 
Remote Sensing Hands-On Lesson, using MPO (FORTRAN)
===========================================================================
 
   March 01, 2023
 
 
Overview
--------------------------------------------------------
 
   In this lesson you will develop a series of simple programs that
   demonstrate the usage of SPICE to compute a variety of different
   geometric quantities applicable to experiments carried out by a remote
   sensing instrument flown on an interplanetary spacecraft. This
   particular lesson focuses on a spectrometer flying on the BepiColombo
   MPO spacecraft, but many of the concepts are easily extended and
   generalized to other scenarios.
 
 
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
   ``toolkit/'' 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 the 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 ``toolkit/exe'' of
   Toolkit installation tree.
 
 
Tutorials
 
   The following SPICE tutorials serve as references for the discussions in
   this lesson:
 
      Name              Lesson steps/routines it describes
      ----------------  -----------------------------------------------
      Time              Time Conversion
      SCLK and LSK      Time Conversion
      SPK               Obtaining Ephemeris Data
      Frames            Reference Frames
      Using Frames      Reference Frames
      PCK               Planetary Constants Data
      CK                Spacecraft Orientation Data
      DSK               Detailed Target Shape (Topography) Data
 
   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 ``toolkit/doc'' directory in the SPICE Toolkit
   installation tree.
 
      Name             Lesson steps/routines that it describes
      ---------------  -----------------------------------------
      ck.req           Obtaining spacecraft orientation data
      dsk.req          Obtaining detailed body shape data
      frames.req       Using reference frames
      naif_ids.req     Determining body ID codes
      pck.req          Obtaining planetary constants data
      sclk.req         SCLK time conversion
      spk.req          Obtaining ephemeris data
      time.req         Time conversion
 
 
The Permuted Index
 
   Another useful document distributed with the Toolkit is the permuted
   index. It is located under the ``toolkit/doc'' directory in the FORTRAN
   installation tree.
 
   This text document provides a simple mechanism by which users can
   discover which SPICE routines perform functions of interest, as well as
   the names of the source files that contain these routines. It is
   particularly useful for FORTRAN programmers because some of the routines
   are entry points; the names of these routines do not translate directly
   into the name of the respective source files that contain them.
 
 
API Documentation
 
   The most detailed specification of a given SPICE FORTRAN routine is
   contained in the header section of its source code. The source code is
   distributed with the Toolkit and is located under the
   ``toolkit/src/spicelib'' path.
 
   For example the path of the source code of the STR2ET routine is
 
      toolkit/src/spicelib/str2et.for
 
   Since some of the FORTRAN routines are entry points they may be part of
   a source file that has different name. The ``Permuted Index'' document
   mentioned above can be used to locate the name of their source file.
 
 
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
 
      8.  Low-resolution Mercury DSK:
 
             mercury_lowres.bds
 
      9.  SIMBIO-SYS IK:
 
             bc_mpo_simbio-sys_v08.ti
 
 
   These SPICE kernels are included in the lesson package.
 
   In addition to these kernels, the extra credit exercises require the
   following kernels:
 
      #  FILE NAME       TYPE DESCRIPTION
      -- --------------- ---- ---------------------------------------------
      10 jup365_2027.bsp SPK  Generic Jovian Satellite Ephemeris SPK
 
   These SPICE kernels are available from the NAIF server at JPL, in the
   ``satellites/a_old_versions'' subdurectory:
 
      https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/
 
 
SPICE Modules Used
--------------------------------------------------------
 
   This section provides a complete list of the routines 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   ROUTINES   FUNCTIONS  KERNELS
      ------- ---------  ---------  ---------  ----------
         1    convtm     FURNSH                1,2
                         PROMPT
                         STR2ET
                         ETCAL
                         TIMOUT
                         SCE2S
 
              extra (*)  UNLOAD     UNITIM     1,2
                         SCT2E
                         ET2UTC
                         SCS2E
 
         2    getsta     FURNSH     VNORM      1,3,4
                         PROMPT
                         STR2ET
                         SPKEZR
                         SPKPOS
                         CONVRT
 
              extra (*)  KCLEAR                1,4,10
                         UNLOAD
 
         3    xform      FURNSH     VSEP       1-7
                         PROMPT
                         STR2ET
                         SPKEZR
                         SXFORM
                         MXVG
                         SPKPOS
                         PXFORM
                         MXV
                         CONVRT
 
              extra (*)  KCLEAR                1-7
                         UNLOAD
 
         4    subpts     FURNSH     VNORM      1,3-4,7,8
                         PROMPT
                         STR2ET
                         SUBPNT
                         SUBSLR
 
              extra (*)  KCLEAR     DPR        1,3-4,7,10
                         RECLAT
                         BODVRD
                         RECPGR
 
         5    fovint     FURNSH     DPR        1-9
                         PROMPT
                         STR2ET
                         GETFVN
                         MOVED
                         BODN2C
                         BYEBYE
                         SINCPT
                         RECLAT
                         ILLUMF
                         ET2LST
 
 
         (*) Additional APIs and kernels used in Extra Credit tasks.
 
   Refer to the headers of the various routines listed above, as detailed
   interface specifications are provided with the source code.
 
 
Time Conversion (convtm)
===========================================================================
 
 
Task Statement
--------------------------------------------------------
 
   Write a program that prompts the user for an input UTC time string,
   converts it to the following time systems and output formats:
 
       1.   Ephemeris Time (ET) in seconds past J2000
 
       2.   Calendar Ephemeris Time
 
       3.   Spacecraft Clock Time
 
   and displays the results. Use the program to convert "2027 JAN 05
   02:04:36" UTC into these alternate systems.
 
 
Learning Goals
--------------------------------------------------------
 
   Familiarity with the various time conversion and parsing routines
   available in the Toolkit. Exposure to source code headers and their
   usage in learning to call routines.
 
 
Approach
--------------------------------------------------------
 
   The solution to the problem can be broken down into a series of simple
   steps:
 
       --   Decide which SPICE kernels are necessary. Prepare a meta-kernel
            listing the kernels and load it into the program.
 
       --   Prompt the user for an input UTC time string.
 
       --   Convert the input time string into ephemeris time expressed as
            seconds past J2000 TDB. Display the result.
 
       --   Convert ephemeris time into a calendar format. Display the
            result.
 
       --   Convert ephemeris time into a spacecraft clock string. Display
            the result.
 
   You may find it useful to consult the permuted index, the headers of
   various source modules, and the ``Time Required Reading'' (time.req) and
   ``SCLK Required Reading'' (sclk.req) documents.
 
   When completing the ``calendar format'' step above, consider using one
   of two possible methods: ETCAL or TIMOUT.
 
 
Solution
--------------------------------------------------------
 
 
Solution Meta-Kernel
 
   The meta-kernel we created for the solution to this exercise is named
   'convtm.tm'. Its contents follow:
 
      KPL/MK
 
         This is the meta-kernel used in the solution of the ``Time
         Conversion'' task in the Remote Sensing Hands On Lesson.
 
         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
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
            PROGRAM CONVTM
 
            IMPLICIT NONE
 
      C
      C     Local Parameters
      C
      C     The name of the meta-kernel that lists the kernels
      C     to load into the program.
      C
            CHARACTER*(*)         METAKR
            PARAMETER           ( METAKR = 'convtm.tm' )
 
      C
      C     The spacecraft clock ID code for BepiColombo MPO.
      C
            INTEGER               SCLKID
            PARAMETER           ( SCLKID = -121 )
 
      C
      C     The length of various string variables.
      C
            INTEGER               STRLEN
            PARAMETER           ( STRLEN = 50 )
 
      C
      C     Local Variables
      C
            CHARACTER*(STRLEN)    CALET
            CHARACTER*(STRLEN)    SCLKST
            CHARACTER*(STRLEN)    UTCTIM
 
            DOUBLE PRECISION      ET
 
      C
      C     Load the kernels this program requires.
      C     Both the spacecraft clock kernel and a
      C     leapseconds kernel should be listed
      C     in the meta-kernel.
      C
            CALL FURNSH ( METAKR )
 
      C
      C     Prompt the user for the input time string.
      C
            CALL PROMPT ( 'Input UTC Time: ', UTCTIM )
 
            WRITE (*,*) 'Converting UTC Time: ', UTCTIM
 
      C
      C     Convert UTCTIM to ET.
      C
            CALL STR2ET ( UTCTIM, ET )
 
            WRITE (*,'(A,F16.3)') '   ET Seconds Past J2000: ', ET
 
      C
      C     Now convert ET to a formal calendar time
      C     string.  This can be accomplished in two
      C     ways.
      C
            CALL ETCAL ( ET, CALET )
 
            WRITE (*,*) '   Calendar ET (ETCAL): ', CALET
 
      C
      C     Or use TIMOUT for finer control over the
      C     output format.  The picture below was built
      C     by examining the header of TIMOUT.
      C
            CALL TIMOUT ( ET, 'YYYY-MON-DDTHR:MN:SC ::TDB', CALET )
 
            WRITE (*,*) '   Calendar ET (TIMOUT): ', CALET
 
      C
      C     Convert ET to spacecraft clock time.
      C
            CALL SCE2S ( SCLKID, ET, SCLKST )
 
            WRITE (*,*) '   Spacecraft Clock Time: ', SCLKST
 
            END
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Input UTC Time: 2027 JAN 05 02:04:36
       Converting UTC Time: 2027 JAN 05 02:04:36
         ET Seconds Past J2000:    852386745.184
          Calendar ET (ETCAL): 2027 JAN 05 02:05:45.184
          Calendar ET (TIMOUT): 2027-JAN-05T02:05:45
          Spacecraft Clock Time: 1/0863834674:28127
 
 
Extra Credit
--------------------------------------------------------
 
   In this ``extra credit'' section you will be presented with more complex
   tasks, aimed at improving your understanding of time conversions, the
   Toolkit routines that deal with them, and some common errors that may
   happen during the execution of these conversions.
 
