| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaAltaz ( double ha, double dec, double phi,
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| 4 | double *az, double *azd, double *azdd,
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| 5 | double *el, double *eld, double *eldd,
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| 6 | double *pa, double *pad, double *padd )
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| 7 | /*
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| 8 | ** - - - - - - - - -
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| 9 | ** s l a A l t a z
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| 10 | ** - - - - - - - - -
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| 11 | **
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| 12 | ** Positions, velocities and accelerations for an altazimuth
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| 13 | ** telescope mount.
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| 14 | **
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| 15 | ** (double precision)
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| 16 | **
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| 17 | ** Given:
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| 18 | ** ha double hour angle
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| 19 | ** dec double declination
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| 20 | ** phi double latitude
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| 21 | **
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| 22 | ** Returned:
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| 23 | ** *az double azimuth
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| 24 | ** *azd double " velocity
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| 25 | ** *azdd double " acceleration
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| 26 | ** *el double elevation
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| 27 | ** *eld double " velocity
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| 28 | ** *eldd double " acceleration
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| 29 | ** *pa double parallactic angle
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| 30 | ** *pad double " " velocity
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| 31 | ** *padd double " " acceleration
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| 32 | **
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| 33 | ** Notes:
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| 34 | **
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| 35 | ** 1) Natural units are used throughout. HA, DEC, PHI, AZ, EL
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| 36 | ** and ZD are in radians. The velocities and accelerations
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| 37 | ** assume constant declination and constant rate of change of
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| 38 | ** hour angle (as for tracking a star); the units of AZD, ELD
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| 39 | ** and PAD are radians per radian of HA, while the units of AZDD,
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| 40 | ** ELDD and PADD are radians per radian of HA squared. To
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| 41 | ** convert into practical degree- and second-based units:
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| 42 | **
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| 43 | ** angles * 360/2pi -> degrees
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| 44 | ** velocities * (2pi/86400)*(360/2pi) -> degree/sec
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| 45 | ** accelerations * ((2pi/86400)**2)*(360/2pi) -> degree/sec/sec
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| 46 | **
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| 47 | ** Note that the seconds here are sidereal rather than SI. One
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| 48 | ** sidereal second is about 0.99727 SI seconds.
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| 49 | **
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| 50 | ** The velocity and acceleration factors assume the sidereal
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| 51 | ** tracking case. Their respective numerical values are (exactly)
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| 52 | ** 1/240 and (approximately) 1/3300236.9.
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| 53 | **
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| 54 | ** 2) Azimuth is returned in the range 0-2pi; north is zero,
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| 55 | ** and east is +pi/2. Elevation and parallactic angle are
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| 56 | ** returned in the range +/-pi/2. Position angle is +ve
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| 57 | ** for a star west of the meridian and is the angle NP-star-zenith.
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| 58 | **
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| 59 | ** 3) The latitude is geodetic as opposed to geocentric. The
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| 60 | ** hour angle and declination are topocentric. Refraction and
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| 61 | ** deficiencies in the telescope mounting are ignored. The
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| 62 | ** purpose of the routine is to give the general form of the
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| 63 | ** quantities. The details of a real telescope could profoundly
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| 64 | ** change the results, especially close to the zenith.
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| 65 | **
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| 66 | ** 4) No range checking of arguments is carried out.
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| 67 | **
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| 68 | ** 5) In applications which involve many such calculations, rather
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| 69 | ** than calling the present routine it will be more efficient to
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| 70 | ** use inline code, having previously computed fixed terms such
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| 71 | ** as sine and cosine of latitude, and (for tracking a star)
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| 72 | ** sine and cosine of declination.
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| 73 | **
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| 74 | ** Defined in slamac.h: DPI, D2PI
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| 75 | **
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| 76 | ** Last revision: 14 March 1997
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| 77 | **
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| 78 | ** Copyright P.T.Wallace. All rights reserved.
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| 79 | */
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| 80 |
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| 81 | #define TINY 1e-30 /* Zone of avoidance around zenith/nadir */
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| 82 |
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| 83 | {
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| 84 | double sh, ch, sd, cd, sp, cp, chcd, sdcp, x, y, z, rsq, r, a, e,
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| 85 | c, s, q, qd, ad, ed, edr, add, edd, qdd;
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| 86 |
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| 87 | /* Useful functions */
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| 88 | sh = sin ( ha );
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| 89 | ch = cos ( ha );
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| 90 | sd = sin ( dec );
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| 91 | cd = cos ( dec );
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| 92 | sp = sin ( phi );
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| 93 | cp = cos ( phi );
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| 94 | chcd = ch * cd;
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| 95 | sdcp = sd * cp;
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| 96 | x = - chcd * sp + sdcp;
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| 97 | y = - sh * cd;
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| 98 | z = chcd * cp + sd * sp;
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| 99 | rsq = x * x + y * y;
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| 100 | r = sqrt ( rsq );
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| 101 |
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| 102 | /* Azimuth and elevation */
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| 103 | if ( rsq == 0.0 ) {
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| 104 | a = 0.0;
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| 105 | } else {
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| 106 | a = atan2 ( y, x );
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| 107 | }
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| 108 | if ( a < 0.0 ) a += D2PI;
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| 109 | e = atan2 ( z, r );
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| 110 |
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| 111 | /* Parallactic angle */
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| 112 | c = cd * sp - ch * sdcp;
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| 113 | s = sh * cp;
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| 114 | if ( c * c + s * s > 0.0 ) {
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| 115 | q = atan2 ( s, c );
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| 116 | } else {
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| 117 | q = DPI - ha;
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| 118 | }
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| 119 |
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| 120 | /* Velocities and accelerations (clamped at zenith/nadir) */
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| 121 | if ( rsq < TINY ) {
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| 122 | rsq = TINY;
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| 123 | r = sqrt ( rsq );
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| 124 | }
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| 125 | qd = - x * cp / rsq;
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| 126 | ad = sp + z * qd;
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| 127 | ed = cp * y / r;
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| 128 | edr = ed / r;
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| 129 | add = edr * ( z * sp + ( 2.0 - rsq ) * qd );
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| 130 | edd = - r * qd * ad;
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| 131 | qdd = edr * ( sp + 2.0 * z * qd );
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| 132 |
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| 133 | /* Results */
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| 134 | *az = a;
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| 135 | *azd = ad;
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| 136 | *azdd = add;
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| 137 | *el = e;
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| 138 | *eld = ed;
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| 139 | *eldd = edd;
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| 140 | *pa = q;
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| 141 | *pad = qd;
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| 142 | *padd = qdd;
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| 143 | }
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