astro.c

/* Adapted from "moontool.c" by John Walker, Release 2.5
**
** Quoting from the original:
**
**   The algorithms used in this program to calculate the positions Sun and
**   Moon as seen from the Earth are given in the book "Practical Astronomy
**   With  Your  Calculator"  by  Peter  Duffett-Smith,   Second   Edition,
**   Cambridge University Press, 1981.  Ignore the word "Calculator" in the
**   title;  this  is  an  essential  reference  if  you're  interested  in
**   developing  software  which  calculates  planetary  positions, orbits,
**   eclipses, and  the  like.   If  you're  interested  in  pursuing  such
**   programming, you should also obtain:
**
**     "Astronomical  Formulae for Calculators" by Jean Meeus, Third Edition,
**     Willmann-Bell, 1985.  A must-have.
**
**     "Planetary  Programs  and  Tables  from  -4000  to  +2800"  by  Pierre
**     Bretagnon  and Jean-Louis Simon, Willmann-Bell, 1986.  If you want the
**     utmost  (outside  of  JPL)  accuracy  for  the  planets,  it's   here.
**
**     "Celestial BASIC" by Eric Burgess, Revised Edition, Sybex, 1985.  Very
**     cookbook oriented, and many of the algorithms are hard to dig  out  of
**     the turgid BASIC code, but you'll probably want it anyway.
**
** See http://www.fourmilab.ch/moontool/
*/

#include <stdio.h>
#include <math.h>
#include <time.h>


#define FALSE 0
#define TRUE 1

/*  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 */


/*
 * UNIX_TO_JULIAN  --  Convert internal Unix date/time to astronomical
 *             Julian time (i.e. Julian date plus day fraction, expressed as
 *	       a double).
 */
double
unix_to_julian( time_t t )
{
	return (double) t / 86400.0 + 2440587.4999996666666666666;
}


/*
 * JYEAR  --  Convert Julian date to year, month, day, which are
 *	       returned via integer pointers to integers.
 */
static void
jyear( double td, int* yy, int* mm, int* 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 time of the mean new Moon for a given
 *		base date.  This argument K to this function is
 *		the precomputed synodic month index, given by:
 *
 *			K = (year - 1900) * 12.3685
 *
 *		where year is expressed as a year and fractional year.
 */
static double
meanphase( double sdate, double k )
{
	double	t, t2, t3, nt1;

	/* 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 */

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

	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 = TRUE;
	} 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 = TRUE;
	}
	if (!apcor) {
	   (void)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( double sdate, double phases[5] )
{
	double	adate, k1, k2, nt1, nt2;
	int	yy, mm, dd;

	adate = sdate - 45;

	jyear(adate, &yy, &mm, &dd);
	k1 = floor((yy + ((mm - 1) * (1.0 / 12.0)) - 1900) * 12.3685);

	adate = nt1 = meanphase(adate, k1);
	while (TRUE) {
		adate += synmonth;
		k2 = k1 + 1;
		nt2 = meanphase(adate, 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( double sdate, double phases[2], double which[2] )
{
	double phases5[5];

	phasehunt5( sdate, phases5 );
	phases[0] = phases5[0];
	which[0] = 0.0;
	phases[1] = phases5[1];
	which[1] = 0.25;
	if ( phases[1] <= sdate ) {
		phases[0] = phases[1];
		which[0] = which[1];
		phases[1] = phases5[2];
		which[1] = 0.5;
		if ( phases[1] <= sdate ) {
			phases[0] = phases[1];
			which[0] = which[1];
			phases[1] = phases5[3];
			which[1] = 0.75;
			if ( phases[1] <= sdate ) {
				phases[0] = phases[1];
				which[0] = which[1];
				phases[1] = phases5[4];
				which[1] = 0.0;
			}
		}
	}
}


/*
 * 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.
 *
 * 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
phase( double pdate, double* pphase, double* mage, double* dist, double* angdia, double* sudist, double* suangdia )
{

	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 fixangle(MoonAge) / 360.0;
}