 
In-situ Sensing Hands-On Lesson, using BepiColombo MPO (MATLAB)
===========================================================================
 
   March 01, 2023
 
 
Overview
--------------------------------------------------------
 
   In this lesson you will develop a simple program illustrating how SPICE
   can be used to compute various kinds of geometry information applicable
   to the experiments carried out by an in-situ instrument flown on an
   interplanetary spacecraft.
 
 
Note About HTML Links
--------------------------------------------------------
 
   The HTML version of this lesson contains links pointing to various HTML
   documents provided with the Toolkit. All of these links are relative
   and, in order to function, require this document to be in a certain
   location in the Toolkit HTML documentation directory tree.
 
   In order for the links to be resolved, if not done already by installing
   the lessons package under the Toolkit's ``doc/html'' directory, create a
   subdirectory called ``lessons'' under the ``doc/html'' directory of the
   ``mice/'' tree and copy this document to that subdirectory before
   loading it into a Web browser.
 
 
References
--------------------------------------------------------
 
   This section lists SPICE documents referred to in this lesson.
 
   Of these documents, the ``Tutorials'' contains the highest level
   descriptions with the least number of details while the ``Required
   Reading'' documents contain much more detailed specifications. The most
   complete specifications are provided in the ``API Documentation''.
 
   In some cases the lesson explanations also refer to the information
   provided in the meta-data area of the kernels used in the lesson
   examples. It is especially true in case of the FK and IK files, which
   often contain comprehensive descriptions of the frames, instrument FOVs,
   etc. Since both FK and IK are text kernels, the information provided in
   them can be viewed using any text editor, while the meta information
   provided in binary kernels -- SPKs and CKs -- can be viewed using
   ``commnt'' or ``spacit'' utility programs located in ``mice/exe'' of
   Toolkit installation tree.
 
 
Tutorials
 
   The following SPICE tutorials serve as references for the discussions in
   this lesson:
 
 
      Name              Lesson steps/functions it describes
      ----------------  -----------------------------------------------
      Time              UTC to ET and SCLK to ET
      Loading Kernels   Loading SPICE kernels
      SCLK              SCLK to ET time conversion
      SPK               Computing positions and velocities
      Frames            Computing transformations between frames
 
   These tutorials are available from the NAIF server at JPL:
 
      http://naif.jpl.nasa.gov/naif/tutorials.html
 
 
Required Readings
 
   The Required Reading documents are provided with the Toolkit and are
   located under the ``mice/doc'' directory in the Mice installation tree.
 
      Name             Lesson steps/functions that it describes
      ---------------  -----------------------------------------
      kernel.req       Loading SPICE kernels
      naif_ids.req     Body and reference frame names
      spk.req          Computing positions and velocities
      sclk.req         SCLK to ET time conversion
      time.req         UTC to ET time conversion
      mice.req         The Mice API
 
 
The Permuted Index
 
   Another useful document distributed with the Toolkit is the permuted
   index. It is located under the ``mice/doc'' directory in the MATLAB
   installation tree.
 
   This text document provides a simple mechanism by which users can
   discover which Mice functions perform functions of interest, as well as
   the names of the source files that contain these functions.
 
 
 
Mice API Documentation
 
   A Mice routine's specification is found in the HTML API documentation
   page located under ``mice/doc/html/mice''.
 
   For example, the document
 
      mice/doc/html/mice/cspice_str2et.html
 
   describes the cspice_str2et routine.
 
 
Kernels Used
--------------------------------------------------------
 
   The following kernels are used in examples provided in this lesson:
 
      1.  Generic LSK:
 
             naif0012.tls
 
      2.  BepiColombo MPO SCLK:
 
             bc_mpo_step_20230117.tsc
 
      3.  Solar System Ephemeris SPK, subsetted to cover only the time
          range of interest:
 
             de432s.bsp
 
      4.  BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover
          only the time range of interest:
 
             bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
      5.  BepiColombo MPO FK:
 
             bc_mpo_v32.tf
 
      6.  BepiColombo MPO Spacecraft CK, subsetted to cover only the time
          range of interest:
 
             bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
      7.  Generic PCK:
 
             pck00011.tpc
 
 
   These SPICE kernels are included in the lesson package.
 
 
Mice Modules Used
--------------------------------------------------------
 
   This section provides a complete list of the functions and kernels that
   are suggested for usage in each of the exercises in this lesson. (You
   may wish to not look at this list unless/until you ``get stuck'' while
   working on your own.)
 
