| 1 | #include "sofa.h"
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| 2 |
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| 3 | void iauPrec76(double date01, double date02, double date11, double date12,
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| 4 | double *zeta, double *z, double *theta)
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| 5 | /*
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| 6 | ** - - - - - - - - - -
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| 7 | ** i a u P r e c 7 6
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| 8 | ** - - - - - - - - - -
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| 9 | **
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| 10 | ** IAU 1976 precession model.
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| 11 | **
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| 12 | ** This function forms the three Euler angles which implement general
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| 13 | ** precession between two dates, using the IAU 1976 model (as for the
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| 14 | ** FK5 catalog).
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| 15 | **
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| 16 | ** This function is part of the International Astronomical Union's
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| 17 | ** SOFA (Standards Of Fundamental Astronomy) software collection.
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| 18 | **
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| 19 | ** Status: canonical model.
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| 20 | **
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| 21 | ** Given:
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| 22 | ** date01,date02 double TDB starting date (Note 1)
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| 23 | ** date11,date12 double TDB ending date (Note 1)
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| 24 | **
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| 25 | ** Returned:
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| 26 | ** zeta double 1st rotation: radians cw around z
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| 27 | ** z double 3rd rotation: radians cw around z
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| 28 | ** theta double 2nd rotation: radians ccw around y
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| 29 | **
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| 30 | ** Notes:
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| 31 | **
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| 32 | ** 1) The dates date01+date02 and date11+date12 are Julian Dates,
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| 33 | ** apportioned in any convenient way between the arguments daten1
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| 34 | ** and daten2. For example, JD(TDB)=2450123.7 could be expressed in
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| 35 | ** any of these ways, among others:
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| 36 | **
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| 37 | ** daten1 daten2
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| 38 | **
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| 39 | ** 2450123.7 0.0 (JD method)
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| 40 | ** 2451545.0 -1421.3 (J2000 method)
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| 41 | ** 2400000.5 50123.2 (MJD method)
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| 42 | ** 2450123.5 0.2 (date & time method)
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| 43 | **
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| 44 | ** The JD method is the most natural and convenient to use in cases
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| 45 | ** where the loss of several decimal digits of resolution is
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| 46 | ** acceptable. The J2000 method is best matched to the way the
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| 47 | ** argument is handled internally and will deliver the optimum
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| 48 | ** optimum resolution. The MJD method and the date & time methods
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| 49 | ** are both good compromises between resolution and convenience.
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| 50 | ** The two dates may be expressed using different methods, but at
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| 51 | ** the risk of losing some resolution.
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| 52 | **
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| 53 | ** 2) The accumulated precession angles zeta, z, theta are expressed
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| 54 | ** through canonical polynomials which are valid only for a limited
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| 55 | ** time span. In addition, the IAU 1976 precession rate is known to
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| 56 | ** be imperfect. The absolute accuracy of the present formulation
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| 57 | ** is better than 0.1 arcsec from 1960AD to 2040AD, better than
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| 58 | ** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
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| 59 | ** the whole of the period 500BC to 3000AD. The errors exceed
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| 60 | ** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
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| 61 | ** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
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| 62 | ** 8200AD.
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| 63 | **
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| 64 | ** 3) The three angles are returned in the conventional order, which
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| 65 | ** is not the same as the order of the corresponding Euler
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| 66 | ** rotations. The precession matrix is
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| 67 | ** R_3(-z) x R_2(+theta) x R_3(-zeta).
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| 68 | **
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| 69 | ** Reference:
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| 70 | **
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| 71 | ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
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| 72 | ** (6) & (7), p283.
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| 73 | **
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| 74 | ** This revision: 2013 November 19
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| 75 | **
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| 76 | ** SOFA release 2015-02-09
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| 77 | **
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| 78 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 79 | */
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| 80 | {
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| 81 | double t0, t, tas2r, w;
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| 82 |
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| 83 | /* Interval between fundamental epoch J2000.0 and start date (JC). */
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| 84 | t0 = ((date01 - DJ00) + date02) / DJC;
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| 85 |
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| 86 | /* Interval over which precession required (JC). */
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| 87 | t = ((date11 - date01) + (date12 - date02)) / DJC;
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| 88 |
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| 89 | /* Euler angles. */
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| 90 | tas2r = t * DAS2R;
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| 91 | w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
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| 92 |
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| 93 | *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
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| 94 |
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| 95 | *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
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| 96 |
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| 97 | *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
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| 98 | + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
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| 99 |
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| 100 | return;
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| 101 |
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| 102 | /*----------------------------------------------------------------------
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| 103 | **
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| 104 | ** Copyright (C) 2015
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| 105 | ** Standards Of Fundamental Astronomy Board
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| 106 | ** of the International Astronomical Union.