   These ``extra credit'' tasks are provided as task statements, and unlike
   the regular tasks, no approach or solution source code is provided. In
   the next section, you will find the numeric solutions (when applicable)
   and answers to the questions asked in these tasks.
 
 
Task statements and questions
 
       1.   Extend your program to convert the input UTC time string to TDB
            Julian Date. Convert "2027 JAN 05 02:04:36" UTC.
 
       2.   Remove the LSK from the original meta-kernel and run your
            program again, using the same inputs as before. Has anything
            changed? Why?
 
       3.   Remove the SCLK from the original meta-kernel and run your
            program again, using the same inputs as before. Has anything
            changed? Why?
 
       4.   Modify your program to perform conversion of UTC or ephemeris
            time, to a spacecraft clock string using the NAIF ID for the
            BepiColombo MPO SIMBIO-SYS HRIC channel. Convert "2027 JAN 05
            02:04:36" UTC.
 
       5.   Find the earliest UTC time that can be converted to BepiColombo
            MPO spacecraft clock.
 
       6.   Extend your program to convert the spacecraft clock time
            obtained in the regular task back to UTC Time and present it in
            ISO calendar date format, with a resolution of milliseconds.
 
       7.   Examine the contents of the generic LSK and the BepiColombo MPO
            SCLK kernels. Can you understand and explain what you see?
 
 
Solutions and answers
 
       1.   Two methods exist in order to convert ephemeris time to Julian
            Date: UNITIM and TIMOUT. The difference between them is the
            type of output produced by each method. UNITIM returns the
            double precision value of an input epoch, while TIMOUT returns
            the string representation of the ephemeris time in Julian Date
            format (when picture input is set to 'JULIAND.#########
            ::TDB'). Refer to the routine header for further details. The
            solution for the requested input UTC string is:
 
         Julian Date TDB:   2461410.5873285
 
       2.   When running the original program without the LSK kernel, an
            error is produced:
 
 
      =====================================================================
      ===========
 
      Toolkit version: N0067
 
      SPICE(NOLEAPSECONDS) --
 
      The variable that points to the leapseconds (DELTET/DELTA_AT) could n
      ot be
      located in the kernel pool. It is likely that the leapseconds kernel
      has not
      been loaded.
 
      A traceback follows.  The name of the highest level module is first.
      STR2ET --> TTRANS
 
      Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
      BLE.  You
      can choose whether the Toolkit aborts or continues when errors occur,
       which
      error messages to output, and where to send the output.  Please read
      the ERROR
      "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
      RT.
 
      =====================================================================
      ===========
 
            This error is triggered by STR2ET because the variable that
            points to the leapseconds is not present in the kernel pool and
            therefore the program lacks data required to perform the
            requested UTC to ephemeris time conversion.
 
            By default, SPICE will report, as a minimum, a short
            descriptive message and a expanded form of this short message
            where more details about the error are provided. If this error
            message is not sufficient for you to understand what has
            happened, you could go to the ``Exceptions'' section in the
            SPICELIB or CSPICE headers of the routine that has triggered
            the error and find out more information about the possible
            causes.
 
       3.   When running the original program without the SCLK kernel, an
            error is produced:
 
 
      =====================================================================
      ===========
 
      Toolkit version: N0067
 
      SPICE(KERNELVARNOTFOUND) -- The Variable Was not Found in the Kernel
      Pool.
 
      Kernel variable SCLK_DATA_TYPE_121 was not found in the kernel pool.
 
      A traceback follows.  The name of the highest level module is first.
      SCE2S --> SCE2T --> SCTYPE --> SCTY01
 
      Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
      BLE.  You
      can choose whether the Toolkit aborts or continues when errors occur,
       which
      error messages to output, and where to send the output.  Please read
      the ERROR
      "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
      RT.
 
      =====================================================================
      ===========
 
            This error is triggered by SCE2S. In this case the error
            message may not give you enough information to understand what
            has actually happened. Nevertheless, the expanded form of this
            short message clearly indicates that the SCLK kernel for the
            spacecraft ID -121 has not been loaded.
 
            The UTC string to ephemeris time conversion and the conversion
            of ephemeris time into a calendar format worked normally as
            these conversions only require the LSK kernel to be loaded.
 
       4.   The first thing you need to do is to find out what the NAIF ID
            is for the SIMBIO-SYS HRIC channel. In order to do so, examine
            the BepiColombo MPO frames definitions kernel listed above and
            look for the ``BepiColombo MPO Mission NAIF ID Codes'' or for
            the ``BepiColombo MPO NAIF ID Codes to Name Mapping'' and
            there, for the NAIF ID given to MPO_SIMBIO-SYS_HRIC_FPA (which
            is -121610). Then replace in your code the SCLK ID -121 with
            -121610. After compiling and executing the program using the
            original meta-kernel, you will be getting the same error as in
            the previous task. Despite the error being exactly the same,
            this case is different. Generally, spacecraft clocks are
            associated with the spacecraft ID and not with its payload,
            sensors or structures IDs. Therefore, in order to do
            conversions from/to spacecraft clock for payload, sensors or
            spacecraft structures, the spacecraft ID must be used.
 
            Note that this does not need to be true for all missions or
            payloads, as SPICE does not restrict the SCLKs to spacecraft
            IDs only. Please refer to your mission's SCLK kernels for
            particulars.
 
       5.   Use SCT2E with the encoding of the MPO spacecraft clock time
            set to 0.0 ticks and convert the resulting ephemeris time to
            UTC using either TIMOUT or ET2UTC. The solution for the
            requested SCLK string is:
 
         Earliest UTC convertible to SCLK: 1999-08-22T00:00:05.204
 
       6.   Use SCS2E with the SCLK string obtained in the computations
            performed in the regular tasks and convert the resulting
            ephemeris time to UTC using either ET2UTC, with 'ISOC' format
            and 3 digits precision, or using TIMOUT using the time picture
            'YYYY-MM-DDTHR:MN:SC.### ::RND'. The solution of the requested
            conversion is:
 
         Spacecraft Clock Time:          1/0863834674:28127
         UTC time from spacecraft clock: 2027-01-05T02:04:36.000
 
 
Obtaining Target States and Positions (getsta)
===========================================================================
 
 
Task Statement
--------------------------------------------------------
 
   Write a program that prompts the user for an input UTC time string,
   computes the following quantities at that epoch:
 
       1.   The apparent state of Mercury as seen from BepiColombo MPO in
            the J2000 frame, in kilometers and kilometers/second. This
            vector itself is not of any particular interest, but it is a
            useful intermediate quantity in some geometry calculations.
 
       2.   The apparent position of the Earth as seen from BepiColombo MPO
            in the J2000 frame, in kilometers.
 
       3.   The one-way light time between BepiColombo MPO and the apparent
            position of Earth, in seconds.
 
       4.   The apparent position of the Sun as seen from Mercury in the
            J2000 frame (J2000), in kilometers.
 
       5.   The actual (geometric) distance between the Sun and Mercury, in
            astronomical units.
 
   and displays the results. Use the program to compute these quantities at
   "2027 JAN 05 02:04:36" UTC.
 
 
Learning Goals
--------------------------------------------------------
 
   Understand the anatomy of an SPKEZR call. Discover the difference
   between SPKEZR and SPKPOS. Familiarity with the Toolkit utility
   ``brief''. Exposure to unit conversion with SPICE.
 
 
Approach
--------------------------------------------------------
 
   The solution to the problem can be broken down into a series of simple
   steps:
 
       --   Decide which SPICE kernels are necessary. Prepare a meta-kernel
            listing the kernels and load it into the program.
 
       --   Prompt the user for an input time string.
 
       --   Convert the input time string into ephemeris time expressed as
            seconds past J2000 TDB.
 
       --   Compute the state of Mercury relative to BepiColombo MPO in the
            J2000 reference frame, corrected for aberrations.
 
       --   Compute the position of Earth relative to BepiColombo MPO in
            the J2000 reference frame, corrected for aberrations. (The
            routine in the library that computes this also returns the
            one-way light time between BepiColombo MPO and Earth.)
 
       --   Compute the position of the Sun relative to Mercury in the
            J2000 reference frame, corrected for aberrations.
 
       --   Compute the position of the Sun relative to Mercury without
            correcting for aberration.
 
            Compute the length of this vector. This provides the desired
            distance in kilometers.
 
       --   Convert the distance in kilometers into AU.
 
   You may find it useful to consult the permuted index, the headers of
   various source modules, and the ``SPK Required Reading'' (spk.req)
   document.
 
   When deciding which SPK files to load, the Toolkit utility ``brief'' may
   be of some use.
 
   ``brief'' is located in the ``toolkit/exe'' directory for FORTRAN
   toolkits. Consult its user's guide available in ``toolkit/doc/brief.ug''
   for details.
 
