Main Page Remote Sensing Hands-On Lesson, using MPO (Python)
## Table of Contents
       Remote Sensing Hands-On Lesson, using MPO (Python)
          Overview
          Note About HTML Links
          References
             Tutorials
             Required Readings
             The Permuted Index
             SpiceyPy API Documentation
          Kernels Used
          SpiceyPy Modules Used

       Time Conversion (convtm)
          Task Statement
          Learning Goals
          Approach
          Solution
             Solution Meta-Kernel
             Solution Source Code
             Solution Sample Output
          Extra Credit
             Task statements and questions
             Solutions and answers

       Obtaining Target States and Positions (getsta)
          Task Statement
          Learning Goals
          Approach
          Solution
             Solution Meta-Kernel
             Solution Source Code
             Solution Sample Output
          Extra Credit
             Task statements and questions
             Solutions and answers

       Spacecraft Orientation and Reference Frames (xform)
          Task Statement
          Learning Goals
          Approach
          Solution
             Solution Meta-Kernel
             Solution Source Code
             Solution Sample Output
          Extra Credit
             Task statements and questions
             Solutions and answers

       Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts)
          Task Statement
          Learning Goals
          Approach
          Solution
             Solution Meta-Kernel
             Solution Source Code
             Solution Sample Output
          Extra Credit
             Task statements and questions
             Solutions and answers

       Intersecting Vectors with an Ellipsoid and a DSK (fovint)
          Task Statement
          Learning Goals
          Approach
          Solution
             Solution Meta-Kernel
             Solution Source Code
             Solution Sample Output
          Extra Credit
Top # Remote Sensing Hands-On Lesson, using MPO (Python) March 01, 2023 Top ## Overview In this lesson you will develop a series of simple programs that demonstrate the usage of SpiceyPy 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. Top ## 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 ``cspice/'' tree and copy this document to that subdirectory before loading it into a Web browser. Top ## 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 ``cspice/exe'' of Toolkit installation tree. Top ### Tutorials The following SPICE tutorials serve as references for the discussions in this lesson:
       Name              Lesson steps/functions 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:
       https://naif.jpl.nasa.gov/naif/tutorials.html
Top ### Required Readings The Required Reading documents are provided with the Toolkit and are located under the ``cspice/doc'' directory in the CSPICE Toolkit installation tree.
       Name             Lesson steps/functions 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
Top ### The Permuted Index Another useful document distributed with the Toolkit is the permuted index. It is located under the ``cspice/doc'' directory in the C installation tree. This text document provides a simple mechanism by which users can discover which SpiceyPy functions perform functions of interest, as well as the names of the source files that contain these functions.
Top ### SpiceyPy API Documentation A SpiceyPy function's parameters specification is available using the built-in Python help system. A more detailed specification of the API can be found in the CSPICE HTML API documentation page located under ``cspice/doc/html/cspice''. For example, the Python help function
       >>> import spiceypy
       >>> help(spiceypy.str2et)
describes of the str2et function's parameters, while the document
       cspice/doc/html/cspice/str2et_c.html
describes extensively the str2et functionality. Top ## 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/
Top ## SpiceyPy Modules Used This section provides a complete list of the functions and kernels that are suggested for usage in each of the exercises in this lesson. (You may wish to not look at this list unless/until you ``get stuck'' while working on your own.)
       CHAPTER EXERCISE   FUNCTIONS        NON-VOID         KERNELS
       ------- ---------  ---------------  ---------------  ----------
          1    convtm     spiceypy.furnsh  spiceypy.str2et  1,2
                          spiceypy.unload  spiceypy.etcal
                                           spiceypy.timout
                                           spiceypy.sce2s

               extra (*)                   spiceypy.unitim  1,2
                                           spiceypy.sct2e
                                           spiceypy.et2utc
                                           spiceypy.scs2e

