| 1 | #include "sofa.h"
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| 2 |
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| 3 | void iauLd(double bm, double p[3], double q[3], double e[3],
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| 4 | double em, double dlim, double p1[3])
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| 5 | /*
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| 6 | ** - - - - - -
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| 7 | ** i a u L d
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| 8 | ** - - - - - -
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| 9 | **
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| 10 | ** Apply light deflection by a solar-system body, as part of
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| 11 | ** transforming coordinate direction into natural direction.
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| 12 | **
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| 13 | ** This function is part of the International Astronomical Union's
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| 14 | ** SOFA (Standards of Fundamental Astronomy) software collection.
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| 15 | **
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| 16 | ** Status: support function.
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| 17 | **
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| 18 | ** Given:
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| 19 | ** bm double mass of the gravitating body (solar masses)
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| 20 | ** p double[3] direction from observer to source (unit vector)
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| 21 | ** q double[3] direction from body to source (unit vector)
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| 22 | ** e double[3] direction from body to observer (unit vector)
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| 23 | ** em double distance from body to observer (au)
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| 24 | ** dlim double deflection limiter (Note 4)
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| 25 | **
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| 26 | ** Returned:
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| 27 | ** p1 double[3] observer to deflected source (unit vector)
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| 28 | **
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| 29 | ** Notes:
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| 30 | **
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| 31 | ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and
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| 32 | ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
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| 33 | ** 2013), with some rearrangement to minimize the effects of machine
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| 34 | ** precision.
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| 35 | **
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| 36 | ** 2) The mass parameter bm can, as required, be adjusted in order to
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| 37 | ** allow for such effects as quadrupole field.
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| 38 | **
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| 39 | ** 3) The barycentric position of the deflecting body should ideally
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| 40 | ** correspond to the time of closest approach of the light ray to
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| 41 | ** the body.
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| 42 | **
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| 43 | ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is
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| 44 | ** the angular separation (in radians) between source and body at
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| 45 | ** which limiting is applied. As phi shrinks below the chosen
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| 46 | ** threshold, the deflection is artificially reduced, reaching zero
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| 47 | ** for phi = 0.
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| 48 | **
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| 49 | ** 5) The returned vector p1 is not normalized, but the consequential
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| 50 | ** departure from unit magnitude is always negligible.
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| 51 | **
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| 52 | ** 6) The arguments p and p1 can be the same array.
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| 53 | **
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| 54 | ** 7) To accumulate total light deflection taking into account the
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| 55 | ** contributions from several bodies, call the present function for
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| 56 | ** each body in succession, in decreasing order of distance from the
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| 57 | ** observer.
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| 58 | **
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| 59 | ** 8) For efficiency, validation is omitted. The supplied vectors must
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| 60 | ** be of unit magnitude, and the deflection limiter non-zero and
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| 61 | ** positive.
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| 62 | **
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| 63 | ** References:
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| 64 | **
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| 65 | ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
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| 66 | ** the Astronomical Almanac, 3rd ed., University Science Books
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| 67 | ** (2013).
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| 68 | **
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| 69 | ** Klioner, Sergei A., "A practical relativistic model for micro-
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| 70 | ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
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| 71 | **
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| 72 | ** Called:
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| 73 | ** iauPdp scalar product of two p-vectors
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| 74 | ** iauPxp vector product of two p-vectors
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| 75 | **
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| 76 | ** This revision: 2013 October 9
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| 77 | **
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| 78 | ** SOFA release 2015-02-09
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| 79 | **
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| 80 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 81 | */
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| 82 | {
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| 83 | int i;
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| 84 | double qpe[3], qdqpe, w, eq[3], peq[3];
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| 85 |
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| 86 | /* q . (q + e). */
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| 87 | for (i = 0; i < 3; i++) {
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| 88 | qpe[i] = q[i] + e[i];
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| 89 | }
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| 90 | qdqpe = iauPdp(q, qpe);
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| 91 |
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| 92 | /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
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| 93 | w = bm * SRS / em / gmax(qdqpe,dlim);
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| 94 |
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| 95 | /* p x (e x q). */
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| 96 | iauPxp(e, q, eq);
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| 97 | iauPxp(p, eq, peq);
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| 98 |
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| 99 | /* Apply the deflection. */
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| 100 | for (i = 0; i < 3; i++) {
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| 101 | p1[i] = p[i] + w*peq[i];
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| 102 | }
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| 103 |
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| 104 | /* Finished. */
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| 105 |
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| 106 | /*----------------------------------------------------------------------
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| 107 | **
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| 108 | ** Copyright (C) 2015
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| 109 | ** Standards Of Fundamental Astronomy Board
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| 110 | ** of the International Astronomical Union.
