Main Page Remote Sensing Hands-On Lesson, using TGO (C)
## Table of Contents
       Remote Sensing Hands-On Lesson, using TGO (C)
          Overview
          Note About HTML Links
          References
             Tutorials
             Required Readings
             The Permuted Index
             API Documentation
          Kernels Used
          CSPICE 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 (C) May 21, 2018 Top ## Overview In this lesson you will develop a series of simple programs that demonstrate the usage of CSPICE 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 ``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 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 ``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. This 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 CSPICE functions perform functions of interest, as well as the names of the source files that contain these functions. Top ### API Documentation The most detailed specification of a given SPICE C routine is contained in the header section of its source code. The source code is distributed with the Toolkit and is located under the ``cspice/src/cspice'' path. For example the path of the source code of the str2et_c routine is
       cspice/src/cspice/str2et_c.c
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 ## CSPICE 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     furnsh_c              1,2
                          prompt_c
                          str2et_c
                          etcal_c
                          timout_c
                          sce2s_c

               extra (*)  unload_c   unitim_c   1,2
                          sct2e_c
                          et2utc_c
                          scs2e_c

          2    getsta     furnsh_c   vnorm_c    1,3-5
                          prompt_c
                          str2et_c
                          spkezr_c
                          spkpos_c
                          convrt_c

               extra (*)  kclear_c              1,3-6,11-13
                          unload_c
                          bodn2c_c

          3    xform      furnsh_c   vsep_c     1-8
                          prompt_c
                          str2et_c
                          spkezr_c
                          sxform_c
                          mxvg_c
                          spkpos_c
                          pxform_c
                          mxv_c
                          convrt_c

               extra (*)  kclear_c              1-8
                          unload_c

          4    subpts     furnsh_c   vnorm_c    1,3-6,9
                          prompt_c
                          str2et_c
                          subpnt_c
                          subslr_c

               extra (*)  kclear_c   dpr_c      1,3-6
                          reclat_c
                          bodvrd_c
                          recpgr_c

          5    fovint     furnsh_c   dpr_c      1-10
                          prompt_c
                          str2et_c
                          bodn2c_c
                          getfov_c
                          sincpt_c
                          reclat_c
                          illumf_c
                          et2lst_c

          (*) Additional APIs and kernels used in Extra Credit tasks.
Refer to the headers of the various functions listed above, as detailed interface specifications are provided with the source code. 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 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: etcal_c or timout_c. 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:
          #include <stdio.h>

          /*
          Standard CSPICE User Include File
          */
          #include "SpiceUsr.h"

          /*
          Local Parameters
          */

          #define METAKR "convtm.tm"
          #define SCLKID -143
          #define STRLEN 50

          int main (void)
          {

             /*
             Local Variables
             */
             SpiceChar               calet  [STRLEN];
             SpiceChar               sclkst [STRLEN];
             SpiceChar               utctim [STRLEN];

             SpiceDouble             et;

             /*
             Load the kernels this program requires.
             Both the spacecraft clock kernel and a
             leapseconds kernel should be listed in
             the meta-kernel.
             */
             furnsh_c ( METAKR );

             /*
             Prompt the user for the input time string.
             */
             prompt_c ( "Input UTC Time: ", STRLEN, utctim );

             printf ( "Converting UTC Time: %s\n", utctim );

             /*
             Convert utctim to ET.
             */
             str2et_c ( utctim, &et );

             printf ( "   ET Seconds Past J2000: %16.3f\n", et );

             /*
             Now convert ET to a calendar time
             string.  This can be accomplished in two
             ways.
             */
             etcal_c ( et, STRLEN, calet );

             printf ( "   Calendar ET (etcal_c): %s\n", calet );

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

             printf ( "   Calendar ET (timout_c): %s\n", calet );

             /*
             Convert ET to spacecraft clock time.
             */
             sce2s_c ( SCLKID, et, STRLEN, sclkst );

             printf ( "   Spacecraft Clock Time: %s\n", sclkst );

             return(0);
          }
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 (etcal_c): 2018 JUN 11 19:33:09.184
          Calendar ET (timout_c): 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: unitim_c and timout_c. The difference between them is the type of output produced by each method. unitim_c returns the double precision value of an input epoch, while timout_c 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:   2458281.3146896
`2.` When running the original program without the LSK kernel, an error is produced:
       =====================================================================
       ===========

       Toolkit version: N0066

       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 via the routine FURNSH.

