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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_EDTERM computes a set of points on the umbral or penumbral
   terminator of a specified target body, where the target shape is modeled
   as an ellipsoid.

I/O


   Given:

      trmtyp   string indicating the type of terminator to
               compute: umbral or penumbral. The umbral terminator is
               the boundary of the portion of the ellipsoid surface in
               total shadow. The penumbral terminator is the boundary
               of the portion of the surface that is completely
               illuminated. Note that in astronomy references, the
               unqualified word "terminator" refers to the umbral
               terminator. Here, the unqualified word refers to either
               type of terminator.

               Possible values of 'trmtyp' are

                  'UMBRAL'
                  'PENUMBRAL'

               Case and leading or trailing blanks in 'trmtyp' are
               not significant.

               [1,c1] = size(trmtyp); char = class(trmtyp)

      source   string name of the body acting as a light source.
               'source' is case-insensitive, and leading and trailing
               blanks in 'target' are not significant. Optionally, you
               may supply a string containing the integer ID code for
               the object. For example both "SUN" and "10" are
               legitimate strings that indicate the Sun is the light
               source.

               This routine assumes that a kernel variable representing
               the light source's radii is present in the kernel pool.
               Normally the kernel variable would be defined by loading
               a PCK file.

               The shape of the light source is always modeled as a
               sphere, regardless of whether radii defining a triaxial
               ellipsoidal shape model are available in the kernel
               pool. The maximum radius of the body is used as the
               radius of the sphere.

               [1,c2] = size(source); char = class(source)

      target   string name of the target body. 'target' is
               case-insensitive, and leading and trailing blanks in
               'target' are not significant. Optionally, you may supply
               a string containing the integer ID code for the object.
               For example both "MOON" and "301" are legitimate strings
               that indicate the moon is the target body.

               This routine assumes that a kernel variable representing
               the target's radii is present in the kernel pool.
               Normally the kernel variable would be defined by loading
               a PCK file.

               [1,c3] = size(target); char = class(target)

      et       epoch of participation of the observer, expressed
               as ephemeris seconds past J2000 TDB: 'et' is the epoch
               at which the observer's position is computed.

               When aberration corrections are not used, 'et' is also
               the epoch at which the position and orientation of the
               target body and position of the light source are
               computed.

               When aberration corrections are used, 'et' is the epoch
               at which the observer's position relative to the solar
               system barycenter is computed; in this case the position
               and orientation of the target body are computed at
               et-lt, where lt is the one-way light time between the
               target body's center and the observer. See the
               description of 'abcorr' below for details.

               [1,1] = size(et); double = class(et)

      fixref   string name of the reference frame relative to
               which the output terminator points are expressed. This must
               be a body-centered, body-fixed frame associated with the
               target. The frame's axes must be compatible with the
               triaxial ellipsoidal shape model associated with the
               target body (normally provide via a PCK): this routine
               assumes that the first, second, and third axis lengths
               correspond, respectively, to the x, y, and z-axes of the
               frame designated by 'fixref'.

               'fixref' may refer to a built-in frame (documented in
               the Frames Required Reading) or a frame defined by a
               loaded frame kernel (FK).

               The orientation of the frame designated by 'fixref' is
               evaluated at epoch of participation of the target body.
               See the descriptions of 'et' and 'abcorr' for details.

               [1,c4] = size(fixref); char = class(fixref)

      abcorr   string indicating the aberration correction to be
               applied when computing the observer-target position, the
               orientation of the target body, and the target-
               source position vector. 'abcorr' may be any of
               the following.

                  'NONE'     Apply no correction. Compute the
                             terminator points using the position
                             of the light source and target, and
                             the orientation of the target, at 'et'.

               Let 'lt' represent the one-way light time between the
               observer and the target body's center. The following
               values of 'abcorr' apply to the "reception" case in
               which photons depart from the target body's center at
               the light-time corrected epoch et-lt and *arrive* at
               the observer's location at 'et':


                  'LT'       Correct for one-way light time (also
                             called "planetary aberration") using a
                             Newtonian formulation. This correction
                             yields the location of the terminator
                             points at the approximate time they
                             emitted photons arriving at the
                             observer at 'et' (the difference between
                             light time to the target center and
                             light time to the terminator points
                             is ignored).

                             The light time correction uses an
                             iterative solution of the light time
                             equation. The solution invoked by the
                             'LT' option uses one iteration.

                             The target position as seen by the
                             observer, the position of the light
                             source as seen from the target at
                             et-lt, and the rotation of the target
                             body, are corrected for light time.

                  'LT+S'     Correct for one-way light time and
                             stellar aberration using a Newtonian
                             formulation. This option modifies the
                             positions obtained with the 'LT' option
                             to account for the observer's velocity
                             relative to the solar system
                             barycenter. This correction also
                             applies to the position of the light
                             source relative to the target. The
                             result is the apparent terminator as
                              seen by the observer.

                  'CN'       Converged Newtonian light time
                             correction. In solving the light time
                             equation, the 'CN' correction iterates
                             until the solution converges. The
                             position and rotation of the target
                             body and the position of the light
                             source relative to the target are
                             corrected for light time.

                  'CN+S'     Converged Newtonian light time
                             and stellar aberration corrections.

               [1,c5] = size(abcorr); char = class(abcorr)

      obsrvr   string name of the observing body. This is typically
               a spacecraft, the Earth, or a surface point on the
               Earth. 'obsrvr' is case-insensitive, and leading and
               trailing blanks in 'obsrvr' are not significant.
               Optionally, you may supply a string containing the
               integer ID code for the object. For example both
               'EARTH' and '399' are legitimate strings that indicate
               the Earth is the observer.

               [1,c5] = size(obsrvr); char = class(obsrvr)

      npts     number of terminator points to compute.

               [1,1] = size(npts); int32 = class(npts)

   the call:

     [ trgepc, obspos, termpts] = cspice_edterm( trmtyp, source, ...
                                                 target, et,     ...
                                                 fixfrm, abcorr, ...
                                                 obsrvr, npts)

   returns:

      trgepc   the "target epoch" of the calculation. 'trgepc' is
               defined as follows: letting 'lt' be the one-way light
               time between the target center and observer, 'trgepc' is
               either the epoch et-lt or 'et' depending on whether the
               requested aberration correction is, respectively, for
               received radiation or omitted. 'lt' is computed using the
               method indicated by 'abcorr'.

               'trgepc' is expressed as seconds past J2000 TDB.

               [1,1] = size(trgepc); double = class(trgepc)

      obspos   position vector from the center of the target body
               at epoch 'trgepc' to the observer at epoch 'et'. 'obspos' is
               expressed in the target body-fixed reference frame
               'fixref', which is evaluated at 'trgepc'.

               'obspos' is returned to simplify various related
               computations that would otherwise be cumbersome. For
               example, the vector 'xvec' from the observer to the
               ith terminator point can be calculated via the call

                  xvec = trmpts(*,i) - obspos

               To transform the vector 'obspos' from a reference frame
               'fixref' at time 'trgepc' to a time-dependent reference
               frame 'ref' at time 'et', the routine pxfrm2_c should be
               called. Let 'xform' be the 3x3 matrix representing the
               rotation from the reference frame 'fixref' at time
               'trgepc' to the reference frame 'ref' at time 'et'. Then
               'obspos' can be transformed to the result 'refvec' as
               follows:

                   xform  = cspice_pxfrm2( fixref, ref, trgepc, et )
                   refvec = xform*obspos

               [3,1] = size(obspos); double = class(obspos)

      trmpts   array of points on the umbral or penumbral terminator
               of the ellipsoid, as specified by the input argument
               'trmtyp'. The ith point is contained in the array

                   pos_i = trmpts(*,i)

               Each terminator point is the point of tangency of a
               plane that is also tangent to the light source. These
               associated points of tangency on the light source have
               uniform distribution in longitude when expressed in a
               cylindrical coordinate system whose Z-axis is the target
               center to source center vector. The magnitude of the
               separation in longitude between the tangency points on
               the light source is

                  2*pi / npts

               If the target is spherical, the terminator points
               also are uniformly distributed in longitude in the
               cylindrical system described above. If the target is
               non-spherical, the longitude distribution of the
               points generally is not uniform.

               The terminator points are expressed in the body-fixed
               reference frame designated by 'fixref'. Units are km.

               [3,npts] = size(trmpts); double = class(trmpts)

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

      Use the meta-kernel shown below to load the required SPICE
      kernels.

         KPL/MK

         File name: standard.tm

         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
            ---------                     --------
            de421.bsp                     Planetary ephemeris
            pck00010.tpc                  Planet orientation and
                                          radii
            naif0010.tls                  Leapseconds

         \begindata

            KERNELS_TO_LOAD = ( 'de421.bsp',
                                'pck00010.tpc',
                                'naif0010.tls'  )

         \begintext

   Example:

      Compute sets of umbral and penumbral terminator points on the
      Moon. Perform a consistency check using the solar incidence
      angle at each point. We expect to see a solar incidence angle of
      approximately 90 degrees. Since the solar incidence angle is
      measured between the local outward normal and the direction to
      the center of the Sun, the solar incidence angle at an umbral
      terminator point should exceed 90 degrees by approximately the
      angular radius of the Sun, while the angle at a penumbral
      terminator points should be less than 90 degrees by that amount.

      META    = 'standard.tm';
      NPTS    =  3;
      first   = true;
      trmtyps = { 'UMBRAL', 'PENUMBRAL' };
      s       = [ -1, 1];
      R2D     = cspice_dpr();

      %
      % Load meta-kernel.
      %
      cspice_furnsh( META )

      %
      % Set observation time.
      %
      utc    = '2007 FEB 3 00:00:00.000';

      et = cspice_str2et( utc );

      %
      % Set participating objects, frame, and aberration
      % corrections.
      %
      obsrvr = 'EARTH';
      target = 'MOON';
      source = 'SUN';
      fixref = 'IAU_MOON';
      abcorr = 'LT+S';

      %
      % Look up the radii of the sun.
      %
      srcrad = cspice_bodvrd( source, 'RADII', 3 );

      %
      % Compute terminator points.
      %
      for trmidx=1:2

         [ trgepc, obspos, trmpts] = cspice_edterm(      ...
                        trmtyps(trmidx), source, target, ...
                        et,              fixref, abcorr, ...
                        obsrvr,          NPTS );

         %
         % Validate terminator points.
         %
         % Look up the target-sun vector at the light-time
         % corrected target epoch.
         %
         if ( first )
            [srcpos, ltime] = cspice_spkpos( source, trgepc, ...
                                             fixref, abcorr, ...
                                             target );

            first = false;
         end

         fprintf(' Terminator type: %s\n', char(trmtyps(trmidx)) )

         for i = 1:NPTS

            %
            % Convert the ith terminator point to latitudinal
            % coordinates. Display the point.
            %
            [radius, lon, lat] = cspice_reclat( trmpts(:,i) );

            fprintf('Terminator point :%d\n', i )
            fprintf('  Radius                     (km):  %f\n', radius)
            fprintf('  Planetocentric longitude   (deg): %f\n', lon *R2D)
            fprintf('  Planetocentric latitude    (deg): %f\n', lat *R2D)

            %
            % Find the illumination angles at the
            % ith terminator point.
            %
            [trgepc, srfvec, phase, solar, emissn] = ...
                                     cspice_ilumin( 'Ellipsoid', ...
                                            target, et,          ...
                                            fixref, abcorr,      ...
                                            obsrvr, trmpts(:,i) );

            fprintf('  Solar incidence angle      (deg): %f\n', solar *R2D)


            %
            % Find the angular radius of the Sun as seen from
            % the terminator point.
            %
            angrad = asin( srcrad(1)/cspice_vdist( srcpos, trmpts(:,i)) );


            %
            % Display the solar incidence angle after
            % adjusting the angular radius of the Sun
            % as seen from the terminator point.The
            % result should be approximately 90 degrees.
            %
            fprintf('  Solar incidence angle adjusted for\n' )
            fprintf('  sun''s angular radius (deg): %18.9f\n\n', ...
                         ( solar + ( s(trmidx)*angrad ) ) *R2D)

         end

      end

      %
      % It's always good form to unload kernels after use,
      % particularly in IDL due to data persistence.
      %
      cspice_kclear

   MATLAB outputs:

       Terminator type: UMBRAL
      Terminator point :1
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): -95.084553
        Planetocentric latitude    (deg): 0.004053
        Solar incidence angle      (deg): 90.269766
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000125

      Terminator point :2
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): 84.228092
        Planetocentric latitude    (deg): 59.995756
        Solar incidence angle      (deg): 90.269766
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000019

      Terminator point :3
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): 87.216418
        Planetocentric latitude    (deg): -59.979551
        Solar incidence angle      (deg): 90.269766
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000043

       Terminator type: PENUMBRAL
      Terminator point :1
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): 84.914101
        Planetocentric latitude    (deg): -0.004073
        Solar incidence angle      (deg): 89.730234
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000122

      Terminator point :2
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): -95.769216
        Planetocentric latitude    (deg): -59.995785
        Solar incidence angle      (deg): 89.730234
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000021

      Terminator point :3
        Radius                     (km):  1737.400000
        Planetocentric longitude   (deg): -92.780892
        Planetocentric latitude    (deg): 59.979499
        Solar incidence angle      (deg): 89.730234
        Solar incidence angle adjusted for
        sun's angular radius (deg):       90.000000044

Particulars


   This routine models the boundaries of shadow regions on an
   ellipsoidal target body "illuminated" by a spherical light
   source. Light rays are assumed to travel along straight lines;
   refraction is not modeled.

   Points on the target body's surface are classified according to
   their illumination as follows:

      -  A target surface point X for which no vector from X to any
         point in the light source intersects the target, except at
         X, is considered to be "completely illuminated."

      -  A target surface point X for which each vector from X to a
         point in the light source intersects the target at points
         other than X is considered to be "in total shadow."

      -  All other target points are considered to be in partial
         shadow.

   In this routine, we use the term "umbral terminator" to denote
   the curve usually called the "terminator": this curve is the
   boundary of the portion of the target body's surface that lies in
   total shadow. We use the term "penumbral terminator" to denote
   the boundary of the completely illuminated portion of the
   surface.

   In general, the terminator on an ellipsoid is a more complicated
   curve than the limb (which is always an ellipse). Aside from
   various special cases, the terminator does not lie in a plane.

   However, the condition for a point X on the ellipsoid to lie on
   the terminator is simple: a plane tangent to the ellipsoid at X
   must also be tangent to the light source. If this tangent plane
   does not intersect the vector from the center of the ellipsoid to
   the center of the light source, then X lies on the umbral
   terminator; otherwise X lies on the penumbral terminator.

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine edterm_c.

   MICE.REQ

Version


   -Mice Version 1.0.0, 18-JUN-2012, EDW (JPL)

Index_Entries


   find terminator on ellipsoid
   find umbral terminator on ellipsoid
   find penumbral terminator on ellipsoid


Wed Apr  5 18:00:31 2017