gfsep_c

Index Page gfsep_c
A B C D E F G H I J K L M N O P Q R S T U V W X
Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries
#### Procedure
       void gfsep_c (  ConstSpiceChar     * targ1,
                       ConstSpiceChar     * shape1,
                       ConstSpiceChar     * frame1,
                       ConstSpiceChar     * targ2,
                       ConstSpiceChar     * shape2,
                       ConstSpiceChar     * frame2,
                       ConstSpiceChar     * abcorr,
                       ConstSpiceChar     * obsrvr,
                       ConstSpiceChar     * relate,
                       SpiceDouble          refval,
                       SpiceDouble          adjust,
                       SpiceDouble          step,
                       SpiceInt             nintvls,
                       SpiceCell          * cnfine,
                       SpiceCell          * result  )
#### Abstract
       Determine time intervals when the angular separation between
       the position vectors of two target bodies relative to an observer
       satisfies a numerical relationship.
#### Required_Reading
       GF
       NAIF_IDS
       SPK
       TIME
       WINDOWS
#### Keywords
       SEPARATION
       GEOMETRY
       SEARCH
       EVENT
#### Brief_I/O
       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       SPICE_GF_CNVTOL
                  P   Convergence tolerance.
       targ1      I   Name of first body
       shape1     I   Name of shape model describing the first body
       frame1     I   The body-fixed reference frame of the first body
       targ2      I   Name of second body
       shape2     I   Name of the shape model describing the second body
       frame2     I   The body-fixed reference frame of the second body
       abcorr     I   Aberration correction flag
       obsrvr     I   Name of the observing body
       relate     I   Operator that either looks for an extreme value
                      (max, min, local, absolute) or compares the
                      angular separation value and refval
       refval     I   Reference value
       adjust     I   Absolute extremum adjustment value
       step       I   Step size in seconds for finding angular separation
                      events
       nintvls    I   Workspace window interval count
       cnfine    I-O  SPICE window to which the search is restricted
       result     O   SPICE window containing results
#### Detailed_Input
       targ1       the string naming the first body of interest. You can
                   also supply the integer ID code for the object as an
                   integer string.  For example both 'MOON' and '301'
                   are legitimate strings that indicate the moon is the
                   target body.

       shape1      the string naming the geometric model used to represent
                   the shape of the targ1 body. Models supported by this routine:

                     'ELLIPSOID'     Use a triaxial ellipsoid model,
                                     with radius values provided by the
                                     kernel pool. A kernel variable
                                     having a name of the form

                                        'BODYnnn_RADII'

                                     where nnn represents the NAIF
                                     integer code associated with the
                                     body, must be present in the kernel
                                     pool. This variable must be
                                     associated with three numeric
                                     values giving the lengths of the
                                     ellipsoid's X, Y, and Z semi-axes.

                                     *This option not yet implemented.*

                     'SPHERE'        Treat the body as a sphere with radius
                                     equal to the maximum value of
                                     BODYnnn_RADII

                     'POINT'         Treat the body as a point;
                                     radius has value zero.

                   The shape1 string lacks sensitivity to case, leading
                   and trailing blanks.

       frame1      the string naming the body-fixed reference frame
                   corresponding to targ1.

       targ2       the string naming the second body of interest. You can
                   also supply the integer ID code for the object as an
                   integer string.  For example both 'MOON' and '301'
                   are legitimate strings that indicate the moon is the
                   target body.

       shape2      the string naming the geometric model used to represent
                   the shape of the targ2. Models supported by this routine:

                     'ELLIPSOID'     Use a triaxial ellipsoid model,
                                     with radius values provided by the
                                     kernel pool. A kernel variable
                                     having a name of the form

                                        'BODYnnn_RADII'

                                     where nnn represents the NAIF
                                     integer code associated with the
                                     body, must be present in the kernel
                                     pool. This variable must be
                                     associated with three numeric
                                     values giving the lengths of the
                                     ellipsoid's X, Y, and Z semi-axes.

                     'SPHERE'        Treat the body as a sphere with radius
                                     equal to the maximum value of
                                     BODYnnn_RADII

                     'POINT'         Treat the body as a single point;
                                     radius has value zero.