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| 111 | **
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| 112 | ** =====================
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| 113 | ** SOFA Software License
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| 114 | ** =====================
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| 115 | **
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| 116 | ** NOTICE TO USER:
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| 117 | **
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| 118 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 119 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 120 | **
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| 121 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 122 | **
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| 123 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 124 | ** purpose, including commercial applications, free of charge and
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| 125 | ** without payment of royalties, subject to the conditions and
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| 126 | ** restrictions listed below.
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| 127 | **
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| 128 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 129 | ** and use and adapt its code and algorithms in your own software,
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| 130 | ** on a world-wide, royalty-free basis. That portion of your
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| 131 | ** distribution that does not consist of intact and unchanged copies
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| 132 | ** of SOFA source code files is a "derived work" that must comply
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| 133 | ** with the following requirements:
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| 134 | **
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| 135 | ** a) Your work shall be marked or carry a statement that it
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| 136 | ** (i) uses routines and computations derived by you from
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| 137 | ** software provided by SOFA under license to you; and
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| 138 | ** (ii) does not itself constitute software provided by and/or
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| 139 | ** endorsed by SOFA.
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| 140 | **
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| 141 | ** b) The source code of your derived work must contain descriptions
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| 142 | ** of how the derived work is based upon, contains and/or differs
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| 143 | ** from the original SOFA software.
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| 144 | **
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| 145 | ** c) The names of all routines in your derived work shall not
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| 146 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 147 | ** thereof such as changes of case.
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| 148 | **
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| 149 | ** d) The origin of the SOFA components of your derived work must
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| 150 | ** not be misrepresented; you must not claim that you wrote the
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| 151 | ** original software, nor file a patent application for SOFA
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| 152 | ** software or algorithms embedded in the SOFA software.
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| 153 | **
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| 154 | ** e) These requirements must be reproduced intact in any source
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| 155 | ** distribution and shall apply to anyone to whom you have
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| 156 | ** granted a further right to modify the source code of your
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| 157 | ** derived work.
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| 158 | **
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| 159 | ** Note that, as originally distributed, the SOFA software is
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| 160 | ** intended to be a definitive implementation of the IAU standards,
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| 161 | ** and consequently third-party modifications are discouraged. All
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| 162 | ** variations, no matter how minor, must be explicitly marked as
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| 163 | ** such, as explained above.
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| 164 | **
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| 165 | ** 4. You shall not cause the SOFA software to be brought into
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| 166 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 167 | ** by inappropriate modification.
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| 168 | **
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| 169 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 170 | ** as to its use or performance. SOFA does not and cannot warrant
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| 171 | ** the performance or results which the user may obtain by using the
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| 172 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 173 | ** to non-infringement of third party rights, merchantability, or
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| 174 | ** fitness for any particular purpose. In no event will SOFA be
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| 175 | ** liable to the user for any consequential, incidental, or special
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| 176 | ** damages, including any lost profits or lost savings, even if a
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| 177 | ** SOFA representative has been advised of such damages, or for any
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| 178 | ** claim by any third party.
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| 179 | **
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| 180 | ** 6. The provision of any version of the SOFA software under the terms
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| 181 | ** and conditions specified herein does not imply that future
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| 182 | ** versions will also be made available under the same terms and
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| 183 | ** conditions.
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| 184 | *
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| 185 | ** In any published work or commercial product which uses the SOFA
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| 186 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 187 | ** appreciated.
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| 188 | **
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| 189 | ** Correspondence concerning SOFA software should be addressed as
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| 190 | ** follows:
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| 191 | **
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| 192 | ** By email: sofa@ukho.gov.uk
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| 193 | ** By post: IAU SOFA Center
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| 194 | ** HM Nautical Almanac Office
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| 195 | ** UK Hydrographic Office
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| 196 | ** Admiralty Way, Taunton
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| 197 | ** Somerset, TA1 2DN
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| 198 | ** United Kingdom
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| 199 | **
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| 200 | **--------------------------------------------------------------------*/
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| 201 |
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| 202 | }
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