void slaEqecl ( double dr, double dd, double date,
double *dl, double *db )
/*
** - - - - - - - - -
** s l a E q e c l
** - - - - - - - - -
**
** Transformation from J2000.0 equatorial coordinates to
** ecliptic coordinates.
**
** (double precision)
**
** Given:
** dr,dd double J2000.0 mean RA,Dec (radians)
** date double TDB (loosely ET) as Modified Julian Date
** (JD-2400000.5)
** Returned:
** *dl,*db double ecliptic longitude and latitude
** (mean of date, IAU 1980 theory, radians)
**
**
** Called:
** slaDcs2c, slaPrec, slaEpj, slaDmxv, slaEcmat, slaDcc2s,
** slaDranrm, slaDrange
**
**
** Last revision: 31 October 1993
**
** Copyright P.T.Wallace. All rights reserved.
*/
{
double rmat[3][3], v1[3], v2[3];
/* Spherical to Cartesian */
slaDcs2c ( dr, dd, v1 );
/* Mean J2000 to mean of date */
slaPrec ( 2000.0, slaEpj ( date ), rmat );
slaDmxv ( rmat, v1, v2 );
/* Equatorial to ecliptic */
slaEcmat ( date, rmat );
slaDmxv ( rmat, v2, v1 );
/* Cartesian to spherical */
slaDcc2s ( v1, dl, db );
/* Express in conventional ranges */
*dl = slaDranrm ( *dl );
*db = slaDrange ( *db );
}
void slaDcmpf ( double coeffs[6],
double *xz, double *yz, double *xs,
double *ys, double *perp, double *orient )