       A traceback follows.  The name of the highest level module is first.
       str2et_c --> STR2ET --> TTRANS

       Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
       BLE.  You
       can choose whether the Toolkit aborts or continues when errors occur,
        which
       error messages to output, and where to send the output.  Please read
       the ERROR
       "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
       RT.

       =====================================================================
       ===========
`` This error is triggered by str2et_c 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:
       =====================================================================
       ===========

       Toolkit version: N0066

       SPICE(KERNELVARNOTFOUND) -- The Variable Was not Found in the Kernel
       Pool.

       SCLK_DATA_TYPE_143 not found. Did you load the SCLK kernel?

       A traceback follows.  The name of the highest level module is first.
       sce2s_c --> SCE2S --> SCE2T --> SCTYPE --> SCLI01

       Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
       BLE.  You
       can choose whether the Toolkit aborts or continues when errors occur,
        which
       error messages to output, and where to send the output.  Please read
       the ERROR
       "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
       RT.

       =====================================================================
       ===========
`` This error is triggered by sce2s_c. 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 sct2e_c with the encoding of the TGO spacecraft clock time set to 0.0 ticks and convert the resulting ephemeris time to UTC using either timout_c or et2utc_c. The solution for the requested SCLK string is:
          Earliest UTC convertible to SCLK: 2016-03-13T21:34:13.194
`6.` Use scs2e_c with the SCLK string obtained in the computations performed in the regular tasks and convert the resulting ephemeris time to UTC using either et2utc_c, with 'ISOC' format and 3 digits precision, or using timout_c 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 spkezr_c call. Discover the difference between spkezr_c and spkpos_c. Familiarity with the Toolkit utility ``brief''. Exposure to unit conversion with CSPICE. 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 function 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 ``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:

                   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:
       #include <stdio.h>

       /*
       Standard CSPICE User Include File
       */
       #include "SpiceUsr.h"

       /*
       Local Parameters
       */

       #define METAKR "getsta.tm"
       #define STRLEN 50

       int main (void)
       {
          /*
          Local Variables
          */
          SpiceChar               utctim [STRLEN];

          SpiceDouble             dist;
          SpiceDouble             et;
          SpiceDouble             ltime;
          SpiceDouble             pos   [3];
          SpiceDouble             state [6];

          /*
          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.
          */
          furnsh_c ( METAKR );

          /*
          Prompt the user for the input time string.
          */
          prompt_c (  "Input UTC Time: ", STRLEN, utctim );

          printf ( "Converting UTC Time: %s\n", utctim  );

          /*
          Convert utctim to ET.
          */
          str2et_c ( utctim, &et );

          printf ( "   ET seconds past J2000: %16.3f\n", 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.
          */
          spkezr_c ( "MARS", et,    "J2000", "LT+S",
                     "TGO",  state, &ltime              );

          printf ( "   Apparent state of Mars as seen "
                   "from ExoMars-16 TGO in the J2000\n" );
          printf ( "      frame (km, km/s):\n"          );
          printf ( "      X = %16.3f\n", state[0]       );
          printf ( "      Y = %16.3f\n", state[1]       );
          printf ( "      Z = %16.3f\n", state[2]       );
          printf ( "     VX = %16.3f\n", state[3]       );
          printf ( "     VY = %16.3f\n", state[4]       );
          printf ( "     VZ = %16.3f\n", state[5]       );

          /*
          Compute the apparent position of Earth as seen from
          ExoMars-16 TGO in the J2000 frame.  Note: We could have
          continued using spkezr_c and simply ignored the velocity
          components.
          */
          spkpos_c ( "EARTH", et,  "J2000", "LT+S",
                     "TGO",   pos, &ltime                   );

          printf ( "   Apparent position of Earth as seen "
                   "from ExoMars-16 TGO in the\n"           );
          printf ( "      J2000 frame (km): \n"             );
          printf ( "      X = %16.3f\n", pos[0]             );
          printf ( "      Y = %16.3f\n", pos[1]             );
          printf ( "      Z = %16.3f\n", pos[2]             );

          /*
          We need only display LTIME, as it is precisely the
          light time in which we are interested.
          */
          printf ( "   One way light time between ExoMars-16 "
                   "TGO and the apparent\n"                    );
          printf ( "      position of Earth (seconds): "
                   "%16.3f\n", ltime                           );

