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Remote Sensing Hands-On Lesson (MATLAB)

Table of Contents 

   Remote Sensing Hands-On Lesson (MATLAB)
      Overview
      Note About HTML Links
      References
         Tutorials
         Required Readings
         The Permuted Index
         Mice API Documentation
      Kernels Used
      Mice 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-spacecraft and Sub-solar Points (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 a Triaxial Ellipsoid (fovint)
      Task Statement
      Learning Goals
      Approach
      Solution
         Solution Meta-Kernel
         Solution Source Code
         Solution Sample Output
      Extra Credit


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Remote Sensing Hands-On Lesson (MATLAB)




September 2, 2016



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Overview



In this lesson you will develop a series of simple programs that demonstrate the usage of Mice 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.



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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, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the Toolkit tree and copy this document to that subdirectory before loading it into a Web browser.



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References





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Tutorials



The following SPICE tutorials are referred to by 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
These tutorials are available from the NAIF ftp server at JPL: 

   http://naif.jpl.nasa.gov/naif/tutorials.html


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Required Readings



The Required Reading documents are provided with the Toolkit and are located under the ``mice/doc'' directory in the MATLAB installation tree. 

   Name             Lesson steps/functions that it describes
   ---------------  -----------------------------------------
   time.req         Time Conversion
   sclk.req         SCLK Time Conversion
   spk.req          Obtaining Ephemeris Data
   frames.req       Using Reference Frames
   pck.req          Obtaining Planetary Constants Data
   ck.req           Obtaining Spacecraft Orientation Data
   naif_ids.req     Determining Body ID Codes


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The Permuted Index



Another useful document distributed with the Toolkit is the permuted index. This is located under the ``mice/doc'' directory in the MATLAB installation tree.

This text document provides a simple mechanism to discover what Mice functions perform a particular function of interest as well as the name of the source module that contains the function.



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Mice API Documentation



A Mice routine's specification is found in the API documentation page located under ``mice/doc/html/mice''.

For example, the document 

   mice/doc/html/mice/cspice_str2et.html
describes the cspice_str2et routine.



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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.  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
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/


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Mice Modules Used



This section provides a complete summary of the functions, and the kernels that are suggested for usage in each of the exercises in this tutorial. (You may wish to not look at this list unless/until you ``get stuck'' while working on your own.) 

   CHAPTER EXERCISE   FUNCTIONS      NON-VOID       KERNELS
   ------- ---------  -------------  ---------      -------
     1     convtm     cspice_furnsh                 1,2
                      cspice_str2et
                      cspice_etcal
                      cspice_timout
                      cspice_sce2s
 
     2     getsta     cspice_furnsh                 1,3-6
                      cspice_str2et
                      cspice_spkezr
                      cspice_spkpos
                      cspice_convrt
 
     3     xform      cspice_furnsh  cspice_vsep    1-8
                      cspice_str2et
                      cspice_spkezr
                      cspice_sxform
                      cspice_spkpos
                      cspice_pxform
                      cspice_convrt
 
     4     subpts     cspice_furnsh                 1,3-6,8
                      cspice_str2et
                      cspice_subpt
                      cspice_subsol
 
     5     fovint     cspice_furnsh  cspice_dpr     1-9
                      cspice_str2et
                      cspice_bodn2c
                      cspice_getfov
                      cspice_sincpt
                      cspice_reclat
                      cspice_ilumin
                      cspice_et2lst
Refer to the headers of the various functions listed above, as detailed interface specifications are provided with the source code.



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Time Conversion (convtm)






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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.



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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.



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Approach



The solution to the problem can be broken down into a series of simple steps:

    -- Decide which SPICE kernels are necessary. Prepare a meta-kernel listing the kernels and load it into the program.

    -- Prompt the user for an input UTC time string.

    -- Convert the input time string into ephemeris time expressed as seconds past J2000 TDB. Display the result.