                   The shape2 string lacks sensitivity to case, leading
                   and trailing blanks.

       frame2      the string naming the body-fixed reference frame
                   corresponding to targ2.

       abcorr      the string indicating the aberration corrections to apply
                   to the observer-target position vector to account for
                   one-way light time and stellar aberration.

                   This routine accepts the same aberration corrections as does
                   the SPICE routine SPKEZR. See the header of SPKEZR for a
                   detailed description of the aberration correction options.
                   For convenience, the options are listed below:

                      'NONE'     Apply no correction.

                      'LT'       "Reception" case:  correct for
                                 one-way light time using a Newtonian
                                 formulation.

                      'LT+S'     "Reception" case:  correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation.

                      'CN'       "Reception" case:  converged
                                 Newtonian light time correction.

                      'CN+S'     "Reception" case:  converged
                                 Newtonian light time and stellar
                                 aberration corrections.

                      'XLT'      "Transmission" case:  correct for
                                 one-way light time using a Newtonian
                                 formulation.

                      'XLT+S'    "Transmission" case:  correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation.

                      'XCN'      "Transmission" case:  converged
                                 Newtonian light time correction.

                      'XCN+S'    "Transmission" case:  converged
                                 Newtonian light time and stellar
                                 aberration corrections.

                   The abcorr string lacks sensitivity to case, leading
                   and trailing blanks.

       obsrvr      the string naming the observing body. Optionally, you
                   may supply the ID code of the object as an integer
                   string. For example, both 'EARTH' and '399' are
                   legitimate strings to supply to indicate the
                   observer is Earth.

       relate      the string identifying the relational operator used to
                   define a constraint on the angular separation. The result
                   window found by this routine indicates the time intervals
                   where the constraint is satisfied. Supported values of
                   relate and corresponding meanings are shown below:

                      '>'      Separation is greater than the reference
                               value refval.

                      '='      Separation is equal to the reference
                               value refval.

                      '<'      Separation is less than the reference
                               value refval.

                     'ABSMAX'  Separation is at an absolute maximum.

                     'ABSMIN'  Separation is at an absolute  minimum.

                     'LOCMAX'  Separation is at a local maximum.

                     'LOCMIN'  Separation is at a local minimum.

                  The caller may indicate that the region of interest
                  is the set of time intervals where the quantity is
                  within a specified angular separation of an absolute extremum.
                  The argument adjust (described below) is used to
                  specify this angular separation.

                  Local extrema are considered to exist only in the
                  interiors of the intervals comprising the confinement
                  window:  a local extremum cannot exist at a boundary
                  point of the confinement window.

                  The relate string lacks sensitivity to case, leading
                  and trailing blanks.

       refval     the double precision reference value used together with
                  relate argument to define an equality or inequality to be
                  satisfied by the angular separation between the specified target
                  and observer. See the discussion of relate above for
                  further information.

                  The units of refval are radians.

       adjust     a double precision value used to modify searches for
                  absolute extrema: when relate is set to ABSMAX or ABSMIN and
                  adjust is set to a positive value, GFSEP finds times when the
                  angular separation between the bodies is within adjust radians
                  of the specified extreme value.

                  For relate set to ABSMAX, the result window contains
                  time intervals when the angular separation has
                  values between ABSMAX - adjust and ABSMAX.

                  For relate set to ABSMIN, the result window contains
                  time intervals when the angular separation has
                  values between ABSMIN and ABSMIN + adjust.

                  adjust is not used for searches for local extrema,
                  equality or inequality conditions.

       step       a double precision value defining the step size to use in
                  the search. step must be short enough for a search using step
                  to locate the time intervals where the specified
                  angular separation function is monotone increasing or
                  decreasing. However, step must not be *too* short, or
                  the search will take an unreasonable amount of time.

                  The choice of step affects the completeness but not
                  the precision of solutions found by this routine; the
                  precision is controlled by the convergence tolerance.
                  See the discussion of the parameter SPICE_GF_CNVTOL for
                  details.

