Main Page Remote Sensing Hands-On Lesson, using TGO (IDL)
## Table of Contents
       Remote Sensing Hands-On Lesson, using TGO (IDL)
          Overview
          Note About HTML Links
          References
             Tutorials
             Required Readings
             The Permuted Index
             Icy API Documentation
          Kernels Used
          Icy 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 TGO (IDL) May 21, 2018 Top ## Overview In this lesson you will develop a series of simple programs that demonstrate the usage of Icy 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 ExoMars-16 TGO 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 ``icy/'' 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 ``icy/exe'' of Toolkit installation tree. Top ### Tutorials The following SPICE tutorials serve as references for the discussions in this lesson:
       Name              Lesson steps/routines it describes
       ----------------  -----------------------------------------------
       Time              Time Conversion
       SCLK and LSK      Time Conversion
       SPK               Obtaining Ephemeris Data
       Frames            Reference Frames
       Using Frames      Reference Frames
       PCK               Planetary Constants Data
       CK                Spacecraft Orientation Data
       DSK               Detailed Target Shape (Topography) Data
These tutorials are available from the NAIF ftp server at JPL:
       http://naif.jpl.nasa.gov/naif/tutorials.html
Top ### Required Readings The Required Reading documents are provided with the Toolkit and are located under the ``icy/doc'' directory in the Icy installation tree.
       Name             Lesson steps/routines that it describes
       ---------------  -----------------------------------------
       ck.req           Obtaining spacecraft orientation data
       dsk.req          Obtaining detailed body shape data
       frames.req       Using reference frames
       naif_ids.req     Determining body ID codes
       pck.req          Obtaining planetary constants data
       sclk.req         SCLK time conversion
       spk.req          Obtaining ephemeris data
       time.req         Time conversion
       icy.req          The Icy API
Top ### The Permuted Index Another useful document distributed with the Toolkit is the permuted index. This is located under the ``icy/doc'' directory in the IDL installation tree. This text document provides a simple mechanism by which users can discover which Icy procedures perform functions of interest, as well as the names of the source files that contain these procedures.
Top ### Icy API Documentation An Icy routine's specification is found in the HTML API documentation page located under ``icy/doc/html/icy''. For example, the document
       icy/doc/html/icy/cspice_str2et.html
describes the cspice_str2et routine. Top ## Kernels Used The following kernels are used in examples provided in this lesson:
       1.  Generic LSK:

              naif0012.tls

       2.  ExoMars-16 TGO SCLK:

              em16_tgo_step_20160414.tsc

       3.  Solar System Ephemeris SPK, subsetted to cover only the time
           range of interest:

              de430.bsp

       4.  Martian Satellite Ephemeris SPK, subsetted to cover only the time
           range of interest:

              mar085.bsp

       5.  ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted to cover only
           the time range of interest:

              em16_tgo_mlt_20171205_20230115_v01.bsp

       6.  Generic PCK:

              pck00010.tpc

       7.  ExoMars-16 TGO FK:

              em16_tgo_v07.tf

       8.  ExoMars-16 TGO Spacecraft CK, subsetted to cover only the time
           range of interest:

              em16_tgo_sc_slt_npo_20171205_20230115_s20160414_v01.bc

       9.  Low-resolution Mars DSK:

              mars_lowres.bds

       10. NOMAD IK:

              em16_tgo_nomad_v02.ti
These SPICE kernels are included in the lesson package available from the NAIF server at JPL:
       ftp://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Lessons/
In addition to these kernels, the extra credit exercises require the following kernels:
       11. Generic Jovian Satellite Ephemeris SPK:

              jup310_2018.bsp

       12. EDM lander FK:

              em16_edm_v00.tf

       13. EDM landing site SPK:

              em16_edm_sot_landing_site_20161020_21000101_v01.bsp
These SPICE kernels are available from the NAIF server at JPL:
       https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/
       https://naif.jpl.nasa.gov/pub/naif/EXOMARS2016/kernels/
Top ## Icy Modules Used This section provides a complete list of the procedures 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     cspice_furnsh                 1,2
                          cspice_str2et
                          cspice_etcal
                          cspice_timout
                          cspice_sce2s
                          cspice_unload

               extra (*)  cspice_sct2e   cspice_unitim  1,2
                          cspice_et2utc
                          cspice_scs2e

          2    getsta     cspice_furnsh  cspice_vnorm   1,3-5
                          cspice_str2et
                          cspice_spkezr
                          cspice_spkpos
                          cspice_convrt
                          cspice_kclear

               extra (*)  cspice_unload                 1,3-6,11-13
                          cspice_bodn2c

          3    xform      cspice_furnsh  cspice_vsep    1-8
                          cspice_str2et
                          cspice_spkezr
                          cspice_sxform
                          cspice_spkpos
                          cspice_pxform
                          cspice_mxv
                          cspice_convrt
                          cspice_kclear

               extra (*)  cspice_unload                 1-8

          4    subpts     cspice_furnsh  cspice_vnorm   1,3-6,9
                          cspice_str2et
                          cspice_subpnt
                          cspice_subslr
                          cspice_unload

               extra (*)  cspice_kclear  cspice_dpr     1,3-6
                          cspice_reclat
                          cspice_bodvrd
                          cspice_recpgr

          5    fovint     cspice_furnsh  cspice_dpr     1-10
                          cspice_str2et
                          cspice_bodn2c
                          cspice_getfov
                          cspice_sincpt
                          cspice_reclat
                          cspice_illumf
                          cspice_et2lst
                          cspice_kclear

          (*) Additional APIs and kernels used in Extra Credit tasks.
Refer to the Icy HTML API documentation pages located under ``icy/doc/html/icy'' for detailed interface specifications of these procedures. 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 "2018 JUN 11 19:32:00" UTC into these alternate systems. Top ## Learning Goals Familiarity with the various time conversion and parsing procedures available in the Toolkit. Exposure to source code headers and their usage in learning to call procedures. 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: cspice_etcal or cspice_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. ExoMars-16 TGO SCLK:

                   em16_tgo_step_20160414.tsc

       \begindata

        KERNELS_TO_LOAD = (

        'kernels/lsk/naif0012.tls',
        'kernels/sclk/em16_tgo_step_20160414.tsc'

                          )

       \begintext
Top ### Solution Source Code A sample solution to the problem follows:
       PRO convtm

          ;;
          ;; Local Parameters
          ;;

          METAKR = "convtm.tm"
          SCLKID = -143
          STRLEN = 50
          utctim = ''

          ;;
          ;; Load the kernels this program requires.
          ;; Both the spacecraft clock kernel and a
          ;; leapseconds kernel should be listed in
          ;; the meta-kernel.
          ;;
          cspice_furnsh, METAKR