          /*
          Compute the apparent position of the Sun as seen
          from Mars in the J2000 frame.
          */
          spkpos_c ( "SUN",  et,  "J2000", "LT+S",
                     "MARS", pos, &ltime                  );

          printf ( "   Apparent position of Sun as seen "
                   "from Mars in the\n"                   );
          printf ( "      J2000 frame (km): \n"           );
          printf ( "      X = %16.3f\n", pos[0]           );
          printf ( "      Y = %16.3f\n", pos[1]           );
          printf ( "      Z = %16.3f\n", 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.
          */
          spkpos_c ( "SUN",  et,  "J2000", "NONE",
                     "MARS", pos, &ltime                  );

          /*
          Compute the distance between the body centers in
          kilometers.
          */
          dist = vnorm_c ( pos );

          /*
          Convert this value to AU using convrt_c.
          */
          convrt_c ( dist, "KM", "AU", &dist );

          printf ( "   Actual distance between Sun and "
                   "Mars body centers:\n"                 );
          printf ( "      (AU): %16.3f\n", dist           );

          return(0);
       }
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 spkezr_c 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 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 spkezr_c:
       =====================================================================
       ===========

       Toolkit version: N0066

       SPICE(SPKINSUFFDATA) --

       Insufficient ephemeris data has been loaded to compute the state of -
       143
       (EXOMARS 2016 TGO) relative to 0 (SOLAR SYSTEM BARYCENTER) at the eph
       emeris
       epoch 2018 JUN 11 19:33:09.184.

       A traceback follows.  The name of the highest level module is first.
       spkezr_c --> SPKEZR --> SPKEZ --> SPKACS --> SPKGEO

       Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
       BLE.  You
       can choose whether the Toolkit aborts or continues when errors occur,
        which
       error messages to output, and where to send the output.  Please read
       the ERROR
       "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
       RT.

       =====================================================================
       ===========
`` This error is generated when trying to compute the apparent state of 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 spkpos_c function 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, spkpos_c 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 functions. Understand the difference between pxform_c and sxform_c. 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 CSPICE functions with which you are already familiar. The ``long way'' presented above is intended to facilitate the introduction of the functions pxform_c and sxform_c. 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:
       #include <stdio.h>

       /*
       Standard CSPICE User Include File
       */
       #include "SpiceUsr.h"

       /*
       Local Parameters
       */

       #define METAKR "xform.tm"
       #define STRLEN 50

       int main (void)
       {

          /*
          Local Variables
          */
          SpiceChar               utctim [STRLEN];

          SpiceDouble             et;
          SpiceDouble             ltime;
          SpiceDouble             state  [6];
          SpiceDouble             bfixst [6];
          SpiceDouble             pos    [3];
          SpiceDouble             sform  [6][6];
          SpiceDouble             pform  [3][3];
          SpiceDouble             bsight [3];
          SpiceDouble             sep;

          /*
          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)
          */
          furnsh_c ( METAKR );

          /*
          Prompt the user for the input time string.
          */
          prompt_c ( "Input UTC Time: ", STRLEN, utctim );

          printf ( "Converting UTC Time: %s\n", utctim );

          /*
          Convert utctim to ET.
          */
          str2et_c ( utctim, &et );

          printf ( "   ET seconds past J2000: %16.3f\n", et );

          /*
          Compute the apparent state of Mars as seen from
          ExoMars-16 TGO in the J2000 reference frame.
          */
          spkezr_c ( "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 position, we
          need to subtract ltime from et.
          */
          sxform_c ( "J2000", "IAU_MARS", et-ltime, sform );

          /*
          Now rotate the apparent J2000 state into IAU_MARS
          with the following matrix multiplication:
          */
          mxvg_c ( sform, state, 6, 6, bfixst );

          /*
          Display the results.
          */
          printf ( "   Apparent state of Mars as seen "
                   "from ExoMars-16 TGO in the IAU_MARS\n" );
          printf ( "      body-fixed frame (km, km/s):\n"  );
          printf ( "      X = %19.6f\n", bfixst[0]         );
          printf ( "      Y = %19.6f\n", bfixst[1]         );
          printf ( "      Z = %19.6f\n", bfixst[2]         );
          printf ( "     VX = %19.6f\n", bfixst[3]         );
          printf ( "     VY = %19.6f\n", bfixst[4]         );
          printf ( "     VZ = %19.6f\n", bfixst[5]         );

          /*
          It is worth pointing out, all of the above could
          have been done with a single use of spkezr_c:
          */
          spkezr_c ( "MARS", et,    "IAU_MARS", "LT+S",
                     "TGO",  state, &ltime                 );

