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#ifndef lint
static char rcsid[] =
"@(#) $Header: phase.c,v 1.2 88/08/26 22:29:42 jef Exp $ (LBL)";
#endif
/* phase.c - routines to calculate the phase of the moon
**
** Adapted from "moontool.c" by John Walker, Release 2.0.
*/
#include <stdio.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;
}
/* jhms - convert Julian time to hour, minutes, and seconds */
static void jhms(j, h, m, s)
double j;
int *h, *m, *s;
{
long ij;
j += 0.5; /* astronomical to civil */
ij = (j - floor(j)) * 86400.0;
*h = ij / 3600L;
*m = (ij / 60L) % 60L;
*s = ij % 60L;
}
/* 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) {
fprintf(stderr, "truephase() called with invalid phase selector.\n");
abort();
}
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, MN, Ev, Ae, A3, MmP,
mEc, A4, lP, V, lPP, NP, y, x, Lambdamoon, BetaM,
MoonAge, MoonPhase,
MoonDist, MoonDFrac, MoonAng, MoonPar,
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);
/* Moon's ascending node mean longitude. */
MN = fixangle(mlnode - 0.0529539 * Day);
/* 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;
/* Corrected longitude of the node. */
NP = MN - 0.16 * sin(torad(M));
/* Y inclination coordinate. */
y = sin(torad(lPP - NP)) * cos(torad(minc));
/* X inclination coordinate. */
x = cos(torad(lPP - NP));
/* Ecliptic longitude. */
Lambdamoon = todeg(atan2(y, x));
Lambdamoon += NP;
/* Ecliptic latitude. */
BetaM = todeg(asin(sin(torad(lPP - NP)) * sin(torad(minc))));
/* 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;
/* Calculate Moon's parallax. */
MoonPar = mparallax / MoonDFrac;
*pphase = MoonPhase;
*mage = synmonth * (fixangle(MoonAge) / 360.0);
*dist = MoonDist;
*angdia = MoonAng;
*sudist = SunDist;
*suangdia = SunAng;
return torad(fixangle(MoonAge));
}
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