/*
** - - - - - - - - -
** s l a D c m p f
** - - - - - - - - -
**
** Decompose an [x,y] linear fit into its constituent parameters:
** zero points, scales, nonperpendicularity and orientation.
**
** Given:
** coeffs double[6] transformation coefficients (see note)
**
** Returned:
** *xz double x zero point
** *yz double y zero point
** *xs double x scale
** *ys double y scale
** *perp double nonperpendicularity (radians)
** *orient double orientation (radians)
**
** Called: slaDrange
**
** The model relates two sets of [x,y] coordinates as follows.
** Naming the elements of coeffs:
**
** coeffs[0] = a
** coeffs[1] = b
** coeffs[2] = c
** coeffs[3] = d
** coeffs[4] = e
** coeffs[5] = f
**
** The model transforms coordinates [x1,y1] into coordinates
** [x2,y2] as follows:
**
** x2 = a + b*x1 + c*y1
** y2 = d + e*x1 + f*y1
**
** The transformation can be decomposed into four steps:
**
** 1) Zero points:
**
** x' = xz + x1
** y' = yz + y1
**
** 2) Scales:
**
** x'' = xs*x'
** y'' = ys*y'
**
** 3) Nonperpendicularity:
**
** x''' = cos(perp/2)*x'' + sin(perp/2)*y''
** y''' = sin(perp/2)*x'' + cos(perp/2)*y''
**
** 4) Orientation:
**
** x2 = cos(orient)*x''' + sin(orient)*y'''
** y2 =-sin(orient)*y''' + cos(orient)*y'''
**
** See also slaFitxy, slaPxy, slaInvf, slaXy2xy
**
** Last revision: 19 December 2001
**
** Copyright P.T.Wallace. All rights reserved.
*/
{
double a, b, c, d, e, f, rb2e2, rc2f2, xsc, ysc, p,
ws, wc, or, hp, shp, chp, sor, cor, det, x0, y0;
/* Copy the six coefficients. */
a = coeffs[0];
b = coeffs[1];
c = coeffs[2];
d = coeffs[3];
e = coeffs[4];
f = coeffs[5];
/* Scales. */
rb2e2 = sqrt ( b * b + e * e );
rc2f2 = sqrt ( c * c + f * f );
if ( ( b * f - c * e ) >= 0.0 )
xsc = rb2e2;
else {
b = -b;
e = -e;
xsc = -rb2e2;
}
ysc = rc2f2;
/* Non-perpendicularity. */
p = slaDrange ( ( ( c != 0.0 || f != 0.0 ) ? atan2 ( c, f ) : 0.0 ) +
( ( e != 0.0 || b != 0.0 ) ? atan2 ( e, b ) : 0.0 ) );
/* Orientation. */
ws = ( c * rb2e2 ) - ( e * rc2f2 );
wc = ( b * rc2f2 ) + ( f * rb2e2 );
or = ( ws != 0.0 || wc != 0.0 ) ? atan2 ( ws, wc ) : 0.0;
/* Zero points. */
hp = p / 2.0;
shp = sin ( hp );
chp = cos ( hp );
sor = sin ( or );
cor = cos ( or );
det = xsc * ysc * ( chp + shp ) * ( chp - shp );
if ( fabs ( det ) > 0.0 ) {
x0 = ysc * ( a * ( ( chp * cor ) - ( shp * sor ) )
- d * ( ( chp * sor ) + ( shp * cor ) ) ) / det;
y0 = xsc * ( a * ( ( chp * sor ) - ( shp * cor ) )
+ d * ( ( chp * cor ) + ( shp * sor ) ) ) / det;
}
else {
x0 = 0.0;
y0 = 0.0;
}
/* Results. */
*xz = x0;
*yz = y0;
*xs = xsc;
*ys = ysc;
*perp = p;
*orient = or;
}
void slaNutc ( double date, double *dpsi, double *deps, double *eps0 )
/*
