| 1 | #include "sofa.h"
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| 2 |
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| 3 | int iauPvstar(double pv[2][3], double *ra, double *dec,
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| 4 | double *pmr, double *pmd, double *px, double *rv)
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| 5 | /*
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| 6 | ** - - - - - - - - - -
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| 7 | ** i a u P v s t a r
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| 8 | ** - - - - - - - - - -
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| 9 | **
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| 10 | ** Convert star position+velocity vector to catalog coordinates.
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| 11 | **
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| 12 | ** This function is part of the International Astronomical Union's
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| 13 | ** SOFA (Standards Of Fundamental Astronomy) software collection.
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| 14 | **
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| 15 | ** Status: support function.
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| 16 | **
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| 17 | ** Given (Note 1):
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| 18 | ** pv double[2][3] pv-vector (AU, AU/day)
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| 19 | **
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| 20 | ** Returned (Note 2):
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| 21 | ** ra double right ascension (radians)
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| 22 | ** dec double declination (radians)
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| 23 | ** pmr double RA proper motion (radians/year)
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| 24 | ** pmd double Dec proper motion (radians/year)
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| 25 | ** px double parallax (arcsec)
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| 26 | ** rv double radial velocity (km/s, positive = receding)
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| 27 | **
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| 28 | ** Returned (function value):
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| 29 | ** int status:
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| 30 | ** 0 = OK
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| 31 | ** -1 = superluminal speed (Note 5)
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| 32 | ** -2 = null position vector
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| 33 | **
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| 34 | ** Notes:
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| 35 | **
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| 36 | ** 1) The specified pv-vector is the coordinate direction (and its rate
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| 37 | ** of change) for the date at which the light leaving the star
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| 38 | ** reached the solar-system barycenter.
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| 39 | **
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| 40 | ** 2) The star data returned by this function are "observables" for an
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| 41 | ** imaginary observer at the solar-system barycenter. Proper motion
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| 42 | ** and radial velocity are, strictly, in terms of barycentric
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| 43 | ** coordinate time, TCB. For most practical applications, it is
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| 44 | ** permissible to neglect the distinction between TCB and ordinary
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| 45 | ** "proper" time on Earth (TT/TAI). The result will, as a rule, be
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| 46 | ** limited by the intrinsic accuracy of the proper-motion and
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| 47 | ** radial-velocity data; moreover, the supplied pv-vector is likely
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| 48 | ** to be merely an intermediate result (for example generated by the
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| 49 | ** function iauStarpv), so that a change of time unit will cancel
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| 50 | ** out overall.
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| 51 | **
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| 52 | ** In accordance with normal star-catalog conventions, the object's
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| 53 | ** right ascension and declination are freed from the effects of
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| 54 | ** secular aberration. The frame, which is aligned to the catalog
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| 55 | ** equator and equinox, is Lorentzian and centered on the SSB.
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| 56 | **
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| 57 | ** Summarizing, the specified pv-vector is for most stars almost
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| 58 | ** identical to the result of applying the standard geometrical
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| 59 | ** "space motion" transformation to the catalog data. The
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| 60 | ** differences, which are the subject of the Stumpff paper cited
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| 61 | ** below, are:
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| 62 | **
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| 63 | ** (i) In stars with significant radial velocity and proper motion,
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| 64 | ** the constantly changing light-time distorts the apparent proper
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| 65 | ** motion. Note that this is a classical, not a relativistic,
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| 66 | ** effect.
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| 67 | **
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| 68 | ** (ii) The transformation complies with special relativity.
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| 69 | **
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| 70 | ** 3) Care is needed with units. The star coordinates are in radians
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| 71 | ** and the proper motions in radians per Julian year, but the
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| 72 | ** parallax is in arcseconds; the radial velocity is in km/s, but
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| 73 | ** the pv-vector result is in AU and AU/day.
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| 74 | **
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| 75 | ** 4) The proper motions are the rate of change of the right ascension
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| 76 | ** and declination at the catalog epoch and are in radians per Julian
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| 77 | ** year. The RA proper motion is in terms of coordinate angle, not
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| 78 | ** true angle, and will thus be numerically larger at high
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| 79 | ** declinations.