 
Solution
--------------------------------------------------------
 
 
Solution Meta-Kernel
 
   The meta-kernel we created for the solution to this exercise is named
   'getsta.tm'. Its contents follow:
 
      KPL/MK
 
         This is the meta-kernel used in the solution of the
         ``Obtaining Target States and Positions'' task in the
         Remote Sensing Hands On Lesson.
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            3. 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/spk/de432s.bsp',
       'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp',
 
                           )
 
      \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
            PROGRAM GETSTA
 
            IMPLICIT NONE
 
      C
      C     SPICELIB Functions
      C
            DOUBLE PRECISION      VNORM
 
      C
      C     Local Parameters
      C
      C
      C     The name of the meta-kernel that lists the kernels
      C     to load into the program.
      C
            CHARACTER*(*)         METAKR
            PARAMETER           ( METAKR = 'getsta.tm' )
 
      C
      C     The length of various string variables.
      C
            INTEGER               STRLEN
            PARAMETER           ( STRLEN = 50 )
 
      C
      C     Local Variables
      C
            CHARACTER*(STRLEN)    UTCTIM
 
            DOUBLE PRECISION      DIST
            DOUBLE PRECISION      ET
            DOUBLE PRECISION      LTIME
            DOUBLE PRECISION      POS   ( 3 )
            DOUBLE PRECISION      STATE ( 6 )
 
      C
      C     Load the kernels that this program requires.  We
      C     will need a leapseconds kernel to convert input
      C     UTC time strings into ET.  We also will need the
      C     necessary SPK files with coverage for the bodies
      C     in which we are interested.
      C
            CALL FURNSH ( METAKR )
 
      C
      C     Prompt the user for the input time string.
      C
            CALL PROMPT ( 'Input UTC Time: ', UTCTIM )
 
            WRITE (*,*) 'Converting UTC Time: ', UTCTIM
 
      C
      C     Convert UTCTIM to ET.
      C
            CALL STR2ET ( UTCTIM, ET )
 
            WRITE (*,'(A,F16.3)') '   ET seconds past J2000: ', ET
 
      C
      C     Compute the apparent state of Mercury as seen from
      C     BepiColombo MPO in the J2000 frame.  All of the ephemeris
      C     readers return states in units of kilometers and
      C     kilometers per second.
      C
            CALL SPKEZR ( 'MERCURY', ET,    'J2000', 'LT+S',
           .              'MPO',     STATE, LTIME            )
 
            WRITE (*,*) '   Apparent state of Mercury as seen from '
           .//          'BepiColombo MPO in the'
            WRITE (*,*) '     J2000 frame (km, km/s):'
 
            WRITE (*,'(A,F16.3)') '      X = ', STATE(1)
            WRITE (*,'(A,F16.3)') '      Y = ', STATE(2)
            WRITE (*,'(A,F16.3)') '      Z = ', STATE(3)
            WRITE (*,'(A,F16.3)') '     VX = ', STATE(4)
            WRITE (*,'(A,F16.3)') '     VY = ', STATE(5)
            WRITE (*,'(A,F16.3)') '     VZ = ', STATE(6)
 
      C
      C     Compute the apparent position of Earth as seen from
      C     BepiColombo MPO in the J2000 frame.  Note: We could have
      C     continued using SPKEZR and simply ignored the velocity
      C     components.
      C
            CALL SPKPOS ( 'EARTH', ET,  'J2000', 'LT+S',
           .              'MPO',   POS, LTIME               )
 
            WRITE (*,*) '   Apparent position of Earth as seen from '
           .//          'BepiColombo MPO in the'
            WRITE (*,*) '     J2000 frame (km):'
 
            WRITE (*,'(A,F16.3)') '      X = ', POS(1)
            WRITE (*,'(A,F16.3)') '      Y = ', POS(2)
            WRITE (*,'(A,F16.3)') '      Z = ', POS(3)
 
      C
      C     We need only display LTIME, as it is precisely the light
      C     time in which we are interested.
      C
            WRITE (*,*) '   One way light time between BepiColombo MPO '
           .//          'and the apparent'
            WRITE (*,'(A,F16.3)') '      position of Earth '
           .//          '(seconds): ', LTIME
 
      C
      C     Compute the apparent position of the Sun as seen from
      C     Mercury in the J2000 frame.
      C
            CALL SPKPOS ( 'SUN',     ET,  'J2000', 'LT+S',
           .              'MERCURY', POS, LTIME            )
 
            WRITE (*,*) '   Apparent position of Sun as seen from '
           .//          'Mercury in the'
            WRITE (*,*) '     J2000 frame (km):'
 
            WRITE (*,'(A,F16.3)') '      X = ', POS(1)
            WRITE (*,'(A,F16.3)') '      Y = ', POS(2)
            WRITE (*,'(A,F16.3)') '      Z = ', POS(3)
 
      C
      C     Now we need to compute the actual distance between the Sun
      C     and Mercury.  The above SPKPOS call gives us the apparent
      C     distance, so we need to adjust our aberration correction
      C     appropriately.
      C
            CALL SPKPOS ( 'SUN',     ET,  'J2000', 'NONE',
           .              'MERCURY', POS, LTIME            )
 
      C
      C     Compute the distance between the body centers in
      C     kilometers.
      C
            DIST = VNORM(POS)
 
      C
      C     Convert this value to AU using CONVRT.
      C
            CALL CONVRT ( DIST, 'KM', 'AU', DIST )
 
            WRITE (*,*) '   Actual distance between Sun and Mercury body '
           .//          'centers: '
            WRITE (*,'(A,F16.3)') '      (AU):', DIST
 
            END
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Input UTC Time: 2027 JAN 05 02:04:36
       Converting UTC Time: 2027 JAN 05 02:04:36
         ET seconds past J2000:    852386745.184
          Apparent state of Mercury as seen from BepiColombo MPO in the
            J2000 frame (km, km/s):
            X =         -683.207
            Y =        -1438.946
            Z =        -2427.819
           VX =            0.036
           VY =            2.360
           VZ =           -1.783
          Apparent position of Earth as seen from BepiColombo MPO in the
            J2000 frame (km):
            X =    -59257854.691
            Y =    185201786.218
            Z =     88178321.179
          One way light time between BepiColombo MPO and the apparent
            position of Earth (seconds):          712.193
          Apparent position of Sun as seen from Mercury in the
            J2000 frame (km):
            X =    -23429947.239
            Y =     54297427.572
            Z =     31434173.468
          Actual distance between Sun and Mercury body centers:
            (AU):           0.448
 
 
Extra Credit
--------------------------------------------------------
 
   In this ``extra credit'' section you will be presented with more complex
   tasks, aimed at improving your understanding of state computations,
   particularly the application of the different light time and stellar
   aberration corrections available in the SPKEZR routine, and some common
   errors that may happen when computing these states.
 
   These ``extra credit'' tasks are provided as task statements, and unlike
   the regular tasks, no approach or solution source code is provided. In
   the next section, you will find the numeric solutions (when applicable)
   and answers to the questions asked in these tasks.
 
 
Task statements and questions
 
       1.   Remove the planetary ephemerides SPK from the original
            meta-kernel and run your program again, using the same inputs
            as before. Has anything changed? Why?
 
       2.   Extend your program to compute the geometric position of
            Jupiter as seen from Mercury in the J2000 frame (J2000), in
            kilometers.
 
       3.   Extend, or modify, your program to compute the position of the
            Sun as seen from Mercury in the J2000 frame (J2000), in
            kilometers, using the following light time and aberration
            corrections: NONE, LT and LT+S. Explain the differences.
 
       4.   Examine the BepiColombo MPO frames definition kernel to find
            the SPICE ID/name definitions.
 
 
Solutions and answers
 
       1.   When running the original program without the planetary
            ephemerides SPK, an error is produced by SPKEZR:
 
 
      =====================================================================
      ===========
 
      Toolkit version: N0067
 
      SPICE(SPKINSUFFDATA) --
 
      Insufficient ephemeris data has been loaded to compute the state of -
      121
      (BEPICOLOMBO MPO) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephe
      meris
      epoch 2027 JAN 05 02:05:45.184.
 
      A traceback follows.  The name of the highest level module is first.
      SPKEZR --> SPKEZ --> SPKACS --> SPKGEO
 
      Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
      BLE.  You
      can choose whether the Toolkit aborts or continues when errors occur,
       which
      error messages to output, and where to send the output.  Please read
      the ERROR
      "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
      RT.
 
      =====================================================================
      ===========
 
            This error is generated when trying to compute the apparent
            state of Mercury as seen from BepiColombo MPO in the J2000
            frame because despite the BepiColombo MPO ephemeris data being
            relative to Mercury, the state of the spacecraft with respect
            to the solar system barycenter is required to compute the light
            time and stellar aberrations. The loaded SPK data are enough to
            compute geometric states of BepiColombo MPO with respect to
            Mercury center, and geometric states of Mercury barycenter with
            respect to the Solar System Barycenter, but insufficient to
            compute the state of the spacecraft relative to the Solar
            System Barycenter because the SPK data needed to compute
            geometric states of Mercury center relative to its barycenter
            are no longer loaded. Run ``brief'' on the SPKs used in the
            original task to find out which ephemeris objects are available
            from those kernels. If you want to find out what is the 'center
            of motion' for the ephemeris object(s) included in an SPK, use
            the -c option when running ``brief'':
 
 
      BRIEF -- Version 4.1.0, September 17, 2021 -- Toolkit Version N0067
 
 
      Summary for: kernels/spk/de432s.bsp
 
      Bodies: MERCURY BARYCENTER (1) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              VENUS BARYCENTER (2) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              EARTH BARYCENTER (3) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              MARS BARYCENTER (4) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              JUPITER BARYCENTER (5) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              SATURN BARYCENTER (6) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              URANUS BARYCENTER (7) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              NEPTUNE BARYCENTER (8) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              PLUTO BARYCENTER (9) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              SUN (10) w.r.t. SOLAR SYSTEM BARYCENTER (0)
              MERCURY (199) w.r.t. MERCURY BARYCENTER (1)
              VENUS (299) w.r.t. VENUS BARYCENTER (2)
              MOON (301) w.r.t. EARTH BARYCENTER (3)
              EARTH (399) w.r.t. EARTH BARYCENTER (3)
              Start of Interval (UTC)             End of Interval (UTC)
              -----------------------------       -------------------------
      ----
              2027-JAN-02 23:01:53.350            2027-JAN-08 00:59:37.932
 
 
      Summary for: kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
      Body: BEPICOLOMBO MPO (-121) w.r.t. MERCURY (199)
            Start of Interval (UTC)             End of Interval (UTC)
            -----------------------------       ---------------------------
      --
            2027-JAN-02 23:01:53.350            2027-JAN-08 00:59:37.932
 