          ;;
          ;; Prompt the user for the input time string.
          ;;
          read, utctim, PROMPT="Input UTC Time: "

          print, "Converting UTC Time: ", utctim

          ;;
          ;; Convert utctim to et.
          ;;
          cspice_str2et, utctim, et

          print, FORMAT="(A,F16.3)", "   ET Seconds Past J2000: ", et

          ;;
          ;; Now convert ET to a formal calendar time
          ;; string.  This can be accomplished in two
          ;; ways.
          ;;
          cspice_etcal, et, calet

          print, "   Calendar ET (cspice_etcal): ", calet

          ;;
          ;; Or use cspice_timout for finer control over the
          ;; output format.  The picture below was built
          ;; by examining the header of cspice_timout.
          ;;
          cspice_timout, et   , "YYYY-MON-DDTHR:MN:SC ::TDB", $
                        STRLEN, calet

          print, "   Calendar ET (cspice_timout): ", calet

          ;;
          ;; Convert ET to spacecraft clock time.
          ;;
          cspice_sce2s, SCLKID, et, sclkst

          print, "   Spacecraft Clock Time: ", sclkst

          cspice_unload, METAKR

       END
Top ### Solution Sample Output After compiling the program, execute it:
       Input UTC Time: 2018 JUN 11 19:32:00
       Converting UTC Time: 2018 JUN 11 19:32:00
          ET Seconds Past J2000:    582017589.185
          Calendar ET (cspice_etcal): 2018 JUN 11 19:33:09.184
          Calendar ET (cspice_timout): 2018-JUN-11T19:33:09
          Spacecraft Clock Time: 1/0070841719.26698
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 "2018 JUN 11 19:32:00" 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 ExoMars-16 TGO NOMAD LNO Nadir aperture. Convert "2018 JUN 11 19:32:00" UTC. `5.` Find the earliest UTC time that can be converted to ExoMars-16 TGO 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 ExoMars-16 TGO 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: cspice_unitim and cspice_timout. The difference between them is the type of output produced by each method. cspice_unitim returns the double precision value of an input epoch, while cspice_timout returns the string representation of the ephemeris time in Julian Date format (when picture input is set to 'JULIAND.######### ::TDB'). Refer to the routine header for further details. The solution for the requested input UTC string is:
          Julian Date TDB:   2458281.3146896
`2.` When running the original program without the LSK kernel, an error is produced:
       % CSPICE_STR2ET: SPICE(NOLEAPSECONDS): [str2et_c->STR2ET->TTRANS]
                         The variable that points to the leapseconds
                         (DELTET/DELTA_AT) could not be located in the
                         kernel pool.  It is likely that the leapseconds
                         kernel has not been loaded via the routine
                         FURNSH.
       % Execution halted at: CONVTM             32
          /home/bsemenov/tmp/lessons_180518/lessons/remote_sensing_tgo/co
         nvtm.pro
       %                      $MAIN$
`` This error is triggered by cspice_str2et because the variable that points to the leapseconds is not present in the kernel pool and therefore the program lacks data required to perform the requested UTC to ephemeris time conversion. `` By default, SPICE will report, as a minimum, a short descriptive message and a expanded form of this short message where more details about the error are provided. If this error message is not sufficient for you to understand what has happened, you could go to the ``Exceptions'' section in the SPICELIB or CSPICE headers of the routine that has triggered the error and find out more information about the possible causes. `3.` When running the original program without the SCLK kernel, an error is produced:
       % CSPICE_SCE2S: SPICE(KERNELVARNOTFOUND):
                        [sce2s_c->SCE2S->SCE2T->SCTYPE->SCLI01]
                        SCLK_DATA_TYPE_143 not found. Did you load the
                        SCLK kernel?
       % Execution halted at: CONVTM             63
          /home/bsemenov/tmp/lessons_180518/lessons/remote_sensing_tgo/co
         nvtm.pro
       %                      $MAIN$
`` This error is triggered by cspice_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 -143 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 NOMAD LNO Nadir aperture. In order to do so, examine the ExoMars-16 TGO frames definitions kernel listed above and look for the ``TGO NAIF ID Codes -- Summary Section'' or for the ``TGO NAIF ID Codes -- Definitions'' and there, for the NAIF ID given to TGO_NOMAD_LNO_NAD (which is -143311). Then replace in your code the SCLK ID -143 with -143311. After compiling and executing the program using the original meta-kernel, you will be getting the same error as in the previous task. Despite the error being exactly the same, this case is different. Generally, spacecraft clocks are associated with the spacecraft ID and not with its payload, sensors or structures IDs. Therefore, in order to do conversions from/to spacecraft clock for payload, sensors or spacecraft structures, the spacecraft ID must be used. `` Note that this does not need to be true for all missions or payloads, as SPICE does not restrict the SCLKs to spacecraft IDs only. Please refer to your mission's SCLK kernels for particulars. `5.` Use cspice_sct2e with the encoding of the TGO spacecraft clock time set to 0.0 ticks and convert the resulting ephemeris time to UTC using either cspice_timout or cspice_et2utc. The solution for the requested SCLK string is:
          Earliest UTC convertible to SCLK: 2016-03-13T21:34:13.194
`6.` Use cspice_scs2e with the SCLK string obtained in the computations performed in the regular tasks and convert the resulting ephemeris time to UTC using either cspice_et2utc, with 'ISOC' format and 3 digits precision, or using cspice_timout using the time picture 'YYYY-MM-DDTHR:MN:SC.### ::RND'. The solution of the requested conversion is:
          Spacecraft Clock Time:          1/0070841719.26698
          UTC time from spacecraft clock: 2018-06-11T19:32:00.000
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 Mars as seen from ExoMars-16 TGO 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 ExoMars-16 TGO in the J2000 frame, in kilometers. `3.` The one-way light time between ExoMars-16 TGO and the apparent position of Earth, in seconds. `4.` The apparent position of the Sun as seen from Mars in the J2000 frame (J2000), in kilometers. `5.` The actual (geometric) distance between the Sun and Mars, in astronomical units. and displays the results. Use the program to compute these quantities at "2018 JUN 11 19:32:00" UTC. Top ## Learning Goals Understand the anatomy of an cspice_spkezr call. Discover the difference between cspice_spkezr and cspice_spkpos. Familiarity with the Toolkit utility ``brief''. Exposure to unit conversion with Icy. 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 Mars relative to ExoMars-16 TGO in the J2000 reference frame, corrected for aberrations. `--` Compute the position of Earth relative to ExoMars-16 TGO in the J2000 reference frame, corrected for aberrations. (The procedure in the library that computes this also returns the one-way light time between ExoMars-16 TGO and Earth.) `--` Compute the position of the Sun relative to Mars in the J2000 reference frame, corrected for aberrations. `--` Compute the position of the Sun relative to Mars 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 ``icy/exe'' directory for IDL toolkits. Consult its user's guide available in ``icy/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:

                   de430.bsp

             3. Martian Satellite Ephemeris SPK, subsetted to cover
                only the time range of interest:

                   mar085.bsp

             4. ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted
                to cover only the time range of interest:

                   em16_tgo_mlt_20171205_20230115_v01.bsp

       \begindata

        KERNELS_TO_LOAD = (

        'kernels/lsk/naif0012.tls',
        'kernels/spk/de430.bsp',
        'kernels/spk/mar085.bsp',
        'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp',

                            )

       \begintext
Top ### Solution Source Code A sample solution to the problem follows:
       PRO getsta

          ;;
          ;; Local Parameters
          ;;

          METAKR = 'getsta.tm'
          STRLEN = 50
          utctim = ''

          ;;
          ;; 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.
          ;;
          cspice_furnsh, METAKR