          2    getsta     spiceypy.furnsh  spiceypy.str2et  1,3,4
                          spiceypy.unload  spiceypy.spkezr
                                           spiceypy.spkpos
                                           spiceypy.vnorm
                                           spiceypy.convrt

               extra (*)  spiceypy.kclear                   1,4,10

          3    xform      spiceypy.furnsh  spiceypy.str2et  1-7
                          spiceypy.unload  spiceypy.spkezr
                                           spiceypy.sxform
                                           spiceypy.mxvg
                                           spiceypy.spkpos
                                           spiceypy.pxform
                                           spiceypy.mxv
                                           spiceypy.convrt
                                           spiceypy.vsep

               extra (*)  spiceypy.kclear                   1-7

          4    subpts     spiceypy.furnsh  spiceypy.str2et  1,3-4,7,8
                          spiceypy.unload  spiceypy.subpnt
                                           spiceypy.vnorm
                                           spiceypy.subslr

               extra (*)  spiceypy.kclear  spiceypy.reclat  1,3-4,7,10
                                           spiceypy.dpr
                                           spiceypy.bodvrd
                                           spiceypy.recpgr

          5    fovint     spiceypy.furnsh  spiceypy.str2et  1-9
                          spiceypy.no_found_check  spiceypy.getfvn
                          spiceypy.unload  spiceypy.bodn2c
                                           spiceypy.sincpt
                                           spiceypy.reclat
                                           spiceypy.dpr
                                           spiceypy.illumf
                                           spiceypy.et2lst

          (*) Additional APIs and kernels used in Extra Credit tasks.
Use the Python built-in help system on the various functions listed above for the API parameters' description, and refer to the headers of their corresponding CSPICE versions for detailed interface specifications. Top # Time Conversion (convtm) Top ## 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. Top ## Learning Goals Familiarity with the various time conversion and parsing functions available in the Toolkit. Exposure to source code headers and their usage in learning to call functions. Top ## 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: spiceypy.etcal or spiceypy.timout. Top ## Solution Top ### 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
Top ### Solution Source Code A sample solution to the problem follows:
       #
       # Solution convtm
       #
       from __future__ import print_function
       from builtins import input

       import spiceypy

       def convtm():
           #
           # Local Parameters
           #
           METAKR = 'convtm.tm'
           SCLKID = -121

           #
           # Load the kernels this program requires.
           # Both the spacecraft clock kernel and a
           # leapseconds kernel should be listed in
           # the meta-kernel.
           #
           spiceypy.furnsh( METAKR )

           #
           # Prompt the user for the input time string.
           #
           utctim = input( 'Input UTC Time: ' )

           print( 'Converting UTC Time: {:s}'.format( utctim ) )

           #
           # Convert utctim to ET.
           #
           et = spiceypy.str2et( utctim )

           print( '   ET Seconds Past J2000: {:16.3f}'.format( et ) )

           #
           # Now convert ET to a calendar time string.
           # This can be accomplished in two ways.
           #
           calet = spiceypy.etcal( et )

           print( '   Calendar ET (etcal):   {:s}'.format( calet ) )

           #
           # Or use timout for finer control over the
           # output format. The picture below was built
           # by examining the header of timout.
           #
           calet = spiceypy.timout( et, 'YYYY-MON-DDTHR:MN:SC ::TDB' )

           print( '   Calendar ET (timout):  {:s}'.format( calet ) )

           #
           # Convert ET to spacecraft clock time.
           #
           sclkst = spiceypy.sce2s( SCLKID, et )

           print( '   Spacecraft Clock Time: {:s}'.format( sclkst ) )

           spiceypy.unload( METAKR )

       if __name__ == '__main__':
           convtm()
Top ### Solution Sample Output Execute the program:
       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
Top ## 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. Top ### 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? Top ### Solutions and answers `1.` Two methods exist in order to convert ephemeris time to Julian Date: spiceypy.unitim and spiceypy.timout. The difference between them is the type of output produced by each method. spiceypy.unitim returns the double precision value of an input epoch, while spiceypy.timout returns the string representation of the ephemeris time in Julian Date format (when picture input is set to 'JULIAND.######### ::TDB'). Refer to the function 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:
       Traceback (most recent call last):
         File "convtm.py", line 73, in <module>
           convtm()
         File "convtm.py", line 36, in convtm
           et = spiceypy.str2et( utctim )
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 139, in with_errcheck
           check_for_spice_error(f)
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 122, in check_for_spice_error
           raise dynamically_instantiate_spiceyerror(
       spiceypy.utils.exceptions.SpiceNOLEAPSECONDS:
       =====================================================================
       ===========

       Toolkit version: CSPICE_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.

