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
|
#include "astro.h"
static double elem[] =
{
36525.0, /* [0] eday of epoc */
30.06896348, /* [1] semi major axis (au) */
0.00858587, /* [2] eccentricity */
1.76917, /* [3] inclination (deg) */
131.72169, /* [4] longitude of the ascending node (deg) */
44.97135, /* [5] longitude of perihelion (deg) */
304.88003, /* [6] mean longitude (deg) */
-0.00125196, /* [1+6] (au/julian century) */
0.0000251, /* [2+6] (e/julian century) */
-3.64, /* [3+6] (arcsec/julian century) */
-151.25, /* [4+6] (arcsec/julian century) */
-844.43, /* [5+6] (arcsec/julian century) */
786449.21, /* [6+6] (arcsec/julian century) */
};
void
nept(void)
{
double pturbl, pturbb, pturbr;
double lograd;
double dele, enom, vnom, nd, sl;
double capj, capn, eye, comg, omg;
double sb, su, cu, u, b, up;
double sd, ca, sa;
double cy;
cy = (eday - elem[0]) / 36525.; /* per julian century */
mrad = elem[1] + elem[1+6]*cy;
ecc = elem[2] + elem[2+6]*cy;
cy = cy / 3600; /* arcsec/deg per julian century */
incl = elem[3] + elem[3+6]*cy;
node = elem[4] + elem[4+6]*cy;
argp = elem[5] + elem[5+6]*cy;
anom = elem[6] + elem[6+6]*cy - argp;
motion = elem[6+6] / 36525. / 3600;
incl *= radian;
node *= radian;
argp *= radian;
anom = fmod(anom,360.)*radian;
enom = anom + ecc*sin(anom);
do {
dele = (anom - enom + ecc * sin(enom)) /
(1. - ecc*cos(enom));
enom += dele;
} while(fabs(dele) > converge);
vnom = 2.*atan2(sqrt((1.+ecc)/(1.-ecc))*sin(enom/2.),
cos(enom/2.));
rad = mrad*(1. - ecc*cos(enom));
lambda = vnom + argp;
pturbl = 0.;
lambda += pturbl*radsec;
pturbb = 0.;
pturbr = 0.;
/*
* reduce to the ecliptic
*/
nd = lambda - node;
lambda = node + atan2(sin(nd)*cos(incl),cos(nd));
sl = sin(incl)*sin(nd) + pturbb*radsec;
beta = atan2(sl, pyth(sl));
lograd = pturbr*2.30258509;
rad *= 1. + lograd;
lambda -= 1185.*radsec;
beta -= 51.*radsec;
motion *= radian*mrad*mrad/(rad*rad);
semi = 83.33;
/*
* here begins the computation of magnitude
* first find the geocentric equatorial coordinates of Saturn
*/
sd = rad*(cos(beta)*sin(lambda)*sin(obliq) +
sin(beta)*cos(obliq));
sa = rad*(cos(beta)*sin(lambda)*cos(obliq) -
sin(beta)*sin(obliq));
ca = rad*cos(beta)*cos(lambda);
sd += zms;
sa += yms;
ca += xms;
alpha = atan2(sa,ca);
delta = atan2(sd,sqrt(sa*sa+ca*ca));
/*
* here are the necessary elements of Saturn's rings
* cf. Exp. Supp. p. 363ff.
*/
capj = 6.9056 - 0.4322*capt;
capn = 126.3615 + 3.9894*capt + 0.2403*capt2;
eye = 28.0743 - 0.0128*capt;
comg = 168.1179 + 1.3936*capt;
omg = 42.9236 - 2.7390*capt - 0.2344*capt2;
capj *= radian;
capn *= radian;
eye *= radian;
comg *= radian;
omg *= radian;
/*
* now find saturnicentric ring-plane coords of the earth
*/
sb = sin(capj)*cos(delta)*sin(alpha-capn) -
cos(capj)*sin(delta);
su = cos(capj)*cos(delta)*sin(alpha-capn) +
sin(capj)*sin(delta);
cu = cos(delta)*cos(alpha-capn);
u = atan2(su,cu);
b = atan2(sb,sqrt(su*su+cu*cu));
/*
* and then the saturnicentric ring-plane coords of the sun
*/
su = sin(eye)*sin(beta) +
cos(eye)*cos(beta)*sin(lambda-comg);
cu = cos(beta)*cos(lambda-comg);
up = atan2(su,cu);
/*
* at last, the magnitude
*/
sb = sin(b);
mag = -8.68 +2.52*fabs(up+omg-u)-
2.60*fabs(sb) + 1.25*(sb*sb);
helio();
geo();
}
|