      Bodies: -121000 w.r.t. BEPICOLOMBO MPO (-121)
              -121540 w.r.t. BEPICOLOMBO MPO (-121)
              -121600 w.r.t. BEPICOLOMBO MPO (-121)
              Start of Interval (UTC)             End of Interval (UTC)
              -----------------------------       -------------------------
      ----
              2027-JAN-02 23:01:53.350            2027-JAN-08 00:59:37.932
 
 
 
       2.   If you run your extended program with the original meta-kernel,
            the SPICE(SPKINSUFFDATA) error should be produced by the SPKPOS
            routine because you have not loaded enough ephemeris data to
            compute the position of Jupiter with respect to Mercury. The
            loaded SPKs contain data for Mercury relative to the Solar
            System Barycenter, and for the Jupiter System Barycenter
            relative to the Solar System Barycenter, but the data for
            Jupiter relative to the Jupiter System Barycenter are missing:
 
 
         Additional kernels required for this task:
 
            1. Generic Jovian Satellite Ephemeris SPK:
 
                  jup365_2027.bsp
 
         available in the NAIF server at:
 
      https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/
      satellites/a_old_versions
 
 
            Download the relevant SPK, add it to the meta-kernel and run
            again your extended program. The solution for the input UTC
            time "2027 JAN 05 02:04:36" when using the downloaded Jovian
            Satellite Ephemeris SPK:
 
         Actual position of Jupiter as seen from Mercury in the
            J2000 frame (km):
            X =   -623644094.418
            Y =    532767093.112
            Z =    251130102.035
 
       3.   When using 'NONE' aberration corrections, SPKPOS returns the
            geometric position of the target body relative to the observer.
            If 'LT' is used, the returned vector corresponds to the
            position of the target at the moment it emitted photons
            arriving at the observer at `et'. If 'LT+S' is used instead,
            the returned vector takes into account the observer's velocity
            relative to the solar system barycenter. The solution for the
            input UTC time "2027 JAN 05 02:04:36" is:
 
         Actual (geometric) position of Sun as seen from Mercury in the
            J2000 frame (km):
            X =    -23438490.402
            Y =     54294213.485
            Z =     31433347.025
         Light-time corrected position of Sun as seen from Mercury in the
            J2000 frame (km):
            X =    -23438492.550
            Y =     54294212.272
            Z =     31433346.550
         Apparent position of Sun as seen from Mercury in the
            J2000 frame (km):
            X =    -23430052.903
            Y =     54297381.156
            Z =     31434164.775
 
 
Spacecraft Orientation and Reference Frames (xform)
===========================================================================
 
 
Task Statement
--------------------------------------------------------
 
   Write a program that prompts the user for an input time string, and
   computes and displays the following at the epoch of interest:
 
       1.   The apparent state of Mercury as seen from BepiColombo MPO in
            the IAU_MERCURY body-fixed frame. This vector itself is not of
            any particular interest, but it is a useful intermediate
            quantity in some geometry calculations.
 
       2.   The angular separation between the apparent position of Mercury
            as seen from BepiColombo MPO and the nominal instrument view
            direction.
 
            The nominal instrument view direction is not provided by any
            kernel variable, but it is indicated in the BepiColombo MPO
            frame kernel cited above in the section ``Kernels Used'' to be
            the +Z axis of the MPO_SPACECRAFT frame.
 
   Use the program to compute these quantities at the epoch "2027 JAN 05
   02:04:36" UTC.
 
 
Learning Goals
--------------------------------------------------------
 
   Familiarity with the different types of kernels involved in chaining
   reference frames together, both inertial and non-inertial. Discover some
   of the matrix and vector math routines. Understand the difference
   between PXFORM and SXFORM.
 
 
Approach
--------------------------------------------------------
 
   The solution to the problem can be broken down into a series of simple
   steps:
 
       --   Decide which SPICE kernels are necessary. Prepare a meta-kernel
            listing the kernels and load it into the program.
 
       --   Prompt the user for an input time string.
 
       --   Convert the input time string into ephemeris time expressed as
            seconds past J2000 TDB.
 
       --   Compute the state of Mercury relative to BepiColombo MPO in the
            J2000 reference frame, corrected for aberrations.
 
       --   Compute the state transformation matrix from J2000 to
            IAU_MERCURY at the epoch, adjusted for light time.
 
       --   Multiply the state of Mercury relative to BepiColombo MPO in
            the J2000 reference frame by the state transformation matrix
            computed in the previous step.
 
       --   Compute the position of Mercury relative to BepiColombo MPO in
            the J2000 reference frame, corrected for aberrations.
 
       --   Determine what the nominal instrument view direction of the
            BepiColombo MPO spacecraft is by examining the frame kernel's
            content.
 
       --   Compute the rotation matrix from the BepiColombo MPO spacecraft
            frame to J2000.
 
       --   Multiply the nominal instrument view direction expressed in the
            BepiColombo MPO spacecraft frame by the rotation matrix from
            the previous step.
 
       --   Compute the separation between the result of the previous step
            and the apparent position of Mercury relative to BepiColombo
            MPO in the J2000 frame.
 
   HINT: Several of the steps above may be compressed into a single step
   using SPICE routines with which you are already familiar. The ``long
   way'' presented above is intended to facilitate the introduction of the
   routines PXFORM and SXFORM.
 
   You may find it useful to consult the permuted index, the headers of
   various source modules, and the following toolkit documentation:
 
       1.   Frames Required Reading (frames.req)
 
       2.   PCK Required Reading (pck.req)
 
       3.   SPK Required Reading (spk.req)
 
       4.   CK Required Reading (ck.req)
 
   This particular example makes use of many of the different types of
   SPICE kernels. You should spend a few moments thinking about which
   kernels you will need and what data they provide.
 
 
Solution
--------------------------------------------------------
 
 
Solution Meta-Kernel
 
   The meta-kernel we created for the solution to this exercise is named
   'xform.tm'. Its contents follow:
 
      KPL/MK
 
         This is the meta-kernel used in the solution of the ``Spacecraft
         Orientation and Reference Frames'' task in the Remote Sensing
         Hands On Lesson.
 
         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
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
            PROGRAM XFORM
 
            IMPLICIT NONE
 
      C
      C     SPICELIB Functions
      C
            DOUBLE PRECISION      VSEP
 
      C
      C     Local Parameters
      C
      C
      C     The name of the meta-kernel that lists the kernels
      C     to load into the program.
      C
            CHARACTER*(*)         METAKR
            PARAMETER           ( METAKR = 'xform.tm' )
 
      C
      C     The length of various string variables.
      C
            INTEGER               STRLEN
            PARAMETER           ( STRLEN = 50 )
 
      C
      C     Local Variables
      C
            CHARACTER*(STRLEN)    UTCTIM
 
            DOUBLE PRECISION      ET
            DOUBLE PRECISION      LTIME
            DOUBLE PRECISION      STATE  ( 6 )
            DOUBLE PRECISION      BFIXST ( 6 )
            DOUBLE PRECISION      POS    ( 3 )
            DOUBLE PRECISION      SXFMAT ( 6, 6 )
            DOUBLE PRECISION      PFORM  ( 3, 3 )
            DOUBLE PRECISION      BSIGHT ( 3 )
            DOUBLE PRECISION      SEP
 
      C
      C     Load the kernels that this program requires.  We
      C     will need:
      C
      C        A leapseconds kernel
      C        A spacecraft clock kernel for BepiColombo MPO
      C        The necessary ephemerides
      C        A planetary constants file (PCK)
      C        A spacecraft orientation kernel for BepiColombo MPO (CK)
      C        A frame kernel (TF)
      C
            CALL FURNSH ( METAKR )
 
      C
      C     Prompt the user for the input time string.
      C
            CALL PROMPT ( 'Input UTC Time: ', UTCTIM )
 
            WRITE (*,'(2A)') 'Converting UTC Time: ', UTCTIM
 
      C
      C     Convert UTCTIM to ET.
      C
            CALL STR2ET ( UTCTIM, ET )
 
            WRITE (*,'(A,F16.3)') '   ET seconds past J2000: ', ET
 
      C
      C     Compute the apparent state of Mercury as seen from BepiColombo
      C     MPO in the J2000 reference frame.
      C
            CALL SPKEZR ( 'MERCURY', ET,    'J2000', 'LT+S',
           .              'MPO',     STATE, LTIME           )
 
      C
      C     Now obtain the transformation from the inertial
      C     J2000 frame to the non-inertial, body-fixed IAU_MERCURY
      C     frame. Since we'll use this transformation to produce
      C     the apparent state in the IAU_MERCURY reference frame,
      C     we need to correct the orientation of this frame for
      C     one-way light time; hence we subtract LTIME from ET
      C     in the call below.
      C
            CALL SXFORM ( 'J2000', 'IAU_MERCURY', ET-LTIME, SXFMAT )
 
      C
      C     Now transform the apparent J2000 state into IAU_MERCURY
      C     with the following matrix multiplication:
      C
            CALL MXVG ( SXFMAT, STATE, 6, 6, BFIXST )
 
      C
      C     Display the results.
      C
            WRITE (*,'(A)') '   Apparent state of Mercury as seen from '
           .//          'BepiColombo MPO in the'
            WRITE (*,'(A)') '      IAU_MERCURY body-fixed frame (km, km/s):
      '
            WRITE (*,'(A,F19.6)') '      X = ', BFIXST(1)
            WRITE (*,'(A,F19.6)') '      Y = ', BFIXST(2)
            WRITE (*,'(A,F19.6)') '      Z = ', BFIXST(3)
            WRITE (*,'(A,F19.6)') '     VX = ', BFIXST(4)
            WRITE (*,'(A,F19.6)') '     VY = ', BFIXST(5)
            WRITE (*,'(A,F19.6)') '     VZ = ', BFIXST(6)
 
