void palSubet ( double rc, double dc, double eq, double *rm, double *dm ) { double a[3]; /* The E-terms */ double v[3]; double f; int i; /* Note the preference for IAU routines */ /* Retrieve the E-terms */ palEtrms( eq, a ); /* Spherical to Cartesian */ iauS2c( rc, dc, v ); /* Include the E-terms */ f = 1.0 + iauPdp( v, a ); for (i=0; i<3; i++) { v[i] = f*v[i] - a[i]; } /* Cartesian to spherical */ iauC2s( v, rm, dm ); /* Bring RA into conventional range */ *rm = iauAnp( *rm ); }
int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv) /* ** - - - - - - - - - - ** i a u P v s t a r ** - - - - - - - - - - ** ** Convert star position+velocity vector to catalog coordinates. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given (Note 1): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (Note 2): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcsec) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (function value): ** int status: ** 0 = OK ** -1 = superluminal speed (Note 5) ** -2 = null position vector ** ** Notes: ** ** 1) The specified pv-vector is the coordinate direction (and its rate ** of change) for the date at which the light leaving the star ** reached the solar-system barycenter. ** ** 2) The star data returned by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the supplied pv-vector is likely ** to be merely an intermediate result (for example generated by the ** function iauStarpv), so that a change of time unit will cancel ** out overall. ** ** 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. ** ** Summarizing, the specified pv-vector is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation to the catalog data. The ** differences, which are the subject of the Stumpff paper cited ** below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 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; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 4) The proper motions are the rate of change of the right ascension ** and declination at the catalog epoch and are in radians per Julian ** year. The RA proper motion is in terms of coordinate angle, not ** true angle, and will thus be numerically larger at high ** declinations. ** ** 5) Straight-line motion at constant speed in the inertial frame is ** assumed. If the speed is greater than or equal to the speed of ** light, the function aborts with an error status. ** ** 6) The inverse transformation is performed by the function iauStarpv. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPm modulus of p-vector ** iauPpp p-vector plus p-vector ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** ** This revision: 2013 June 18 ** ** SOFA release 2015-02-09 ** ** Copyright (C) 2015 IAU SOFA Board. See notes at end. */ { double r, x[3], vr, ur[3], vt, ut[3], bett, betr, d, w, del, usr[3], ust[3], a, rad, decd, rd; /* Isolate the radial component of the velocity (AU/day, inertial). */ iauPn(pv[0], &r, x); vr = iauPdp(x, pv[1]); iauSxp(vr, x, ur); /* Isolate the transverse component of the velocity (AU/day, inertial). */ iauPmp(pv[1], ur, ut); vt = iauPm(ut); /* Special-relativity dimensionless parameters. */ bett = vt / DC; betr = vr / DC; /* The inertial-to-observed correction terms. */ d = 1.0 + betr; w = 1.0 - betr*betr - bett*bett; if (d == 0.0 || w < 0) return -1; del = sqrt(w) - 1.0; /* Apply relativistic correction factor to radial velocity component. */ w = (betr != 0) ? (betr - del) / (betr * d) : 1.0; iauSxp(w, ur, usr); /* Apply relativistic correction factor to tangential velocity */ /* component. */ iauSxp(1.0/d, ut, ust); /* Combine the two to obtain the observed velocity vector (AU/day). */ iauPpp(usr, ust, pv[1]); /* Cartesian to spherical. */ iauPv2s(pv, &a, dec, &r, &rad, &decd, &rd); if (r == 0.0) return -2; /* Return RA in range 0 to 2pi. */ *ra = iauAnp(a); /* Return proper motions in radians per year. */ *pmr = rad * DJY; *pmd = decd * DJY; /* Return parallax in arcsec. */ *px = DR2AS / r; /* Return radial velocity in km/s. */ *rv = 1e-3 * rd * DAU / DAYSEC; /* OK status. */ return 0; /*---------------------------------------------------------------------- ** ** Copyright (C) 2015 ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]) /* ** - - - - - - ** i a u L d ** - - - - - - ** ** Apply light deflection by a solar-system body, as part of ** transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** bm double mass of the gravitating body (solar masses) ** p double[3] direction from observer to source (unit vector) ** q double[3] direction from body to source (unit vector) ** e double[3] direction from body to observer (unit vector) ** em double distance from body to observer (au) ** dlim double deflection limiter (Note 4) ** ** Returned: ** p1 double[3] observer to deflected source (unit vector) ** ** Notes: ** ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann ** 2013), with some rearrangement to minimize the effects of machine ** precision. ** ** 2) The mass parameter bm can, as required, be adjusted in order to ** allow for such effects as quadrupole field. ** ** 3) The barycentric position of the deflecting body should ideally ** correspond to the time of closest approach of the light ray to ** the body. ** ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is ** the angular separation (in radians) between source and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. ** ** 5) The returned vector p1 is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 6) The arguments p and p1 can be the same array. ** ** 7) To accumulate total light deflection taking into account the ** contributions from several bodies, call the present function for ** each body in succession, in decreasing order of distance from the ** observer. ** ** 8) For efficiency, validation is omitted. The supplied vectors must ** be of unit magnitude, and the deflection limiter non-zero and ** positive. ** ** References: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013). ** ** Klioner, Sergei A., "A practical relativistic model for micro- ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). ** ** Called: ** iauPdp scalar product of two p-vectors ** iauPxp vector product of two p-vectors ** ** This revision: 2013 October 9 ** ** SOFA release 2015-02-09 ** ** Copyright (C) 2015 IAU SOFA Board. See notes at end. */ { int i; double qpe[3], qdqpe, w, eq[3], peq[3]; /* q . (q + e). */ for (i = 0; i < 3; i++) { qpe[i] = q[i] + e[i]; } qdqpe = iauPdp(q, qpe); /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */ w = bm * SRS / em / gmax(qdqpe,dlim); /* p x (e x q). */ iauPxp(e, q, eq); iauPxp(p, eq, peq); /* Apply the deflection. */ for (i = 0; i < 3; i++) { p1[i] = p[i] + w*peq[i]; } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2015 ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]) /* ** - - - - - - - - - - ** i a u S t a r p v ** - - - - - - - - - - ** ** Convert star catalog coordinates to position+velocity vector. ** ** Status: support function. ** ** Given (Note 1): ** ra double right ascension (radians) ** dec double declination (radians) ** pmr double RA proper motion (radians/year) ** pmd double Dec proper motion (radians/year) ** px double parallax (arcseconds) ** rv double radial velocity (km/s, positive = receding) ** ** Returned (Note 2): ** pv double[2][3] pv-vector (AU, AU/day) ** ** Returned (function value): ** int status: ** 0 = no warnings ** 1 = distance overridden (Note 6) ** 2 = excessive speed (Note 7) ** 4 = solution didn't converge (Note 8) ** else = binary logical OR of the above ** ** Notes: ** ** 1) The star data accepted by this function are "observables" for an ** imaginary observer at the solar-system barycenter. Proper motion ** and radial velocity are, strictly, in terms of barycentric ** coordinate time, TCB. For most practical applications, it is ** permissible to neglect the distinction between TCB and ordinary ** "proper" time on Earth (TT/TAI). The result will, as a rule, be ** limited by the intrinsic accuracy of the proper-motion and ** radial-velocity data; moreover, the pv-vector is likely to be ** merely an intermediate result, so that a change of time unit ** would cancel out overall. ** ** 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. ** ** 2) The resulting position and velocity pv-vector is with respect to ** the same frame and, like the catalog coordinates, is freed from ** the effects of secular aberration. Should the "coordinate ** direction", where the object was located at the catalog epoch, be ** required, it may be obtained by calculating the magnitude of the ** position vector pv[0][0-2] dividing by the speed of light in ** AU/day to give the light-time, and then multiplying the space ** velocity pv[1][0-2] by this light-time and adding the result to ** pv[0][0-2]. ** ** Summarizing, the pv-vector returned is for most stars almost ** identical to the result of applying the standard geometrical ** "space motion" transformation. The differences, which are the ** subject of the Stumpff paper referenced below, are: ** ** (i) In stars with significant radial velocity and proper motion, ** the constantly changing light-time distorts the apparent proper ** motion. Note that this is a classical, not a relativistic, ** effect. ** ** (ii) The transformation complies with special relativity. ** ** 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; the radial velocity is in km/s, but ** the pv-vector result is in AU and AU/day. ** ** 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 constant PXMIN). ** 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), it is arbitrarily set to zero. When this action ** occurs, 2 is added to the status. ** ** 8) The relativistic adjustment involves an iterative calculation. ** If the process fails to converge within a set number (IMAX) of ** iterations, 4 is added to the status. ** ** 9) The inverse transformation is performed by the function ** iauPvstar. ** ** Called: ** iauS2pv spherical coordinates to pv-vector ** iauPm modulus of p-vector ** iauZp zero p-vector ** iauPn decompose p-vector into modulus and direction ** iauPdp scalar product of two p-vectors ** iauSxp multiply p-vector by scalar ** iauPmp p-vector minus p-vector ** iauPpp p-vector plus p-vector ** ** Reference: ** ** Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. ** ** This revision: 2009 July 6 ** ** Original version 2012-03-01 ** ** Copyright (C) 2013 Naoki Arita. See notes at end. */ { /* Smallest allowed parallax */ static const double PXMIN = 1e-7; /* Largest allowed speed (fraction of c) */ static const double VMAX = 0.5; /* Maximum number of iterations for relativistic solution */ static const int IMAX = 100; int i, iwarn; double w, r, rd, rad, decd, v, x[3], usr[3], ust[3], vsr, vst, betst, betsr, bett, betr, dd, ddel, ur[3], ut[3], d = 0.0, del = 0.0, /* to prevent */ odd = 0.0, oddel = 0.0, /* compiler */ od = 0.0, odel = 0.0; /* warnings */ /* Distance (AU). */ if (px >= PXMIN) { w = px; iwarn = 0; } else { w = PXMIN; iwarn = 1; } r = DR2AS / w; /* Radial velocity (AU/day). */ rd = DAYSEC * rv * 1e3 / DAU; /* Proper motion (radian/day). */ rad = pmr / DJY; decd = pmd / DJY; /* To pv-vector (AU,AU/day). */ iauS2pv(ra, dec, r, rad, decd, rd, pv); /* If excessive velocity, arbitrarily set it to zero. */ v = iauPm(pv[1]); if (v / DC > VMAX) { iauZp(pv[1]); iwarn += 2; } /* Isolate the radial component of the velocity (AU/day). */ iauPn(pv[0], &w, x); vsr = iauPdp(x, pv[1]); iauSxp(vsr, x, usr); /* Isolate the transverse component of the velocity (AU/day). */ iauPmp(pv[1], usr, ust); vst = iauPm(ust); /* Special-relativity dimensionless parameters. */ betsr = vsr / DC; betst = vst / DC; /* Determine the inertial-to-observed relativistic correction terms. */ bett = betst; betr = betsr; for (i = 0; i < IMAX; i++) { d = 1.0 + betr; del = sqrt(1.0 - betr*betr - bett*bett) - 1.0; betr = d * betsr + del; bett = d * betst; if (i > 0) { dd = fabs(d - od); ddel = fabs(del - odel); if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break; odd = dd; oddel = ddel; } od = d; odel = del; } if (i >= IMAX) iwarn += 4; /* Replace observed radial velocity with inertial value. */ w = (betsr != 0.0) ? d + del / betsr : 1.0; iauSxp(w, usr, ur); /* Replace observed tangential velocity with inertial value. */ iauSxp(d, ust, ut); /* Combine the two to obtain the inertial space velocity. */ iauPpp(ur, ut, pv[1]); /* Return the status. */ return iwarn; /*---------------------------------------------------------------------- ** ** Celes is a wrapper of the SOFA Library for Ruby. ** ** This file is redistributed and relicensed in accordance with ** the SOFA Software License (http://www.iausofa.org/tandc.html). ** ** The original library is available from IAU Standards of ** Fundamental Astronomy (http://www.iausofa.org/). ** ** ** ** ** ** Copyright (C) 2013, Naoki Arita ** All rights reserved. ** ** 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. ** **--------------------------------------------------------------------*/ }
double iauSepp(double a[3], double b[3]) /* ** - - - - - - - - ** i a u S e p p ** - - - - - - - - ** ** Angular separation between two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] first p-vector (not necessarily unit length) ** b double[3] second p-vector (not necessarily unit length) ** ** Returned (function value): ** double angular separation (radians, always positive) ** ** Notes: ** ** 1) If either vector is null, a zero result is returned. ** ** 2) The angular separation is most simply formulated in terms of ** scalar product. However, this gives poor accuracy for angles ** near zero and pi. The present algorithm uses both cross product ** and dot product, to deliver full accuracy whatever the size of ** the angle. ** ** Called: ** iauPxp vector product of two p-vectors ** iauPm modulus of p-vector ** iauPdp scalar product of two p-vectors ** ** This revision: 2008 May 22 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 IAU SOFA Board. See notes at end. */ { double axb[3], ss, cs, s; /* Sine of angle between the vectors, multiplied by the two moduli. */ iauPxp(a, b, axb); ss = iauPm(axb); /* Cosine of the angle, multiplied by the two moduli. */ cs = iauPdp(a, b); /* The angle. */ s = ((ss != 0.0) || (cs != 0.0)) ? atan2(ss, cs) : 0.0; return s; /*---------------------------------------------------------------------- ** ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
double iauPap(double a[3], double b[3]) /* ** - - - - - - - ** i a u P a p ** - - - - - - - ** ** Position-angle from two p-vectors. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: vector/matrix support function. ** ** Given: ** a double[3] direction of reference point ** b double[3] direction of point whose PA is required ** ** Returned (function value): ** double position angle of b with respect to a (radians) ** ** Notes: ** ** 1) The result is the position angle, in radians, of direction b with ** respect to direction a. It is in the range -pi to +pi. The ** sense is such that if b is a small distance "north" of a the ** position angle is approximately zero, and if b is a small ** distance "east" of a the position angle is approximately +pi/2. ** ** 2) The vectors a and b need not be of unit length. ** ** 3) Zero is returned if the two directions are the same or if either ** vector is null. ** ** 4) If vector a is at a pole, the result is ill-defined. ** ** Called: ** iauPn decompose p-vector into modulus and direction ** iauPm modulus of p-vector ** iauPxp vector product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPdp scalar product of two p-vectors ** ** This revision: 2008 May 25 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 IAU SOFA Board. See notes at end. */ { double am, au[3], bm, st, ct, xa, ya, za, eta[3], xi[3], a2b[3], pa; /* Modulus and direction of the a vector. */ iauPn(a, &am, au); /* Modulus of the b vector. */ bm = iauPm(b); /* Deal with the case of a null vector. */ if ((am == 0.0) || (bm == 0.0)) { st = 0.0; ct = 1.0; } else { /* The "north" axis tangential from a (arbitrary length). */ xa = a[0]; ya = a[1]; za = a[2]; eta[0] = -xa * za; eta[1] = -ya * za; eta[2] = xa*xa + ya*ya; /* The "east" axis tangential from a (same length). */ iauPxp(eta, au, xi); /* The vector from a to b. */ iauPmp(b, a, a2b); /* Resolve into components along the north and east axes. */ st = iauPdp(a2b, xi); ct = iauPdp(a2b, eta); /* Deal with degenerate cases. */ if ((st == 0.0) && (ct == 0.0)) ct = 1.0; } /* Position angle. */ pa = atan2(st, ct); return pa; /*---------------------------------------------------------------------- ** ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]) /*+ ** - - - - - - - ** i a u L d n ** - - - - - - - ** ** For a star, apply light deflection by multiple solar-system bodies, ** as part of transforming coordinate direction into natural direction. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** n int number of bodies (note 1) ** b iauLDBODY[n] data for each of the n bodies (Notes 1,2): ** bm double mass of the body (solar masses, Note 3) ** dl double deflection limiter (Note 4) ** pv [2][3] barycentric PV of the body (au, au/day) ** ob double[3] barycentric position of the observer (au) ** sc double[3] observer to star coord direction (unit vector) ** ** Returned: ** sn double[3] observer to deflected star (unit vector) ** ** 1) The array b contains n entries, one for each body to be ** considered. If n = 0, no gravitational light deflection will be ** applied, not even for the Sun. ** ** 2) The array b should include an entry for the Sun as well as for ** any planet or other body to be taken into account. The entries ** should be in the order in which the light passes the body. ** ** 3) In the entry in the b array for body i, the mass parameter ** b[i].bm can, as required, be adjusted in order to allow for such ** effects as quadrupole field. ** ** 4) The deflection limiter parameter b[i].dl is phi^2/2, where phi is ** the angular separation (in radians) between star and body at ** which limiting is applied. As