       str2et_c --> STR2ET --> TTRANS

       =====================================================================
       ===========
`` This error is triggered by spiceypy.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 function 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:
       Traceback (most recent call last):
         File "convtm.py", line 73, in <module>
           convtm()
         File "convtm.py", line 64, in convtm
           sclkst = spiceypy.sce2s( SCLKID, et )
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 139, in with_errcheck
           check_for_spice_error(f)
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 122, in check_for_spice_error
           raise dynamically_instantiate_spiceyerror(
       spiceypy.utils.exceptions.SpiceKERNELVARNOTFOUND:
       =====================================================================
       ===========

       Toolkit version: CSPICE_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.

       sce2s_c --> SCE2S --> SCE2T --> SCTYPE --> SCTY01

       =====================================================================
       ===========
`` This error is triggered by spiceypy.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 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 spiceypy.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 spiceypy.timout or spiceypy.et2utc. The solution for the requested SCLK string is:
          Earliest UTC convertible to SCLK: 1999-08-22T00:00:05.204
`6.` Use spiceypy.scs2e with the SCLK string obtained in the computations performed in the regular tasks and convert the resulting ephemeris time to UTC using either spiceypy.et2utc, with 'ISOC' format and 3 digits precision, or using spiceypy.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
Top # Obtaining Target States and Positions (getsta) Top ## 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. Top ## Learning Goals Understand the anatomy of an spiceypy.spkezr call. Discover the difference between spiceypy.spkezr and spiceypy.spkpos. Familiarity with the Toolkit utility ``brief''. Exposure to unit conversion with SpiceyPy. Top ## 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 function 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 ``cspice/exe'' directory for C toolkits. Consult its user's guide available in ``cspice/doc/brief.ug'' for details. Top ## Solution Top ### 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
Top ### Solution Source Code A sample solution to the problem follows:
       #
       # Solution getsta.py
       #
       from __future__ import print_function
       from builtins import input

       import spiceypy

       def getsta():
           #
           # Local parameters
           #
           METAKR = 'getsta.tm'

           #
           # Load the kernels that this program requires.  We
           # will need a leapseconds kernel to convert input
           # UTC time strings into ET.  We also will need the
           # necessary SPK files with coverage for the bodies
           # in which we are interested.
           #
           spiceypy.furnsh( METAKR )

           #
           #Prompt the user for the input time string.
           #
           utctim = input( 'Input UTC Time: ' )

           print( 'Converting UTC Time: {:s}'.format(utctim)  )

           #
           #Convert utctim to ET.
           #
           et = spiceypy.str2et( utctim )

           print( '   ET seconds past J2000: {:16.3f}'.format(et) )

           #
           # Compute the apparent state of Mercury as seen from
           # BepiColombo MPO in the J2000 frame.  All of the ephemeris
           # readers return states in units of kilometers and
           # kilometers per second.
           #
           [state, ltime] = spiceypy.spkezr( 'MERCURY', et,  'J2000',
                                             'LT+S',   'MPO'       )

           print( '   Apparent state of Mercury as seen '
                  'from BepiColombo MPO in the\n'
                  '      J2000 frame (km, km/s):'             )

           print( '      X = {:16.3f}'.format(state[0])       )
           print( '      Y = {:16.3f}'.format(state[1])       )
           print( '      Z = {:16.3f}'.format(state[2])       )
           print( '     VX = {:16.3f}'.format(state[3])       )
           print( '     VY = {:16.3f}'.format(state[4])       )
           print( '     VZ = {:16.3f}'.format(state[5])       )

           #
           # Compute the apparent position of Earth as seen from
           # BepiColombo MPO in the J2000 frame.  Note: We could have
           # continued using spkezr and simply ignored the
           # velocity components.
           #
           [pos, ltime] = spiceypy.spkpos( 'EARTH', et,    'J2000',
                                           'LT+S',  'MPO',         )

           print( '   Apparent position of Earth as '
                  'seen from BepiColombo MPO in the\n'
                  '      J2000 frame (km):'                )
           print( '      X = {:16.3f}'.format(pos[0])  )
           print( '      Y = {:16.3f}'.format(pos[1])  )
           print( '      Z = {:16.3f}'.format(pos[2])  )

           #
           # We need only display LTIME, as it is precisely the
           # light time in which we are interested.
           #
           print( '   One way light time between BepiColombo '
                  'MPO and the apparent\n'
                  '      position of Earth (seconds):'
                  ' {:16.3f}'.format(ltime) )