                  'step' has units of TDB seconds.

       nintvls    an integer value specifying the number of intervals in the
                  the internal workspace array used by this routine. 'nintvls'
                  should be at least as large as the number of intervals
                  within the search region on which the specified observer-target
                  vector coordinate function is monotone increasing or decreasing.
                  It does no harm to pick a value of 'nintvls' larger than the
                  minimum required to execute the specified search, but if chosen
                  too small, the search will fail.

       cnfine     a double precision SPICE window that confines the time
                  period over which the specified search is conducted.
                  cnfine may consist of a single interval or a collection
                  of intervals.

                  In some cases the confinement window can be used to
                  greatly reduce the time period that must be searched
                  for the desired solution. See the Particulars section
                  below for further discussion.

                  See the Examples section below for a code example
                  that shows how to create a confinement window.
#### Detailed_Output
       cnfine     is the input confinement window, updated if necessary
                  so the control area of its data array indicates the
                  window's size and cardinality. The window data are
                  unchanged.

       result     the SPICE window of intervals, contained within the
                  confinement window cnfine, on which the specified
                  constraint is satisfied.

                  If result is non-empty on input, its contents
                  will be discarded before gfsep_c conducts its
                  search.

                  result must be declared and initialized with sufficient
                  size to capture the full set of time intervals
                  within the search region on which the specified constraint
                  is satisfied.

                  If the search is for local extrema, or for absolute
                  extrema with adjust set to zero, then normally each
                  interval of result will be a singleton: the left and
                  right endpoints of each interval will be identical.

                  If no times within the confinement window satisfy the
                  constraint, result will be returned with a
                  cardinality of zero.
#### Parameters
       SPICE_GF_CNVTOL

                  is the convergence tolerance used for finding endpoints
                  of the intervals comprising the result window.
                  SPICE_GF_CNVTOL is used to determine when binary searches
                  for roots should terminate: when a root is bracketed
                  within an interval of length SPICE_GF_CNVTOL; the root is
                  considered to have been found.

                  The accuracy, as opposed to precision, of roots found by
                  this routine depends on the accuracy of the input data.
                  In most cases, the accuracy of solutions will be inferior
                  to their precision.

                  SPICE_GF_CNVTOL has the value 1.0e-6. Units are TDB
                  seconds.
#### Exceptions
       1)  In order for this routine to produce correct results,
           the step size must be appropriate for the problem at hand.
           Step sizes that are too large may cause this routine to miss
           roots; step sizes that are too small may cause this routine
           to run unacceptably slowly and in some cases, find spurious
           roots.

           This routine does not diagnose invalid step sizes, except
           that if the step size is non-positive, an error is signaled
           by a routine in the call tree of this routine.

       2)  Due to numerical errors, in particular,

              - Truncation error in time values
              - Finite tolerance value
              - Errors in computed geometric quantities

           it is *normal* for the condition of interest to not always be
           satisfied near the endpoints of the intervals comprising the
           result window.

           The result window may need to be contracted slightly by the
           caller to achieve desired results. The SPICE window routine
           wncond_c can be used to contract the result window.

       3)  If an error (typically cell overflow) occurs while performing
           window arithmetic, the error will be diagnosed by a routine
           in the call tree of this routine.

       4)  If the relational operator `relate' is not recognized, an
           error is signaled by a routine in the call tree of this
           routine.

       5)   If the aberration correction specifier contains an
            unrecognized value, an error is signaled by a routine in the
            call tree of this routine.

       6)  If `adjust' is negative, an error is signaled by a routine in
           the call tree of this routine.

       7)  If either of the input body names do not map to NAIF ID
           codes, an error is signaled by a routine in the call tree of
           this routine.

       8)  If required ephemerides or other kernel data are not
           available, an error is signaled by a routine in the call tree
           of this routine.

       9)  If any input string argument pointer is null, the error
           SPICE(NULLPOINTER) will be signaled.

       10) If any input string argument is empty, the error
           SPICE(EMPTYSTRING) will be signaled.

       11) If the workspace interval count 'nintvls' is less than 1, the
           error SPICE(VALUEOUTOFRANGE) will be signaled.

       12) If the required amount of workspace memory cannot be
           allocated, the error SPICE(MALLOCFAILURE) will be
           signaled.
#### Files
       Appropriate SPK and PCK kernels must be loaded by the
       calling program before this routine is called.