      CHAPTER EXERCISE   FUNCTIONS      NON-VOID       KERNELS
      ------- ---------  -------------  -------------  ----------
         1    convrt     cspice_furnsh  cspice_str2et  1
                         cspice_unload
 
         2    sclket     cspice_furnsh  cspice_str2et  1,2
                         cspice_unload  cspice_scs2e
 
         3    getsta     cspice_furnsh  cspice_str2et  1-4
                         cspice_unload  cspice_scs2e
                                        cspice_spkezr
 
         4    soldir     cspice_furnsh  cspice_str2et  1-6
                         cspice_unload  cspice_scs2e
                                        cspice_spkezr
                                        cspice_spkpos
 
         5    sscpnt     cspice_furnsh  cspice_str2et  1-7
                         cspice_unload  cspice_scs2e
                                        cspice_spkezr
                                        cspice_spkpos
                                        cspice_subpnt
                                        cspice_reclat
                                        cspice_pxform
                                        cspice_dpr
 
         6    scvel      cspice_furnsh  cspice_str2et  1-7
                         cspice_unload  cspice_scs2e
                                        cspice_spkezr
                                        cspice_spkpos
                                        cspice_subpnt
                                        cspice_reclat
                                        cspice_pxform
                                        cspice_dpr
 
   Refer to the Mice HTML API documentation pages located under
   ``mice/doc/html/mice'' for detailed interface specifications of these
   functions.
 
 
Step-1: ``UTC to ET''
===========================================================================
 
 
``UTC to ET'' Task Statement
--------------------------------------------------------
 
   Write a program that computes and prints the Ephemeris Time (ET)
   corresponding to ``2027 JAN 05 02:04:36'' UTC, as the number of
   ephemeris seconds past J2000, .
 
 
``UTC to ET'' Hints
--------------------------------------------------------
 
   Find out what SPICE kernel(s) is(are) needed to support this conversion.
   Reference the ``time.req'' and/or ``Time'' tutorial.
 
   Find out what routine should be called to load necessary kernel(s).
   Reference the ``kernel.req'' and/or ``Loading Kernels'' tutorial.
 
   Find the ``loader'' routine calling sequence specification. Look at the
   ``time.req'' and that routine's source code header. This routine may be
   an entry point, in which case there will be no source file with the same
   name. To find out in which source file this entry point is, search for
   its name in the ``Permuted Index''.
 
   Find the routine(s) used to convert time between UTC and ET. Look at the
   ``time.req'' and/or ``Time'' tutorial.
 
   Find the ``converter'' routine(s) calling sequence specification. Look
   in the ``time.req'' and the routine's source code header.
 
   Put all calls together in a program, add variable declarations (the
   routine header's ``Declarations'' and ``Examples'' sections are a good
   place to look for declaration specification and examples) and output
   print statements.
 
 
``UTC to ET'' Solution Steps
--------------------------------------------------------
 
   Only one kernel file is needed to support this conversion -- an LSK file
   ``naif0012.tls''.
 
   As any other SPICE kernel this file can be loaded by the cspice_furnsh
   routine. For that, the name of the file can be provided as a sole
   argument of this routine:
 
      ...
      lskfle =  'naif0012.tls';
 
      cspice_furnsh( lskfle )
 
   or it can be listed in a meta-kernel:
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
 
                        )
 
      \begintext
 
   the name of which, let's call it ``convrt.tm'', can be then provided as
   a sole argument of the cspice_furnsh routine:
 
         mkfile  =  'convrt.tm';
         cspice_furnsh( mkfile )
 
   While the second option seems to involve a bit more work -- it requires
   making an extra file -- it is a much better way to go if you plan to
   load more kernels as you extend the program. With the meta-kernel
   approach simply adding more kernels to the list in KERNEL_TO_LOAD
   without changing the program code will accomplish that.
 
   The highest level Mice time routine converting UTC to ET is
   cspice_str2et (``mice/doc/html/mice/cspice_str2et.html'').
 
   It has two arguments -- input time string representing UTC in a variety
   of formats (see cspice_str2et header's section ``Particulars'' for the
   complete description of input time formats) and output DP number of ET
   seconds past J2000. A call to cspice_str2et converting a given UTC to ET
   could look like this:
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
   By combining cspice_furnsh and cspice_str2et calls and required
   declarations and by adding a simple print statement, one would get a
   complete program that prints ET for the given UTC epoch.
 
   Use of Mice calls in a MATLAB script requires the MATLAB search path
   include the Mice source, ``mice/src/mice'', and Mice library,
   ``mice/lib'', directories. Add those directories to the path using the
   ``addpath'' command.
 
   When you execute the script, ``convrt'', it produces the following
   output:
 
      >> convrt
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
 
 
``UTC to ET'' Code
--------------------------------------------------------
 
   Program ``convrt.m'':
 
      function convrt()
 
         mkfile  =  'convrt.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``convrt.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
 
                        )
 
      \begintext
 
 
Step-2: ``SCLK to ET''
===========================================================================
 
 
``SCLK to ET'' Task Statement
--------------------------------------------------------
 
   Extend the program from Step-1 to compute and print ET for the following
   BepiColombo MPO on-board clock epoch ``863834674:28127''.
 