           #
           # Compute the apparent position of the Sun as seen from
           # Mercury in the J2000 frame.
           #
           [pos, ltime] = spiceypy.spkpos( 'SUN',  et,        'J2000',
                                           'LT+S', 'MERCURY',         )

           print( '   Apparent position of Sun as '
                  'seen from Mercury in the\n'
                  '       J2000 frame (km):'           )
           print( '      X = {:16.3f}'.format(pos[0])  )
           print( '      Y = {:16.3f}'.format(pos[1])  )
           print( '      Z = {:16.3f}'.format(pos[2])  )

           #
           # Now we need to compute the actual distance between
           # the Sun and Mercury.  The above spkpos call gives us
           # the apparent distance, so we need to adjust our
           # aberration correction appropriately.
           #
           [pos, ltime] = spiceypy.spkpos( 'SUN',  et,      'J2000',
                                           'NONE', 'MERCURY'         )

           #
           # Compute the distance between the body centers in
           # kilometers.
           #
           dist = spiceypy.vnorm( pos )

           #
           # Convert this value to AU using convrt.
           #
           dist = spiceypy.convrt( dist, 'KM', 'AU' )

           print( '   Actual distance between Sun and '
                  'Mercury body centers:\n'
                  '      (AU): {:16.3f}'.format(dist) )

           spiceypy.unload( METAKR )

       if __name__ == '__main__':
           getsta()
Top ### Solution Sample Output Execute the program:
       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
Top ## 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 spiceypy.spkezr function, 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. Top ### 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. Top ### Solutions and answers `1.` When running the original program without the planetary ephemerides SPK, an error is produced by spiceypy.spkezr:
       Traceback (most recent call last):
         File "getsta.py", line 128, in <module>
           getsta()
         File "getsta.py", line 46, in getsta
           [state, ltime] = spiceypy.spkezr( 'MERCURY', et,  'J2000',
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 139, in with_errcheck
           check_for_spice_error(f)
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 122, in check_for_spice_error
           raise dynamically_instantiate_spiceyerror(
       spiceypy.utils.exceptions.SpiceSPKINSUFFDATA:
       =====================================================================
       ===========

       Toolkit version: CSPICE_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
       ephemeris epoch 2027 JAN 05 02:05:45.184.

       spkezr_c --> SPKEZR --> SPKEZ --> SPKACS --> SPKGEO

       =====================================================================
       ===========
`` 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 spiceypy.spkpos function 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, spiceypy.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
Top # Spacecraft Orientation and Reference Frames (xform) Top ## 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. Top ## 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 functions. Understand the difference between spiceypy.pxform and spiceypy.sxform. Top ## 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 SpiceyPy functions with which you are already familiar. The ``long way'' presented above is intended to facilitate the introduction of the functions spiceypy.pxform and spiceypy.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. Top ## Solution Top ### 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
Top ### Solution Source Code A sample solution to the problem follows:
       #
       # Solution xform.py
       #
       from __future__ import print_function
       from builtins import input

       import spiceypy

       def xform():
           #
           # Local parameters
           #
           METAKR = 'xform.tm'

           #
           # Load the kernels that this program requires.  We
           # will need:
           #
           #    A leapseconds kernel
           #    A spacecraft clock kernel for BepiColombo MPO
           #    The necessary ephemerides
           #    A planetary constants file (PCK)
           #    A spacecraft orientation kernel for BepiColombo MPO (CK)
           #    A frame kernel (TF)
           #
           spiceypy.furnsh( METAKR )

           #
           #  Prompt the user for the input time string.
           #
           utctim = input( 'Input UTC Time: ' )

           print( 'Converting UTC Time: {:s}'.format(utctim)  )

           #
           #Convert utctim to ET.
           #
           et = spiceypy.str2et( utctim )

           print( '   ET seconds past J2000: {:16.3f}'.format(et) )

           #
           # Compute the apparent state of Mercury as seen from
           # BepiColombo MPO in the J2000 frame.
           #
           [state, ltime] = spiceypy.spkezr( 'MERCURY', et,   'J2000',
                                             'LT+S',    'MPO'         )
           #
           # Now obtain the transformation from the inertial
           # J2000 frame to the non-inertial body-fixed IAU_MERCURY
           # frame.  Since we want the apparent position, we
           # need to subtract ltime from et.
           #
           sform = spiceypy.sxform( 'J2000', 'IAU_MERCURY', et-ltime )

           #
           # Now rotate the apparent J2000 state into IAU_MERCURY
           # with the following matrix multiplication:
           #
           bfixst = spiceypy.mxvg ( sform, state )