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| 107 | **
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| 108 | ** =====================
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| 109 | ** SOFA Software License
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| 110 | ** =====================
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| 111 | **
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| 112 | ** NOTICE TO USER:
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| 113 | **
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| 114 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 115 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 116 | **
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| 117 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 118 | **
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| 119 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 120 | ** purpose, including commercial applications, free of charge and
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| 121 | ** without payment of royalties, subject to the conditions and
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| 122 | ** restrictions listed below.
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| 123 | **
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| 124 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 125 | ** and use and adapt its code and algorithms in your own software,
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| 126 | ** on a world-wide, royalty-free basis. That portion of your
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| 127 | ** distribution that does not consist of intact and unchanged copies
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| 128 | ** of SOFA source code files is a "derived work" that must comply
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| 129 | ** with the following requirements:
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| 130 | **
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| 131 | ** a) Your work shall be marked or carry a statement that it
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| 132 | ** (i) uses routines and computations derived by you from
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| 133 | ** software provided by SOFA under license to you; and
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| 134 | ** (ii) does not itself constitute software provided by and/or
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| 135 | ** endorsed by SOFA.
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| 136 | **
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| 137 | ** b) The source code of your derived work must contain descriptions
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| 138 | ** of how the derived work is based upon, contains and/or differs
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| 139 | ** from the original SOFA software.
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| 140 | **
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| 141 | ** c) The names of all routines in your derived work shall not
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| 142 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 143 | ** thereof such as changes of case.
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| 144 | **
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| 145 | ** d) The origin of the SOFA components of your derived work must
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| 146 | ** not be misrepresented; you must not claim that you wrote the
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| 147 | ** original software, nor file a patent application for SOFA
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| 148 | ** software or algorithms embedded in the SOFA software.
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| 149 | **
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| 150 | ** e) These requirements must be reproduced intact in any source
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| 151 | ** distribution and shall apply to anyone to whom you have
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| 152 | ** granted a further right to modify the source code of your
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| 153 | ** derived work.
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| 154 | **
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| 155 | ** Note that, as originally distributed, the SOFA software is
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| 156 | ** intended to be a definitive implementation of the IAU standards,
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| 157 | ** and consequently third-party modifications are discouraged. All
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| 158 | ** variations, no matter how minor, must be explicitly marked as
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| 159 | ** such, as explained above.
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| 160 | **
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| 161 | ** 4. You shall not cause the SOFA software to be brought into
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| 162 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 163 | ** by inappropriate modification.
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| 164 | **
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| 165 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 166 | ** as to its use or performance. SOFA does not and cannot warrant
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| 167 | ** the performance or results which the user may obtain by using the
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| 168 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 169 | ** to non-infringement of third party rights, merchantability, or
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| 170 | ** fitness for any particular purpose. In no event will SOFA be
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| 171 | ** liable to the user for any consequential, incidental, or special
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| 172 | ** damages, including any lost profits or lost savings, even if a
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| 173 | ** SOFA representative has been advised of such damages, or for any
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| 174 | ** claim by any third party.
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| 175 | **
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| 176 | ** 6. The provision of any version of the SOFA software under the terms
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| 177 | ** and conditions specified herein does not imply that future
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| 178 | ** versions will also be made available under the same terms and
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| 179 | ** conditions.
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| 180 | *
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| 181 | ** In any published work or commercial product which uses the SOFA
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| 182 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 183 | ** appreciated.
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| 184 | **
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| 185 | ** Correspondence concerning SOFA software should be addressed as
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| 186 | ** follows:
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| 187 | **
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| 188 | ** By email: sofa@ukho.gov.uk
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| 189 | ** By post: IAU SOFA Center
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| 190 | ** HM Nautical Almanac Office
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| 191 | ** UK Hydrographic Office
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| 192 | ** Admiralty Way, Taunton
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| 193 | ** Somerset, TA1 2DN
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| 194 | ** United Kingdom
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| 195 | **
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| 196 | **--------------------------------------------------------------------*/
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| 197 | }
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