      C
      C     It is worth pointing out, all of the above could have
      C     been done with a single call to SPKEZR:
      C
            CALL SPKEZR ( 'MERCURY', ET,    'IAU_MERCURY', 'LT+S',
           .              'MPO',     STATE, LTIME               )
 
      C
      C     Display the results.
      C
            WRITE (*,'(A)') '   Apparent state of Mercury as seen from '
           .//          'BepiColombo MPO in the'
            WRITE (*,'(A)') '      IAU_MERCURY body-fixed frame '
           .//          '(km, km/s) obtained using'
            WRITE (*,'(A)') '      SPKEZR directly:'
            WRITE (*,'(A,F19.6)') '      X = ', STATE(1)
            WRITE (*,'(A,F19.6)') '      Y = ', STATE(2)
            WRITE (*,'(A,F19.6)') '      Z = ', STATE(3)
            WRITE (*,'(A,F19.6)') '     VX = ', STATE(4)
            WRITE (*,'(A,F19.6)') '     VY = ', STATE(5)
            WRITE (*,'(A,F19.6)') '     VZ = ', STATE(6)
 
      C
      C     Note that the velocity found by using SPKEZR
      C     to compute the state in the IAU_MERCURY frame differs
      C     at the few mm/second level from that found previously
      C     by calling SPKEZR and then SXFORM. Computing velocity
      C     via a single call to SPKEZR as we've done immediately
      C     above is slightly more accurate because it accounts for
      C     the effect of the rate of change of light time on the
      C     apparent angular velocity of the target's body-fixed
      C     reference frame.
      C
      C     Now we are to compute the angular separation between
      C     the apparent position of Mercury as seen from the orbiter
      C     and the nominal instrument view direction.  First,
      C     compute the apparent position of Mercury as seen from
      C     BepiColombo MPO in the J2000 frame.
      C
            CALL SPKPOS ( 'MERCURY', ET,  'J2000', 'LT+S',
           .              'MPO',     POS, LTIME            )
 
      C
      C     Now compute the location of the nominal instrument view
      C     direction.  From reading the frame kernel we know that
      C     the instrument view direction is nominally the +Z axis
      C     of the MPO_SPACECRAFT frame defined there.
      C
            BSIGHT(1) = 0.0D0
            BSIGHT(2) = 0.0D0
            BSIGHT(3) = 1.0D0
 
      C
      C     Now compute the rotation matrix from MPO_SPACECRAFT into
      C     J2000.
      C
            CALL PXFORM ( 'MPO_SPACECRAFT', 'J2000', ET, PFORM )
 
      C
      C     And multiply the result to obtain the nominal instrument
      C     view direction in the J2000 reference frame.
      C
            CALL MXV ( PFORM, BSIGHT, BSIGHT )
 
      C
      C     Lastly compute the angular separation.
      C
            CALL CONVRT ( VSEP(BSIGHT, POS), 'RADIANS',
           .              'DEGREES',         SEP        )
 
            WRITE (*,'(A)') '   Angular separation between the '
           .//          'apparent position of Mercury and'
            WRITE (*,'(A)') '      the BepiColombo MPO nominal '
           .//          'instrument view direction'
            WRITE (*,'(A)') '      (degrees):'
            WRITE (*,'(A,F19.3)') '      ', SEP
 
      C
      C     Or, alternately we can work in the spacecraft
      C     frame directly.
      C
            CALL SPKPOS ( 'MERCURY', ET,  'MPO_SPACECRAFT', 'LT+S',
           .              'MPO',  POS, LTIME                    )
 
      C
      C     The nominal instrument view direction is the +Z-axis
      C     in the MPO_SPACECRAFT frame.
      C
            BSIGHT(1) = 0.0D0
            BSIGHT(2) = 0.0D0
            BSIGHT(3) = 1.0D0
 
      C
      C     Lastly compute the angular separation.
      C
            CALL CONVRT ( VSEP(BSIGHT, POS), 'RADIANS',
           .              'DEGREES',         SEP        )
 
            WRITE (*,'(A)') '   Angular separation between the '
           .//          'apparent position of Mercury and'
            WRITE (*,'(A)') '      the BepiColombo MPO nominal '
           .//          'instrument view direction computed'
            WRITE (*,'(A)') '      using vectors in the '
           .//          'MPO_SPACECRAFT frame (degrees): '
            WRITE (*,'(A,F19.3)') '      ', SEP
 
            END
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Input UTC Time: 2027 JAN 05 02:04:36
      Converting UTC Time: 2027 JAN 05 02:04:36
         ET seconds past J2000:    852386745.184
         Apparent state of Mercury as seen from BepiColombo MPO in the
            IAU_MERCURY body-fixed frame (km, km/s):
            X =        -2354.697620
            Y =         -762.547549
            Z =        -1518.408470
           VX =            1.208589
           VY =            0.394259
           VZ =           -2.671125
         Apparent state of Mercury as seen from BepiColombo MPO in the
            IAU_MERCURY body-fixed frame (km, km/s) obtained using
            SPKEZR directly:
            X =        -2354.697620
            Y =         -762.547549
            Z =        -1518.408470
           VX =            1.208589
           VY =            0.394259
           VZ =           -2.671125
         Angular separation between the apparent position of Mercury and
            the BepiColombo MPO nominal instrument view direction
            (degrees):
                          0.009
         Angular separation between the apparent position of Mercury and
            the BepiColombo MPO nominal instrument view direction computed
            using vectors in the MPO_SPACECRAFT frame (degrees):
                          0.009
 
 
Extra Credit
--------------------------------------------------------
 
   In this ``extra credit'' section you will be presented with more complex
   tasks, aimed at improving your understanding of frame transformations,
   and some common errors that may happen when computing them.
 
   These ``extra credit'' tasks are provided as task statements, and unlike
   the regular tasks, no approach or solution source code is provided. In
   the next section, you will find the numeric solutions (when applicable)
   and answers to the questions asked in these tasks.
 
 
Task statements and questions
 
       1.   Run the original program using the input UTC time "2027 JAN 06
            15:32:05". Explain what happens.
 
       2.   Compute the angular separation between the apparent position of
            the Sun as seen from BepiColombo MPO and the nominal instrument
            view direction. Is the science deck illuminated?
 
 
Solutions and answers
 
       1.   When running the original software using as input the UTC time
            string "2027 JAN 06 15:32:05":
 
 
      =====================================================================
      ===========
 
      Toolkit version: N0067
 
      SPICE(NOFRAMECONNECT) --
 
      At epoch 8.5252159418408E+08 TDB (2027 JAN 06 15:33:14.184 TDB), ther
      e is
      insufficient information available to transform from reference frame
      -121000
      (MPO_SPACECRAFT) to reference frame 1 (J2000). MPO_SPACECRAFT is a CK
       frame; a
      CK file containing data for instrument or structure -121000 at the ep
      och shown
      above, as well as a corresponding SCLK kernel, must be loaded in orde
      r to use
      this frame. Failure to find required CK data could be due to one or m
      ore CK
      files not having been loaded, or to the epoch shown above lying withi
      n a
      coverage gap or beyond the coverage bounds of the loaded CK files. It
       is also
      possible that no loaded CK file has required angular velocity data fo
      r the
      input epoch, even if a loaded CK does have attitude data for that epo
      ch. You
      can use CKBRIEF with the -dump option to display coverage intervals o
      f a CK
      file.
 
      A traceback follows.  The name of the highest level module is first.
      PXFORM --> REFCHG
 
      Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
      BLE.  You
      can choose whether the Toolkit aborts or continues when errors occur,
       which
      error messages to output, and where to send the output.  Please read
      the ERROR
      "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
      RT.
 
      =====================================================================
      ===========
 
            PXFORM returns the SPICE(NOFRAMECONNECT) error, which indicates
            that there are not sufficient data to perform the
            transformation from the MPO_SPACECRAFT frame to J2000 at the
            requested epoch. If you summarize the BepiColombo MPO
            spacecraft CK using the ``ckbrief'' utility program with the
            -dump option (display interpolation intervals boundaries) you
            will find that the CK contains gaps within its segment:
 
 
      CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067
 
 
      Summary for: kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f201811
      27_v03.bc
 
      Segment No.: 1
 
      Object:  -121000
        Interval Begin UTC       Interval End UTC         AV
        ------------------------ ------------------------ ---
        2027-JAN-02 23:01:53.350 2027-JAN-06 11:04:56.368 Y
        2027-JAN-06 11:08:00.779 2027-JAN-06 15:30:56.685 Y
        2027-JAN-06 15:33:04.016 2027-JAN-06 22:05:57.865 Y
        2027-JAN-06 22:10:03.746 2027-JAN-08 00:59:37.932 Y
 
 
 
            whereas if you had used ckbrief without -dump you would have
            gotten the following information (only CK segment begin/end
            times):
 
 
      CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067
 
 
      Summary for: kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f201811
      27_v03.bc
 
      Object:  -121000
        Interval Begin UTC       Interval End UTC         AV
        ------------------------ ------------------------ ---
        2027-JAN-02 23:01:53.350 2027-JAN-08 00:59:37.932 Y
 
 
 
            which has insufficient detail to reveal the problem.
 
       2.   By computing the apparent position of the Sun as seen from
            BepiColombo MPO in the MPO_SPACECRAFT frame, and the angular
            separation between this vector and the nominal instrument view
            direction (+Z-axis of the MPO_SPACECRAFT frame), you will find
            whether the science deck is illuminated. The solution for the
            input UTC time "2027 JAN 05 02:04:36" is:
 
      Angular separation between the apparent position of the Sun and the
      BepiColombo MPO nominal instrument view direction (degrees):
          135.393
 
      Science Deck illumination:
         BepiColombo MPO Science Deck IS NOT illuminated.
 
            since the angular separation is greater than 90 degrees.
 