          /*
          Display the results.
          */
          printf ( "   Apparent state of Mars as seen "
                   "from ExoMars-16 TGO in the IAU_MARS\n" );
          printf ( "      body-fixed frame (km, km/s) "
                   "obtained using spkezr_c directly:\n"   );
          printf ( "      X = %19.6f\n", state[0]          );
          printf ( "      Y = %19.6f\n", state[1]          );
          printf ( "      Z = %19.6f\n", state[2]          );
          printf ( "     VX = %19.6f\n", state[3]          );
          printf ( "     VY = %19.6f\n", state[4]          );
          printf ( "     VZ = %19.6f\n", state[5]          );

          /*
          Note that the velocity found by using spkezr_c
          to compute the state in the IAU_MARS frame differs
          at the few mm/second level from that found previously
          by calling spkezr_c and then sxform_c. Computing
          velocity via a single call to spkezr_c 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.
          */
          spkpos_c ( "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] =  0.0;
          bsight[1] = -1.0;
          bsight[2] =  0.0;

          /*
          Now compute the rotation matrix from TGO_SPACECRAFT
          into J2000.
          */
          pxform_c ( "TGO_SPACECRAFT", "J2000", et, pform  );

          /*
          And multiply the result to obtain the nominal instrument
          view direction in the J2000 reference frame.
          */
          mxv_c ( pform, bsight, bsight );

          /*
          Lastly compute the angular separation.
          */
          convrt_c ( vsep_c(bsight, pos), "RADIANS",
                     "DEGREES",           &sep               );

          printf ( "   Angular separation between the "
                   "apparent position of Mars and the\n"     );
          printf ( "      ExoMars-16 TGO nominal "
                   "instrument view direction (degrees): \n" );
          printf ( "      %16.3f\n", sep                     );

          /*
          Or alternatively we can work in the spacecraft
          frame directly.
          */
          spkpos_c ( "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] =  0.0;
          bsight[1] = -1.0;
          bsight[2] =  0.0;

          /*
          Lastly compute the angular separation.
          */
          convrt_c ( vsep_c(bsight, pos), "RADIANS",
                     "DEGREES",           &sep              );

          printf ( "   Angular separation between the "
                   "apparent position of Mars and the\n"    );
          printf ( "      ExoMars-16 TGO nominal "
                   "instrument view direction computed\n"   );
          printf ( "      using vectors in the "
                   "TGO_SPACECRAFT frame (degrees):\n"      );
          printf ( "      %16.3f\n", sep                    );

          return(0);
       }
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 spkezr_c 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":
       =====================================================================
       ===========

       Toolkit version: N0066

       SPICE(NOFRAMECONNECT) --

       At epoch 5.8209996918462E+08 TDB (2018 JUN 12 18:26:09.184 TDB), ther
       e 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 ep
       och shown
       above, as well as a corresponding SCLK kernel, must be loaded in orde
       r to use
       this frame. Failure to find required CK data could be due to one or m
       ore CK
       files not having been loaded, or to the epoch shown above lying withi
       n a
       coverage gap or beyond the coverage bounds of the loaded CK files. It
        is also
       possible that no loaded CK file has required angular velocity data fo
       r the
       input epoch, even if a loaded CK does have attitude data for that epo
       ch. You
       can use CKBRIEF with the -dump option to display coverage intervals o
       f a CK
       file.

       A traceback follows.  The name of the highest level module is first.
       pxform_c --> PXFORM --> REFCHG

       Oh, by the way:  The SPICELIB error handling actions are USER-TAILORA
       BLE.  You
       can choose whether the Toolkit aborts or continues when errors occur,
        which
       error messages to output, and where to send the output.  Please read
       the ERROR
       "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP
       RT.

