt3;
28 	argp = 334.329556 + .1114040803*eday - .010325*capt2
29 		 - 12.e-6*capt3;
30 	node = 259.183275 - .0529539222*eday + .002078*capt2
31 		 + 2.e-6*capt3;
32 	lsun = 279.696678 + .9856473354*eday + .000303*capt2;
33 	psun = 281.220833 + .0000470684*eday + .000453*capt2
34 		 + 3.e-6*capt3;
35 
36 	dlong = fmod(dlong, 360.);
37 	argp = fmod(argp, 360.);
38 	node = fmod(node, 360.);
39 	lsun = fmod(lsun, 360.);
40 	psun = fmod(psun, 360.);
41 
42 	eccm = 22639.550;
43 	eccs = .01675104 - .00004180*capt;
44 	incl = 18461.400;
45 	cpe = 124.986;
46 	chp = 3422.451;
47 
48 /*
49  *	some subsidiary elements - they are all longitudes
50  *	and they are referred to the epoch 1/0.5 1900 and
51  *	to the fixed mean equinox of 1850.0.
52  */
53 
54 	v0 = 342.069128 + 1.6021304820*eday;
55 	t0 =  98.998753 + 0.9856091138*eday;
56 	m0 = 293.049675 + 0.5240329445*eday;
57 	j0 = 237.352319 + 0.0830912295*eday;
58 
59 /*
60  *	the following are periodic corrections to the
61  *	fundamental elements and constants.
62  *	arg3 is the "Great Venus Inequality".
63  */
64 
65 	arg1 = 41.1 + 20.2*(capt+.5);
66 	arg2 = dlong - argp + 33. + 3.*t0 - 10.*v0 - 2.6*(capt+.5);
67 	arg3 = dlong - argp + 151.1 + 16.*t0 - 18.*v0 - (capt+.5);
68 	arg4 = node;
69 	arg5 = node + 276.2 - 2.3*(capt+.5);
70 	arg6 = 313.9 + 13.*t0 - 8.*v0;
71 	arg7 = dlong - argp + 112.0 + 29.*t0 - 26.*v0;
72 	arg8 = dlong + argp - 2.*lsun + 273. + 21.*t0 - 20.*v0;
73 	arg9 = node + 290.1 - 0.9*(capt+.5);
74 	arg10 = 115. + 38.5*(capt+.5);
75 	arg1 *= radian;
76 	arg2 *= radian;
77 	arg3 *= radian;
78 	arg4 *= radian;
79 	arg5 *= radian;
80 	arg6 *= radian;
81 	arg7 *= radian;
82 	arg8 *= radian;
83 	arg9 *= radian;
84 	arg10 *= radian;
85 
86 	dlong +=
87 		   (0.84 *sin(arg1)
88 		 +  0.31 *sin(arg2)
89 		 + 14.27 *sin(arg3)
90 		 +  7.261*sin(arg4)
91 		 +  0.282*sin(arg5)
92 		 +  0.237*sin(arg6)
93 		 +  0.108*sin(arg7)
94 		 +  0.126*sin(arg8))/3600.;
95 
96 	argp +=
97 		 (- 2.10 *sin(arg1)
98 		 -  0.118*sin(arg3)
99 		 -  2.076*sin(arg4)
100 		 -  0.840*sin(arg5)
101 		 -  0.593*sin(arg6))/3600.;
102 
103 	node +=
104 		   (0.63*sin(arg1)
105 		 +  0.17*sin(arg3)
106 		 + 95.96*sin(arg4)
107 		 + 15.58*sin(arg5)
108 		 +  1.86*sin(arg9))/3600.;
109 
110 	t0 +=
111 		 (- 6.40*sin(arg1)
112 		 -  1.89*sin(arg6))/3600.;
113 
114 	psun +=
115 		   (6.40*sin(arg1)
116 		 +  1.89*sin(arg6))/3600.;
117 
118 	dgamma = -  4.318*cos(arg4)
119 		 -  0.698*cos(arg5)
120 		 -  0.083*cos(arg9);
121 
122 	j0 +=
123 		   0.33*sin(arg10);
124 
125 /*
126  *	the following factors account for the fact that the
127  *	eccentricity, solar eccentricity, inclination and
128  *	parallax used by Brown to make up his coefficients
129  *	are both wrong and out of date.  Brown did the same
130  *	thing in a different way.
131  */
132 
133 	k1 = eccm/22639.500;
134 	k2 = eccs/.01675104;
135 	k3 = 1. + 2.708e-6 + .000108008*dgamma;
136 	k4 = cpe/125.154;
137 	k5 = chp/3422.700;
138 
139 /*
140  *	the principal arguments that are used to compute
141  *	perturbations are the following differences of the
142  *	fundamental elements.