 
Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts)
===========================================================================
 
 
Task Statement
--------------------------------------------------------
 
   Write a program that prompts the user for an input UTC time string and
   computes the following quantities at that epoch:
 
       1.   The apparent sub-observer point of BepiColombo MPO on Mercury,
            in the body fixed frame IAU_MERCURY, in kilometers, and the
            spacecraft altitude as the distance between the spacecraft and
            this point, in kilometers.
 
       2.   The apparent sub-solar point on Mercury, as seen from
            BepiColombo MPO in the body fixed frame IAU_MERCURY, in
            kilometers.
 
   The program computes each point twice: once using an ellipsoidal shape
   model and the
 
           near point/ellipsoid
 
   definition, and once using a DSK shape model and the
 
           nadir/dsk/unprioritized
 
   definition.
 
   The program displays the results. Use the program to compute these
   quantities at "2027 JAN 05 02:04:36" UTC.
 
 
Learning Goals
--------------------------------------------------------
 
   Discover higher level geometry calculation routines in SPICE and their
   usage as it relates to BepiColombo MPO.
 
 
Approach
--------------------------------------------------------
 
   This particular problem is more of an exercise in searching the permuted
   index to find the appropriate routines and then reading their headers to
   understand how to call them.
 
   One point worth considering: how would the results change if the
   sub-solar and sub-observer points were computed using the
 
           intercept/ellipsoid
 
   and
 
           intercept/dsk/unprioritized
 
   definitions? Which definition is appropriate?
 
 
Solution
--------------------------------------------------------
 
 
Solution Meta-Kernel
 
   The meta-kernel we created for the solution to this exercise is named
   'subpts.tm'. Its contents follow:
 
      KPL/MK
 
         This is the meta-kernel used in the solution of the
         ``Computing Sub-s/c and Sub-solar Points on an Ellipsoid
         and a DSK'' task in the Remote Sensing Hands On Lesson.
 
         The names and contents of the kernels referenced by this
         meta-kernel are as follows:
 
            1. Generic LSK:
 
                  naif0012.tls
 
            2. Solar System Ephemeris SPK, subsetted to cover only
               the time range of interest:
 
                  de432s.bsp
 
            3. BepiColombo MPO Spacecraft Trajectory SPK, subsetted
               to cover only the time range of interest:
 
                  bc_mpo_mlt_50037_20260314_20280529_v05.bsp
 
            4. Generic PCK:
 
                  pck00011.tpc
 
            5. Low-resolution Mercury DSK:
 
                  mercury_lowres.bds
 
      \begindata
 
       KERNELS_TO_LOAD = (
 
       'kernels/lsk/naif0012.tls',
       'kernels/spk/de432s.bsp',
       'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp',
       'kernels/pck/pck00011.tpc'
       'kernels/dsk/mercury_lowres.bds'
 
                         )
 
      \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
            PROGRAM SUBPTS
 
            IMPLICIT NONE
      C
      C     SPICELIB functions
      C
            DOUBLE PRECISION      VNORM
 
      C
      C     Local Parameters
      C
      C
      C     The name of the meta-kernel that lists the kernels
      C     to load into the program.
      C
            CHARACTER*(*)         METAKR
            PARAMETER           ( METAKR = 'subpts.tm' )
 
      C
      C     The length of various string variables.
      C
            INTEGER               STRLEN
            PARAMETER           ( STRLEN = 50 )
 
      C
      C     Local Variables
      C
            CHARACTER*(STRLEN)    METHOD
            CHARACTER*(STRLEN)    UTCTIM
 
            DOUBLE PRECISION      ET
            DOUBLE PRECISION      SPOINT ( 3 )
            DOUBLE PRECISION      SRFVEC ( 3 )
            DOUBLE PRECISION      TRGEPC
 
            INTEGER               I
 
      C
      C     Load the kernels that this program requires.  We
      C     will need:
      C
      C        A leapseconds kernel
      C        The necessary ephemerides
      C        A planetary constants file (PCK)
      C        A DSK file containing Mercury shape data
      C
            CALL FURNSH ( METAKR )
 
      C
      C     Prompt the user for the input time string.
      C
            CALL PROMPT ( 'Input UTC Time: ', UTCTIM )
 
            WRITE (*,*) 'Converting UTC Time: ', UTCTIM
 
      C
      C     Convert UTCTIM to ET.
      C
            CALL STR2ET ( UTCTIM, ET )
 
            WRITE (*,'(A,F16.3)') '   ET seconds past J2000: ', ET
 
 
            DO I = 1, 2
 
               IF ( I .EQ. 1 ) THEN
      C
      C           Use the "near point" sub-point definition
      C           and an ellipsoidal model.
      C
                  METHOD = 'NEAR POINT/Ellipsoid'
 
               ELSE
      C
      C           Use the "nadir" sub-point definition and a
      C           DSK model.
      C
                  METHOD = 'NADIR/DSK/Unprioritized'
 
               END IF
 
               WRITE (*,*) ' '
               WRITE (*,*) 'Sub-point/target shape model: '//METHOD
               WRITE (*,*) ' '
 
 
      C
      C        Compute the apparent sub-observer point of BepiColombo MPO
      C        on Mercury.
      C
               CALL SUBPNT ( METHOD,
           .                 'MERCURY', ET,     'IAU_MERCURY', 'LT+S',
           .                 'MPO',     SPOINT, TRGEPC,        SRFVEC  )
 
               WRITE (*,*) '   Apparent sub-observer point of '
           .   //          'BepiColombo MPO on Mercury '
               WRITE (*,*) '   in the IAU_MERCURY frame (km):'
               WRITE (*,'(A,F16.3)') '      X = ', SPOINT(1)
               WRITE (*,'(A,F16.3)') '      Y = ', SPOINT(2)
               WRITE (*,'(A,F16.3)') '      Z = ', SPOINT(3)
               WRITE (*,'(A,F16.3)') '    ALT = ', VNORM(SRFVEC)
 
      C
      C        Compute the apparent sub-solar point on Mercury as seen
      C        from BepiColombo MPO.
      C
               CALL SUBSLR ( METHOD,
           .                 'MERCURY', ET,     'IAU_MERCURY', 'LT+S',
           .                 'MPO',     SPOINT, TRGEPC,        SRFVEC  )
 
               WRITE (*,*) '   Apparent sub-solar point on Mercury as '
           .   //          'seen from BepiColombo'
               WRITE (*,*) '   MPO in the IAU_MERCURY frame (km):'
               WRITE (*,'(A,F16.3)') '      X = ', SPOINT(1)
               WRITE (*,'(A,F16.3)') '      Y = ', SPOINT(2)
               WRITE (*,'(A,F16.3)') '      Z = ', SPOINT(3)
 
            END DO
 
            END
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Input UTC Time: 2027 JAN 05 02:04:36
       Converting UTC Time: 2027 JAN 05 02:04:36
         ET seconds past J2000:    852386745.184
 
       Sub-point/target shape model: NEAR POINT/Ellipsoid
 
          Apparent sub-observer point of BepiColombo MPO on Mercury
          in the IAU_MERCURY frame (km):
            X =         1978.726
            Y =          640.793
            Z =         1275.611
          ALT =          463.634
          Apparent sub-solar point on Mercury as seen from BepiColombo
          MPO in the IAU_MERCURY frame (km):
            X =         1526.831
            Y =         1903.936
            Z =           -1.436
 
       Sub-point/target shape model: NADIR/DSK/Unprioritized
 
          Apparent sub-observer point of BepiColombo MPO on Mercury
          in the IAU_MERCURY frame (km):
            X =         1979.558
            Y =          641.062
            Z =         1276.148
          ALT =          462.608
          Apparent sub-solar point on Mercury as seen from BepiColombo
          MPO in the IAU_MERCURY frame (km):
            X =         1525.673
            Y =         1902.492
            Z =           -1.434
 
 
Extra Credit
--------------------------------------------------------
 
   In this ``extra credit'' section you will be presented with more complex
   tasks, aimed at improving your understanding of SUBPNT and SUBSLR
   routines.
 
   These ``extra credit'' tasks are provided as task statements, and unlike
   the regular tasks, no approach or solution source code is provided. In
   the next section, you will find the numeric solutions (when applicable)
   and answers to the questions asked in these tasks.
 
 
Task statements and questions
 
       1.   Recompute the apparent sub-solar point on Mercury as seen from
            BepiColombo MPO in the body fixed frame IAU_MERCURY in
            kilometers using the 'Intercept/ellipsoid' method at "2027 JAN
            05 02:04:36". Explain the differences.
 
       2.   Compute the geometric sub-spacecraft point of BepiColombo MPO
            on Europa in the body fixed frame IAU_EUROPA in kilometers
            using the 'Near point/ellipsoid' method at "2027 JAN 05
            02:04:36". This point itself is not of any particular interest,
            but it is useful as input to the next ``extra credit'' task.
 
       3.   Transform the sub-spacecraft Cartesian coordinates obtained in
            the previous task to planetocentric and planetographic
            coordinates. When computing planetographic coordinates,
            retrieve Europa' radii by calling BODVRD and use the first
            element of the returned radii values as Europa' equatorial
            radius. Explain why planetocentric and planetographic latitudes
            and longitudes are different. Explain why the planetographic
            altitude for a point on the surface of Europa is not zero and
            whether this is correct or not.
 