       =====================================================================
       ===========
`` pxform_c 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 functions in CSPICE 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 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:

                   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:
       #include <stdio.h>

       /*
       Standard CSPICE User Include File
       */
       #include "SpiceUsr.h"

       /*
       Local Parameters
       */

       #define METAKR "subpts.tm"
       #define STRLEN 50

       int main (void)
       {
          /*
          Local Variables
          */
          SpiceChar             * method;
          SpiceChar               utctim [STRLEN];

          SpiceDouble             et;
          SpiceDouble             spoint [3];
          SpiceDouble             srfvec [3];
          SpiceDouble             trgepc;

          SpiceInt                i;

          /*
          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
          */
          furnsh_c ( METAKR );

          /*
          Prompt the user for the input time string.
          */
          prompt_c ( "Input UTC Time: ", STRLEN, utctim );

          printf ( " Converting UTC Time: %s\n", utctim );

          /*
          Convert utctim to ET.
          */
          str2et_c ( utctim, &et );

          printf ( "   ET seconds past J2000: %16.3f\n", et );

          for ( i = 0;  i < 2;  i++ )
          {
             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";
             }

             printf ( "\n Sub-point/target shape model: %s\n\n",
                      method                                    );

             /*
             Compute the apparent sub-observer point of ExoMars-16 TGO
             on Mars.
             */
             subpnt_c ( method,
                        "MARS",  et,     "IAU_MARS",   "LT+S",
                        "TGO",   spoint, &trgepc,      srfvec );

             printf ( "   Apparent sub-observer point of ExoMars-16 "
                      "TGO on Mars\n"                           );
             printf ( "   in the IAU_MARS frame (km):\n"        );
             printf ( "      X = %16.3f\n", spoint[0]           );
             printf ( "      Y = %16.3f\n", spoint[1]           );
             printf ( "      Z = %16.3f\n", spoint[2]           );
             printf ( "    ALT = %16.3f\n", vnorm_c(srfvec)     );

             /*
             Compute the apparent sub-solar point on Mars
             as seen from ExoMars-16 TGO.
             */
             subslr_c ( method,
                        "MARS",  et,     "IAU_MARS",   "LT+S",
                        "TGO",   spoint, &trgepc,      srfvec );

             printf ( "   Apparent sub-solar point on Mars "
                      "as seen from ExoMars-16\n"               );
             printf ( "   TGO in the IAU_MARS frame (km):\n"    );
             printf ( "      X = %16.3f\n", spoint[0]           );
             printf ( "      Y = %16.3f\n", spoint[1]           );
             printf ( "      Z = %16.3f\n", spoint[2]           );
          }

          printf ( "\n" );

          return(0);
       }
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 subpnt_c and subslr_c 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 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 bodvrd_c 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 subpnt_c 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 function and another time conversion function in CSPICE. 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:
       #include <stdio.h>

       /*
       Standard CSPICE User Include File
       */
       #include "SpiceUsr.h"
       #include <stdlib.h>

       /*
       Local Parameters
       */
       #define METAKR "fovint.tm"
       #define STRLEN 50

       /*
       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.
       */
       #define BCVLEN 5

       int main (void)
       {
          /*
          Local Variables
          */
          SpiceBoolean            lit;
          SpiceBoolean            visibl;

          SpiceChar               ampm   [STRLEN];
          SpiceChar              *boolst [2] = { "false", "true" };
          SpiceChar               insfrm [STRLEN];
          SpiceChar              *method [2];
          SpiceChar               shape  [STRLEN];
          SpiceChar               time   [STRLEN];
          SpiceChar               utctim [STRLEN];
          SpiceChar              *vecnam[] = {
                                    "Boundary Corner 1",
                                    "Boundary Corner 2",
                                    "Boundary Corner 3",
                                    "Boundary Corner 4",
                                    "TGO NOMAD LNO Nadir Boresight" };

          SpiceDouble             bounds [BCVLEN][3];
          SpiceDouble             bsight [3];
          SpiceDouble             emissn;
          SpiceDouble             et;
          SpiceDouble             lat;
          SpiceDouble             lon;
          SpiceDouble             phase;
          SpiceDouble             point  [3];
          SpiceDouble             radius;
          SpiceDouble             solar;
          SpiceDouble             srfvec [3];
          SpiceDouble             trgepc;

          SpiceInt                hr;
          SpiceInt                i;
          SpiceInt                j;
          SpiceInt                mn;
          SpiceInt                n;
          SpiceInt                lnonid;
          SpiceInt                marsid;
          SpiceInt                sc;

          SpiceBoolean            found;

          /*
          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.
          */
          furnsh_c ( METAKR );

          /*
          Prompt the user for the input time string.
          */
          prompt_c ( "Input UTC Time: ", STRLEN, utctim );

          printf ( "Converting UTC Time: %s\n", utctim );

          /*
          Convert utctim to ET.
          */
          str2et_c ( utctim, &et );

          printf ( "  ET seconds past J2000: %16.3f\n\n", et );

