CelestialCoordinates.c

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/*
*  Copyright (C) 2007 Jolien Creighton, Reinhard Prix, Teviet Creighton, John Whelan
*
*  This program is free software; you can redistribute it and/or modify
*  it under the terms of the GNU General Public License as published by
*  the Free Software Foundation; either version 2 of the License, or
*  (at your option) any later version.
*
*  This program is distributed in the hope that it will be useful,
*  but WITHOUT ANY WARRANTY; without even the implied warranty of
*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
*  GNU General Public License for more details.
*
*  You should have received a copy of the GNU General Public License
*  along with with program; see the file COPYING. If not, write to the
*  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
*  MA  02110-1301  USA
*/
 
#include <math.h>
#include <lal/LALStdlib.h>
#include <lal/LALConstants.h>
#include <lal/SkyCoordinates.h>
 
#define LAL_ALPHAGAL (3.366032942)
#define LAL_DELTAGAL (0.473477302)
#define LAL_LGAL     (0.576)
 
/**
 * \author T.D. Creighton
 * \addtogroup CelestialCoordinates_c
 * \brief Converts among Galactic, ecliptic, and equatorial coordinates.
 *
 * These functions perform the specified coordinate transformation on the
 * contents of \a input and store the result in \a *output.  The
 * two pointers may point to the same object, in which case the
 * conversion is done in place.  The functions will also check
 * <tt>input->system</tt> and set <tt>output->system</tt> as appropriate.
 *
 * These routines are collected together because they involve fixed,
 * absolute coordinate systems, so the transformations require no
 * additional parameters such as the time or site of observation.  We
 * also note that there are no direct conversions between Galactic and
 * ecliptic coordinates.  At the risk of additional computational
 * overhead, it is simple to use the equatorial coordinate system as an
 * intermediate step.
 *
 * ### Description ###
 *
 * These functions perform the specified coordinate transformation on the
 * contents of \a input and store the result in \a output.  The
 * two pointers may point to the same object, in which case the
 * conversion is done in place.  The functions will also check
 * <tt>input->system</tt> and set <tt>output->system</tt> as appropriate.
 *
 * These routines are collected together because they involve fixed,
 * absolute coordinate systems, so the transformations require no
 * additional parameters such as the time or site of observation.  We
 * also note that there are no direct conversions between Galactic and
 * ecliptic coordinates.  At the risk of additional computational
 * overhead, it is simple to use the equatorial coordinate system as an
 * intermediate step.
 *
 * ### Algorithm ###
 *
 * These routines follow the spherical angle relations on p. 13
 * of \cite Lang_K1999 .  Note that the actual formulae for Galactic
 * longitude and right ascension in this reference are wrong; we give
 * corrected formulae below derived from the sine and cosine equations.
 * (The Galactic to equatorial transformations can also be found in
 * Sec. 12.3 of \cite GRASP2000 .  All positions are assumed to
 * be in the J2000 epoch.
 *
 * \par Galactic coordinates:
 * The following formulae relate
 * Galactic latitude \f$b\f$ and longitude \f$l\f$ to declination \f$\delta\f$ and
 * right ascension \f$\alpha\f$:
 * \f{eqnarray}{
 * b & = & \arcsin[\cos\delta\cos\delta_\mathrm{NGP}
 * \cos(\alpha-\alpha_\mathrm{NGP}) +
 * \sin\delta\sin\delta_\mathrm{NGP}] \;,\\
 * l & = & \arctan\!2[\sin\delta\cos\delta_\mathrm{NGP} -
 * \cos\delta\cos(\alpha-\alpha_\mathrm{NGP})
 * \sin\delta_\mathrm{NGP},
 * \cos\delta\sin(\alpha-\alpha_\mathrm{NGP})]\\
 * & & \quad + \; l_\mathrm{ascend} \;,
 * \f}
 * where \f$\arctan\!2(y,x)\f$ can be thought of as the argument of the
 * complex number \f$x+iy\f$; unlike \f$\arctan(y/x)\f$, it ranges over the full
 * range \f$[0,2\pi)\f$ instead of just half of it.  The inverse
 * transformations are:
 * \f{eqnarray}{
 * \delta & = & \arcsin[\cos b\cos\delta_\mathrm{NGP}\sin(l-l_\mathrm{ascend}) +
 * \sin b\sin\delta_\mathrm{NGP}] \;,\\
 * \alpha & = & \arctan\!2[\cos b\cos(l-l_\mathrm{ascend}),
 * \sin b\cos\delta_\mathrm{NGP} -
 * \cos b\sin(l-l_\mathrm{ascend})\sin\delta_\mathrm{NGP}] \\
 * & & \quad + \; \alpha_\mathrm{NGP} \;.
 * \f}
 * In these equations we have defined the orientation of the Galaxy with
 * the following parameters (which should eventually be placed in <tt>LALConstants.h</tt>:
 * \f[
 * \begin{array}{r@{\quad=\quad}l@{\quad=\quad}l}
 * \alpha_\mathrm{NGP} & 192.8594813^\circ &
 * \mbox{the right ascension (epoch J2000) of the north Galactic pole} \\
 * \delta_\mathrm{NGP} & 27.1282511^\circ &
 * \mbox{the declination (epoch J2000) of the north Galactic pole} \\
 * l_\mathrm{ascend} & 33^\circ &
 * \mbox{the longitude of the ascending node of the Galactic plane}
 * \end{array}
 * \f]
 * The ascending node of the Galactic plane is defined as the direction
 * along the intersection of the Galactic and equatorial planes where
 * rotation in the positive sense about the Galactic \f$z\f$ axis carries a
 * point from the southern to northern equatorial hemisphere.  That is,
 * if \f$\mathbf{u}\f$ points in the direction \f$\delta=90^\circ\f$
 * (celestial north), and \f$\mathbf{v}\f$ points in the direction
 * \f$b=90^\circ\f$ (Galactic north), then
 * \f$\mathbf{u} \times \mathbf{v}\f$ points along the ascending node.
 *
 * \par Ecliptic coordinates:
 * The following formulae relate
 * Ecliptic latitude \f$\beta\f$ and longitude \f$\lambda\f$ to declination
 * \f$\delta\f$ and right ascension \f$\alpha\f$:
 * \f{eqnarray}{
 * \beta & = & \arcsin(\sin\delta\cos\epsilon -
 * \cos\delta\sin\alpha\sin\epsilon) \;, \\
 * \lambda & = & \arctan\!2(\cos\delta\sin\alpha\cos\epsilon +
 * \sin\delta\sin\epsilon, \cos\delta\cos\alpha) \;.
 * \f}
 * The inverse transformations are:
 * \f{eqnarray}{
 * \delta & = & \arcsin(\cos\beta\sin\lambda\sin\epsilon +
 * \sin\beta\cos\epsilon) \;, \\
 * \alpha & = & \arctan\!2(\cos\beta\sin\lambda\cos\epsilon -
 * \sin\beta\sin\epsilon, \cos\beta\cos\lambda) \;.
 * \f}
 * Here \f$\epsilon\f$ is the obliquity (inclination) of the ecliptic plane,
 * which varies over time; at epoch J200 it has a mean value of:
 * \f[
 * \epsilon = 23.4392911^\circ \; .
 * \f]
 *
 */
/** @{ */
 