 
Solutions and answers
 
       1.   The differences observed are due to the computation method. The
            ``Intercept/ellipsoid'' method defines the sub-solar point as
            the target surface intercept of the line containing the Sun and
            the target's center, while the ``Near point/ellipsoid'' method
            defines the sub-solar point as the the nearest point on the
            target relative to the Sun. Since Mercury is not spherical,
            these two points are not the same:
 
         Apparent sub-solar point on Mercury as seen from BepiColombo MPO
         in the IAU_MERCURY frame using the 'Near Point: ellipsoid' method
         (km):
            X =         1526.828
            Y =         1903.939
            Z =           -1.435
 
         Apparent sub-solar point on Mercury as seen from BepiColombo MPO
         in the IAU_MERCURY frame using the 'Intercept: ellipsoid' method
         (km):
            X =         1526.828
            Y =         1903.939
            Z =           -1.438
 
       2.   Download the relevant SPK prodiving ephemeris data for Europa,
            add it to the meta-kernel and run again your extended program:
 
 
         Additional kernels required for this task:
 
            1. Generic Jovian Satellite Ephemeris SPK:
 
                  jup365_2027.bsp
 
         available in the NAIF server at:
 
      https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/
      satellites/a_old_versions
 
 
            The geometric sub-spacecraft point of BepiColombo MPO on Europa
            in the body fixed frame IAU_EUROPA in kilometers at "2027 JAN
            05 02:04:36" UTC epoch is:
 
         Geometric sub-spacecraft point of BepiColombo MPO on Europa in
         the IAU_EUROPA frame using the 'Near Point: ellipsoid' method
         (km):
            X =         -753.484
            Y =        -1366.703
            Z =          -24.296
 
       3.   The sub-spacecraft point of BepiColombo MPO on Europa in
            planetocentric and planetographic coordinates at "2027 JAN 05
            02:04:36" UTC epoch is:
 
         Planetocentric coordinates of the BepiColombo MPO
         sub-spacecraft point on Europa (degrees, km):
         LAT =           -0.892
         LON =         -118.869
         R   =         1560.835
 
         Planetographic coordinates of the BepiColombo MPO
         sub-spacecraft point on Europa (degrees, km):
         LAT =           -0.895
         LON =          118.869
         ALT =           -1.764
 
            The planetocentric and planetographic longitudes are different
            (``graphic'' = 360 - ``centric'') because planetographic
            longitudes on Europa are measured positive west as defined by
            the Europa' rotation direction.
 
            The planetocentric and planetographic latitudes are different
            because the planetocentric latitude was computed as the angle
            between the direction from the center of the body to the point
            and the equatorial plane, while the planetographic latitude was
            computed as the angle between the surface normal at the point
            and the equatorial plane.
 
            The planetographic altitude is non zero because it was computed
            using a different and incorrect Europa surface model: a
            spheroid with equal equatorial radii. The surface point
            computed by SUBPNT was computed by treating Europa as a
            triaxial ellipsoid with different equatorial radii. The
            planetographic latitude is also incorrect because it is based
            on the normal to the surface of the spheroid rather than the
            ellipsoid, In general planetographic coordinates cannot be used
            for bodies with shapes modeled as triaxial ellipsoids.
 
 
Intersecting Vectors with an Ellipsoid and a DSK (fovint)
===========================================================================
 
 
Task Statement
--------------------------------------------------------
 
   Write a program that prompts the user for an input UTC time string and,
   for that time, computes the intersection of the BepiColombo MPO
   SIMBIO-SYS HRIC channel boresight and field of view (FOV) boundary
   vectors with the surface of Mercury. Compute each intercept twice: once
   with Mercury' shape modeled as an ellipsoid, and once with Mercury'
   shape modeled by DSK data. The program presents each point of
   intersection as
 
       1.   A Cartesian vector in the IAU_MERCURY frame
 
       2.   Planetocentric (latitudinal) coordinates in the IAU_MERCURY
            frame.
 
   For each of the camera FOV boundary and boresight vectors, if an
   intersection is found, the program displays the results of the above
   computations, otherwise it indicates no intersection exists.
 
   At each point of intersection compute the following:
 
       3.   Phase angle
 
       4.   Solar incidence angle
 
       5.   Emission angle
 
   These angles should be computed using both ellipsoidal and DSK shape
   models.
 
   Additionally compute the local solar time at the intercept of the
   spectrometer aperture boresight with the surface of Mercury, using both
   ellipsoidal and DSK shape models.
 
   Use this program to compute values at the UTC epoch:
 
            "2027 JAN 05 02:04:36"
 
 
Learning Goals
--------------------------------------------------------
 
   Understand how field of view parameters are retrieved from instrument
   kernels. Learn how various standard planetary constants are retrieved
   from text PCKs. Discover how to compute the intersection of field of
   view vectors with target bodies whose shapes are modeled as ellipsoids
   or provided by DSKs. Discover another high level geometry routine and
   another time conversion routine in SPICE.
 
 
Approach
--------------------------------------------------------
 
   This problem can be broken down into several simple, small steps:
 
       --   Decide which SPICE kernels are necessary. Prepare a meta-kernel
            listing the kernels and load it into the program. Remember, you
            will need to find a kernel with information about the
            BepiColombo MPO SIMBIO-SYS spectrometer.
 
       --   Prompt the user for an input time string.
 
       --   Convert the input time string into ephemeris time expressed as
            seconds past J2000 TDB.
 
       --   Retrieve the FOV (field of view) configuration for the
            BepiColombo MPO SIMBIO-SYS HRIC channel.
 
   For each vector in the set of boundary corner vectors, and for the
   boresight vector, perform the following operations:
 
       --   Compute the intercept of the vector with Mercury modeled as an
            ellipsoid or using DSK data.
 
       --   If this intercept is found, convert the position vector of the
            intercept into planetocentric coordinates.
 
            Then compute the phase, solar incidence, and emission angles at
            the intercept. Otherwise indicate to the user no intercept was
            found for this vector.
 
       --   Compute the planetocentric longitude of the boresight
            intercept.
 
   Finally
 
       --   Compute the local solar time at the boresight intercept
            longitude on a 24-hour clock. The input time for this
            computation should be the TDB observation epoch minus one-way
            light time from the boresight intercept to the spacecraft.
 
   It may be useful to consult the BepiColombo MPO SIMBIO-SYS instrument
   kernel to determine the name of the SIMBIO-SYS HRIC channel as well as
   its configuration. This exercise may make use of some of the concepts
   and (loosely) code from the ``Spacecraft Orientation and Reference
   Frames'' task.
 
 
Solution
--------------------------------------------------------
 
 
Solution Meta-Kernel
 
   The meta-kernel we created for the solution to this exercise is named
   'fovint.tm'. Its contents follow:
 
      KPL/MK
 
         This is the meta-kernel used in the solution of the
         ``Intersecting Vectors with an Ellipsoid and a DSK'' task
         in the Remote Sensing Hands On Lesson.
 
         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
 
            8. SIMBIO-SYS IK:
 
                  bc_mpo_simbio-sys_v08.ti
 
            9. Low-resolution Mercury DSK:
 
                  mercury_lowres.bds
 
      \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',
       'kernels/ik/bc_mpo_simbio-sys_v08.ti'
       'kernels/dsk/mercury_lowres.bds'
 
                         )
 
      \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
            PROGRAM FOVINT
            IMPLICIT NONE
 
      C
      C     SPICELIB functions
      C
            DOUBLE PRECISION      DPR
      C
      C     Local Parameters
      C
      C     The name of the meta-kernel that lists the kernels
      C     to load into the program.
      C
            CHARACTER*(*)         METAKR
            PARAMETER           ( METAKR = 'fovint.tm' )
 
      C
      C     The length of various string variables.
      C
            INTEGER               STRLEN
            PARAMETER           ( STRLEN = 50 )
 
      C
      C     The maximum number of boundary corner vectors
      C     we can retrieve. We've extended this array by 1
      C     element to make room for the boresight vector.
      C
            INTEGER               BCVLEN
            PARAMETER           ( BCVLEN = 5 )
 
      C
      C     Local Variables
      C
            CHARACTER*(STRLEN)    AMPM
            CHARACTER*(STRLEN)    INSFRM
            CHARACTER*(STRLEN)    METHOD ( 2 )
            CHARACTER*(STRLEN)    SHAPE
            CHARACTER*(STRLEN)    TIME
            CHARACTER*(STRLEN)    UTCTIM
            CHARACTER*(STRLEN)    VECNAM ( BCVLEN )
 
            DOUBLE PRECISION      BOUNDS ( 3, BCVLEN )
            DOUBLE PRECISION      BSIGHT ( 3 )
            DOUBLE PRECISION      EMISSN
            DOUBLE PRECISION      ET
            DOUBLE PRECISION      LAT
            DOUBLE PRECISION      LON
            DOUBLE PRECISION      PHASE
            DOUBLE PRECISION      POINT  ( 3 )
            DOUBLE PRECISION      RADIUS
            DOUBLE PRECISION      SOLAR
            DOUBLE PRECISION      SRFVEC ( 3 )
            DOUBLE PRECISION      TRGEPC
 
            INTEGER               HR
            INTEGER               I
            INTEGER               J
            INTEGER               MN
            INTEGER               N
            INTEGER               MERCID
            INTEGER               SC
 
            LOGICAL               FOUND
            LOGICAL               LIT
            LOGICAL               VISIBL
 
 
      C
      C     Load the kernels that this program requires. We
      C     will need:
      C
      C        A leapseconds kernel.
      C        A SCLK kernel for BepiColombo MPO.
      C        Any necessary ephemerides.
      C        The BepiColombo MPO frame kernel.
      C        An BepiColombo MPO C-kernel.
      C        A PCK file with Mercury constants.
      C        The BepiColombo MPO SIMBIO-SYS I-kernel.
      C        A DSK file containing Mercury shape data.
      C
            CALL FURNSH ( METAKR )
 
      C
      C     Prompt the user for the input time string.
      C
            CALL PROMPT ( 'Input UTC Time: ', UTCTIM )
 
            WRITE (*,*) 'Converting UTC Time: ', UTCTIM
 
      C
      C     Convert UTCTIM to ET.
      C
            CALL STR2ET ( UTCTIM, ET )
 
            WRITE (*,'(A,F16.3)') '   ET seconds past J2000: ', ET
 
      C
      C     Now we need to obtain the FOV configuration of the
      C     SIMBIO-SYS HRIC channel.
      C
            CALL GETFVN ( 'MPO_SIMBIO-SYS_HRIC_FPA', BCVLEN, SHAPE,
           .              INSFRM, BSIGHT, N, BOUNDS )
 