143  */
144 
145 	mnom = dlong - argp;
146 	msun = lsun - psun;
147 	noded = dlong - node;
148 	dmoon = dlong - lsun;
149 
150 /*
151  *	solar terms in longitude
152  */
153 
154 	lterms = 0.0;
155 	mp = moontab;
156 	for(;;) {
157 		if(mp->f == 0.0)
158 			break;
159 		lterms += sinx(mp->f,
160 			mp->c[0], mp->c[1],
161 			mp->c[2], mp->c[3], 0.0);
162 		mp++;
163 	}
164 	mp++;
165 
166 /*
167  *	planetary terms in longitude
168  */
169 
170 	lterms += sinx(0.822, 0,0,0,0, t0-v0);
171 	lterms += sinx(0.307, 0,0,0,0, 2.*t0-2.*v0+179.8);
172 	lterms += sinx(0.348, 0,0,0,0, 3.*t0-2.*v0+272.9);
173 	lterms += sinx(0.176, 0,0,0,0, 4.*t0-3.*v0+271.7);
174 	lterms += sinx(0.092, 0,0,0,0, 5.*t0-3.*v0+199.);
175 	lterms += sinx(0.129, 1,0,0,0, -t0+v0+180.);
176 	lterms += sinx(0.152, 1,0,0,0, t0-v0);
177 	lterms += sinx(0.127, 1,0,0,0, 3.*t0-3.*v0+180.);
178 	lterms += sinx(0.099, 0,0,0,2, t0-v0);
179 	lterms += sinx(0.136, 0,0,0,2, 2.*t0-2.*v0+179.5);
180 	lterms += sinx(0.083, -1,0,0,2, -4.*t0+4.*v0+180.);
181 	lterms += sinx(0.662, -1,0,0,2, -3.*t0+3.*v0+180.0);
182 	lterms += sinx(0.137, -1,0,0,2, -2.*t0+2.*v0);
183 	lterms += sinx(0.133, -1,0,0,2, t0-v0);
184 	lterms += sinx(0.157, -1,0,0,2, 2.*t0-2.*v0+179.6);
185 	lterms += sinx(0.079, -1,0,0,2, -8.*t0+6.*v0+162.6);
186 	lterms += sinx(0.073, 2,0,0,-2, 3.*t0-3.*v0+180.);
187 	lterms += sinx(0.643, 0,0,0,0, -t0+j0+178.8);
188 	lterms += sinx(0.187, 0,0,0,0, -2.*t0+2.*j0+359.6);
189 	lterms += sinx(0.087, 0,0,0,0, j0+289.9);
190 	lterms += sinx(0.165, 0,0,0,0, -t0+2.*j0+241.5);
191 	lterms += sinx(0.144, 1,0,0,0, t0-j0+1.0);
192 	lterms += sinx(0.158, 1,0,0,0, -t0+j0+179.0);
193 	lterms += sinx(0.190, 1,0,0,0, -2.*t0+2.*j0+180.0);
194 	lterms += sinx(0.096, 1,0,0,0, -2.*t0+3.*j0+352.5);
195 	lterms += sinx(0.070, 0,0,0,2, 2.*t0-2.*j0+180.);
196 	lterms += sinx(0.167, 0,0,0,2, -t0+j0+178.5);
197 	lterms += sinx(0.085, 0,0,0,2, -2.*t0+2.*j0+359.2);
198 	lterms += sinx(1.137, -1,0,0,2, 2.*t0-2.*j0+180.3);
199 	lterms += sinx(0.211, -1,0,0,2, -t0+j0+178.4);
200 	lterms += sinx(0.089, -1,0,0,2, -2.*t0+2.*j0+359.2);
201 	lterms += sinx(0.436, -1,0,0,2, 2.*t0-3.*j0+7.5);
202 	lterms += sinx(0.240, 2,0,0,-2, -2.*t0+2.*j0+179.9);
203 	lterms += sinx(0.284, 2,0,0,-2, -2.*t0+3.*j0+172.5);
204 	lterms += sinx(0.195, 0,0,0,0, -2.*t0+2.*m0+180.2);
205 	lterms += sinx(0.327, 0,0,0,0, -t0+2.*m0+224.4);
206 	lterms += sinx(0.093, 0,0,0,0, -2.*t0+4.*m0+244.8);
207 	lterms += sinx(0.073, 1,0,0,0, -t0+2.*m0+223.3);
208 	lterms += sinx(0.074, 1,0,0,0, t0-2.*m0+306.3);
209 	lterms += sinx(0.189, 0,0,0,0, node+180.);
210 
211 /*
212  *	solar terms in latitude
213  */
214 
215 	sterms = 0;
216 	for(;;) {
217 		if(mp->f == 0)
218 			break;
219 		sterms += sinx(mp->f,
220 			mp->c[0], mp->c[1],
221 			mp->c[2], mp->c[3], 0);
222 		mp++;
223 	}
224 	mp++;
225 
226 	cterms = 0;
227 	for(;;) {
228 		if(mp->f == 0)
