/* Nutation -- AA page B20
* using nutation in longitude and obliquity from nutlo()
* and obliquity of the ecliptic from epsiln()
* both calculated for Julian date J.
*
* p[] = equatorial rectangular position vector of object for
* mean ecliptic and equinox of date.
*/
int nutate( double J, double *p )
{
double ce, se, cl, sl, sino, f;
double dp[3], p1[3];
int i;
nutlo(J); /* be sure we calculated nutl and nuto */
epsiln(J); /* and also the obliquity of date */
f = eps + nuto;
ce = cos( f );
se = sin( f );
sino = sin(nuto);
cl = cos( nutl );
sl = sin( nutl );
/* Apply adjustment
* to equatorial rectangular coordinates of object.
*
* This is a composite of three rotations: rotate about x axis
* to ecliptic of date; rotate about new z axis by the nutation
* in longitude; rotate about new x axis back to equator of date
* plus nutation in obliquity.
*/
p1[0] = cl*p[0]
- sl*coseps*p[1]
- sl*sineps*p[2];
p1[1] = sl*ce*p[0]
+ ( cl*coseps*ce + sineps*se )*p[1]
- ( sino + (1.0-cl)*sineps*ce )*p[2];
p1[2] = sl*se*p[0]
+ ( sino + (cl-1.0)*se*coseps )*p[1]
+ ( cl*sineps*se + coseps*ce )*p[2];
for( i=0; i<3; i++ )
dp[i] = p1[i] - p[i];
for( i=0; i<3; i++ )
p[i] = p1[i];
return(0);
}
/* Calculate geometric position of the Moon and apply
* approximate corrections to find apparent position,
* phase of the Moon, etc. for AA.ARC.
*/
int domoon()
{
int i, prtsav;
double ra0, dec0, r;
double x, y, z, lon0;
double c, s, temp;
double pp[3], qq[3];
double acos();
/* Compute obliquity of the ecliptic, coseps, and sineps
*/
epsiln(TDT);
/* Run the orbit calculation twice, at two different times,
* in order to find the rate of change of R.A. and Dec.
*/
/* Calculate for 0.001 day ago
*/
prtsav = prtflg;
prtflg = 0; /* disable display */
moonll(TDT-0.001, moonpp, moonpol);
/*
lonlat( rearth, TDT, eapolar ); // precess earth to date
// lonlat( rearth, TDT, eapolar, 1 );
*/
ra0 = ra;
dec0 = dec;
lon0 = l;
prtflg = prtsav;
/* Calculate for present instant.
*/
moonll(TDT, moonpp, moonpol);
/* The rates of change. These are used by altaz() to
* correct the time of rising, transit, and setting.
*/
dradt = ra - ra0;
if (dradt >= PI)
dradt = dradt - 2.0 * PI;
if (dradt <= -PI)
dradt = dradt + 2.0 * PI;
dradt = 1000.0 * dradt;
ddecdt = 1000.0*(dec-dec0);
/* Post the ecliptic longitude and latitude, in radians,
* and the radius in au.
*/
obpolar[0] = l;
obpolar[1] = B;
r = 1.0/sin(p); /* distance in earth-radii */
ra0 = Rearth*r; /* factor is radius of earth in au */
obpolar[2] = ra0;
/* Rate of change in longitude, degrees per day
* used for phase of the moon
*/
lon0 = 1000.0*RTD*(l - lon0);
/* convert to ecliptic rectangular coordinates */
z = ra0 * cos(B);
x = z * cos(l);
y = z * sin(l);
z = ra0 * sin(B);
/* convert to equatorial coordinates */
pp[0] = x;
pp[1] = y * coseps - z * sineps;
pp[2] = y * sineps + z * coseps;
/* Find sun-moon-earth angles */
precess( rearth, TDT, -1 );
for( i=0; i<3; i++ )
qq[i] = rearth[i] + pp[i];
angles( pp, qq, rearth );
/* Display answers
*/
if( prtflg )
{
/* Apparent ecliptic coordinates.
The nutation in longitude is added to the ecliptic longitude.
See AA page C2. First rotate the coordinate system about the
x axis from mean equator to ecliptic.
Then rotate about the z axis by the nutation in longitude. */
x = Mapp[0];
y = Mapp[1];
z = Mapp[2];
temp = coseps * y + sineps * z;
z = -sineps * y + coseps * z;
y = temp;
c = cos(nutl);
s = sin(nutl);
temp = c * x - s * y;
y = s * x + c * y;
x = temp;
Mapp[0] = zatan2( x, y );
Mapp[1] = asin( z );
Mapp[2] = Rem;
printf( "Apparent geocentric longitude %.3f deg", RTD*Mapp[0] );
printf( " latitude %.3f deg\n", RTD*Mapp[1] );
printf( "Distance %.3f Earth-radii\n", r );
printf( "Horizontal parallax" );
dms( p );
printf( "Semidiameter" );
x = 0.272453 * p + 0.0799/RTS; /* AA page L6 */
dms( x );
x = RTD * acos(-ep);
printf( "\nElongation from sun %.2f deg,", x );
x = 0.5 * (1.0 + pq);
printf( " Illuminated fraction %.2f\n", x );
/* Find phase of the Moon by comparing Moon's longitude
* with Earth's longitude.
*
* The number of days before or past indicated phase is
* estimated by assuming the true longitudes change linearly
* with time. These rates are estimated for the date, but
* do not stay constant. The error can exceed 0.15 day in 4 days.
*/
/* Apparent longitude of sun.
* Moon's longitude was already corrected for light time.
*/
y = eapolar[0] - 20.496/(RTS*eapolar[2]);
x = obpolar[0] - y;
x = modtp( x ) * RTD; /* difference in longitude */
i = x/90; /* number of quarters */
x = (x - i*90.0); /* phase angle mod 90 degrees */
/* days per degree of phase angle */
z = 1.0/(lon0 - (0.9856/eapolar[2]));
if( x > 45.0 )
{
y = -(x - 90.0)*z;
if( y > 1.0 )
printf( "Phase %.1f days before ", y );
else
printf( "Phase %.2f days before ", y );
i = (i+1) & 3;
}
else
{
y = x*z;
if( y > 1.0 )
printf( "Phase %.1f days past ", y );
else
printf( "Phase %.2f days past ", y );
}
switch(i)
{
case 0: printf( "Full Moon\n" ); break;
case 1: printf( "Third Quarter\n" ); break;
case 2: printf( "New Moon\n" ); break;
case 3: printf( "First Quarter\n" ); break;
}
} /* if prtflg */
printf( " Apparent: R.A." );
hms(ra);
printf( "Declination" );
dms(dec);
printf( "\n" );
/* Compute and display topocentric position (altaz.c)
*/
pp[0] = ra;
pp[1] = dec;
pp[2] = r * Rearth;
altaz( pp, UT );
return(0);
}