          ;;
          ;; Prompt the user for the input time string.
          ;;
          read, utctim, PROMPT = 'Input UTC Time: '

          print, 'Converting UTC Time: ', utctim

          ;;
          ;; Convert utctim to et.
          ;;
          cspice_str2et, utctim, et

          print, FORMAT='(A,F16.3)', '   ET seconds past J2000: ', et

          ;;
          ;; Compute the apparent state of Mars as seen from
          ;; ExoMars-16 TGO in the J2000 frame.  All of the ephemeris
          ;; readers return states in units of kilometers and
          ;; kilometers per second.
          ;;
          cspice_spkezr, 'MARS', et   , 'J2000', 'LT+S', $
                         'TGO',  state, ltime

          print, '   Apparent state of Mars as seen ' +$
                 'from ExoMars-16 TGO in the J2000'
          print, '      frame (km, km/s): '
          print, FORMAT='(A,F16.3)', '      X = ', state[0]
          print, FORMAT='(A,F16.3)', '      Y = ', state[1]
          print, FORMAT='(A,F16.3)', '      Z = ', state[2]
          print, FORMAT='(A,F16.3)', '     VX = ', state[3]
          print, FORMAT='(A,F16.3)', '     VY = ', state[4]
          print, FORMAT='(A,F16.3)', '     VZ = ', state[5]

          ;;
          ;; Compute the apparent position of Earth as seen from
          ;; ExoMars-16 TGO in the J2000 frame.  Note: We could have
          ;; continued using cspice_spkezr and simply ignored the
          ;; velocity components.
          ;;
          cspice_spkpos, 'EARTH', et , 'J2000', 'LT+S', $
                         'TGO',   pos, ltime

          print, '   Apparent position of Earth as '    +$
                      'seen from ExoMars-16 TGO in the'
          print, '      J2000 frame (km):  '
          print, FORMAT='(A,F16.3)', '      X = ', pos[0]
          print, FORMAT='(A,F16.3)', '      Y = ', pos[1]
          print, FORMAT='(A,F16.3)', '      Z = ', pos[2]

          ;;
          ;; We need only display LT, as it is precisely the
          ;; light time in which we are interested.
          ;;
          print, '   One way light time between ExoMars-16 ' +$
                 'TGO and the apparent'
          print, FORMAT='(A,F16.3)', '      position of Earth ' +$
                                     '(seconds): ', ltime

          ;;
          ;; Compute the apparent position of the Sun as seen
          ;; from Mars in the J2000 frame.
          ;;
          cspice_spkpos, 'SUN' , et , 'J2000', 'LT+S', $
                         'MARS', pos, ltime

          print, '   Apparent position of Sun as seen ' +$
                 'from Mars in the '
          print, '      J2000 frame (km): '
          print, FORMAT='(A,F16.3)', '      X = ', pos[0]
          print, FORMAT='(A,F16.3)', '      Y = ', pos[1]
          print, FORMAT='(A,F16.3)', '      Z = ', pos[2]

          ;;
          ;; Now we need to compute the actual distance between
          ;; the Sun and Mars.  The above SPKPOS call gives us
          ;; the apparent distance, so we need to adjust our
          ;; aberration correction appropriately.
          ;;
          cspice_spkpos, 'SUN' , et , 'J2000', 'NONE', $
                         'MARS', pos, ltime

          ;;
          ;; Compute the distance between the body centers in
          ;; kilometers.
          ;;
          dist = cspice_vnorm ( pos )

          ;;
          ;; Convert this value to AU using cspice_convrt.
          ;; Recall, cspice_convrt cannot overwrite the
          ;; input with the output. Use 'dist_au' for the
          ;; output value.
          ;;
          cspice_convrt, dist, 'KM', 'AU', dist_au

          print, '   Actual distance between Sun and Mars ' + $
                 'body centers:'
          print, FORMAT='(A,F16.3)', '      (AU): ', dist_au

          cspice_kclear

       END
Top ### Solution Sample Output After compiling the program, execute it:
       Input UTC Time: 2018 JUN 11 19:32:00
       Converting UTC Time: 2018 JUN 11 19:32:00
          ET seconds past J2000:    582017589.185
          Apparent state of Mars as seen from ExoMars-16 TGO in the J2000
             frame (km, km/s):
             X =         2911.822
             Y =        -2033.802
             Z =        -1291.701
            VX =            1.310
            VY =           -0.056
            VZ =            3.104
          Apparent position of Earth as seen from ExoMars-16 TGO in the
             J2000 frame (km):
             X =    -49609884.080
             Y =     57070665.862
             Z =     30304236.930
          One way light time between ExoMars-16 TGO and the apparent
             position of Earth (seconds):          271.738
          Apparent position of Sun as seen from Mars in the
             J2000 frame (km):
             X =    -24712734.289
             Y =    194560532.943
             Z =     89906636.789
          Actual distance between Sun and Mars body centers:
             (AU):            1.442
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 cspice_spkezr procedure, 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 Martian 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 Mars in the J2000 frame (J2000), in kilometers. `3.` Extend your program to compute the apparent position of the Schiaparelli Entry, Descent and Landing Demonstrator Module (EDM) Landing Site as seen from the ExoMars-16 Trace Gas Orbiter (TGO) spacecraft in the J2000 frame (J2000), in kilometers. `4.` Extend, or modify, your program to compute the position of the Sun as seen from Mars in the J2000 frame (J2000), in kilometers, using the following light time and aberration corrections: NONE, LT and LT+S. Explain the differences. `5.` Examine the ExoMars-16 TGO frames definition kernel to find the SPICE ID/name definitions. Top ### Solutions and answers `1.` When running the original program without the Martian planetary ephemerides SPK, an error is produced by cspice_spkezr:
       % CSPICE_SPKEZR: SPICE(SPKINSUFFDATA):
                         [spkezr_c->SPKEZR->SPKEZ->SPKACS->SPKGEO]
                         Insufficient ephemeris data has been loaded to
                         compute the state of -143 (EXOMARS 2016 TGO)
                         relative to 0 (SOLAR SYSTEM BARYCENTER) at the
                         ephemeris epoch 2018 JUN 11 19:33:09.184.
       % Execution halted at: GETSTA             42
          /home/bsemenov/tmp/lessons_180518/lessons/remote_sensing_tgo/ge
         tsta.pro
       %                      $MAIN$
`` This error is generated when trying to compute the apparent state of Mars as seen from ExoMars-16 TGO in the J2000 frame because despite the ExoMars-16 TGO ephemeris data being relative to Mars, 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 ExoMars-16 TGO with respect to Mars center, and geometric states of Mars 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 Mars 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 4.0.0, September 8, 2010 -- Toolkit Version N0066

       Summary for: kernels/spk/de430.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)
               -----------------------------       -------------------------
       ----
               2018-JUN-09 23:30:00.000            2018-JUN-14 12:00:00.000

       Summary for: kernels/spk/mar085.bsp

       Bodies: EARTH BARYCENTER (3) w.r.t. SOLAR SYSTEM BARYCENTER (0)
               MARS BARYCENTER (4) w.r.t. SOLAR SYSTEM BARYCENTER (0)
               SUN (10) w.r.t. SOLAR SYSTEM BARYCENTER (0)
               EARTH (399) w.r.t. EARTH BARYCENTER (3)
               PHOBOS (401) w.r.t. MARS BARYCENTER (4)
               DEIMOS (402) w.r.t. MARS BARYCENTER (4)
               MARS (499) w.r.t. MARS BARYCENTER (4)
               Start of Interval (UTC)             End of Interval (UTC)
               -----------------------------       -------------------------
       ----
               2018-JUN-09 23:30:00.000            2018-JUN-14 12:00:00.000