 
``SCLK to ET'' Hints
--------------------------------------------------------
 
   Find out what additional (to those already loaded in Step-1) SPICE
   kernel(s) is(are) needed to support SCLK to ET conversion. Look at the
   ``sclk.req'' and/or ``SCLK'' tutorial.
 
   Modify the program or meta-kernel to load this(these) kernels.
 
   Find the routine(s) needed to convert time between SCLK and ET. Look at
   the ``sclk.req'' and/or ``Time'' and ``SCLK'' tutorials.
 
   Find the ``converter'' routine's calling sequence specification. Look in
   the ``sclk.req'' and the routine's source code header.
 
   Look at ``naif_ids.req'' and the comments in the additional kernel(s)
   that you have loaded for information on proper values of input arguments
   of this routine.
 
   Add calls to the ``converter'' routine(s), necessary variable
   declarations (the routine header's ``Declarations'' and ``Examples''
   sections are a good place to look for declaration specification and
   examples), and output print statements to the program.
 
 
``SCLK to ET'' Solution Steps
--------------------------------------------------------
 
   A BepiColombo MPO SCLK file is needed additionally to the LSK file
   loaded in the Step-1 to support this conversion.
 
   No code change is needed in the loading portion of the program if a
   meta-kernel approach was used in the Step-1. The program will load the
   file if it will be added to the list of kernels in the KERNELS_TO_LOAD
   variable:
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
 
                        )
 
      \begintext
 
   The highest level Mice routine converting SCLK to ET is cspice_scs2e
   (``mice/doc/html/mice/cspice_scs2e.html'').
 
   It has three arguments -- NAIF ID for BepiColombo MPO s/c (-121 as
   described by ``naif_ids.req'' document), input time string representing
   BepiColombo MPO SCLK, and output DP number of ET seconds past J2000. A
   call to cspice_str2et converting given SCLK to ET could look like this:
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
   By adding the cspice_scs2e call, required declarations and a simple
   print statement, one would get a complete program that prints ET for the
   given SCLK epoch.
 
   When you execute the script, ``sclket'', it produces the following
   output:
 
      >> sclket
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
      SCLK      = 863834674:28127
      ET        =     852386745.184037
 
 
``SCLK to ET'' Code
--------------------------------------------------------
 
   Program ``sclket.m'':
 
      function sclket()
 
         mkfile  =  'sclket.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
         fprintf( 'SCLK      = %s\n',     sclk );
         fprintf( 'ET        = %20.6f\n', et   );
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``sclket.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
 
                        )
 
      \begintext
 
 
Step-3: ``Spacecraft State''
===========================================================================
 
 
``Spacecraft State'' Task Statement
--------------------------------------------------------
 
   Extend the program from Step-2 to compute geometric state -- position
   and velocity -- of the BepiColombo MPO spacecraft with respect to the
   Sun in the Ecliptic frame at the epoch specified by SCLK time from
   Step-2.
 
 
``Spacecraft State'' Hints
--------------------------------------------------------
 
   Find out what additional (to those already loaded in Steps-1&2) SPICE
   kernel(s) is(are) needed to support state computation. Look at the
   ``spk.req'' and/or ``SPK'' tutorial.
 
   Verify that the kernels contain enough data to compute the state of
   interest. Use ``brief'' utility program located under ``toolkit/exe''
   directory for that.
 
   Modify the meta-kernel to load this(these) kernels.
 
   Determine the routine(s) needed to compute states. Look at the
   ``spk.req'' and/or ``SPK'' tutorial presentation.
 
   Find the the routine(s) calling sequence specification. Look in the
   ``spk.req'' and the routine's source code header.
 
   Reference the ``naif_ids.req'' and ``frames.req'' and the routine(s)
   header ``Inputs'' and ``Particulars'' sections to determine proper
   values of the input arguments of this routine.
 
   Add calls to the routine(s), necessary variable declarations and output
   print statements to the program.
 
 
``Spacecraft State'' Solution Steps
--------------------------------------------------------
 
   A BepiColombo MPO spacecraft trajectory SPK and generic planetary
   ephemeris SPK files are needed to support computation of the state of
   interest.
 
   The file names can be added to the meta-kernel to get them loaded into
   the program:
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/spk/de432s.bsp'
 
                        )
 
      \begintext
 
   The highest level Mice routine computing states is cspice_spkezr
   (``mice/doc/html/mice/cspice_spkezr.html'').
 
   We are interested in computing BepiColombo MPO position and velocity
   with respect to the Sun, therefore the target and observer names should
   be set to 'MPO' and 'Sun' (both names can be found in ``naif_ids.req'').
 