           #
           # Display the results.
           #
           print( '   Apparent state of Mercury as seen '
                  'from BepiColombo MPO in the\n'
                  '      IAU_MERCURY body-fixed frame (km, km/s):' )
           print( '      X = {:19.6f}'.format(bfixst[0])    )
           print( '      Y = {:19.6f}'.format(bfixst[1])    )
           print( '      Z = {:19.6f}'.format(bfixst[2])    )
           print( '     VX = {:19.6f}'.format(bfixst[3])    )
           print( '     VY = {:19.6f}'.format(bfixst[4])    )
           print( '     VZ = {:19.6f}'.format(bfixst[5])    )

           #
           # It is worth pointing out, all of the above could
           #  have been done with a single use of spkezr:
           #
           [state, ltime] = spiceypy.spkezr(
                               'MERCURY', et,   'IAU_MERCURY',
                               'LT+S',    'MPO'               )
           #
           # Display the results.
           #
           print( '   Apparent state of Mercury as seen '
                  'from BepiColombo MPO in the\n'
                  '      IAU_MERCURY body-fixed frame '
                  '(km, km/s) obtained using\n'
                  '      spkezr directly:' )
           print( '      X = {:19.6f}'.format(state[0])    )
           print( '      Y = {:19.6f}'.format(state[1])    )
           print( '      Z = {:19.6f}'.format(state[2])    )
           print( '     VX = {:19.6f}'.format(state[3])    )
           print( '     VY = {:19.6f}'.format(state[4])    )
           print( '     VZ = {:19.6f}'.format(state[5])    )

           #
           # Note that the velocity found by using spkezr
           # to compute the state in the IAU_MERCURY frame differs
           # at the few mm/second level from that found previously
           # by calling spkezr and then sxform. Computing
           # velocity via a single call to spkezr as we've
           # done immediately above is slightly more accurate because
           # it accounts for the effect of the rate of change of
           # light time on the apparent angular velocity of the
           # target's body-fixed reference frame.
           #
           # Now we are to compute the angular separation between
           # the apparent position of Mercury as seen from the orbiter
           # and the nominal instrument view direction. First,
           # compute the apparent position of Mercury as seen from
           # BepiColombo MPO in the J2000 frame.
           #
           [pos, ltime] = spiceypy.spkpos( 'MERCURY', et,   'J2000',
                                           'LT+S',    'MPO'         )

           #
           # Now compute the location of the nominal instrument view
           # direction.  From reading the frame kernel we know that
           # the instrument view direction is nominally the +Z axis
           # of the MPO_SPACECRAFT frame defined there.
           #
           bsight = [ 0.0, 0.0, 1.0 ]

           #
           # Now compute the rotation matrix from MPO_SPACECRAFT into
           # J2000.
           #
           pform = spiceypy.pxform( 'MPO_SPACECRAFT', 'J2000', et )

           #
           # And multiply the result to obtain the nominal instrument
           # view direction in the J2000 reference frame.
           #
           bsight = spiceypy.mxv( pform, bsight )

           #
           # Lastly compute the angular separation.
           #
           sep =  spiceypy.convrt( spiceypy.vsep(bsight, pos),
                                   'RADIANS', 'DEGREES'       )

           print( '   Angular separation between the '
                  'apparent position of Mercury and\n'
                  '      the BepiColombo MPO nominal instrument '
                  'view direction\n'
                  '      (degrees):\n'
                  '      {:16.3f}'.format(sep)        )

           #
           # Or alternatively we can work in the spacecraft
           # frame directly.
           #
           [pos, ltime] = spiceypy.spkpos(
                             'MERCURY', et,   'MPO_SPACECRAFT',
                             'LT+S',    'MPO'                 )

           #
           # The nominal instrument view direction is the +Z-axis
           # in the MPO_SPACECRAFT frame.
           #
           bsight = [ 0.0, 0.0, 1.0 ]