phi shrinks below the chosen ** threshold, the deflection is artificially reduced, reaching zero ** for phi = 0. Example values suitable for a terrestrial ** observer, together with masses, are as follows: ** ** body i b[i].bm b[i].dl ** ** Sun 1.0 6e-6 ** Jupiter 0.00095435 3e-9 ** Saturn 0.00028574 3e-10 ** ** 5) For cases where the starlight passes the body before reaching the ** observer, the body is placed back along its barycentric track by ** the light time from that point to the observer. For cases where ** the body is "behind" the observer no such shift is applied. If ** a different treatment is preferred, the user has the option of ** instead using the iauLd function. Similarly, iauLd can be used ** for cases where the source is nearby, not a star. ** ** 6) The returned vector sn is not normalized, but the consequential ** departure from unit magnitude is always negligible. ** ** 7) The arguments sc and sn can be the same array. ** ** 8) For efficiency, validation is omitted. The supplied masses must ** be greater than zero, the position and velocity vectors must be ** right, and the deflection limiter greater than zero. ** ** Reference: ** ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to ** the Astronomical Almanac, 3rd ed., University Science Books ** (2013), Section 7.2.4. ** ** Called: ** iauCp copy p-vector ** iauPdp scalar product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPpsp p-vector plus scaled p-vector ** iauPn decompose p-vector into modulus and direction ** iauLd light deflection by a solar-system body ** ** This revision: 2017 March 16 ** ** SOFA release 2017-04-20 ** ** Copyright (C) 2017 IAU SOFA Board. See notes at end. */ { /* Light time for 1 au (days) */ const double CR = AULT/DAYSEC; int i; double v[3], dt, ev[3], em, e[3]; /* Star direction prior to deflection. */ iauCp(sc, sn); /* Body by body. */ for ( i = 0; i < n; i++ ) { /* Body to observer vector at epoch of observation (au). */ iauPmp ( ob, b[i].pv[0], v ); /* Minus the time since the light passed the body (days). */ dt = iauPdp(sn,v) * CR; /* Neutralize if the star is "behind" the observer. */ dt = gmin(dt, 0.0); /* Backtrack the body to the time the light was passing the body. */ iauPpsp(v, -dt, b[i].pv[1], ev); /* Body to observer vector as magnitude and direction. */ iauPn(ev, &em, e); /* Apply light deflection for this body. */ iauLd ( b[i].bm, sn, sn, e, em, b[i].dl, sn ); /* Next body. */ } /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2017 ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
int iauStarpm(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) /* ** - - - - - - - - - - ** i a u S t a r p m ** - - - - - - - - - - ** ** Star proper motion: update star catalog data for space motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** 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 iauStarpv ** 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 iauStarpv), it is arbitrarily set ** to zero. When this action occurs, 2 is added to the status. ** ** 8) The relativistic adjustment carried out in the iauStarpv function ** involves an iterative calculation. If the process fails to ** converge within a set number of iterations, 4 is added to the ** status. ** ** Called: ** iauStarpv star catalog data to space motion pv-vector ** iauPvu update a pv-vector ** iauPdp scalar product of two p-vectors ** iauPvstar space motion pv-vector to star catalog data ** ** This revision: 2008 May 16 ** ** SOFA release 2012-03-01 ** ** Copyright (C) 2012 IAU SOFA Board. See notes at end. */ { 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 = iauStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1); /* Light time when observed (days). */ tl1 = iauPm(pv1[0]) / 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. */ iauPvu(dt + tl1, pv1, pv); /* From this geometric position, deduce the observed light time (days) */ /* at the "after" epoch (with theoretically unneccessary error check). */ r2 = iauPdp(pv[0], pv[0]); rdv = iauPdp(pv[0], pv[1]); v2 = iauPdp(pv[1], pv[1]); c2mv2 = DC*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. */ iauPvu(dt + (tl1 - tl2), pv1, pv2); /* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */ j2 = iauPvstar(pv2, ra2, dec2, pmr2, pmd2, px2, rv2); /* Final status. */ j = (j2 == 0) ? j1 : -1; return j; /*---------------------------------------------------------------------- ** ** 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: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }