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/* 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 <stdlib.h>
#include "tws.h"
#include "phase.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(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(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;
}
/* kepler - solve the equation of Kepler */
static double kepler(double m, double 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(double pdate, double *pphase, double *mage, double *dist,
double *angdia, double *sudist, double *suangdia)
/* pphase: illuminated fraction */
/* mage: age of moon in days */
/* dist: distance in kilometres */
/* angdia: angular diameter in degrees */
/* sudist: distance to Sun */
/* 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));
}
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