    -- Convert ephemeris time into a calendar format. Display the result.

    -- Convert ephemeris time into a spacecraft clock string. Display the result.

You may find it useful to consult the permuted index, the headers of various source modules, and the ``Time Required Reading'' (time.req) and ``SCLK Required Reading'' (sclk.req) documents.

When completing the ``calendar format'' step above, consider using one of two possible methods: cspice_etcal or cspice_timout.



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Solution





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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.
 
   \begindata
 
    KERNELS_TO_LOAD = (
 
    'kernels/lsk/naif0012.tls',
    'kernels/sclk/em16_tgo_step_20160414.tsc'
 
                      )
 
   \begintext


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Solution Source Code



A sample solution to the problem follows: 

   %
   % Remote sensing lesson:  Time conversion
   %
   function convtm()
 
   %
   % Local parameters
   %
   METAKR = 'convtm.tm';
   SCLKID = -143;
 
   %
   % Load the kernels his program requires.
   % Both the spacecraft clock kernel and a
   % leapseconds kernel should be listed in
   % the meta-kernel.
   %
   cspice_furnsh ( METAKR );
 
   %
   % Prompt the user for the input time string.
   %
   utctim = input ( 'Input UTC Time: ', 's' );
 
   fprintf ( 'Converting UTC Time: %s\n', utctim )
 
   %
   % Convert utctim to et.
   %
   et = cspice_str2et ( utctim );
 
   fprintf ( '   ET Seconds Past J2000: %16.3f\n', et )
 
   %
   % Now convert ET to a formal calendar time
   % string.  This can be accomplished in two
   % ways.
   %
   calet = cspice_etcal ( et );
 
   fprintf ( '   Calendar ET (cspice_etcal):  %s\n', calet )
 
   %
   % Or use cspice_timout for finer control over the
   % output format.  The picture below was built
   % by examining the header of cspice_timout.
   %
   calet = cspice_timout ( et, 'YYYY-MON-DDTHR:MN:SC ::TDB' );
 
   fprintf ( '   Calendar ET (cspice_timout): %s\n', calet )
 
   %
   % Convert ET to spacecraft clock time.
   %
   sclkst = cspice_sce2s ( SCLKID, et );
 
   fprintf ( '   Spacecraft Clock Time: %s\n', sclkst )
 
   %
   % Unload kernels we loaded at the start of the function.
   %
   cspice_unload ( METAKR );
 
   %
   % End of function convtm
   %


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Solution Sample Output



Execute the program: 

   Converting UTC Time: 2018 JUN 11 19:32:00
      ET Seconds Past J2000:    582017589.185
      Calendar ET (cspice_etcal):  2018 JUN 11 19:33:09.184
      Calendar ET (cspice_timout): 2018-JUN-11T19:33:09
      Spacecraft Clock Time: 1/0070841719.26698


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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.



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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?



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Solutions and answers



    1. Two methods exist in order to convert ephemeris time to Julian Date: cspice_unitim and cspice_timout. The difference between them is the type of output produced by each method. cspice_unitim returns the double precision value of an input epoch, while cspice_timout returns the string representation of the ephemeris time in Julian Date format (when picture input is set to 'JULIAND.######### ::TDB'). Refer to the 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: SPICE(NOLEAPSECONDS). This error is triggered by cspice_str2et because the variable that points to the leapseconds is not present in the kernel pool and therefore there is not enough data to perform the requested UTC to ephemeris time conversion.

    By default, SPICE will report, as a minimum, a short descriptive message -- in this case SPICE(NOLEAPSECONDS) -- 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 by cspice_sce2s: SPICE(KERNELVARNOTFOUND), which in this case 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 executing the program using the original meta-kernel, you will be getting the same error as in the previous task. Despite the error being exactly the same, this case is different. Generally, spacecraft clocks are associated with the spacecraft ID and not with its payload, sensors or structures IDs. Therefore, in order to do conversions from/to spacecraft clock for payload, sensors or spacecraft structures, the spacecraft ID must be used.