/** \see See documentation in  \ref CelestialCoordinates_c */
void
LALGalacticToEquatorial( LALStatus   *stat,
                         SkyPosition *output,
                         SkyPosition *input )
{
  REAL8 sinDGal = sin( LAL_DELTAGAL ); /* sin(delta_NGP) */
  REAL8 cosDGal = cos( LAL_DELTAGAL ); /* cos(delta_NGP) */
  REAL8 l = -LAL_LGAL;          /* will be l-l(ascend) */
  REAL8 sinB, cosB, sinL, cosL; /* sin and cos of b and l */
  REAL8 sinD, sinA, cosA;       /* sin and cos of delta and alpha */
 
  INITSTATUS(stat);
 
  /* Make sure parameter structures exist. */
  ASSERT( input, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
  ASSERT( output, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
 
  /* Make sure we're given the right coordinate system. */
  if ( input->system != COORDINATESYSTEM_GALACTIC ) {
    ABORT( stat, SKYCOORDINATESH_ESYS, SKYCOORDINATESH_MSGESYS );
  }
 
  /* Compute intermediates. */
  l += input->longitude;
  sinB = sin( input->latitude );
  cosB = cos( input->latitude );
  sinL = sin( l );
  cosL = cos( l );
 
  /* Compute components. */
  sinD = cosB*cosDGal*sinL + sinB*sinDGal;
  sinA = cosB*cosL;
  cosA = sinB*cosDGal - cosB*sinL*sinDGal;
 
  /* Compute final results. */
  output->system = COORDINATESYSTEM_EQUATORIAL;
  output->latitude = asin( sinD );
  l = atan2( sinA, cosA ) + LAL_ALPHAGAL;
 
  /* Optional phase correction. */
  if ( l < 0.0 )
    l += LAL_TWOPI;
  output->longitude = l;
 
  RETURN( stat );
}
 
/** \see See documentation in  \ref CelestialCoordinates_c */
void
LALEquatorialToGalactic( LALStatus   *stat,
                         SkyPosition *output,
                         SkyPosition *input )
{
  REAL8 sinDGal = sin( LAL_DELTAGAL ); /* sin(delta_NGP) */
  REAL8 cosDGal = cos( LAL_DELTAGAL ); /* cos(delta_NGP) */
  REAL8 a = -LAL_ALPHAGAL;      /* will be alpha-alpha_NGP */
  REAL8 sinD, cosD, sinA, cosA; /* sin and cos of delta and alpha */
  REAL8 sinB, sinL, cosL;       /* sin and cos of b and l */
 