** - - - - - - - -
** s l a N u t c
** - - - - - - - -
**
** Nutation: longitude & obliquity components and
** mean obliquity (IAU 1980 theory).
**
** (double precision)
**
** References:
** Final report of the IAU working group on nutation,
** chairman P.K.Seidelmann, 1980.
** Kaplan,G.H., 1981, USNO circular No. 163, pa3-6.
**
** Given:
** date double TDB (loosely ET) as Modified Julian Date
** (JD-2400000.5)
**
** Returned:
** *dpsi,*deps double nutation in longitude,obliquity
** *eps0 double mean obliquity
**
** Called: slaDrange
**
** Defined in slamac.h: DAS2R, dmod
**
** Last revision: 19 March 1996
**
** Copyright P.T.Wallace. All rights reserved.
*/
#define T2AS 1296000.0 /* Turns to arc seconds */
#define U2R 0.4848136811095359949e-9 /* Units of 0.0001 arcsec to radians */
{
double t, el, el2, el3, elp, elp2,
f, f2, f4,
d, d2, d4,
om, om2,
dp, de, a;
/* Interval between basic epoch J2000.0 and current epoch (JC) */
t = ( date - 51544.5 ) / 36525.0;
/* Fundamental arguments in the FK5 reference system */
/* Mean longitude of the Moon minus mean longitude of the Moon's perigee */
el = slaDrange ( DAS2R * dmod ( 485866.733 + ( 1325.0 * T2AS + 715922.633
+ ( 31.310 + 0.064 * t ) * t ) * t , T2AS ) );
/* Mean longitude of the Sun minus mean longitude of the Sun's perigee */
elp = slaDrange ( DAS2R * dmod ( 1287099.804 + ( 99.0 * T2AS + 1292581.224
+ ( -0.577 - 0.012 * t ) * t ) * t, T2AS ) );
/* Mean longitude of the Moon minus mean longitude of the Moon's node */
f = slaDrange ( DAS2R * dmod ( 335778.877 + ( 1342.0 * T2AS + 295263.137
+ ( -13.257 + 0.011 * t ) * t ) * t, T2AS ) );
/* Mean elongation of the Moon from the Sun */
d = slaDrange ( DAS2R * dmod ( 1072261.307 + ( 1236.0 * T2AS + 1105601.328
+ ( -6.891 + 0.019 * t ) * t ) * t, T2AS ) );
/* Longitude of the mean ascending node of the lunar orbit on the
ecliptic, measured from the mean equinox of date */
om = slaDrange ( DAS2R * dmod ( 450160.280 + ( -5.0 * T2AS - 482890.539
+ ( 7.455 + 0.008 * t ) * t ) * t, T2AS ) );
/* Multiples of arguments */
el2 = el + el;
el3 = el2 + el;
elp2 = elp + elp;
f2 = f + f;
f4 = f2 + f2;
d2 = d + d;
d4 = d2 + d2;
om2 = om + om;
/* Series for the nutation */
dp = 0.0;
de = 0.0;
dp += sin ( elp + d ); /* 106 */
dp -= sin ( f2 + d4 + om2 ); /* 105 */
dp += sin ( el2 + d2 ); /* 104 */
dp -= sin ( el - f2 + d2 ); /* 103 */
dp -= sin ( el + elp - d2 + om ); /* 102 */
dp -= sin ( - elp + f2 + om ); /* 101 */
dp -= sin ( el - f2 - d2 ); /* 100 */
dp -= sin ( elp + d2 ); /* 99 */
dp -= sin ( f2 - d + om2 ); /* 98 */
dp -= sin ( - f2 + om ); /* 97 */
dp += sin ( - el - elp + d2 + om ); /* 96 */
dp += sin ( elp + f2 + om ); /* 95 */
dp -= sin ( el + f2 - d2 ); /* 94 */
dp += sin ( el3 + f2 - d2 + om2 ); /* 93 */
dp += sin ( f4 - d2 + om2 ); /* 92 */
dp -= sin ( el + d2 + om ); /* 91 */
dp -= sin ( el2 + f2 + d2 + om2 ); /* 90 */
a = el2 + f2 - d2 + om; /* 89 */
dp += sin ( a );
de -= cos ( a );
dp += sin ( el - elp - d2 ); /* 88 */
dp += sin ( - el + f4 + om2 ); /* 87 */
a = - el2 + f2 + d4 + om2; /* 86 */
dp -= sin ( a );
de += cos ( a );
a = el + f2 + d2 + om; /* 85 */
dp -= sin ( a );
de += cos ( a );