          /*
          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.
          */
          bodn2c_c ( "TGO_NOMAD_LNO_NAD", &lnonid, &found );

          /*
          Stop the program if the code was not found.
          */
          if ( !found )
          {
             printf ( "Unable to locate the ID code for "
                      "TGO_NOMAD_LNO_NAD\n"                   );
             exit   ( EXIT_FAILURE );
          }

          /*
          Now retrieve the field of view parameters.
          */
          getfov_c ( lnonid, BCVLEN, STRLEN, STRLEN,
                     shape,  insfrm, bsight, &n,     bounds );

          /*
          Rather than treat BSIGHT as a separate vector,
          copy it into the last slot of BOUNDS.
          */
          for ( i=0; i<3; i++ )
          {
             bounds[4][i] = bsight[i];
          }

          /*
          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
          sincpt_c and ilumin_c. Note that some SPICE routines require
          different "method" inputs from those shown here. See the
          API documentation of each routine for details.
          */
          method[0] = "Ellipsoid";
          method[1] = "DSK/Unprioritized";

          /*
          Get Mars ID. We'll use this ID code later, when we
          compute local solar time.
          */
          bodn2c_c ( "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.
          */
          if ( !found )
          {
             printf ( "Unable to locate the body ID code "
                      "for Mars.\n"                      );
             exit   ( EXIT_FAILURE );
          }

          /*
          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=0; i<5; i++ )
          {
             printf ( "Vector: %s\n", vecnam[i] );

             for ( j = 0;  j < 2;  j++ )
             {
                printf ( "\n Target shape model: %s\n\n", method[j] );

                /*
                Call sincpt_c to determine coordinates of the
                intersection of this vector with the surface
                of Mars.
                */
                sincpt_c ( method[j], "MARS",    et,     "IAU_MARS",
                           "LT+S",    "TGO",     insfrm, bounds[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 )
                {
                   printf ( "No intersection point found at "
                            "this epoch for this vector.\n"   );
                }
                else
                {
                   /*
                   Now, we have discovered a point of intersection.
                   Start by displaying the position vector in the
                   IAU_MARS frame of the intersection.
                   */
                   printf ( "  Position vector of surface intercept "
                            "in the IAU_MARS frame (km):\n" );
                   printf ( "     X   = %16.3f\n", point[0] );
                   printf ( "     Y   = %16.3f\n", point[1] );
                   printf ( "     Z   = %16.3f\n", point[2] );

                   /*
                   Display the planetocentric latitude and longitude
                   of the intercept.
                   */
                   reclat_c ( point, &radius, &lon, &lat );

                   printf ( "  Planetocentric coordinates of "
                            "the intercept (degrees):\n"  );
                   printf ( "     LAT = %16.3f\n", lat * dpr_c() );
                   printf ( "     LON = %16.3f\n", lon * dpr_c() );

                   /*
                   Compute the illumination angles at this
                   point.
                   */
                   illumf_c( method[j],    "MARS",   "SUN",     et,
                             "IAU_MARS",   "LT+S",   "TGO", point,
                             &trgepc,      srfvec,   &phase,    &solar,
                             &emissn,      &visibl,  &lit              );

                   printf ( "  Phase angle (degrees):           "
                            "%16.3f\n", phase * dpr_c()          );
                   printf ( "  Solar incidence angle (degrees): "
                            "%16.3f\n", solar * dpr_c()          );
                   printf ( "  Emission angle (degrees):        "
                            "%16.3f\n", emissn * dpr_c()         );
                   printf ( "  Observer visible: %s\n", boolst[visibl] );
                   printf ( "  Sun visible:      %s\n", boolst[lit]    );

                   if ( i == 4 )
                   {
                      /*
                      Compute local solar time corresponding to the TDB
                      light time corrected epoch at the boresignt
                      intercept.
                      */
                      et2lst_c ( trgepc,
                                 marsid,
                                 lon,
                                 "PLANETOCENTRIC",
                                 STRLEN,
                                 STRLEN,
                                 &hr,
                                 &mn,
                                 &sc,
                                 time,
                                 ampm             );

                      printf ( "\n  Local Solar Time at boresight "
                               "intercept (24 Hour Clock):\n"      );
                      printf ( "     %s\n", time                   );
                   }
                   /*
                   End of LST computation block.
                   */
                }
                /*
                End of shape model loop.
                */
             }
             /*
             End of vector loop.
             */
             printf ( "\n" );
          }

          return(0);
       }
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.