#include "erfa.h" int eraStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) /* ** - - - - - - - - - - ** e r a S t a r p m ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion. ** ** Given: ** ra1 double right ascension (radians), before ** dec1 double declination (radians), before ** pmr1 double RA proper motion (radians/year), before ** pmd1 double Dec proper motion (radians/year), before ** px1 double parallax (arcseconds), before ** rv1 double radial velocity (km/s, +ve = receding), before ** ep1a double "before" epoch, part A (Note 1) ** ep1b double "before" epoch, part B (Note 1) ** ep2a double "after" epoch, part A (Note 1) ** ep2b double "after" epoch, part B (Note 1) ** ** Returned: ** ra2 double right ascension (radians), after ** dec2 double declination (radians), after ** pmr2 double RA proper motion (radians/year), after ** pmd2 double Dec proper motion (radians/year), after ** px2 double parallax (arcseconds), after ** rv2 double radial velocity (km/s, +ve = receding), after ** ** Returned (function value): ** int status: ** -1 = system error (should not occur) ** 0 = no warnings or errors ** 1 = distance overridden (Note 6) ** 2 = excessive velocity (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above warnings ** ** Notes: ** ** 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are ** Julian Dates, apportioned in any convenient way between the two ** parts (A and B). For example, JD(TDB)=2450123.7 could be ** expressed in any of these ways, among others: ** ** epna epnb ** ** 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) In accordance with normal star-catalog conventions, the object's ** right ascension and declination are freed from the effects of ** secular aberration. The frame, which is aligned to the catalog ** equator and equinox, is Lorentzian and centered on the SSB. ** ** The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per TDB ** Julian year. ** ** The parallax and radial velocity are in the same frame. ** ** 3) Care is needed with units. The star coordinates are in radians ** and the proper motions in radians per Julian year, but the ** parallax is in arcseconds. ** ** 4) The RA proper motion is in terms of coordinate angle, not true ** angle. If the catalog uses arcseconds for both RA and Dec proper ** motions, the RA proper motion will need to be divided by cos(Dec) ** before use. ** ** 5) Straight-line motion at constant speed, in the inertial frame, ** is assumed. ** ** 6) An extremely small (or zero or negative) parallax is interpreted ** to mean that the object is on the "celestial sphere", the radius ** of which is an arbitrary (large) value (see the eraStarpv ** function for the value used). When the distance is overridden in ** this way, the status, initially zero, has 1 added to it. ** ** 7) If the space velocity is a significant fraction of c (see the ** constant VMAX in the function eraStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the eraStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** eraStarpv star catalog data to space motion pv-vector ** eraPvu update a pv-vector ** eraPdp scalar product of two p-vectors ** eraPvstar space motion pv-vector to star catalog data ** ** Copyright (C) 2013-2016, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double pv1[2][3], tl1, dt, pv[2][3], r2, rdv, v2, c2mv2, tl2, pv2[2][3]; int j1, j2, j; /* RA,Dec etc. at the "before" epoch to space motion pv-vector. */ j1 = eraStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1); /* Light time when observed (days). */ tl1 = eraPm(pv1[0]) / ERFA_DC; /* Time interval, "before" to "after" (days). */ dt = (ep2a - ep1a) + (ep2b - ep1b); /* Move star along track from the "before" observed position to the */ /* "after" geometric position. */ eraPvu(dt + tl1, pv1, pv); /* From this geometric position, deduce the observed light time (days) */ /* at the "after" epoch (with theoretically unneccessary error check). */ r2 = eraPdp(pv[0], pv[0]); rdv = eraPdp(pv[0], pv[1]); v2 = eraPdp(pv[1], pv[1]); c2mv2 = ERFA_DC*ERFA_DC - v2; if (c2mv2 <= 0) return -1; tl2 = (-rdv + sqrt(rdv*rdv + c2mv2*r2)) / c2mv2; /* Move the position along track from the observed place at the */ /* "before" epoch to the observed place at the "after" epoch. */ eraPvu(dt + (tl1 - tl2), pv1, pv2); /* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */ j2 = eraPvstar(pv2, ra2, dec2, pmr2, pmd2, px2, rv2); /* Final status. */ j = (j2 == 0) ? j1 : -1; return j; } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2016, NumFOCUS Foundation. ** All rights reserved. ** ** This library is derived, with permission, from the International ** Astronomical Union's "Standards of Fundamental Astronomy" library, ** available from http://www.iausofa.org. ** ** The ERFA version is intended to retain identical functionality to ** the SOFA library, but made distinct through different function and ** file names, as set out in the SOFA license conditions. The SOFA ** original has a role as a reference standard for the IAU and IERS, ** and consequently redistribution is permitted only in its unaltered ** state. The ERFA version is not subject to this restriction and ** therefore can be included in distributions which do not support the ** concept of "read only" software. ** ** Although the intent is to replicate the SOFA API (other than ** replacement of prefix names) and results (with the exception of ** bugs; any that are discovered will be fixed), SOFA is not ** responsible for any errors found in this version of the library. ** ** If you wish to acknowledge the SOFA heritage, please acknowledge ** that you are using a library derived from SOFA, rather than SOFA ** itself. ** ** ** TERMS AND CONDITIONS ** ** Redistribution and use in source and binary forms, with or without ** modification, are permitted provided that the following conditions ** are met: ** ** 1 Redistributions of source code must retain the above copyright ** notice, this list of conditions and the following disclaimer. ** ** 2 Redistributions in binary form must reproduce the above copyright ** notice, this list of conditions and the following disclaimer in ** the documentation and/or other materials provided with the ** distribution. ** ** 3 Neither the name of the Standards Of Fundamental Astronomy Board, ** the International Astronomical Union nor the names of its ** contributors may be used to endorse or promote products derived ** from this software without specific prior written permission. ** ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ** POSSIBILITY OF SUCH DAMAGE. ** */