229 			break;
230 		cterms += cosx(mp->f,
231 			mp->c[0], mp->c[1],
232 			mp->c[2], mp->c[3], 0);
233 		mp++;
234 	}
235 	mp++;
236 
237 	nterms = 0;
238 	for(;;) {
239 		if(mp->f == 0)
240 			break;
241 		nterms += sinx(mp->f,
242 			mp->c[0], mp->c[1],
243 			mp->c[2], mp->c[3], 0);
244 		mp++;
245 	}
246 	mp++;
247 
248 /*
249  *	planetary terms in latitude
250  */
251 
252 	pterms =
253 		   sinx(0.215, 0,0,0,0, dlong);
254 
255 /*
256  *	solar terms in parallax
257  */
258 
259 	spterms = 3422.700;
260 	for(;;) {
261 		if(mp->f == 0)
262 			break;
263 		spterms += cosx(mp->f,
264 			mp->c[0], mp->c[1],
265 			mp->c[2], mp->c[3], 0);
266 		mp++;
267 	}
268 
269 /*
270  *	planetary terms in parallax
271  */
272 
273 	//spterms = spterms;
274 
275 /*
276  *	computation of longitude
277  */
278 
279 	lambda = (dlong + lterms/3600.)*radian;
280 
281 /*
282  *	computation of latitude
283  */
284 
285 	arglat = (noded + sterms/3600.)*radian;
286 	gamma1 = 18519.700 * k3;
287 	gamma2 = -6.241 * k3*k3*k3;
288 	gamma3 = 0.004 * k3*k3*k3*k3*k3;
289 
290 	k6 = (gamma1 + cterms) / gamma1;
291 
292 	beta = k6 * (gamma1*sin(arglat) + gamma2*sin(3.*arglat)
293 		 + gamma3*sin(5.*arglat) + nterms)
294 		 + pterms;
295 	if(flags['o'])
296 		beta -= 0.6;
297 	beta *= radsec;
298 
299 /*
300  *	computation of parallax
301  */
302 
303 	spterms = k5 * spterms *radsec;
304 	hp = spterms + (spterms*spterms*spterms)/6.;
305 
306 	rad = hp/radsec;
307 	rp = 1.;
308 	semi = .0799 + .272453*(hp/radsec);
309 	if(dmoon < 0.)
310 		dmoon += 360.;
311 	mag = dmoon/360.;
312 
313 /*
314  *	change to equatorial coordinates
315  */
316 
317 	lambda += phi;
318 	obl2 = obliq + eps;
319 	xmp = rp*cos(lambda)*cos(beta);
320 	ymp = rp*(sin(lambda)*cos(beta)*cos(obl2) - sin(obl2)*sin(beta));
321 	zmp = rp*(sin(lambda)*cos(beta)*sin(obl2) + cos(obl2)*sin(beta));
322 
323 	alpha = atan2(ymp, xmp);
324 	delta = atan2(zmp, sqrt(xmp*xmp+ymp*ymp));
325 	meday = eday;
326 	mhp = hp;
327 
328 	geo();
329 }
330 
331 double
332 sinx(double coef, int i, int j, int k, int m, double angle)
333 {
334 	double x;
335 
336 	x = i*mnom + j*msun + k*noded + m*dmoon + angle;
337 	x = coef*sin(x*radian);
338 	if(i < 0)
339 		i = -i;
340 	for(; i>0; i--)
341 		x *= k1;
342 	if(j < 0)
343 		j = -j;
344 	for(; j>0; j--)
345 		x *= k2;
346 	if(k < 0)
347 		k = -k;
348 	for(; k>0; k--)
349 		x *= k3;
350 	if(m & 1)
351 		x *= k4;
352 
353 	return x;
354 }
355 
356 double
357 cosx(double coef, int i, int j, int k, int m, double angle)
358 {
359 	double x;
360 
361 	x = i*mnom + j*msun + k*noded + m*dmoon + angle;
362 	x = coef*cos(x*radian);
363 	if(i < 0)
364 		i = -i;
365 	for(; i>0; i--)
366 		x *= k1;
367 	if(j < 0)
368 		j = -j;
369 	for(; j>0; j--)
370 		x *= k2;
371 	if(k < 0)
372 		k = -k;
373 	for(; k>0; k--)
374 		x *= k3;
375 	if(m & 1)
376 		x *= k4;
377 
378 	return x;
379 }