  INITSTATUS(stat);
 
  /* Make sure parameter structures exist. */
  ASSERT( input, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
  ASSERT( output, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
 
  /* Make sure we're given the right coordinate system. */
  if ( input->system != COORDINATESYSTEM_EQUATORIAL ) {
    ABORT( stat, SKYCOORDINATESH_ESYS, SKYCOORDINATESH_MSGESYS );
  }
 
  /* Compute intermediates. */
  a += input->longitude;
  sinD = sin( input->latitude );
  cosD = cos( input->latitude );
  sinA = sin( a );
  cosA = cos( a );
 
  /* Compute components. */
  sinB = cosD*cosDGal*cosA + sinD*sinDGal;
  sinL = sinD*cosDGal - cosD*cosA*sinDGal;
  cosL = cosD*sinA;
 
  /* Compute final results. */
  output->system = COORDINATESYSTEM_GALACTIC;
  output->latitude = asin( sinB );
  a = atan2( sinL, cosL ) + LAL_LGAL;
 
  /* Optional phase correction. */
  if ( a < 0.0 )
    a += LAL_TWOPI;
  output->longitude = a;
 
  RETURN( stat );
}
 
/** \see See documentation in  \ref CelestialCoordinates_c */
void
LALEclipticToEquatorial( LALStatus   *stat,
                         SkyPosition *output,
                         SkyPosition *input )
{
  REAL8 sinE = sin( LAL_IEARTH ); /* sin(epsilon) */
  REAL8 cosE = cos( LAL_IEARTH ); /* cos(epsilon) */
  REAL8 sinB, cosB, sinL, cosL;   /* sin and cos of b and l */
  REAL8 sinD, sinA, cosA;         /* sin and cos of delta and alpha */
 
  INITSTATUS(stat);
 
  /* Make sure parameter structures exist. */
  ASSERT( input, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
  ASSERT( output, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
 
  /* Make sure we're given the right coordinate system. */
  if ( input->system != COORDINATESYSTEM_ECLIPTIC ) {
    ABORT( stat, SKYCOORDINATESH_ESYS, SKYCOORDINATESH_MSGESYS );
  }
 
  /* Compute intermediates. */
  sinB = sin( input->latitude );
  cosB = cos( input->latitude );
  sinL = sin( input->longitude );
  cosL = cos( input->longitude );
 
  /* Compute components. */
  sinD = cosB*sinL*sinE + sinB*cosE;
  sinA = cosB*sinL*cosE - sinB*sinE;
  cosA = cosB*cosL;
 
  /* Compute final results. */
  output->system = COORDINATESYSTEM_EQUATORIAL;
  output->latitude = asin( sinD );
  output->longitude = atan2( sinA, cosA );
 
  /* Optional phase correction. */
  if ( output->longitude < 0.0 )
    output->longitude += LAL_TWOPI;
 
  RETURN( stat );
}
 
/** \see See documentation in  \ref CelestialCoordinates_c */
void
LALEquatorialToEcliptic( LALStatus   *stat,
                         SkyPosition *output,
                         SkyPosition *input )
{
  REAL8 sinE = sin( LAL_IEARTH ); /* sin(epsilon) */
  REAL8 cosE = cos( LAL_IEARTH ); /* cos(epsilon) */
  REAL8 sinD, cosD, sinA, cosA;   /* sin and cos of delta and alpha */
  REAL8 sinB, sinL, cosL;         /* sin and cos of b and l */
 
  INITSTATUS(stat);
 
  /* Make sure parameter structures exist. */
  ASSERT( input, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
  ASSERT( output, stat, SKYCOORDINATESH_ENUL, SKYCOORDINATESH_MSGENUL );
 
  /* Make sure we're given the right coordinate system. */
  if ( input->system != COORDINATESYSTEM_EQUATORIAL ) {
    ABORT( stat, SKYCOORDINATESH_ESYS, SKYCOORDINATESH_MSGESYS );
  }
 
  /* Compute intermediates. */
  sinD = sin( input->latitude );
  cosD = cos( input->latitude );
  sinA = sin( input->longitude );
  cosA = cos( input->longitude );
 
  /* Compute components. */
  sinB = sinD*cosE - cosD*sinA*sinE;
  sinL = cosD*sinA*cosE + sinD*sinE;
  cosL = cosD*cosA;
 
  /* Compute final results. */
  output->system = COORDINATESYSTEM_ECLIPTIC;
  output->latitude = asin( sinB );
  output->longitude = atan2( sinL, cosL );
 
  /* Optional phase correction. */
  if ( output->longitude < 0.0 )
    output->longitude += LAL_TWOPI;
 
  RETURN( stat );
}
/** @} */