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| 80 | **
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| 81 | ** 5) Straight-line motion at constant speed in the inertial frame is
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| 82 | ** assumed. If the speed is greater than or equal to the speed of
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| 83 | ** light, the function aborts with an error status.
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| 84 | **
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| 85 | ** 6) The inverse transformation is performed by the function iauStarpv.
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| 86 | **
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| 87 | ** Called:
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| 88 | ** iauPn decompose p-vector into modulus and direction
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| 89 | ** iauPdp scalar product of two p-vectors
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| 90 | ** iauSxp multiply p-vector by scalar
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| 91 | ** iauPmp p-vector minus p-vector
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| 92 | ** iauPm modulus of p-vector
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| 93 | ** iauPpp p-vector plus p-vector
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| 94 | ** iauPv2s pv-vector to spherical
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| 95 | ** iauAnp normalize angle into range 0 to 2pi
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| 96 | **
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| 97 | ** Reference:
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| 98 | **
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| 99 | ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
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| 100 | **
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| 101 | ** This revision: 2013 June 18
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| 102 | **
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| 103 | ** SOFA release 2015-02-09
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| 104 | **
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| 105 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 106 | */
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| 107 | {
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| 108 | double r, x[3], vr, ur[3], vt, ut[3], bett, betr, d, w, del,
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| 109 | usr[3], ust[3], a, rad, decd, rd;
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| 110 |
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| 111 | /* Isolate the radial component of the velocity (AU/day, inertial). */
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| 112 | iauPn(pv[0], &r, x);
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| 113 | vr = iauPdp(x, pv[1]);
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| 114 | iauSxp(vr, x, ur);
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| 115 |
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| 116 | /* Isolate the transverse component of the velocity (AU/day, inertial). */
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| 117 | iauPmp(pv[1], ur, ut);
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| 118 | vt = iauPm(ut);
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| 119 |
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| 120 | /* Special-relativity dimensionless parameters. */
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| 121 | bett = vt / DC;
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| 122 | betr = vr / DC;
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| 123 |
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| 124 | /* The inertial-to-observed correction terms. */
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| 125 | d = 1.0 + betr;
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| 126 | w = 1.0 - betr*betr - bett*bett;
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| 127 | if (d == 0.0 || w < 0) return -1;
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| 128 | del = sqrt(w) - 1.0;
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| 129 |
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| 130 | /* Apply relativistic correction factor to radial velocity component. */
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| 131 | w = (betr != 0) ? (betr - del) / (betr * d) : 1.0;
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| 132 | iauSxp(w, ur, usr);
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| 133 |
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| 134 | /* Apply relativistic correction factor to tangential velocity */
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| 135 | /* component. */
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| 136 | iauSxp(1.0/d, ut, ust);
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| 137 |
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| 138 | /* Combine the two to obtain the observed velocity vector (AU/day). */
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| 139 | iauPpp(usr, ust, pv[1]);
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| 140 |
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| 141 | /* Cartesian to spherical. */
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| 142 | iauPv2s(pv, &a, dec, &r, &rad, &decd, &rd);
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| 143 | if (r == 0.0) return -2;
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| 144 |
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| 145 | /* Return RA in range 0 to 2pi. */
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| 146 | *ra = iauAnp(a);
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| 147 |
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| 148 | /* Return proper motions in radians per year. */
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| 149 | *pmr = rad * DJY;
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| 150 | *pmd = decd * DJY;
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| 151 |
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| 152 | /* Return parallax in arcsec. */
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| 153 | *px = DR2AS / r;
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| 154 |
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| 155 | /* Return radial velocity in km/s. */
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| 156 | *rv = 1e-3 * rd * DAU / DAYSEC;
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| 157 |
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| 158 | /* OK status. */
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| 159 | return 0;
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| 160 |
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| 161 | /*----------------------------------------------------------------------
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| 162 | **
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| 163 | ** Copyright (C) 2015
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| 164 | ** Standards Of Fundamental Astronomy Board
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| 165 | ** of the International Astronomical Union.
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| 166 | **
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| 167 | ** =====================
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| 168 | ** SOFA Software License
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| 169 | ** =====================
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| 170 | **
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| 171 | ** NOTICE TO USER:
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| 172 | **
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| 173 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 174 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 175 | **
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| 176 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 177 | **
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| 178 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 179 | ** purpose, including commercial applications, free of charge and
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| 180 | ** without payment of royalties, subject to the conditions and
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| 181 | ** restrictions listed below.
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| 182 | **
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| 183 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 184 | ** and use and adapt its code and algorithms in your own software,
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| 185 | ** on a world-wide, royalty-free basis. That portion of your
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| 186 | ** distribution that does not consist of intact and unchanged copies
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| 187 | ** of SOFA source code files is a "derived work" that must comply
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| 188 | ** with the following requirements:
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| 189 | **
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| 190 | ** a) Your work shall be marked or carry a statement that it
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| 191 | ** (i) uses routines and computations derived by you from
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| 192 | ** software provided by SOFA under license to you; and
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| 193 | ** (ii) does not itself constitute software provided by and/or
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| 194 | ** endorsed by SOFA.
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| 195 | **
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| 196 | ** b) The source code of your derived work must contain descriptions
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| 197 | ** of how the derived work is based upon, contains and/or differs
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| 198 | ** from the original SOFA software.
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| 199 | **
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| 200 | ** c) The names of all routines in your derived work shall not
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| 201 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 202 | ** thereof such as changes of case.
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| 203 | **
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| 204 | ** d) The origin of the SOFA components of your derived work must
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| 205 | ** not be misrepresented; you must not claim that you wrote the
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| 206 | ** original software, nor file a patent application for SOFA
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| 207 | ** software or algorithms embedded in the SOFA software.
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| 208 | **
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| 209 | ** e) These requirements must be reproduced intact in any source
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| 210 | ** distribution and shall apply to anyone to whom you have
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| 211 | ** granted a further right to modify the source code of your
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| 212 | ** derived work.
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| 213 | **
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| 214 | ** Note that, as originally distributed, the SOFA software is
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| 215 | ** intended to be a definitive implementation of the IAU standards,
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| 216 | ** and consequently third-party modifications are discouraged. All
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| 217 | ** variations, no matter how minor, must be explicitly marked as
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| 218 | ** such, as explained above.
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| 219 | **
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| 220 | ** 4. You shall not cause the SOFA software to be brought into
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| 221 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 222 | ** by inappropriate modification.
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| 223 | **
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| 224 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 225 | ** as to its use or performance. SOFA does not and cannot warrant
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| 226 | ** the performance or results which the user may obtain by using the
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| 227 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 228 | ** to non-infringement of third party rights, merchantability, or
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| 229 | ** fitness for any particular purpose. In no event will SOFA be
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| 230 | ** liable to the user for any consequential, incidental, or special
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| 231 | ** damages, including any lost profits or lost savings, even if a
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| 232 | ** SOFA representative has been advised of such damages, or for any
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| 233 | ** claim by any third party.
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| 234 | **
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| 235 | ** 6. The provision of any version of the SOFA software under the terms
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| 236 | ** and conditions specified herein does not imply that future
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| 237 | ** versions will also be made available under the same terms and
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| 238 | ** conditions.
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| 239 | *
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| 240 | ** In any published work or commercial product which uses the SOFA
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| 241 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 242 | ** appreciated.
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| 243 | **
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| 244 | ** Correspondence concerning SOFA software should be addressed as
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| 245 | ** follows:
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| 246 | **
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| 247 | ** By email: sofa@ukho.gov.uk
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| 248 | ** By post: IAU SOFA Center
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| 249 | ** HM Nautical Almanac Office
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| 250 | ** UK Hydrographic Office
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| 251 | ** Admiralty Way, Taunton
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| 252 | ** Somerset, TA1 2DN
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| 253 | ** United Kingdom
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| 254 | **
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| 255 | **--------------------------------------------------------------------*/
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| 256 | }
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