#include "sofam.h" void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5) /* ** - - - - - - - - - ** i a u H f k 5 z ** - - - - - - - - - ** ** Transform a Hipparcos star position into FK5 J2000.0, assuming ** zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** date1,date2 double TDB date (Note 1) ** ** Returned (all FK5, equinox J2000.0, date date1+date2): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double FK5 RA proper motion (rad/year, Note 4) ** dd5 double Dec proper motion (rad/year, Note 4) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. ** ** 3) The FK5 to Hipparcos transformation is modeled as a pure rotation ** and spin; zonal errors in the FK5 catalogue are not taken into ** account. ** ** 4) It was the intention that Hipparcos should be a close ** approximation to an inertial frame, so that distant objects have ** zero proper motion; such objects have (in general) non-zero ** proper motion in FK5, and this function returns those fictitious ** proper motions. ** ** 5) The position returned by this function is in the FK5 J2000.0 ** reference system but at date date1+date2. ** ** 6) See also iauFk52h, iauH2fk5, iauFk5zhz. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauSxp multiply p-vector by scalar ** iauRxr product of two r-matrices ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** ** This revision: 2009 December 17 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 IAU SOFA Board. See notes at end. */ { double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3], rst[3][3], r5ht[3][3], pv5e[2][3], vv[3], w, r, v; /* Time interval from fundamental epoch J2000.0 to given date (JY). */ t = ((date1 - DJ00) + date2) / DJY; /* Hipparcos barycentric position vector (normalized). */ iauS2c(rh, dh, ph); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Rotate the spin into the Hipparcos system. */ iauRxp(r5h, s5h, sh); /* Accumulated Hipparcos wrt FK5 spin over that interval. */ iauSxp(t, s5h, vst); /* Express the accumulated spin as a rotation matrix. */ iauRv2m(vst, rst); /* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */ iauRxr(r5h, rst, r5ht); /* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */ iauTrxp(r5ht, ph, pv5e[0]); /* Apply spin to the position giving a space motion. */ iauPxp(sh, ph, vv); /* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */ iauTrxp(r5ht, vv, pv5e[1]); /* FK5 position/velocity pv-vector to spherical. */ iauPv2s(pv5e, &w, d5, &r, dr5, dd5, &v); *r5 = iauAnp(w); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2012 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }