#include "erfa.h" void eraAtoiq(const char *type, double ob1, double ob2, eraASTROM *astrom, double *ri, double *di) /* ** - - - - - - - - - ** e r a A t o i q ** - - - - - - - - - ** ** Quick observed place to CIRS, given the star-independent astrometry ** parameters. ** ** Use of this function is appropriate when efficiency is important and ** where many star positions are all to be transformed for one date. ** The star-independent astrometry parameters can be obtained by ** calling eraApio[13] or eraApco[13]. ** ** Given: ** type char[] type of coordinates: "R", "H" or "A" (Note 1) ** ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ** ob2 double observed ZD or Dec (radians) ** astrom eraASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Returned: ** ri double* CIRS right ascension (CIO-based, radians) ** di double* CIRS declination (radians) ** ** Notes: ** ** 1) "Observed" Az,El means the position that would be seen by a ** perfect geodetically aligned theodolite. This is related to ** the observed HA,Dec via the standard rotation, using the geodetic ** latitude (corrected for polar motion), while the observed HA and ** RA are related simply through the Earth rotation angle and the ** site longitude. "Observed" RA,Dec or HA,Dec thus means the ** position that would be seen by a perfect equatorial with its ** polar axis aligned to the Earth's axis of rotation. By removing ** from the observed place the effects of atmospheric refraction and ** diurnal aberration, the CIRS RA,Dec is obtained. ** ** 2) Only the first character of the type argument is significant. ** "R" or "r" indicates that ob1 and ob2 are the observed right ** ascension and declination; "H" or "h" indicates that they are ** hour angle (west +ve) and declination; anything else ("A" or ** "a" is recommended) indicates that ob1 and ob2 are azimuth (north ** zero, east 90 deg) and zenith distance. (Zenith distance is used ** rather than altitude in order to reflect the fact that no ** allowance is made for depression of the horizon.) ** ** 3) The accuracy of the result is limited by the corrections for ** refraction, which use a simple A*tan(z) + B*tan^3(z) model. ** Providing the meteorological parameters are known accurately and ** there are no gross local effects, the predicted observed ** coordinates should be within 0.05 arcsec (optical) or 1 arcsec ** (radio) for a zenith distance of less than 70 degrees, better ** than 30 arcsec (optical or radio) at 85 degrees and better than ** 20 arcmin (optical) or 30 arcmin (radio) at the horizon. ** ** Without refraction, the complementary functions eraAtioq and ** eraAtoiq are self-consistent to better than 1 microarcsecond all ** over the celestial sphere. With refraction included, consistency ** falls off at high zenith distances, but is still better than ** 0.05 arcsec at 85 degrees. ** ** 4) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** Called: ** eraS2c spherical coordinates to unit vector ** eraC2s p-vector to spherical ** eraAnp normalize angle into range 0 to 2pi ** ** Copyright (C) 2013-2014, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { int c; double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[3], xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref, zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda, f, xhd, yhd, zhd, xpl, ypl, w, hma; /* Coordinate type. */ c = (int) type[0]; /* Coordinates. */ c1 = ob1; c2 = ob2; /* Sin, cos of latitude. */ sphi = astrom->sphi; cphi = astrom->cphi; /* Standardize coordinate type. */ if ( c == 'r' || c == 'R' ) { c = 'R'; } else if ( c == 'h' || c == 'H' ) { c = 'H'; } else { c = 'A'; } /* If Az,ZD, convert to Cartesian (S=0,E=90). */ if ( c == 'A' ) { ce = sin(c2); xaeo = - cos(c1) * ce; yaeo = sin(c1) * ce; zaeo = cos(c2); } else { /* If RA,Dec, convert to HA,Dec. */ if ( c == 'R' ) c1 = astrom->eral - c1; /* To Cartesian -HA,Dec. */ eraS2c ( -c1, c2, v ); xmhdo = v[0]; ymhdo = v[1]; zmhdo = v[2]; /* To Cartesian Az,El (S=0,E=90). */ xaeo = sphi*xmhdo - cphi*zmhdo; yaeo = ymhdo; zaeo = cphi*xmhdo + sphi*zmhdo; } /* Azimuth (S=0,E=90). */ az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0; /* Sine of observed ZD, and observed ZD. */ sz = sqrt ( xaeo*xaeo + yaeo*yaeo ); zdo = atan2 ( sz, zaeo ); /* ** Refraction ** ---------- */ /* Fast algorithm using two constant model. */ refa = astrom->refa; refb = astrom->refb; tz = sz / zaeo; dref = ( refa + refb*tz*tz ) * tz; zdt = zdo + dref; /* To Cartesian Az,ZD. */ ce = sin(zdt); xaet = cos(az) * ce; yaet = sin(az) * ce; zaet = cos(zdt); /* Cartesian Az,ZD to Cartesian -HA,Dec. */ xmhda = sphi*xaet + cphi*zaet; ymhda = yaet; zmhda = - cphi*xaet + sphi*zaet; /* Diurnal aberration. */ f = ( 1.0 + astrom->diurab*ymhda ); xhd = f * xmhda; yhd = f * ( ymhda - astrom->diurab ); zhd = f * zmhda; /* Polar motion. */ xpl = astrom->xpl; ypl = astrom->ypl; w = xpl*xhd - ypl*yhd + zhd; v[0] = xhd - xpl*w; v[1] = yhd + ypl*w; v[2] = w - ( xpl*xpl + ypl*ypl ) * zhd; /* To spherical -HA,Dec. */ eraC2s(v, &hma, di); /* Right ascension. */ *ri = eraAnp(astrom->eral + hma); /* Finished. */ } /*---------------------------------------------------------------------- ** ** ** Copyright (C) 2013-2014, 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. ** */