a = el + elp + f2 - d2 + om2; /* 84 */
dp += sin ( a );
de -= cos ( a );
dp -= sin ( el2 - d4 ); /* 83 */
a = - el + f2 + d4 + om2; /* 82 */
dp -= 2.0 * sin ( a );
de += cos ( a );
a = - el2 + f2 + d2 + om2; /* 81 */
dp += sin ( a );
de = de - cos ( a );
dp -= sin ( el - d4 ); /* 80 */
a = - el + om2; /* 79 */
dp += sin ( a );
de = de - cos ( a );
a = f2 + d + om2; /* 78 */
dp += 2.0 * sin ( a );
de = de - cos ( a );
dp += 2.0 * sin ( el3 ); /* 77 */
a = el + om2; /* 76 */
dp -= 2.0 * sin ( a );
de += cos ( a );
a = el2 + om; /* 75 */
dp += 2.0 * sin ( a );
de -= cos ( a );
a = - el + f2 - d2 + om; /* 74 */
dp -= 2.0 * sin ( a );
de += cos ( a );
a = el + elp + f2 + om2; /* 73 */
dp += 2.0 * sin ( a );
de = de - cos ( a );
a = - elp + f2 + d2 + om2; /* 72 */
dp -= 3.0 * sin ( a );
de += cos ( a );
a = el3 + f2 + om2; /* 71 */
dp -= 3.0 * sin ( a );
de += cos ( a );
a = - el2 + om; /* 70 */
dp -= 2.0 * sin ( a );
de += cos ( a );
a = - el - elp + f2 + d2 + om2; /* 69 */
dp -= 3.0 * sin ( a );
de += cos ( a );
a = el - elp + f2 + om2; /* 68 */
dp -= 3.0 * sin ( a );
de += cos ( a );
dp += 3.0 * sin ( el + f2 ); /* 67 */
dp -= 3.0 * sin ( el + elp ); /* 66 */
dp -= 4.0 * sin ( d ); /* 65 */
dp += 4.0 * sin ( el - f2 ); /* 64 */
dp -= 4.0 * sin ( elp - d2 ); /* 63 */
a = el2 + f2 + om; /* 62 */
dp -= 5.0 * sin ( a );
de += 3.0 * cos ( a );
dp += 5.0 * sin ( el - elp ); /* 61 */
a = - d2 + om; /* 60 */
dp -= 5.0 * sin ( a );
de += 3.0 * cos ( a );
a = el + f2 - d2 + om; /* 59 */
dp += 6.0 * sin ( a );
de -= 3.0 * cos ( a );
a = f2 + d2 + om; /* 58 */
dp -= 7.0 * sin ( a );
de += 3.0 * cos ( a );
a = d2 + om; /* 57 */
dp -= 6.0 * sin ( a );
de += 3.0 * cos ( a );
a = el2 + f2 - d2 + om2; /* 56 */
dp += 6.0 * sin ( a );
de -= 3.0 * cos ( a );
dp += 6.0 * sin ( el + d2); /* 55 */
a = el + f2 + d2 + om2; /* 54 */
dp -= 8.0 * sin ( a );
de += 3.0 * cos ( a );
a = - elp + f2 + om2; /* 53 */
dp -= 7.0 * sin ( a );
de += 3.0 * cos ( a );
a = elp + f2 + om2; /* 52 */
dp += 7.0 * sin ( a );
de -= 3.0 * cos ( a );
dp -= 7.0 * sin ( el + elp - d2 ); /* 51 */
a = - el + f2 + d2 + om; /* 50 */
dp -= 10.0 * sin ( a );
de += 5.0 * cos ( a );
a = el - d2 + om; /* 49 */
dp -= 13.0 * sin ( a );
de += 7.0 * cos ( a );
a = - el + d2 + om; /* 48 */
dp += 16.0 * sin ( a );
de -= 8.0 * cos ( a );
a = - el + f2 + om; /* 47 */
dp += 21.0 * sin ( a );
de -= 10.0 * cos ( a );
dp += 26.0 * sin ( f2 ); /* 46 */
de -= cos( f2 );
a = el2 + f2 + om2; /* 45 */
dp -= 31.0 * sin ( a );
de += 13.0 * cos ( a );
a = el + f2 - d2 + om2; /* 44 */
dp += 29.0 * sin ( a );
de -= 12.0 * cos ( a );
dp += 29.0 * sin ( el2 ); /* 43 */
de -= cos( el2 );
a = f2 + d2 + om2; /* 42 */
dp -= 38.0 * sin ( a );
de += 16.0 * cos ( a );
a = el + f2 + om; /* 41 */
dp -= 51.0 * sin ( a );
de += 27.0 * cos ( a );
a = - el + f2 + d2 + om2; /* 40 */
dp -= 59.0 * sin ( a );
de += 26.0 * cos ( a );
a = - el + om; /* 39 */
dp += ( - 58.0 - 0.1 * t ) * sin ( a );
de += 32.0 * cos ( a );
a = el + om; /* 38 */
dp += ( 63.0 + 0.1 * t ) * sin ( a );
de -= 33.0 * cos ( a );
dp += 63.0 * sin ( d2 ); /* 37 */
de -= 2.0 * cos( d2 );
a = - el + f2 + om2; /* 36 */
dp += 123.0 * sin ( a );
de -= 53.0 * cos ( a );
a = el - d2; /* 35 */
dp -= 158.0 * sin ( a );
de -= cos ( a );
a = el + f2 + om2; /* 34 */
dp -= 301.0 * sin ( a );
de += ( 129.0 - 0.1 * t ) * cos ( a );
a = f2 + om; /* 33 */
dp += ( - 386.0 - 0.4 * t ) * sin ( a );
de += 200.0 * cos ( a );
dp += ( 712.0 + 0.1 * t ) * sin ( el ); /* 32 */
de -= 7.0 * cos( el );
a = f2 + om2; /* 31 */
dp += ( -2274.0 - 0.2 * t ) * sin ( a );
de += ( 977.0 - 0.5 * t ) * cos ( a );
dp -= sin ( elp + f2 - d2 ); /* 30 */
dp += sin ( - el + d + om ); /* 29 */
dp += sin ( elp + om2 ); /* 28 */
dp -= sin ( elp - f2 + d2 ); /* 27 */
dp += sin ( - f2 + d2 + om ); /* 26 */
dp += sin ( el2 + elp - d2 ); /* 25 */
dp -= 4.0 * sin ( el - d ); /* 24 */
a = elp + f2 - d2 + om; /* 23 */
dp += 4.0 * sin ( a );
de -= 2.0 * cos ( a );
a = el2 - d2 + om; /* 22 */
dp += 4.0 * sin ( a );
de -= 2.0 * cos ( a );
a = - elp + f2 - d2 + om; /* 21 */
dp -= 5.0 * sin ( a );
de += 3.0 * cos ( a );
a = - el2 + d2 + om; /* 20 */
dp -= 6.0 * sin ( a );
de += 3.0 * cos ( a );
a = - elp + om; /* 19 */
dp -= 12.0 * sin ( a );
de += 6.0 * cos ( a );
a = elp2 + f2 - d2 + om2; /* 18 */
dp += ( - 16.0 + 0.1 * t) * sin ( a );
de += 7.0 * cos ( a );
a = elp + om; /* 17 */
dp -= 15.0 * sin ( a );
de += 9.0 * cos ( a );
dp += ( 17.0 - 0.1 * t ) * sin ( elp2 ); /* 16 */
dp -= 22.0 * sin ( f2 - d2 ); /* 15 */
a = el2 - d2; /* 14 */
dp += 48.0 * sin ( a );
de += cos ( a );
a = f2 - d2 + om; /* 13 */
dp += ( 129.0 + 0.1 * t ) * sin ( a );
de -= 70.0 * cos ( a );
a = - elp + f2 - d2 + om2; /* 12 */
dp += ( 217.0 - 0.5 * t ) * sin ( a );
de += ( -95.0 + 0.3 * t ) * cos ( a );
a = elp + f2 - d2 + om2; /* 11 */
dp += ( - 517.0 + 1.2 * t ) * sin ( a );
de += ( 224.0 - 0.6 * t ) * cos ( a );
dp += ( 1426.0 - 3.4 * t ) * sin ( elp ); /* 10 */
de += ( 54.0 - 0.1 * t) * cos ( elp );
a = f2 - d2 + om2; /* 9 */
dp += ( - 13187.0 - 1.6 * t ) * sin ( a );
de += ( 5736.0 - 3.1 * t ) * cos ( a );
dp += sin ( el2 - f2 + om ); /* 8 */
a = - elp2 + f2 - d2 + om; /* 7 */
dp -= 2.0 * sin ( a );
de += cos ( a );
dp -= 3.0 * sin ( el - elp - d ); /* 6 */
a = - el2 + f2 + om2; /* 5 */
dp -= 3.0 * sin ( a );
de += cos ( a );
dp += 11.0 * sin ( el2 - f2 ); /* 4 */
a = - el2 + f2 + om; /* 3 */
dp += 46.0 * sin ( a );
de -= 24.0 * cos ( a );
dp += ( 2062.0 + 0.2 * t ) * sin ( om2 ); /* 2 */
de += ( - 895.0 + 0.5 * t ) * cos ( om2 );
dp += ( - 171996.0 - 174.2 * t) * sin ( om ); /* 1 */
de += ( 92025.0 + 8.9 * t ) * cos ( om );
/* Convert results to radians */
*dpsi = dp * U2R;
*deps = de * U2R;
/* Mean obliquity */
*eps0 = DAS2R * ( 84381.448 +
( - 46.8150 +
( - 0.00059 + 0.001813 * t ) * t ) * t );
}