           #
           # Lastly compute the angular separation.
           #
           sep =  spiceypy.convrt( spiceypy.vsep(bsight, pos),
                                   'RADIANS', 'DEGREES'       )

           print( '   Angular separation between the '
                  'apparent position of Mercury and\n'
                  '      the BepiColombo MPO nominal instrument '
                  'view direction computed\n'
                  '      using vectors in the '
                  'MPO_SPACECRAFT frame (degrees):\n'
                  '      {:16.3f}'.format(sep)            )

           spiceypy.unload( METAKR )

       if __name__ == '__main__':
           xform()
Top ### Solution Sample Output Execute the program:
       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
Top ## 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. Top ### 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? Top ### Solutions and answers `1.` When running the original software using as input the UTC time string "2027 JAN 06 15:32:05":
       Traceback (most recent call last):
         File "xform.py", line 185, in <module>
           xform()
         File "xform.py", line 131, in xform
           pform = spiceypy.pxform( 'MPO_SPACECRAFT', 'J2000', et )
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 139, in with_errcheck
           check_for_spice_error(f)
         File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
       piceypy/spiceypy.py", line 122, in check_for_spice_error
           raise dynamically_instantiate_spiceyerror(
       spiceypy.utils.exceptions.SpiceNOFRAMECONNECT:
       =====================================================================
       ===========

       Toolkit version: CSPICE_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 f
       rame -121000 (MPO_SPACECRAFT) to reference frame 1 (J2000). MPO_SPACE
       CRAFT is a CK frame; a CK file containing data for instrument or stru
       cture -121000 at the epoch shown above, as well as a corresponding SC
       LK kernel, must be loaded in order to use this frame. Failure to find
        required CK data could be due to one or more CK files not having bee
       n loaded, or to the epoch shown above lying within a coverage gap or
       beyond the coverage bounds of the loaded CK files. It is also possibl
       e that no loaded CK file has required angular velocity data for the i
       nput epoch, even if a loaded CK does have attitude data for that epoc
       h. You can use CKBRIEF with the -dump option to display coverage inte
       rvals of a CK file.

       pxform_c --> PXFORM --> REFCHG

       =====================================================================
       ===========
`` spiceypy.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. Top # Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts) Top ## 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. Top ## Learning Goals Discover higher level geometry calculation functions in SpiceyPy and their usage as it relates to BepiColombo MPO. Top ## Approach This particular problem is more of an exercise in searching the permuted index to find the appropriate functions 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? Top ## Solution Top ### 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
Top ### Solution Source Code A sample solution to the problem follows:
       #
       # Solution subpts.py
       #
       from __future__ import print_function
       from builtins import input

       #
       # SpiceyPy package:
       #
       import spiceypy

       def subpts():
           #
           # Local parameters
           #
           METAKR = 'subpts.tm'

           #
           # Load the kernels that this program requires.  We
           # will need:
           #
           #    A leapseconds kernel
           #    The necessary ephemerides
           #    A planetary constants file (PCK)
           #    A DSK file containing Mercury shape data
           #
           spiceypy.furnsh( METAKR )

           #
           #Prompt the user for the input time string.
           #
           utctim = input( 'Input UTC Time: ' )

           print( ' Converting UTC Time: {:s}'.format(utctim)  )

           #
           #Convert utctim to ET.
           #
           et = spiceypy.str2et( utctim )

           print( '   ET seconds past J2000: {:16.3f}'.format(et) )

           for  i  in range(2):

               if  i  == 0:
                   #
                   # Use the "near point" sub-point definition
                   # and an ellipsoidal model.
                   #
                   method = 'NEAR POINT/Ellipsoid'

               else:
                   #
                   # Use the "nadir" sub-point definition
                   # and a DSK model.
                   #
                   method = 'NADIR/DSK/Unprioritized'

               print( '\n Sub-point/target shape model: {:s}\n'.format(
                   method )  )

               #
               # Compute the apparent sub-observer point of BepiColombo MPO
               # on Mercury.
               #
               [spoint, trgepc, srfvec] = spiceypy.subpnt(
                                       method,        'MERCURY', et,
                                       'IAU_MERCURY', 'LT+S',    'MPO' )

               print( '   Apparent sub-observer point of BepiColombo '
                      'MPO on Mercury\n'
                      '   in the IAU_MERCURY frame (km):' )
               print( '      X = {:16.3f}'.format(spoint[0])              )
               print( '      Y = {:16.3f}'.format(spoint[1])              )
               print( '      Z = {:16.3f}'.format(spoint[2])              )
               print( '    ALT = {:16.3f}'.format(spiceypy.vnorm(srfvec)) )