       The following data are required:

          - SPK data: the calling application must load ephemeris data
            for the targets, observer, and any intermediate objects in
            a chain connecting the targets and observer that cover the time
            period specified by the window CNFINE. If aberration
            corrections are used, the states of target and observer
            relative to the solar system barycenter must be calculable
            from the available ephemeris data. Typically ephemeris data
            are made available by loading one or more SPK files using
            FURNSH.

          - PCK data: bodies modeled as triaxial ellipsoids must have
            semi-axis lengths provided by variables in the kernel pool.
            Typically these data are made available by loading a text
            PCK file using FURNSH.

          - If non-inertial reference frames are used, then PCK
            files, frame kernels, C-kernels, and SCLK kernels may be
            needed.

       Such kernel data are normally loaded once per program
       run, NOT every time this routine is called.
#### Particulars
       This routine provides a simpler, but less flexible interface
       than does the routine gfevnt_c for conducting searches for
       angular separation events. Applications that require support for
       progress reporting, interrupt handling, non-default step or
       refinement functions, or non-default convergence tolerance should
       call gfevnt_c rather than this routine.

       This routine determines a set of one or more time intervals
       within the confinement window for which the angular separation
       between the two bodies satisfies some defined relationship.
       The resulting set of intervals is returned as a SPICE window.

       Below we discuss in greater detail aspects of this routine's
       solution process that are relevant to correct and efficient
       use of this routine in user applications.

       The Search Process
       ==================

       Regardless of the type of constraint selected by the caller, this
       routine starts the search for solutions by determining the time
       periods, within the confinement window, over which the specified
       angular separation function is monotone increasing and monotone
       decreasing. Each of these time periods is represented by a SPICE window.
       Having found these windows, all of the angular separation function's
       local extrema within the confinement window are known. Absolute extrema
       then can be found very easily.

       Within any interval of these "monotone" windows, there will be at
       most one solution of any equality constraint. Since the boundary
       of the solution set for any inequality constraint is the set
       of points where an equality constraint is met, the solutions of
       both equality and inequality constraints can be found easily
       once the monotone windows have been found.

       Step Size
       =========

       The monotone windows (described above) are found using a two-step
       search process. Each interval of the confinement window is
       searched as follows: first, the input step size is used to
       determine the time separation at which the sign of the rate of
       change of angular separation (angular separation rate) will be
       sampled. Starting at the left endpoint of an interval, samples
       will be taken at each step. If a change of sign is found, a
       root has been bracketed; at that point, the time at which the
       angular separation rate is zero can be found by a refinement
       process, for example, using a binary search.

       Note that the optimal choice of step size depends on the lengths
       of the intervals over which the distance function is monotone:
       the step size should be shorter than the shortest of these
       intervals (within the confinement window).

       The optimal step size is *not* necessarily related to the lengths
       of the intervals comprising the result window. For example, if
       the shortest monotone interval has length 10 days, and if the
       shortest result window interval has length 5 minutes, a step size
       of 9.9 days is still adequate to find all of the intervals in the
       result window. In situations like this, the technique of using
       monotone windows yields a dramatic efficiency improvement over a
       state-based search that simply tests at each step whether the
       specified constraint is satisfied. The latter type of search can
       miss solution intervals if the step size is shorter than the
       shortest solution interval.

       Having some knowledge of the relative geometry of the target and
       observer can be a valuable aid in picking a reasonable step size.
       In general, the user can compensate for lack of such knowledge by
       picking a very short step size; the cost is increased computation
       time.

       Note that the step size is not related to the precision with which
       the endpoints of the intervals of the result window are computed.
       That precision level is controlled by the convergence tolerance.

       Convergence Tolerance
       =====================

       As described above, the root-finding process used by this routine
       involves first bracketing roots and then using a search process
       to locate them. "Roots" are both times when local extrema are
       attained and times when the distance function is equal to a
       reference value. All endpoints of the intervals comprising the
       result window are either endpoints of intervals of the
       confinement window or roots.

       Once a root has been bracketed, a refinement process is used to
       narrow down the time interval within which the root must lie.
       This refinement process terminates when the location of the root
       has been determined to within an error margin called the
       "convergence tolerance." The convergence tolerance used by this
       routine is set by the parameter SPICE_GF_CNVTOL.