       Summary for: kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp

       Body: EXOMARS 2016 TGO (-143) w.r.t. MARS (499)
             Start of Interval (UTC)             End of Interval (UTC)
             -----------------------------       ---------------------------
       --
             2018-JUN-09 23:30:00.000            2018-JUN-14 12:00:00.000
`2.` If you run your extended program with the original meta-kernel, the SPICE(SPKINSUFFDATA) error should be produced by the cspice_spkpos procedure because you have not loaded enough ephemeris data to compute the position of Jupiter with respect to Mars. The loaded SPKs contain data for Mars 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:

                   jup310_2018.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 "2018 JUN 11 19:32:00" when using the downloaded Jovian Satellite Ephemeris SPK:
          Actual position of Jupiter as seen from Mars in the
             J2000 frame (km):
             X =   -536521483.294
             Y =   -384722940.461
             Z =   -145930841.439
`3.` Once you have extended your program, download the required data from the official ExoMars-16 SPICE FTP site and update your meta-kernel:
          Additional kernels required for this task:

             1. EDM lander FK:

                   em16_edm_v00.tf

             2. EDM landing site SPK:

                   em16_edm_sot_landing_site_20161020_21000101_v01.bsp

             3. Generic PCK:

                   pck00010.tpc

          available in the NAIF server at:

             https://naif.jpl.nasa.gov/pub/naif/EXOMARS2016/kernels/
`` This is the solution for the input UTC time "2018 JUN 11 19:32:00" when using the following data for the EDM lander:
          EDM_LANDING_SITE NAIF ID:      -117900
          Apparent position of EDM Landing Site as seen from
             ExoMars-16 TGO in the J2000 frame (km):
             X =         -131.716
             Y =        -2168.989
             Z =          208.792
`4.` When using 'NONE' aberration corrections, cspice_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 "2018 JUN 11 19:32:00" is:
          Actual (geometric) position of Sun as seen from Mars in the
             J2000 frame (km):
             X =    -24730874.909
             Y =    194558449.463
             Z =     89906170.829
          Light-time corrected position of Sun as seen from Mars in the
             J2000 frame (km):
             X =    -24730866.197
             Y =    194558445.149
             Z =     89906168.728
          Apparent position of Sun as seen from Mars in the
             J2000 frame (km):
             X =    -24712733.997
             Y =    194560532.846
             Z =     89906636.764
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 Mars as seen from ExoMars-16 TGO in the IAU_MARS 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 Mars as seen from ExoMars-16 TGO and the nominal instrument view direction. `` The nominal instrument view direction is not provided by any kernel variable, but it is indicated in the ExoMars-16 TGO frame kernel cited above in the section ``Kernels Used'' to be the -Y axis of the TGO_SPACECRAFT frame. Use the program to compute these quantities at the epoch "2018 JUN 11 19:32:00" 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 procedures. Understand the difference between cspice_pxform and cspice_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 Mars relative to ExoMars-16 TGO in the J2000 reference frame, corrected for aberrations. `--` Compute the state transformation matrix from J2000 to IAU_MARS at the epoch, adjusted for light time. `--` Multiply the state of Mars relative to ExoMars-16 TGO in the J2000 reference frame by the state transformation matrix computed in the previous step. `--` Compute the position of Mars relative to ExoMars-16 TGO in the J2000 reference frame, corrected for aberrations. `--` Determine what the nominal instrument view direction of the ExoMars-16 TGO spacecraft is by examining the frame kernel's content. `--` Compute the rotation matrix from the ExoMars-16 TGO spacecraft frame to J2000. `--` Multiply the nominal instrument view direction expressed in the ExoMars-16 TGO 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 Mars relative to ExoMars-16 TGO in the J2000 frame. HINT: Several of the steps above may be compressed into a single step using Icy procedures with which you are already familiar. The ``long way'' presented above is intended to facilitate the introduction of the procedures cspice_pxform and cspice_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. ExoMars-16 TGO SCLK:

                   em16_tgo_step_20160414.tsc

             3. Solar System Ephemeris SPK, subsetted to cover only
                the time range of interest:

                   de430.bsp

             4. Martian Satellite Ephemeris SPK, subsetted to cover
                only the time range of interest:

                   mar085.bsp

             5. ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted
                to cover only the time range of interest:

                   em16_tgo_mlt_20171205_20230115_v01.bsp

             6. ExoMars-16 TGO FK:

                   em16_tgo_v07.tf

             7. ExoMars-16 TGO Spacecraft CK, subsetted to cover only
                the time range of interest:

                   em16_tgo_sc_slt_npo_20171205_20230115_s20160414_v01.bc

             8. Generic PCK:

                   pck00010.tpc

       \begindata

        KERNELS_TO_LOAD = (

        'kernels/lsk/naif0012.tls',
        'kernels/sclk/em16_tgo_step_20160414.tsc',
        'kernels/spk/de430.bsp',
        'kernels/spk/mar085.bsp',
        'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp',
        'kernels/fk/em16_tgo_v07.tf',
        'kernels/ck/em16_tgo_sc_slt_npo_20171205_20230115_s20160414_v01.bc',
        'kernels/pck/pck00010.tpc'

                           )

       \begintext
Top ### Solution Source Code A sample solution to the problem follows:
       PRO xform

          ;;
          ;; Local Parameters
          ;;

          METAKR = 'xform.tm'
          STRLEN = 50
          utctim = ''

          ;;
          ;; Load the kernels that this program requires. We
          ;; will need:
          ;;
          ;;    A leapseconds kernel
          ;;    A spacecraft clock kernel for ExoMars-16 TGO
          ;;    The necessary ephemerides
          ;;    A planetary constants file (PCK)
          ;;    A spacecraft orientation kernel for ExoMars-16 TGO (CK)
          ;;    A frame kernel (TF)
          ;;
          cspice_furnsh, METAKR

          ;;
          ;; Prompt the user for the input time string.
          ;;
          read, utctim, PROMPT = 'Input UTC Time: '

          print, 'Converting UTC Time: ', utctim

          ;;
          ;; Convert utctim to et.
          ;;
          cspice_str2et, utctim, et

          print, FORMAT='(A,F16.3)', '   ET seconds past J2000: ', et

          ;;
          ;; Compute the apparent state of Mars as seen from
          ;; ExoMars-16 TGO in the J2000 frame. All of the ephemeris
          ;; readers return states in units of kilometers and
          ;; kilometers per second.
          ;;
          cspice_spkezr, 'MARS', et,    'J2000', 'LT+S', $
                         'TGO',  state, ltime

          ;;
          ;; Now obtain the transformation from the inertial
          ;; J2000 frame to the non-inertial body-fixed IAU_MARS
          ;; frame. Since we want the apparent state in the
          ;; IAU_MARS reference frame, we need to correct the
          ;; orientation and angular velocity of this frame
          ;; for one-way light time; hence we subtract ltime from
          ;; et in the call below.
          ;;
          cspice_sxform, 'J2000', 'IAU_MARS', et-ltime, sxfmat

          ;;
          ;; Now transform the apparent J2000 state into IAU_MARS
          ;; with the following matrix multiplication:
          ;;
          bfixst = transpose(sxfmat) # state

          ;;
          ;; Display the results.
          ;;
          print, '   Apparent state of Mars as seen ' +$
                      'from ExoMars-16 TGO in the IAU_MARS'
          print, '      body-fixed frame (km, km/s):'
          print, FORMAT='(A,F19.6)', '      X = ', bfixst[0]
          print, FORMAT='(A,F19.6)', '      Y = ', bfixst[1]
          print, FORMAT='(A,F19.6)', '      Z = ', bfixst[2]
          print, FORMAT='(A,F19.6)', '     VX = ', bfixst[3]
          print, FORMAT='(A,F19.6)', '     VY = ', bfixst[4]
          print, FORMAT='(A,F19.6)', '     VZ = ', bfixst[5]