               #
               # Compute the apparent sub-solar point on Mercury
               # as seen from BepiColombo MPO.
               #
               [spoint, trgepc, srfvec] = spiceypy.subslr(
                                       method,        'MERCURY', et,
                                       'IAU_MERCURY', 'LT+S',    'MPO' )

               print( '   Apparent sub-solar point on Mercury '
                      'as seen from BepiColombo \n'
                      '   MPO in the IAU_MERCURY frame (km):'  )
               print( '      X = {:16.3f}'.format(spoint[0])   )
               print( '      Y = {:16.3f}'.format(spoint[1])   )
               print( '      Z = {:16.3f}'.format(spoint[2])   )

           #
           # End of computation block for "method"
           #
           print( '' )

           spiceypy.unload( METAKR )

       if __name__ == '__main__':
           subpts()
Top ### Solution Sample Output Execute the program:
       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
Top ## Extra Credit In this ``extra credit'' section you will be presented with more complex tasks, aimed at improving your understanding of spiceypy.subpnt and spiceypy.subslr functions. 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. Top ### 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 spiceypy.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. Top ### 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 spiceypy.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. Top # Intersecting Vectors with an Ellipsoid and a DSK (fovint) Top ## 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" Top ## 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 function and another time conversion function in SpiceyPy. Top ## 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. Top ## Solution Top ### 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
Top ### Solution Source Code A sample solution to the problem follows:
       #
       # Solution fovint.py
       #
       from __future__ import print_function
       from builtins import input

       #
       # SpiceyPy package:
       #
       import spiceypy
       from spiceypy.utils.support_types import SpiceyError

       def fovint():
           #
           # Local parameters
           #
           METAKR = 'fovint.tm'
           ROOM   = 4

           #
           # Load the kernels that this program requires.  We
           # will need:
           #
           #    A leapseconds kernel.
           #    A SCLK kernel for BepiColombo MPO.
           #    Any necessary ephemerides.
           #    The BepiColombo MPO frame kernel.
           #    An BepiColombo MPO C-kernel.
           #    A PCK file with Mercury constants.
           #    The BepiColombo MPO SIMBIO-SYS I-kernel.
           #    A DSK file containing Mercury shape data.
           #
           spiceypy.furnsh( METAKR )

           #
           # Prompt the user for the input time string.
           #
           utctim = input( 'Input UTC Time: ' )

           print( 'Converting UTC Time: {:s}'.format(utctim)  )

           #
           # Convert utctim to ET.
           #
           et = spiceypy.str2et( utctim )

           print( '  ET seconds past J2000: {:16.3f}\n'.format(et) )

           #
           # Now we need to obtain the FOV configuration of
           # the SIMBIO-SYS HRIC channel.
           #
           [ shape, insfrm, bsight,
             n, bounds ] = spiceypy.getfvn( 'MPO_SIMBIO-SYS_HRIC_FPA', ROOM
       )

           #
           # `bounds' is a numpy array. We'll convert it to a list.
           #
           # Rather than treat BSIGHT as a separate vector,
           # copy it into the last slot of BOUNDS.
           #
           bounds = bounds.tolist()
           bounds.append( bsight )

           #
           # Set vector names to be used for output.
           #
           vecnam = [ 'Boundary Corner 1',
                      'Boundary Corner 2',
                      'Boundary Corner 3',
                      'Boundary Corner 4',
                      'MPO SIMBIO-SYS HRIC Boresight' ]

           #
           # Set values of "method" string that specify use of
           # ellipsoidal and DSK (topographic) shape models.
           #
           # In this case, we can use the same methods for calls to both
           # spiceypy.sincpt and spiceypy.ilumin. Note that some SPICE
           # routines require different "method" inputs from those
           # shown here. See the API documentation of each routine
           # for details.
           #
           method = [ 'Ellipsoid', 'DSK/Unprioritized' ]

           #
           # Get ID code of Mercury. We'll use this ID code later, when we
           # compute local solar time.
           #
           try:
               marsid = spiceypy.bodn2c( 'MERCURY' )

           except SpiceyError as exc:
               #
               # The ID code for MERCURY is built-in to the library.
               # However, it is good programming practice to get
               # in the habit of handling exceptions that may
               # be thrown when a quantity is not found.
               #
               #
               # Also see the call to spiceypy.sincpt below for an
               # example of handling a "not found" condition that is
               # not an error.
               #
               print( 'Exception message is: {:s}'.format( exc.message ) )

               raise

           #
           # Now perform the same set of calculations for each
           # vector listed in the BOUNDS array. Use both
           # ellipsoidal and detailed (DSK) shape models.
           #
           for i  in  range(5):
               #
               # Call sincpt to determine coordinates of the
               # intersection of this vector with the surface
               # of Mercury.
               #
               print( 'Vector: {:s}\n'.format( vecnam[i] ) )

               for  j  in range(2):

                   print ( ' Target shape model: {:s}\n'.format(
                                                method[j]      )  )

                   #
                   # Treat an "intercept not found" condition as a normal
                   # case rather than as an exception. This way we
                   # distinguish between this condition and other
                   # exceptions, in particular, any other "not found"
                   # exceptions.
                   #
                   with spiceypy.no_found_check():

                       [point, trgepc, srfvec, found ] = spiceypy.sincpt(
                           method[j],   'MERCURY',     et,
                           'IAU_MERCURY',  'LT+S',    'MPO',
                           insfrm,      bounds[i]         )

                   if found:
                       #
                       # Now, we have discovered a point of intersection.
                       # Start by displaying the position vector in the
                       # IAU_MERCURY frame of the intersection.
                       #
                       print( '  Position vector of surface intercept '
                              'in the IAU_MERCURY frame (km):'           )
                       print( '     X   = {:16.3f}'.format( point[0] )  )
                       print( '     Y   = {:16.3f}'.format( point[1] )  )
                       print( '     Z   = {:16.3f}'.format( point[2] )  )

                       #
                       # Display the planetocentric latitude and longitude
                       # of the intercept.
                       #
                       [radius, lon, lat] = spiceypy.reclat( point )

                       print( '  Planetocentric coordinates of '
                              'the intercept (degrees):'          )
                       print( '     LAT = {:16.3f}'.format(
                                          lat * spiceypy.dpr() )  )
                       print( '     LON = {:16.3f}'.format(
                                          lon * spiceypy.dpr() )  )
                       #
                       # Compute the illumination angles at this
                       # point.
                       #
                       [ trgepc, srfvec, phase, solar,
                         emissn, visibl, lit           ] = spiceypy.illumf(
                            method[j],   'MERCURY', 'SUN',     et,
                           'IAU_MERCURY', 'LT+S',   'MPO', point )

                       print( '  Phase angle (degrees):           '
                              '{:16.3f}'.format( phase*spiceypy.dpr() )  )
                       print( '  Solar incidence angle (degrees): '
                              '{:16.3f}'.format( solar*spiceypy.dpr() )  )
                       print( '  Emission angle (degrees):        '
                              '{:16.3f}'.format( emissn*spiceypy.dpr())  )
                       print( '  Observer visible:  {:s}'.format(
                           str(visibl) )  )
                       print( '  Sun visible:       {:s}'.format(
                           str(lit)    )  )

                       if  i  ==  4:
                           #
                           # Compute local solar time corresponding
                           # to the light time corrected TDB epoch
                           # at the boresight intercept.
                           #
                           [hr, mn, sc, time, ampm] = spiceypy.et2lst(
                               trgepc,
                               marsid,
                               lon,
                               'PLANETOCENTRIC' )

                           print( '\n  Local Solar Time at boresight '
                                  'intercept (24 Hour Clock):\n'
                                  '     {:s}'.format( time )       )
                       #
                       # End of LST computation block.
                       #

                   else:
                       #
                       # Display a message if no intercept was found.
                       # Otherwise, continue with the calculations.
                       #
                       print( 'No intersection point found at '
                              'this epoch for this vector.\n'  )

                   #
                   # End of spiceypy.sincpt intercept handling block.
                   #
                   print( '' )
               #
               # End of target shape model loop.
               #
           #
           # End of vector loop.
           #

           spiceypy.unload( METAKR )

       if __name__ == '__main__':
            fovint()
Top ### Solution Sample Output Execute the program:
       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:  true
         Sun visible:       true

        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:  true
         Sun visible:       true

       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:  true
         Sun visible:       true

        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:  true
         Sun visible:       true

       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:  true
         Sun visible:       true

        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:  true
         Sun visible:       true

       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:  true
         Sun visible:       true

        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:  true
         Sun visible:       true

       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:  true
         Sun visible:       true

         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:  true
         Sun visible:       true

         Local Solar Time at boresight intercept (24 Hour Clock):
            09:46:41
Top ## Extra Credit There are no ``extra credit'' tasks for this step of the lesson.