      C
      C     Rather than treat BSIGHT as a separate vector,
      C     copy it into the last slot of BOUNDS.
      C
            CALL MOVED ( BSIGHT, 3, BOUNDS(1,5) )
 
      C
      C     Define names for each of the vectors for display
      C     purposes.
      C
            VECNAM (1) = 'Boundary Corner 1'
            VECNAM (2) = 'Boundary Corner 2'
            VECNAM (3) = 'Boundary Corner 3'
            VECNAM (4) = 'Boundary Corner 4'
            VECNAM (5) = 'MPO SIMBIO-SYS HRIC Boresight'
 
      C
      C     Set values of "method" string that specify use of
      C     ellipsoidal and DSK (topographic) shape models.
      C
      C     In this case, we can use the same methods for calls to both
      C     SINCPT and ILUMIN. Note that some SPICE routines require
      C     different "method" inputs from those shown here. See the
      C     API documentation of each routine for details.
      C
            METHOD(1) = 'Ellipsoid'
            METHOD(2) = 'DSK/Unprioritized'
 
      C
      C     Get Mercury ID. We'll use this ID code later, when we
      C     compute local solar time.
      C
            CALL BODN2C ( 'MERCURY', MERCID, FOUND )
      C
      C     Stop the program if the code was not found.
      C
            IF ( .NOT. FOUND ) THEN
               WRITE (*,*) 'Unable to locate the ID code for MERCURY'
               CALL BYEBYE ( 'FAILURE' )
            END IF
 
      C
      C     Now perform the same set of calculations for each
      C     vector listed in the BOUNDS array. Use both
      C     ellipsoidal and detailed (DSK) shape models.
      C
            DO I = 1, 5
 
               WRITE (*,*) ' '
               WRITE (*,*) 'Vector: ', VECNAM(I)
               WRITE (*,*) ' '
 
               DO J = 1, 2
 
                  WRITE (*,*) ' Target shape model: '//METHOD(J)
                  WRITE (*,*) ' '
      C
      C           Call SINCPT to determine coordinates of the
      C           intersection of this vector with the surface
      C           of Mercury.
      C
                  CALL SINCPT ( METHOD(J),     'MERCURY',   ET,
           .                    'IAU_MERCURY', 'LT+S',      'MPO',
           .                    INSFRM,        BOUNDS(1,I), POINT,
           .                    TRGEPC,        SRFVEC,      FOUND )
      C
      C           Check the found flag. Display a message if the point
      C           of intersection was not found, otherwise continue with
      C           the calculations.
      C
                  IF ( .NOT. FOUND ) THEN
 
                     WRITE (*,*) 'No intersection point found at '
           .         //          'this epoch for this vector.'
 
                  ELSE
      C
      C              Now, we have discovered a point of intersection.
      C              Start by displaying the position vector in the
      C              IAU_MERCURY frame of the intersection.
      C
                     WRITE (*,*) '  Position vector of '
           .         //          'surface intercept in '
           .         //          'the IAU_MERCURY'
                     WRITE (*,*) '  frame (km):'
                     WRITE (*,'(A,F16.3)') '      X   = ', POINT(1)
                     WRITE (*,'(A,F16.3)') '      Y   = ', POINT(2)
                     WRITE (*,'(A,F16.3)') '      Z   = ', POINT(3)
 
      C
      C              Display the planetocentric latitude and longitude
      C              of the intercept.
      C
                     CALL RECLAT ( POINT, RADIUS, LON, LAT )
 
                     WRITE (*,*) '  Planetocentric coordinates of the '
           .         //          'intercept (degrees):'
                     WRITE (*,'(A,F16.3)') '      LAT = ', LAT * DPR()
                     WRITE (*,'(A,F16.3)') '      LON = ', LON * DPR()
 
      C
      C              Compute the illumination angles at this
      C              point.
      C
                     CALL ILLUMF ( METHOD(J),  'MERCURY',       'SUN',
           .                       ET,         'IAU_MERCURY',   'LT+S',
           .                       'MPO',      POINT,        TRGEPC,
           .                       SRFVEC,     PHASE,        SOLAR,
           .                       EMISSN,     VISIBL,       LIT    )
 
                     WRITE (*,'(A,F16.3)') '   Phase angle (degrees):'
           .         //                    '           ', PHASE * DPR()
                     WRITE (*,'(A,F16.3)') '   Solar incidence angle '
           .         //                    '(degrees): ', SOLAR * DPR()
                     WRITE (*,'(A,F16.3)') '   Emission angle (degree'
           .         //                    's):        ', EMISSN* DPR()
                     WRITE (*,'(A,L2)'   ) '   Observer visible: ', VISIBL
                     WRITE (*,'(A,L2)'   ) '   Sun visible:      ', LIT
 
                     IF ( I .EQ. 5 ) THEN
      C
      C                 Compute local time corresponding to the TDB
      C                 light time corrected epoch at the boresight
      C                 intercept.
      C
                        CALL ET2LST ( TRGEPC,
           .                          MERCID,
           .                          LON,
           .                          'PLANETOCENTRIC',
           .                          HR,
           .                          MN,
           .                          SC,
           .                          TIME,
           .                          AMPM              )
 
                        WRITE (*,*) ' '
                        WRITE (*,*) '  Local Solar Time at boresight '
           .            //          'intercept (24 Hour Clock): '
                        WRITE (*,*) '     ', TIME
 
                     END IF
 
                  END IF
 
                  WRITE (*,*) ' '
 
               END DO
      C
      C        End of shape model loop.
      C
            END DO
      C
      C     End of vector loop.
      C
            END
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Input UTC Time: 2027 JAN 05 02:04:36
       Converting UTC Time: 2027 JAN 05 02:04:36
         ET seconds past J2000:    852386745.184
 
       Vector: Boundary Corner 1
 
        Target shape model: Ellipsoid
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1973.717
            Y   =          645.436
            Z   =         1281.009
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.670
            LON =           18.109
         Phase angle (degrees):                     44.735
         Solar incidence angle (degrees):           44.622
         Emission angle (degrees):                   1.280
         Observer visible:  T
         Sun visible:       T
 
        Target shape model: DSK/Unprioritized
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1974.257
            Y   =          645.602
            Z   =         1281.346
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.670
            LON =           18.108
         Phase angle (degrees):                     44.735
         Solar incidence angle (degrees):           46.703
         Emission angle (degrees):                   4.145
         Observer visible:  T
         Sun visible:       T
 
 
       Vector: Boundary Corner 2
 
        Target shape model: Ellipsoid
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1979.643
            Y   =          647.354
            Z   =         1270.875
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.391
            LON =           18.108
         Phase angle (degrees):                     45.641
         Solar incidence angle (degrees):           44.447
         Emission angle (degrees):                   1.198
         Observer visible:  T
         Sun visible:       T
 
        Target shape model: DSK/Unprioritized
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1980.449
            Y   =          647.601
            Z   =         1271.407
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.391
            LON =           18.108
         Phase angle (degrees):                     45.641
         Solar incidence angle (degrees):           43.796
         Emission angle (degrees):                   1.894
         Observer visible:  T
         Sun visible:       T
 
 
       Vector: Boundary Corner 3
 
        Target shape model: Ellipsoid
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1983.307
            Y   =          636.037
            Z   =         1270.876
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.391
            LON =           17.781
         Phase angle (degrees):                     44.501
         Solar incidence angle (degrees):           44.666
         Emission angle (degrees):                   1.195
         Observer visible:  T
         Sun visible:       T
 
        Target shape model: DSK/Unprioritized
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1984.034
            Y   =          636.285
            Z   =         1271.361
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.391
            LON =           17.781
         Phase angle (degrees):                     44.501
         Solar incidence angle (degrees):           45.429
         Emission angle (degrees):                   2.027
         Observer visible:  T
         Sun visible:       T
 
 
       Vector: Boundary Corner 4
 
        Target shape model: Ellipsoid
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1977.381
            Y   =          634.119
            Z   =         1281.010
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.670
            LON =           17.780
         Phase angle (degrees):                     43.576
         Solar incidence angle (degrees):           44.840
         Emission angle (degrees):                   1.278
         Observer visible:  T
         Sun visible:       T
 
        Target shape model: DSK/Unprioritized
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1978.158
            Y   =          634.384
            Z   =         1281.499
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.670
            LON =           17.781
         Phase angle (degrees):                     43.576
         Solar incidence angle (degrees):           45.349
         Emission angle (degrees):                   1.920
         Observer visible:  T
         Sun visible:       T
 
 
       Vector: MPO SIMBIO-SYS HRIC Boresight
 
        Target shape model: Ellipsoid
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1978.524
            Y   =          640.740
            Z   =         1275.950
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.530
            LON =           17.944
         Phase angle (degrees):                     44.609
         Solar incidence angle (degrees):           44.644
         Emission angle (degrees):                   0.059
         Observer visible:  T
         Sun visible:       T
 
         Local Solar Time at boresight intercept (24 Hour Clock):
            09:46:41
 
        Target shape model: DSK/Unprioritized
 
         Position vector of surface intercept in the IAU_MERCURY
         frame (km):
            X   =         1979.357
            Y   =          641.010
            Z   =         1276.487
         Planetocentric coordinates of the intercept (degrees):
            LAT =           31.530
            LON =           17.944
         Phase angle (degrees):                     44.609
         Solar incidence angle (degrees):           45.349
         Emission angle (degrees):                   1.138
         Observer visible:  T
         Sun visible:       T
 
         Local Solar Time at boresight intercept (24 Hour Clock):
            09:46:41
 
 
 
Extra Credit
--------------------------------------------------------
 
   There are no ``extra credit'' tasks for this step of the lesson.
 