          ;;
          ;; It is worth pointing out, all of the above could
          ;; have been done with a single use of cspice_spkezr:
          ;;
          ;;
          cspice_spkezr, 'MARS', et,    'IAU_MARS', 'LT+S', $
                         'TGO',  state, ltime

          ;;
          ;; Display the results.
          ;;
          print, '   Apparent state of Mars as seen ' +$
                      'from ExoMars-16 TGO in the IAU_MARS'
          print, '      body-fixed frame (km, km/s) '  +$
                 'obtained using cspice_spkezr'
          print, '      directly:'
          print, FORMAT='(A,F19.6)', '      X = ', state[0]
          print, FORMAT='(A,F19.6)', '      Y = ', state[1]
          print, FORMAT='(A,F19.6)', '      Z = ', state[2]
          print, FORMAT='(A,F19.6)', '     VX = ', state[3]
          print, FORMAT='(A,F19.6)', '     VY = ', state[4]
          print, FORMAT='(A,F19.6)', '     VZ = ', state[5]

          ;;
          ;; Note that the velocity found by using cspice_spkezr
          ;; to compute the state in the IAU_MARS frame differs
          ;; at the few mm/second level from that found previously
          ;; by calling cspice_spkezr and then cspice_sxform. Computing
          ;; velocity via a single call to cspice_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 Mars as seen from the orbiter
          ;; and the nominal instrument view direction.  First,
          ;; compute the apparent position of Mars as seen from
          ;; ExoMars-16 TGO in the J2000 frame.
          ;;
          cspice_spkpos, 'MARS', et,  'J2000', 'LT+S', $
                         'TGO',  pos,  ltime

          ;;
          ;; 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 -Y axis
          ;; of the TGO_SPACECRAFT frame defined there.
          ;;
          bsight = [ 0.D0, -1.D0, 0.D0]

          ;;
          ;; Now compute the rotation matrix from TGO_SPACECRAFT into
          ;; J2000.
          ;;
          cspice_pxform, 'TGO_SPACECRAFT', 'J2000', et, pform

          ;;
          ;; And multiply the result to obtain the nominal instrument
          ;; view direction in the J2000 reference frame.
          ;;
          cspice_mxv, pform, bsight, bsight

          ;;
          ;; Lastly compute the angular separation.
          ;;
          cspice_convrt, cspice_vsep(bsight, pos), 'RADIANS', $
                        'DEGREES', sep

          print, '   Angular separation between the '        +$
                      'apparent position of Mars and the'
          print, '      ExoMars-16 TGO nominal instrument '  +$
                      'view direction (degrees):'
          print, FORMAT='(A,F16.3)', '      ', sep

          ;;
          ;; Or alternatively we can work in the spacecraft
          ;; frame directly.
          ;;
          cspice_spkpos, 'MARS', et,  'TGO_SPACECRAFT', 'LT+S', $
                         'TGO',  pos, ltime

          ;;
          ;; The nominal instrument view direction is the -Y-axis
          ;; in the TGO_SPACECRAFT frame.
          ;;
          bsight = [ 0.D0, -1.D0, 0.D0]

          ;;
          ;; Lastly compute the angular separation.
          ;;
          cspice_convrt, cspice_vsep(bsight, pos), 'RADIANS', $
                        'DEGREES', sep

          print, '   Angular separation between the '        +$
                      'apparent position of Mars and the'
          print, '      ExoMars-16 TGO nominal instrument '  +$
                      'view direction computed'
          print, '      using vectors in the '               +$
                      'TGO_SPACECRAFT frame (degrees):'
          print, FORMAT='(A,F16.3)', '      ', sep

          cspice_kclear

       END
Top ### Solution Sample Output After compiling the program, execute it:
       Input UTC Time: 2018 JUN 11 19:32:00
       Converting UTC Time: 2018 JUN 11 19:32:00
          ET seconds past J2000:    582017589.185
          Apparent state of Mars as seen from ExoMars-16 TGO in the IAU_MARS
             body-fixed frame (km, km/s):
             X =        -2843.464125
             Y =         2235.459544
             Z =         1095.894969
            VX =            0.311443
            VY =           -1.151929
            VZ =            3.082123
          Apparent state of Mars as seen from ExoMars-16 TGO in the IAU_MARS
             body-fixed frame (km, km/s) obtained using cspice_spkezr
             directly:
             X =        -2843.464125
             Y =         2235.459544
             Z =         1095.894969
            VX =            0.311443
            VY =           -1.151929
            VZ =            3.082123
          Angular separation between the apparent position of Mars and the
             ExoMars-16 TGO nominal instrument view direction (degrees):
                        5.438
          Angular separation between the apparent position of Mars and the
             ExoMars-16 TGO nominal instrument view direction computed
             using vectors in the TGO_SPACECRAFT frame (degrees):
                        5.438
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 "2018 jun 12 18:25:00". Explain what happens. `2.` Compute the angular separation between the apparent position of the Sun as seen from ExoMars-16 TGO 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 "2018 jun 12 18:25:00":
       % CSPICE_PXFORM: SPICE(NOFRAMECONNECT): [pxform_c->PXFORM->REFCHG]
                         At epoch 5.8209996918462E+08 TDB (2018 JUN 12
                         18:26:09.184 TDB), there is insufficient
                         information available to transform from
                         reference frame -143000 (TGO_SPACECRAFT) to
                         reference frame 1 (J2000). TGO_SPACECRAFT is a
                         CK frame; a CK file containing data for
                         instrument or structure -143000 at the epoch
                         shown above, as well as a corresponding SCLK
                         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 been
                         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
                         possible that no loaded CK file has required
                         angular velocity data for the input epoch, even
                         if a loaded CK does have attitude data for that
                         epoch. You can use CKBRIEF with the -dump
                         option to display coverage intervals of a CK
                         file.
       % Execution halted at: XFORM             134
          /home/bsemenov/tmp/lessons_180518/lessons/remote_sensing_tgo/xf
         orm.pro
       %                      $MAIN$
`` cspice_pxform returns the SPICE(NOFRAMECONNECT) error, which indicates that there are not sufficient data to perform the transformation from the TGO_SPACECRAFT frame to J2000 at the requested epoch. If you summarize the ExoMars-16 TGO 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 N0066

       Summary for: kernels/ck/em16_tgo_sc_slt_npo_20171205_20230115_s201604
       14_v01.bc

       Segment No.: 1

       Object:  -143000
         Interval Begin UTC       Interval End UTC         AV
         ------------------------ ------------------------ ---
         2018-JUN-10 23:59:59.999 2018-JUN-12 06:26:53.918 Y
         2018-JUN-12 06:56:53.918 2018-JUN-12 18:14:33.918 Y
         2018-JUN-12 18:44:33.918 2018-JUN-13 04:02:13.918 Y
         2018-JUN-13 04:32:13.918 2018-JUN-13 07:58:33.918 Y
         2018-JUN-13 08:28:33.918 2018-JUN-13 11:59:59.999 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 N0066

       Summary for: kernels/ck/em16_tgo_sc_slt_npo_20171205_20230115_s201604
       14_v01.bc

       Object:  -143000
         Interval Begin UTC       Interval End UTC         AV
         ------------------------ ------------------------ ---
         2018-JUN-10 23:59:59.999 2018-JUN-13 11:59:59.999 Y
`` which has insufficient detail to reveal the problem. `2.` By computing the apparent position of the Sun as seen from ExoMars-16 TGO in the TGO_SPACECRAFT frame, and the angular separation between this vector and the nominal instrument view direction (-Y-axis of the TGO_SPACECRAFT frame), you will find whether the science deck is illuminated. The solution for the input UTC time "2018 JUN 11 19:32:00" is:
       Angular separation between the apparent position of the Sun and the
       ExoMars-16 TGO nominal instrument view direction (degrees):
           130.543

       Science Deck illumination:
          ExoMars-16 TGO 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 ExoMars-16 TGO on Mars, in the body fixed frame IAU_MARS, in kilometers. `2.` The apparent sub-solar point on Mars, as seen from ExoMars-16 TGO in the body fixed frame IAU_MARS, 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 "2018 JUN 11 19:32:00" UTC. Top ## Learning Goals Discover higher level geometry calculation procedures in Icy and their usage as it relates to ExoMars-16 TGO. Top ## Approach This particular problem is more of an exercise in searching the permuted index to find the appropriate procedures 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:

                   de430.bsp

             3. Martian Satellite Ephemeris SPK, subsetted to cover
                only the time range of interest:

                   mar085.bsp

             4. ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted
                to cover only the time range of interest:

                   em16_tgo_mlt_20171205_20230115_v01.bsp

             5. Generic PCK:

                   pck00010.tpc

             6. Low-resolution Mars DSK:

                   mars_lowres.bds

       \begindata

        KERNELS_TO_LOAD = (

        'kernels/lsk/naif0012.tls',
        'kernels/spk/de430.bsp',
        'kernels/spk/mar085.bsp',
        'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp',
        'kernels/pck/pck00010.tpc'
        'kernels/dsk/mars_lowres.bds'

                          )

       \begintext
Top ### Solution Source Code A sample solution to the problem follows:
       PRO subpts

          ;;
          ;; Local Parameters
          ;;
          METAKR = 'subpts.tm'
          STRLEN = 50
          utctim = ''

          ;;
          ;; 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 Mars shape data
          ;;
          cspice_furnsh, METAKR

          ;;
          ;; Prompt the user for the input time string.
          ;;
          read, utctim, PROMPT = 'Input UTC Time: '

          print, 'Converting UTC Time: ', utctim

          ;;
          ;; Convert utctim to et.
          ;;
          cspice_str2et, utctim, et

          print, FORMAT='(A,F16.3)', '   ET seconds past J2000: ', et

          for i = 0, 1  do begin

             if i eq 0 then begin

                ;;
                ;; Use the "near point" sub-point definition
                ;; and an ellipsoidal model.
                ;;
                method = 'NEAR POINT/Ellipsoid'

             endif else begin

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

             endelse

             print
             print, FORMAT='(A)', ' Sub-point/target shape model: ' $
                    + method
             print

             ;;
             ;; Compute the apparent sub-observer point of ExoMars-16 TGO
             ;; on Mars.
             ;;
             cspice_subpnt, method,                                  $
                            'MARS',  et,     'IAU_MARS',   'LT+S',   $
                            'TGO',   spoint, trgepc,       srfvec

             print, '   Apparent sub-observer point of ExoMars-16 ' +$
                    'TGO on Mars'
             print, '   in the IAU_MARS frame (km):'
             print, FORMAT='(A,F16.3)', '      X = ', spoint[0]
             print, FORMAT='(A,F16.3)', '      Y = ', spoint[1]
             print, FORMAT='(A,F16.3)', '      Z = ', spoint[2]
             print, FORMAT='(A,F16.3)', '    ALT = ', cspice_vnorm(srfvec)

             ;;
             ;; Compute the apparent sub-solar point on Mars
             ;; as seen from ExoMars-16 TGO.
             ;;
             cspice_subslr, method,                                  $
                            'MARS',  et,     'IAU_MARS',   'LT+S',   $
                            'TGO',   spoint, trgepc,       srfvec

             print, '   Apparent sub-solar point on Mars ' +$
                    'as seen from ExoMars-16'
             print, '   TGO in the IAU_MARS frame (km):'
             print, FORMAT='(A,F16.3)', '      X = ', spoint[0]
             print, FORMAT='(A,F16.3)', '      Y = ', spoint[1]
             print, FORMAT='(A,F16.3)', '      Z = ', spoint[2]

          endfor

          print

          cspice_unload, METAKR

       END
Top ### Solution Sample Output After compiling the program, execute it:
       Input UTC Time: 2018 JUN 11 19:32:00
       Converting UTC Time: 2018 JUN 11 19:32:00
          ET seconds past J2000:    582017589.185

        Sub-point/target shape model: NEAR POINT/Ellipsoid

          Apparent sub-observer point of ExoMars-16 TGO on Mars
          in the IAU_MARS frame (km):
             X =         2554.165
             Y =        -2008.010
             Z =         -983.240
           ALT =          385.045
          Apparent sub-solar point on Mars as seen from ExoMars-16
          TGO in the IAU_MARS frame (km):
             X =          487.589
             Y =        -3348.610
             Z =         -286.697

        Sub-point/target shape model: NADIR/DSK/Unprioritized

          Apparent sub-observer point of ExoMars-16 TGO on Mars
          in the IAU_MARS frame (km):
             X =         2554.223
             Y =        -2008.057
             Z =         -983.263
           ALT =          384.967
          Apparent sub-solar point on Mars as seen from ExoMars-16
          TGO in the IAU_MARS frame (km):
             X =          488.096
             Y =        -3352.093
             Z =         -286.999
Top ## Extra Credit In this ``extra credit'' section you will be presented with more complex tasks, aimed at improving your understanding of cspice_subpnt and cspice_subslr procedures. 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 Mars as seen from ExoMars-16 TGO in the body fixed frame IAU_MARS in kilometers using the 'Intercept/ellipsoid' method at "2018 JUN 11 19:32:00". Explain the differences. `2.` Compute the geometric sub-spacecraft point of ExoMars-16 TGO on Phobos in the body fixed frame IAU_PHOBOS in kilometers using the 'Near point/ellipsoid' method at "2018 JUN 11 19:32:00". `3.` Transform the sub-spacecraft Cartesian coordinates obtained in the previous task to planetocentric and planetographic coordinates. When computing planetographic coordinates, retrieve Phobos' radii by calling cspice_bodvrd and use the first element of the returned radii values as Phobos' equatorial radius. Explain why planetocentric and planetographic latitudes and longitudes are different. Explain why the planetographic altitude for a point on the surface of Phobos 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 Mars is not spherical, these two points are not the same:
          Apparent sub-solar point on Mars as seen from ExoMars-16 TGO in
          the IAU_MARS frame using the 'Near Point: ellipsoid' method
          (km):
             X =          487.589
             Y =        -3348.610
             Z =         -286.697

          Apparent sub-solar point on Mars as seen from ExoMars-16 TGO in
          the IAU_MARS frame using the 'Intercept: ellipsoid' method
          (km):
             X =          487.547
             Y =        -3348.322
             Z =         -290.077
`2.` The geometric sub-spacecraft point of ExoMars-16 TGO on Phobos in the body fixed frame IAU_PHOBOS in kilometers at "2018 JUN 11 19:32:00" UTC epoch is:
          Geometric sub-spacecraft point of ExoMars-16 TGO on Phobos in
          the IAU_PHOBOS frame using the 'Near Point: ellipsoid' method
          (km):
             X =           12.059
             Y =            4.173
             Z =           -0.676
`3.` The sub-spacecraft point of ExoMars-16 TGO on Phobos in planetocentric and planetographic coordinates at "2018 JUN 11 19:32:00" UTC epoch is:
          Planetocentric coordinates of the ExoMars-16 TGO
          sub-spacecraft point on Phobos (degrees, km):
          LAT =           -3.030
          LON =           19.088
          R   =           12.779

          Planetographic coordinates of the ExoMars-16 TGO
          sub-spacecraft point on Phobos (degrees, km):
          LAT =           -6.268
          LON =          340.912
          ALT =           -0.202
`` The planetocentric and planetographic longitudes are different (``graphic'' = 360 - ``centric'') because planetographic longitudes on Phobos are measured positive west as defined by the Phobos' 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 Phobos surface model: a spheroid with equal equatorial radii. The surface point computed by cspice_subpnt was computed by treating Phobos 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 ExoMars-16 TGO NOMAD LNO Nadir aperture boresight and field of view (FOV) boundary vectors with the surface of Mars. Compute each intercept twice: once with Mars' shape modeled as an ellipsoid, and once with Mars' shape modeled by DSK data. The program presents each point of intersection as `1.` A Cartesian vector in the IAU_MARS frame `2.` Planetocentric (latitudinal) coordinates in the IAU_MARS 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 Mars, using both ellipsoidal and DSK shape models. Use this program to compute values at the UTC epoch: `` "2018 JUN 11 19:32:00" 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 procedure and another time conversion procedure in Icy. 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 ExoMars-16 TGO NOMAD 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 ExoMars-16 TGO NOMAD LNO Nadir aperture. 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 Mars 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 ExoMars-16 TGO NOMAD instrument kernel to determine the name of the NOMAD LNO Nadir aperture 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. ExoMars-16 TGO SCLK:

                   em16_tgo_step_20160414.tsc

             3. Solar System Ephemeris SPK, subsetted to cover only
                the time range of interest:

                   de430.bsp

             4. Martian Satellite Ephemeris SPK, subsetted to cover
                only the time range of interest:

                   mar085.bsp

             5. ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted
                to cover only the time range of interest:

                   em16_tgo_mlt_20171205_20230115_v01.bsp

             6. ExoMars-16 TGO FK:

                   em16_tgo_v07.tf

             7. ExoMars-16 TGO Spacecraft CK, subsetted to cover only
                the time range of interest:

                   em16_tgo_sc_slt_npo_20171205_20230115_s20160414_v01.bc

             8. Generic PCK:

                   pck00010.tpc

             9. NOMAD IK:

                   em16_tgo_nomad_v02.ti

            10. Low-resolution Mars DSK:

                   mars_lowres.bds

       \begindata

        KERNELS_TO_LOAD = (

        'kernels/lsk/naif0012.tls',
        'kernels/sclk/em16_tgo_step_20160414.tsc',
        'kernels/spk/de430.bsp',
        'kernels/spk/mar085.bsp',
        'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp',
        'kernels/fk/em16_tgo_v07.tf',
        'kernels/ck/em16_tgo_sc_slt_npo_20171205_20230115_s20160414_v01.bc',
        'kernels/pck/pck00010.tpc',
        'kernels/ik/em16_tgo_nomad_v02.ti'
        'kernels/dsk/mars_lowres.bds'

                          )

       \begintext
Top ### Solution Source Code A sample solution to the problem follows:
       PRO fovint

          ;;
          ;; Local Parameters
          ;;

          METAKR     = 'fovint.tm'
          STRLEN     = 50
          boolstr    = [ 'false', 'true' ]

          ;;
          ;; BCVLEN is the maximum number of boundary corner
          ;; vectors we can retrieve. We've extended this array by 1
          ;; element to make room for the boresight vector.
          ;;
          BCVLEN     = 5
          utctim     = ''
          scan_vecs = dblarr( 3, BCVLEN )

          vecnam  = ['Boundary Corner 1', $
                     'Boundary Corner 2', $
                     'Boundary Corner 3', $
                     'Boundary Corner 4', $
                     'TGO NOMAD LNO Nadir Boresight' ]

          ;;
          ;; Load the kernels that this program requires.  We
          ;; will need:
          ;;
          ;;    A leapseconds kernel.
          ;;    A SCLK kernel for ExoMars-16 TGO.
          ;;    Any necessary ephemerides.
          ;;    The ExoMars-16 TGO frame kernel.
          ;;    An ExoMars-16 TGO C-kernel.
          ;;    A PCK file with Mars constants.
          ;;    The ExoMars-16 TGO NOMAD I-kernel.
          ;;    A DSK file containing Mars shape data.
          ;;
          cspice_furnsh, METAKR

          ;;
          ;; Prompt the user for the input time string.
          ;;
          read, utctim, PROMPT = 'Input UTC Time: '

          print, 'Converting UTC Time: ', utctim

          ;;
          ;; Convert utctim to et.
          ;;
          cspice_str2et,  utctim, et

          print, FORMAT='(A,F16.3)', '  ET seconds past J2000: ', et
          print

          ;;
          ;; Now we need to obtain the FOV configuration of
          ;; the NOMAD LNO Nadir aperture.  To do this we will
          ;; need the ID code for TGO_NOMAD_LNO_NAD.
          ;;
          cspice_bodn2c, 'TGO_NOMAD_LNO_NAD', lnonid, found

          ;;
          ;; Stop the program if the code was not found.
          ;;
          if ( ~ found ) then begin
             print, 'Unable to locate the ID code for ' +$
                    'TGO_NOMAD_LNO_NAD'
             return
          endif

          ;;
          ;; Now retrieve the field of view parameters.
          ;;
          cspice_getfov, lnonid, BCVLEN, shape, insfrm, bsight, bounds

          ;;
          ;; Rather than treat 'bsight' as a separate vector,
          ;; copy it and 'bounds' to 'scan_vecs'.
          ;;
          scan_vecs[ 0:11] = bounds[0:11]
          scan_vecs[12:14] = bsight[0:2]

          ;;
          ;; 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
          ;; cspice_sincpt and cspice_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 Mars ID. We'll use this ID code later, when we
          ;; compute local solar time.
          ;;
          cspice_bodn2c, 'MARS', marsid, found

          ;;
          ;; The ID code for MARS is built in to the library.
          ;; However, it is good programming practice to get
          ;; in the habit of checking your found-flags.
          ;; Return if the code was not found.
          ;;
          if ( ~found ) then begin
             print, 'Unable to locate the ID code for Mars.'
             return
          endif

          ;;
          ;; Now perform the same set of calculations for each
          ;; vector listed in the 'bounds' array.
          ;;
          for i = 0, 4 do begin

             print, 'Vector: ', vecnam[i]

             for j = 0, 1 do begin

                print
                print, FORMAT = '(A)', ' Target shape model: ' + method[j]
                print

                ;;
                ;; Call sincpt to determine coordinates of the
                ;; intersection of this vector with the surface
                ;; of Mars.
                ;;
                cspice_sincpt, method[j],    'MARS',         et,        $
                               'IAU_MARS',   'LT+S',         'TGO',     $
                                insfrm,      scan_vecs[*,i], point,     $
                                trgepc,      srfvec,         found
                ;;
                ;; Check the found flag.  Display a message if
                ;; the point of intersection was not found,
                ;; otherwise continue with the calculations.
                ;;

                if ( ~ found ) then begin

                   print, 'No intersection point found at '  +$
                               'this epoch for this vector.'

                endif else begin

                   ;;
                   ;; Now, we have discovered a point of intersection.
                   ;; Start by displaying the position vector in the
                   ;; IAU_MARS frame of the intersection.
                   ;;
                   print, '  Position vector of surface intercept ' +$
                          'in the IAU_MARS frame (km):'
                   print, FORMAT='(A,F16.3)', '     X   = ', point[0]
                   print, FORMAT='(A,F16.3)', '     Y   = ', point[1]
                   print, FORMAT='(A,F16.3)', '     Z   = ', point[2]

                   ;;
                   ;; Display the planetocentric latitude and longitude
                   ;; of the intercept.
                   ;;
                   cspice_reclat, point, radius, lon, lat

                   print, '  Planetocentric coordinates of ' +$
                          'the intercept (degrees):'
                   print, FORMAT='(A,F16.3)', '     LAT = ', $
                          lat * cspice_dpr()
                   print, FORMAT='(A,F16.3)', '     LON = ', $
                          lon * cspice_dpr()

                   ;;
                   ;; Compute the illumination angles at this
                   ;; point.
                   ;;
                   cspice_illumf, method[j],  'MARS',       'SUN',  $
                                  et,         'IAU_MARS',   'LT+S', $
                                  'TGO',      point,        trgepc, $
                                  srfvec,     phase,        solar,  $
                                  emissn,     visibl,       lit

                   print, FORMAT='(A,F16.3)', $
                          '  Phase angle (degrees):           ', $
                          phase * cspice_dpr()
                   print, FORMAT='(A,F16.3)', $
                          '  Solar incidence angle (degrees): ', $
                          solar * cspice_dpr()
                   print, FORMAT='(A,F16.3)', $
                          '  Emission angle (degrees):        ', $
                          emissn * cspice_dpr()
                   print, FORMAT='(A)',                          $
                          '  Observer visible:  ' + boolstr[visibl]
                   print, FORMAT='(A)',                          $
                          '  Sun visible:       ' + boolstr[lit]

                   ;;
                   ;; Lastly compute the local solar time at the boresight
                   ;; intersection.
                   ;;
                   if  i eq 4  then begin

                      ;; Compute local solar time corresponding to
                      ;; the TDB light time corrected epoch at the
                      ;; intercept.
                      ;;
                      cspice_et2lst, trgepc, marsid, lon, 'PLANETOCENTRIC',$
                                     hr,     min,    sc,  time,  ampm

                      print
                      print, '  Local Solar Time at boresight ' +$
                             'intercept (24 Hour Clock):'
                      print, '     ' + time

                   endif
                   ;;
                   ;; End of LST computation block.
                   ;;

                endelse
                ;;
                ;; End of intercept processing block.
                ;;

             endfor
             ;;
             ;; End of shape model loop.
             ;;

             print

          endfor
          ;;
          ;; End of vector loop.
          ;;

          cspice_kclear

       END
Top ### Solution Sample Output After compiling the program, execute it:
       Input UTC Time: 2018 JUN 11 19:32:00
       Converting UTC Time: 2018 JUN 11 19:32:00
         ET seconds past J2000:    582017589.185

       Vector: Boundary Corner 1

        Target shape model: Ellipsoid

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2535.004
            Y   =        -2028.528
            Z   =         -990.594
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.967
            LON =          -38.667
         Phase angle (degrees):                     48.207
         Solar incidence angle (degrees):           43.872
         Emission angle (degrees):                   4.798
         Observer visible:  true
         Sun visible:       true

        Target shape model: DSK/Unprioritized

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2535.278
            Y   =        -2028.712
            Z   =         -990.688
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.967
            LON =          -38.667
         Phase angle (degrees):                     48.207
         Solar incidence angle (degrees):           44.387
         Emission angle (degrees):                   4.326
         Observer visible:  true
         Sun visible:       true

       Vector: Boundary Corner 2

        Target shape model: Ellipsoid

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2525.056
            Y   =        -2042.075
            Z   =         -988.196
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.925
            LON =          -38.963
         Phase angle (degrees):                     50.707
         Solar incidence angle (degrees):           43.586
         Emission angle (degrees):                   7.432
         Observer visible:  true
         Sun visible:       true

        Target shape model: DSK/Unprioritized

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2525.359
            Y   =        -2042.259
            Z   =         -988.299
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.925
            LON =          -38.962
         Phase angle (degrees):                     50.707
         Solar incidence angle (degrees):           42.457
         Emission angle (degrees):                   8.610
         Observer visible:  true
         Sun visible:       true

       Vector: Boundary Corner 3

        Target shape model: Ellipsoid

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2525.201
            Y   =        -2042.104
            Z   =         -987.770
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.917
            LON =          -38.962
         Phase angle (degrees):                     50.708
         Solar incidence angle (degrees):           43.585
         Emission angle (degrees):                   7.413
         Observer visible:  true
         Sun visible:       true

        Target shape model: DSK/Unprioritized

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2525.506
            Y   =        -2042.289
            Z   =         -987.874
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.917
            LON =          -38.961
         Phase angle (degrees):                     50.708
         Solar incidence angle (degrees):           42.457
         Emission angle (degrees):                   8.593
         Observer visible:  true
         Sun visible:       true

       Vector: Boundary Corner 4

        Target shape model: Ellipsoid

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2535.149
            Y   =        -2028.558
            Z   =         -990.170
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.960
            LON =          -38.666
         Phase angle (degrees):                     48.208
         Solar incidence angle (degrees):           43.871
         Emission angle (degrees):                   4.769
         Observer visible:  true
         Sun visible:       true

        Target shape model: DSK/Unprioritized

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2535.423
            Y   =        -2028.741
            Z   =         -990.263
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.960
            LON =          -38.665
         Phase angle (degrees):                     48.208
         Solar incidence angle (degrees):           44.387
         Emission angle (degrees):                   4.297
         Observer visible:  true
         Sun visible:       true

       Vector: TGO NOMAD LNO Nadir Boresight

        Target shape model: Ellipsoid

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2530.122
            Y   =        -2035.307
            Z   =         -989.188
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.942
            LON =          -38.814
         Phase angle (degrees):                     49.457
         Solar incidence angle (degrees):           43.729
         Emission angle (degrees):                   6.086
         Observer visible:  true
         Sun visible:       true

         Local Solar Time at boresight intercept (24 Hour Clock):
            14:51:36

        Target shape model: DSK/Unprioritized

         Position vector of surface intercept in the IAU_MARS frame (km):
            X   =         2530.471
            Y   =        -2035.529
            Z   =         -989.307
         Planetocentric coordinates of the intercept (degrees):
            LAT =          -16.942
            LON =          -38.813
         Phase angle (degrees):                     49.457
         Solar incidence angle (degrees):           44.387
         Emission angle (degrees):                   5.462
         Observer visible:  true
         Sun visible:       true

         Local Solar Time at boresight intercept (24 Hour Clock):
            14:51:36
Top ## Extra Credit There are no ``extra credit'' tasks for this step of the lesson.