       The value of SPICE_GF_CNVTOL is set to a "tight" value in the f2c'd
       routine so that the tolerance doesn't become the limiting factor
       in the accuracy of solutions found by this routine. In general the
       accuracy of input data will be the limiting factor.

       To use a different tolerance value, a lower-level GF routine such
       as gfevnt_c must be called. Making the tolerance tighter than
       SPICE_GF_CNVTOL is unlikely to be useful, since the results are unlikely
       to be more accurate. Making the tolerance looser will speed up
       searches somewhat, since a few convergence steps will be omitted.
       However, in most cases, the step size is likely to have a much
       greater effect on processing time than would the convergence
       tolerance.

       The Confinement Window
       ======================

       The simplest use of the confinement window is to specify a time
       interval within which a solution is sought. However, the
       confinement window can, in some cases, be used to make searches
       more efficient. Sometimes it's possible to do an efficient search
       to reduce the size of the time period over which a relatively
       slow search of interest must be performed.

       Negative Angular Separation
       ===========================

       For those searches using a SPHERE shape identifier for both
       target bodies, the angular separation function returns a
       negative value when the bodies overlap (occult), e.g.
       a search for an ABSMIN of angular separation in a
       confinement window covering an occultation event will
       return the time when the apparent center of the
       occulting body passes closest to the apparent center of
       the occulted body.

       Elongation
       ===========================

       The angular separation of two targets as seen from an observer
       where one of those targets is the sun is known as elongation.
#### Examples
       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       The examples shown below require a "standard" set of SPICE
       kernels. We list these kernels in a meta kernel named 'standard.tm'.

          KPL/MK

                This meta-kernel is intended to support operation of SPICE
                example programs. The kernels shown here should not be
                assumed to contain adequate or correct versions of data
                required by SPICE-based user applications.

                In order for an application to use this meta-kernel, the
                kernels referenced here must be present in the user's
                current working directory.

                The names and contents of the kernels referenced
                by this meta-kernel are as follows:

                   File name                     Contents
                   ---------                     --------
                   de414.bsp                     Planetary ephemeris
                   pck00008.tpc                  Planet orientation and
                                                 radii
                   naif0008.tls                  Leapseconds

          \begindata

          KERNELS_TO_LOAD = ( '/kernels/gen/lsk/naif0008.tls'
                              '/kernels/gen/spk/de414.bsp'
                              '/kernels/gen/pck/pck00008.tpc'
                            )

       Example(1):

          Determine the times of local maxima of the angular separation
          between the moon and earth as observed from the sun from
          Jan 1, 2007 to Jan 1 2008.

          #include <stdio.h>
          #include <stdlib.h>
          #include <string.h>

          #include "SpiceUsr.h"

          #define       MAXWIN    1000
          #define       TIMFMT    "YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND"
          #define       TIMLEN   41

          int main( int argc, char **argv )
             {

             /.
             Create the needed windows. Note, one window
             consists of two values, so the total number
             of cell values to allocate equals twice
             the number of windows.
             ./
             SPICEDOUBLE_CELL ( result, 2*MAXWIN );
             SPICEDOUBLE_CELL ( cnfine, 2       );

             SpiceDouble       begtim;
             SpiceDouble       endtim;
             SpiceDouble       step;
             SpiceDouble       adjust;
             SpiceDouble       refval;
             SpiceDouble       beg;
             SpiceDouble       end;

             SpiceChar         begstr [ TIMLEN ];
             SpiceChar         endstr [ TIMLEN ];

             SpiceChar       * targ1  = "MOON";
             SpiceChar       * frame1 = "NULL";
             SpiceChar       * shape1 = "SPHERE";

             SpiceChar       * targ2  = "EARTH";
             SpiceChar       * frame2 = "NULL";
             SpiceChar       * shape2 = "SPHERE";

             SpiceChar       * abcorr = "NONE";
             SpiceChar       * relate = "LOCMAX";

             SpiceChar       * obsrvr = "SUN";

             SpiceInt          count;
             SpiceInt          i;

             /.
             Load kernels.
             ./
             furnsh_c( "standard.tm" );

             /.
             Store the time bounds of our search interval in
             the cnfine confinement window.
             ./
             str2et_c( "2007 JAN 01", &begtim );
             str2et_c( "2008 JAN 01", &endtim );

             wninsd_c ( begtim, endtim, &cnfine );

             /.
             Search using a step size of 6 days (in units of seconds).
             ./
             step   = 6.*spd_c();
             adjust = 0.;
             refval = 0.;

             /.
             List the beginning and ending points in each interval
             if result contains data.
             ./
             gfsep_c ( targ1,
                      shape1,
                      frame1,
                      targ2,
                      shape2,
                      frame2,
                      abcorr,
                      obsrvr,
                      relate,
                      refval,
                      adjust,
                      step,
                      MAXWIN,
                      &cnfine,
                      &result );

             count = wncard_c( &result );

             /.
             Display the results.
             ./
             if (count == 0 )
                {
                printf ( "Result window is empty.\n\n" );
                }
             else
                {
                for ( i = 0;  i < count;  i++ )
                   {

                   /.
                   Fetch the endpoints of the Ith interval
                   of the result window.
                   ./
                   wnfetd_c ( &result, i, &beg, &end );

                   timout_c ( beg, TIMFMT, TIMLEN, begstr );
                   timout_c ( end, TIMFMT, TIMLEN, endstr );

                   printf ( "Interval %d\n", i + 1);
                   printf ( "Beginning TDB %s \n", begstr );
                   printf ( "Ending TDB    %s \n", endstr );

                   }
                }

             kclear_c();
             return( 0 );
             }

          The program's partial output:

             Interval 1
             Beginning TDB 2007-JAN-11 11:21:20.213872 (TDB)
             Ending TDB    2007-JAN-11 11:21:20.213872 (TDB)

             Interval 2
             Beginning TDB 2007-JAN-26 01:43:41.029955 (TDB)
             Ending TDB    2007-JAN-26 01:43:41.029955 (TDB)

                ...

             Interval 24
             Beginning TDB 2007-DEC-17 04:04:46.935442 (TDB)
             Ending TDB    2007-DEC-17 04:04:46.935442 (TDB)

             Interval 25
             Beginning TDB 2007-DEC-31 13:43:52.558897 (TDB)
             Ending TDB    2007-DEC-31 13:43:52.558897 (TDB)

       Example(2):

          Determine the time of local maxima elongation of the
          Moon as seen from earth for the same time interval
          as the previous example:

          Edit the Example(1) program to use the assignments:

             SpiceChar       * targ1  = "MOON";
             SpiceChar       * targ2  = "SUN";
             SpiceChar       * obsrvr = "EARTH";

          The program's partial output:

             Interval 1
             Beginning TDB 2007-JAN-03 14:20:24.618884 (TDB)
             Ending TDB    2007-JAN-03 14:20:24.618884 (TDB)

             Interval 2
             Beginning TDB 2007-FEB-02 06:16:24.101655 (TDB)
             Ending TDB    2007-FEB-02 06:16:24.101655 (TDB)

                ...

             Interval 12
             Beginning TDB 2007-NOV-24 14:31:04.334590 (TDB)
             Ending TDB    2007-NOV-24 14:31:04.334590 (TDB)

             Interval 13
             Beginning TDB 2007-DEC-24 01:40:12.238389 (TDB)
             Ending TDB    2007-DEC-24 01:40:12.238389 (TDB)
#### Restrictions
       1) The kernel files to be used by this routine must be loaded
          (normally via the CSPICE routine furnsh_c) before this routine
          is called.

       2) This routine has the side effect of re-initializing the
          angular separation quantity utility package.  Callers may
          need to re-initialize the package after calling this routine.

       3) Due to the current logic implemented in zzgfspu, a direct
          search for zero angular separation of two point targets will
          always fails, i.e.,

               'relate' has value "="
               'refval' has value 0.

            Use 'relate' values of "ABSMIN" or "LOCMIN" to detect such an event(s).
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman   (JPL)
       E.D. Wright    (JPL)
#### Version
       -CSPICE Version 1.0.0, 10-FEB-2009 (NJB) (EDW)
#### Index_Entries
       GF angular separation search
#### Link to routine gfsep_c source file gfsep_c.c

    Thu Apr 16 08:58:15 2009