   The state should be in ecliptic frame, therefore the name of the frame
   in which the state should be computed is 'ECLIPJ2000' (see
   ``frames.req'' document.)
 
   Since we need only the geometric position, the `abcorr' argument of the
   routine should be set to 'NONE' (see aberration correction discussion in
   the (``mice/src/cspice/spkezr_c.c''). header).
 
   Putting it all together, we get:
 
         target = 'MPO';
         frame  = 'ECLIPJ2000';
         corrtn = 'NONE';
         observ = 'SUN';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
 
   When you execute the script, ``getsta'', it produces the following
   output:
 
      >> getsta
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
      SCLK      = 863834674:28127
      ET        =     852386745.184037
       X        =      23439067.896105
       Y        =     -62315194.638947
       Z        =      -7240868.738598
      VX        =            35.799323
      VY        =            18.151988
      VZ        =             0.890570
 
 
``Spacecraft State'' Code
--------------------------------------------------------
 
   Program ``getsta.m'':
 
      function getsta()
 
         mkfile  =  'getsta.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
         fprintf( 'SCLK      = %s\n',     sclk );
         fprintf( 'ET        = %20.6f\n', et   );
 
         target = 'MPO';
         frame  = 'ECLIPJ2000';
         corrtn = 'NONE';
         observ = 'SUN';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
 
         fprintf( ' X        = %20.6f\n', state(1) )
         fprintf( ' Y        = %20.6f\n', state(2) )
         fprintf( ' Z        = %20.6f\n', state(3) )
         fprintf( 'VX        = %20.6f\n', state(4) )
         fprintf( 'VY        = %20.6f\n', state(5) )
         fprintf( 'VZ        = %20.6f\n', state(6) )
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``getsta.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/spk/de432s.bsp'
 
                        )
 
      \begintext
 
 
Step-4: ``Sun Direction''
===========================================================================
 
 
``Sun Direction'' Task Statement
--------------------------------------------------------
 
   Extend the program from Step-3 to compute apparent direction of the Sun
   in the SERENA STROFIO +X Buffle frame at the epoch specified by SCLK
   time from Step-2.
 
 
``Sun Direction'' Hints
--------------------------------------------------------
 
   Determine the additional SPICE kernels needed to support the direction
   computation, knowing that they should provide the s/c and instrument
   frame orientation.
 
   Verify that the orientation data in the kernels have adequate coverage
   to support computation of the direction of interest. Use ``ckbrief''
   utility program located under ``toolkit/exe'' directory for that.
 
   Modify the meta-kernel to load this(these) kernels.
 
   Determine the proper input arguments for the cspice_spkpos call to
   calculate the direction (which is the position portion of the output
   state). Look through the Frames Kernel find the name of the frame to
   used.
 
   Add calls to the routine(s), necessary variable declarations and output
   print statements to the program.
 
 
``Sun Direction'' Solution Steps
--------------------------------------------------------
 
   A BepiColombo MPO spacecraft orientation CK file, providing s/c
   orientation with respect to an inertial frame, and BepiColombo MPO FK
   file, providing orientation of the SERENA STROFIO +X Buffle frame with
   respect to the s/c frame, are needed additionally to already loaded
   kernels to support computation of this direction.
 
   The file names can be added to the meta-kernel to get them loaded into
   the program:
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            5. BepiColombo MPO FK:
 
                  bc_mpo_v32.tf
 
            6. BepiColombo MPO Spacecraft CK, subsetted to cover only
               the time range of interest:
 
                  bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/de432s.bsp'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/fk/bc_mpo_v32.tf'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
 
                        )
 
      \begintext
 
   The same highest level Mice routine computing positions, cspice_spkpos,
   can be used to compute this direction.
 
   Since this is the direction of the Sun as seen from the s/c, the target
   argument should be set to 'Sun' and the observer argument should be set
   to 'MPO'. The name of the SERENA STROFIO +X Buffle frame is
   'MPO_SERENA_STROFIO+X', the definition and description of this frame are
   provided in the BepiColombo MPO FK file, ``bc_mpo_v32.tf''.
 
   Since the apparent, or ``as seen'', position is sought for, the `abcorr'
   argument of the routine should be set to 'LT+S' (see aberration
   correction discussion in the (``mice/src/cspice/spkpos_c.c'') header).
 
   Putting it all together, we get:
 
         target = 'SUN';
         frame  = 'MPO_SERENA_STROFIO+X';
         corrtn = 'LT+S';
         observ = 'MPO';
 
         [ sundir, ltime ] = cspice_spkpos( target, et, frame, ...
                                                corrtn, observ );
         sundir = sundir/norm(sundir);
 
   When you execute the script, ``soldir'', it produces the following
   output:
 
      >> soldir
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
      SCLK      = 863834674:28127
      ET        =     852386745.184037
       X        =      23439067.896105
       Y        =     -62315194.638947
       Z        =      -7240868.738598
      VX        =            35.799323
      VY        =            18.151988
      VZ        =             0.890570
      SUNDIR(X) =             0.711937
      SUNDIR(Y) =             0.549505
      SUNDIR(Z) =            -0.437252
 
 
``Sun Direction'' Code
--------------------------------------------------------
 
   Program ``soldir.m'':
 
      function soldir()
 
         mkfile  =  'soldir.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
         fprintf( 'SCLK      = %s\n',     sclk );
         fprintf( 'ET        = %20.6f\n', et   );
 
         target = 'MPO';
         frame  = 'ECLIPJ2000';
         corrtn = 'NONE';
         observ = 'SUN';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
 
         fprintf( ' X        = %20.6f\n', state(1) )
         fprintf( ' Y        = %20.6f\n', state(2) )
         fprintf( ' Z        = %20.6f\n', state(3) )
         fprintf( 'VX        = %20.6f\n', state(4) )
         fprintf( 'VY        = %20.6f\n', state(5) )
         fprintf( 'VZ        = %20.6f\n', state(6) )
 
         target = 'SUN';
         frame  = 'MPO_SERENA_STROFIO+X';
         corrtn = 'LT+S';
         observ = 'MPO';
 
         [ sundir, ltime ] = cspice_spkpos( target, et, frame, ...
                                                corrtn, observ );
         sundir = sundir/norm(sundir);
 
         fprintf( 'SUNDIR(X) = %20.6f\n', sundir(1) )
         fprintf( 'SUNDIR(Y) = %20.6f\n', sundir(2) )
         fprintf( 'SUNDIR(Z) = %20.6f\n', sundir(3) )
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``soldir.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            5. BepiColombo MPO FK:
 
                  bc_mpo_v32.tf
 
            6. BepiColombo MPO Spacecraft CK, subsetted to cover only
               the time range of interest:
 
                  bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/de432s.bsp'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/fk/bc_mpo_v32.tf'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
 
                        )
 
      \begintext
 
 
Step-5: ``Sub-Spacecraft Point''
===========================================================================
 
 
``Sub-Spacecraft Point'' Task Statement
--------------------------------------------------------
 
   Extend the program from Step-4 to compute planetocentric longitude and
   and latitude of the sub-spacecraft point on Mercury, and the direction
   from the spacecraft to that point in the SERENA STROFIO +X Buffle frame.
 
 
``Sub-Spacecraft Point'' Hints
--------------------------------------------------------
 
   Find the Mice routine that computes sub-observer point coordinates. Use
   ``Most Used Mice APIs'' or ``subpt'' cookbook program for that.
 
   Refer to the routine's header to determine the additional kernels needed
   for this direction computation. Modify the meta-kernel to load
   this(these) kernels.
 
   Determine the proper input arguments for the routine. Refer to the
   routine's header for that information.
 
   Convert the surface point Cartesian vector returned by this routine to
   latitudinal coordinates. Use ``Permuted Index'' to find the routine that
   does this conversion. Refer to the routine's header for input/output
   argument specifications.
 
   Since the Cartesian vector from the spacecraft to the sub-spacecraft
   point is computed in the Mercury body-fixed frame, it should be
   transformed into the instrument frame get the direction we are looking
   for. Refer to ``frames.req'' and/or ``Frames'' tutorial to determine the
   name of the routine computing transformations and use it to compute
   transformation from Mercury body-fixed to the SERENA STROFIO +X Buffle
   frame.
 
   Using ``Permuted Index'' find the routine that multiplies 3x3 matrix by
   3d vector and use it to rotate the vector to the instrument frame.
 
   Add calls to the routine(s), necessary variable declarations and output
   print statements to the program.
 
 
``Sub-Spacecraft Point'' Solution Steps
--------------------------------------------------------
 
   The cspice_subpnt routine (``mice/doc/html/icy/cspice_subpnt.html'') can
   be used to compute the sub-observer point and the vector from the
   observer to that point with a single call. To determine this point as
   the closest point on the Mercury ellipsoid, the `method' argument has to
   be set to 'NEAR POINT: ELLIPSOID'. For our case the `target' is
   'MERCURY', the target body-fixed frame is 'IAU_MERCURY', and the
   observer is 'MPO'.
 
   Since the s/c is close to Mercury, light time does not need to be taken
   into account and, therefore, the `abcorr' argument can be set to 'NONE'.
 
   In order for cspice_subpnt to compute the nearest point location, a PCK
   file containing Mercury radii has to be loaded into the program (see
   ``Files'' section of the routine's header.) All other files required for
   this computation are already being loaded by the program. With PCK file
   name added to it, the updated meta-kernel will look like this:
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            5. BepiColombo MPO FK:
 
                  bc_mpo_v32.tf
 
            6. BepiColombo MPO Spacecraft CK, subsetted to cover only
               the time range of interest:
 
                  bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
            7. Generic PCK:
 
                  pck00011.tpc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/de432s.bsp'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/fk/bc_mpo_v32.tf'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
      'kernels/pck/pck00011.tpc'
 
                        )
 
      \begintext
 
   The sub-spacecraft point Cartesian vector can be converted to
   planetocentric radius, longitude and latitude using the cspice_reclat
   routine (``mice/doc/html/mice/cspice_reclat.html'').
 
   The vector from the spacecraft to the sub-spacecraft point returned by
   cspice_subpnt has to be rotated from the body-fixed frame to the
   instrument frame. The name of the routine that computes 3x3 matrices
   rotating vectors from one frame to another is cspice_pxform
   (``mice/doc/html/mice/cspice_pxform.html'').
 
   In our case the `from' argument should be set to 'IAU_MERCURY' and the
   `to' argument should be set to 'MPO_SERENA_STROFIO+X'
 
   The vector should be then multiplied by this matrix to rotate it to the
   instrument frame.
 
   After applying the rotation, normalize the resultant vector by dividing
   the vector by its norm.
 
   For output the longitude and latitude angles returned by cspice_reclat
   in radians can be converted to degrees by multiplying by cspice_dpr
   function (``mice/doc/html/mice/cspice_dpr.html'').
 
   Putting it all together, we get:
 
         method = 'NEAR POINT: ELLIPSOID';
         target = 'MERCURY';
         frame  = 'IAU_MERCURY';
         corrtn = 'NONE';
         observ = 'MPO';
 
         [spoint, trgepc, srfvec] = cspice_subpnt( method, target, ...
                                            et, frame, corrtn, observ);
 
         [srad, slon, slat] = cspice_reclat( spoint );
 
         fromfr = 'IAU_MERCURY';
         tofr   = 'MPO_SERENA_STROFIO+X';
 
         m2imat = cspice_pxform( fromfr, tofr, et);
 
         sbpdir =  m2imat * srfvec;
         sbpdir = sbpdir/norm(sbpdir);
 
         fprintf( 'LON       = %20.6f\n', slon * cspice_dpr )
         fprintf( 'LAT       = %20.6f\n', slat * cspice_dpr )
 
   When you execute the script, ``sscpnt'', it produces the following
   output:
 
      >> sscpnt
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
      SCLK      = 863834674:28127
      ET        =     852386745.184037
       X        =      23439067.896105
       Y        =     -62315194.638947
       Z        =      -7240868.738598
      VX        =            35.799323
      VY        =            18.151988
      VZ        =             0.890570
      SUNDIR(X) =             0.711937
      SUNDIR(Y) =             0.549505
      SUNDIR(Z) =            -0.437252
      LON       =            17.944077
      LAT       =            31.521072
      SBPDIR(X) =            -1.000000
      SBPDIR(Y) =             0.000000
      SBPDIR(Z) =            -0.000864
 
 
``Sub-Spacecraft Point'' Code
--------------------------------------------------------
 
   Program ``sscpnt.m'':
 
      function sscpnt()
 
         mkfile  =  'sscpnt.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
         fprintf( 'SCLK      = %s\n',     sclk );
         fprintf( 'ET        = %20.6f\n', et   );
 
         target = 'MPO';
         frame  = 'ECLIPJ2000';
         corrtn = 'NONE';
         observ = 'SUN';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
 
         fprintf( ' X        = %20.6f\n', state(1) )
         fprintf( ' Y        = %20.6f\n', state(2) )
         fprintf( ' Z        = %20.6f\n', state(3) )
         fprintf( 'VX        = %20.6f\n', state(4) )
         fprintf( 'VY        = %20.6f\n', state(5) )
         fprintf( 'VZ        = %20.6f\n', state(6) )
 
         target = 'SUN';
         frame  = 'MPO_SERENA_STROFIO+X';
         corrtn = 'LT+S';
         observ = 'MPO';
 
         [ sundir, ltime ] = cspice_spkpos( target, et, frame, ...
                                                       corrtn, observ );
         sundir = sundir/norm(sundir);
 
         fprintf( 'SUNDIR(X) = %20.6f\n', sundir(1) )
         fprintf( 'SUNDIR(Y) = %20.6f\n', sundir(2) )
         fprintf( 'SUNDIR(Z) = %20.6f\n', sundir(3) )
 
         method = 'NEAR POINT: ELLIPSOID';
         target = 'MERCURY';
         frame  = 'IAU_MERCURY';
         corrtn = 'NONE';
         observ = 'MPO';
 
         [spoint, trgepc, srfvec] = cspice_subpnt( method, target, ...
                                            et, frame, corrtn, observ);
 
         [srad, slon, slat] = cspice_reclat( spoint );
 
         fromfr = 'IAU_MERCURY';
         tofr   = 'MPO_SERENA_STROFIO+X';
 
         m2imat = cspice_pxform( fromfr, tofr, et);
 
         sbpdir =  m2imat * srfvec;
         sbpdir = sbpdir/norm(sbpdir);
 
         fprintf( 'LON       = %20.6f\n', slon * cspice_dpr )
         fprintf( 'LAT       = %20.6f\n', slat * cspice_dpr )
         fprintf( 'SBPDIR(X) = %20.6f\n', sbpdir(1)         )
         fprintf( 'SBPDIR(Y) = %20.6f\n', sbpdir(2)         )
         fprintf( 'SBPDIR(Z) = %20.6f\n', sbpdir(3)         )
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``sscpnt.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            5. BepiColombo MPO FK:
 
                  bc_mpo_v32.tf
 
            6. BepiColombo MPO Spacecraft CK, subsetted to cover only
               the time range of interest:
 
                  bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
            7. Generic PCK:
 
                  pck00011.tpc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/de432s.bsp'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/fk/bc_mpo_v32.tf'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
      'kernels/pck/pck00011.tpc'
 
                        )
 
      \begintext
 
 
Step-6: ``Spacecraft Velocity''
===========================================================================
 
 
``Spacecraft Velocity'' Task Statement
--------------------------------------------------------
 
   Extend the program from Step-5 to compute the spacecraft velocity with
   respect to Mercury in the SERENA STROFIO +X Buffle frame.
 
 
``Spacecraft Velocity'' Hints
--------------------------------------------------------
 
   Compute velocity of the spacecraft with respect to Mercury in some
   inertial frame, for example J2000. Recall that velocity is the last
   three components of the state vector returned by cspice_spkezr.
 
   Since the velocity vector is computed in the inertial frame, it should
   be rotated to the instrument frame. Look at the previous step the
   routine that compute necessary rotation and rotate vectors.
 
   Add calls to the routine(s), necessary variable declarations and output
   print statements to the program.
 
 
``Spacecraft Velocity'' Solution Steps
--------------------------------------------------------
 
   All kernels required for computations in this step are already being
   loaded by the program, therefore, the meta-kernel does not need to be
   changed.
 
   The spacecraft velocity vector is the last three components of the state
   returned by cspice_spkezr. To compute velocity of BepiColombo MPO with
   respect to Mercury in the J2000 inertial frame the cspice_spkezr
   arguments should be set to 'MPO' (TARG), 'MERCURY' (OBS), 'J2000' (REF)
   and 'NONE' (ABCORR).
 
   The computed velocity vector has to be rotated from the J2000 frame to
   the instrument frame. The cspice_pxform routine used in the previous
   step can be used to compute the rotation matrix needed for that. In this
   case the frame name arguments should be set to 'J2000' (FROM) and
   'MPO_SERENA_STROFIO+X' (TO).
 
   As in the previous step the difference vector should be then multiplied
   by this rotation matrix. After applying the rotation, normalize the
   resultant vector by dividing the vector by its norm.
 
   Putting it all together, we get:
 
         target = 'MPO';
         frame  = 'J2000';
         corrtn = 'NONE';
         observ = 'MERCURY';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
         scvdir = state(4:6);
 
         fromfr = 'J2000';
         tofr   = 'MPO_SERENA_STROFIO+X';
         j2imat = cspice_pxform( fromfr, tofr, et );
 
         scvdir = j2imat * scvdir;
         scvdir = scvdir/norm(scvdir);
 
   When you execute the script, ``scvel'', it produces the following
   output:
 
      >> scvel
      UTC       = 2027 JAN 05 02:04:36
      ET        =     852386745.184031
      SCLK      = 863834674:28127
      ET        =     852386745.184037
       X        =      23439067.896105
       Y        =     -62315194.638947
       Z        =      -7240868.738598
      VX        =            35.799323
      VY        =            18.151988
      VZ        =             0.890570
      SUNDIR(X) =             0.711937
      SUNDIR(Y) =             0.549505
      SUNDIR(Z) =            -0.437252
      LON       =            17.944077
      LAT       =            31.521072
      SBPDIR(X) =            -1.000000
      SBPDIR(Y) =             0.000000
      SBPDIR(Z) =            -0.000864
      SCVDIR(X) =             0.105745
      SCVDIR(Y) =             0.000009
      SCVDIR(Z) =             0.994393
 
   Note that computing the spacecraft velocity in the instrument frame by a
   single call to cspice_spkezr by specifying 'MPO_SERENA_STROFIO+X' in the
   `ref' argument returns an incorrect result. Such computation will take
   into account the spacecraft angular velocity from the CK files, which
   should not be considered in this case.
 
 
``Spacecraft Velocity'' Code Program ``scvel.m'':
--------------------------------------------------------
 
      function scvel()
 
         mkfile  =  'scvel.tm';
         cspice_furnsh( mkfile )
 
         utc = '2027 JAN 05 02:04:36';
         et  = cspice_str2et( utc );
 
         fprintf( 'UTC       = %s\n',     utc );
         fprintf( 'ET        = %20.6f\n', et  );
 
         scid = -121;
         sclk = '863834674:28127';
         et   = cspice_scs2e( scid, sclk);
 
         fprintf( 'SCLK      = %s\n',     sclk );
         fprintf( 'ET        = %20.6f\n', et   );
 
         target = 'MPO';
         frame  = 'ECLIPJ2000';
         corrtn = 'NONE';
         observ = 'SUN';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
 
         fprintf( ' X        = %20.6f\n', state(1) )
         fprintf( ' Y        = %20.6f\n', state(2) )
         fprintf( ' Z        = %20.6f\n', state(3) )
         fprintf( 'VX        = %20.6f\n', state(4) )
         fprintf( 'VY        = %20.6f\n', state(5) )
         fprintf( 'VZ        = %20.6f\n', state(6) )
 
         target = 'SUN';
         frame  = 'MPO_SERENA_STROFIO+X';
         corrtn = 'LT+S';
         observ = 'MPO';
 
         [ sundir, ltime ] = cspice_spkpos( target, et, frame, ...
                                                corrtn, observ );
         sundir = sundir/norm(sundir);
 
         fprintf( 'SUNDIR(X) = %20.6f\n', sundir(1) )
         fprintf( 'SUNDIR(Y) = %20.6f\n', sundir(2) )
         fprintf( 'SUNDIR(Z) = %20.6f\n', sundir(3) )
 
         method = 'NEAR POINT: ELLIPSOID';
         target = 'MERCURY';
         frame  = 'IAU_MERCURY';
         corrtn = 'NONE';
         observ = 'MPO';
 
         [spoint, trgepc, srfvec] = cspice_subpnt( method, target, ...
                                            et, frame, corrtn, observ);
 
         [srad, slon, slat] = cspice_reclat( spoint );
 
         fromfr = 'IAU_MERCURY';
         tofr   = 'MPO_SERENA_STROFIO+X';
 
         m2imat = cspice_pxform( fromfr, tofr, et);
 
         sbpdir =  m2imat * srfvec;
         sbpdir = sbpdir/norm(sbpdir);
 
         fprintf( 'LON       = %20.6f\n', slon * cspice_dpr )
         fprintf( 'LAT       = %20.6f\n', slat * cspice_dpr )
         fprintf( 'SBPDIR(X) = %20.6f\n', sbpdir(1)         )
         fprintf( 'SBPDIR(Y) = %20.6f\n', sbpdir(2)         )
         fprintf( 'SBPDIR(Z) = %20.6f\n', sbpdir(3)         )
 
         target = 'MPO';
         frame  = 'J2000';
         corrtn = 'NONE';
         observ = 'MERCURY';
 
         [state, ltime] = cspice_spkezr( target, et, frame, ...
                                             corrtn, observ );
         scvdir = state(4:6);
 
         fromfr = 'J2000';
         tofr   = 'MPO_SERENA_STROFIO+X';
         j2imat = cspice_pxform( fromfr, tofr, et );
 
         scvdir = j2imat * scvdir;
         scvdir = scvdir/norm(scvdir);
 
         fprintf( 'SCVDIR(X) = %20.6f\n', scvdir(1)         )
         fprintf( 'SCVDIR(Y) = %20.6f\n', scvdir(2)         )
         fprintf( 'SCVDIR(Z) = %20.6f\n', scvdir(3)         )
 
         cspice_unload( mkfile )
 
   Meta-kernel file ``scvel.tm'':
 
      KPL/MK
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. BepiColombo MPO SCLK:
 
                  bc_mpo_step_20230117.tsc
 
            3. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            5. BepiColombo MPO FK:
 
                  bc_mpo_v32.tf
 
            6. BepiColombo MPO Spacecraft CK, subsetted to cover only
               the time range of interest:
 
                  bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc
 
            7. Generic PCK:
 
                  pck00011.tpc
 
      \begindata
 
      KERNELS_TO_LOAD = (
 
      'kernels/lsk/naif0012.tls'
      'kernels/sclk/bc_mpo_step_20230117.tsc'
      'kernels/spk/de432s.bsp'
      'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp'
      'kernels/fk/bc_mpo_v32.tf'
      'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc'
      'kernels/pck/pck00011.tpc'
 
                        )
 
      \begintext
 