    Note that this does not need to be true for all missions or payloads, as SPICE does not restrict the SCLKs to spacecraft IDs only. Please refer to your mission's SCLK kernels for particulars.

    5. Use cspice_scs2e with the input SCLK string set to ``0.0'' and convert the resulting ephemeris time to UTC using either cspice_timout or cspice_et2utc. The solution for the requested SCLK string is: 

         Earliest UTC convertible to SCLK: 2016-03-13T21:34:13.194
    6. Use cspice_scs2e with the SCLK string obtained in the computations performed in the regular tasks (1/0070841719.26698) and convert the resulting ephemeris time to UTC using either cspice_et2utc, with 'ISOC' format and 3 digits precision, or using cspice_timout using the time picture 'YYYY-MM-DDTHR:MN:SC.### ::RND'. The solution of the requested conversion is: 

         UTC time from spacecraft clock: 2018-06-11T19:32:00.000


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Obtaining Target States and Positions (getsta)






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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.



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Learning Goals



Understand the anatomy of an cspice_spkezr call. Discover the difference between cspice_spkezr and cspice_spkpos. Familiarity with the Toolkit utility ``brief''. Exposure to unit conversion with Mice.



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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 ``mice/exe'' directory for MATLAB toolkits. Consult its user's guide available in ``mice/doc/brief.ug'' for details.



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Solution





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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.
 
   \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/fk/em16_tgo_v07.tf'
 
                        )
 
   \begintext


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Solution Source Code



A sample solution to the problem follows: 

   %
   % Remote sensing lesson:  State vector lookup
   %
   function getsta()
 
   %
   % Local parameters
   %
   METAKR = 'getsta.tm';
 
   %
   % Load the kernels that this program requires.  We
   % will need a leapseconds kernel to convert input
   % UTC time strings into ET.  We also will need
   % SPK files with coverage for the bodies
   % in which we are interested.
   %
   % Since the SPICE body/ID mapping for TGO is not
   % yet included in the standard library, we will
   % need the frame kernel where the mapping is
   % defined.
   %
   cspice_furnsh ( METAKR );
 
   %
   % Prompt the user for the input time string.
   %
   utctim = input ( 'Input UTC Time: ', 's' );
 
   fprintf ( 'Converting UTC Time: %s\n', utctim )
 
   %
   % Convert utctim to ET.
   %
   et = cspice_str2et ( utctim );
 
   fprintf ( '   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.
   %
   [state, ltime] = cspice_spkezr ( 'MARS',  et,    ...
                                    'J2000', 'LT+S', 'TGO' );
 
   fprintf ( [ '   Apparent state of Mars as seen ', ...
               'from ExoMars-16 TGO in the J2000\n', ...
               '      frame (km, km/s):\n']                )
 
   fprintf ( '      X = %16.3f\n', state(1) )
   fprintf ( '      Y = %16.3f\n', state(2) )
   fprintf ( '      Z = %16.3f\n', state(3) )
   fprintf ( '     VX = %16.3f\n', state(4) )
   fprintf ( '     VY = %16.3f\n', state(5) )
   fprintf ( '     VZ = %16.3f\n', state(6) )
 
 
   %
   % Compute the apparent position of Earth as seen from
   % ExoMars-16 TGO in the J2000 frame.  Note: We could have
   % continued using cspice_spkezr and simply ignored the
   % velocity components.
   %
   [pos, ltime] = cspice_spkpos ( 'EARTH', et,     ...
                                  'J2000', 'LT+S', 'TGO' );
 
   fprintf ( [ '   Apparent position of Earth as seen ', ...
               'from ExoMars-16 TGO in the\n',           ...
               '      J2000 frame (km):\n' ]               )
 
   fprintf ( '      X = %16.3f\n', pos(1) )
   fprintf ( '      Y = %16.3f\n', pos(2) )
   fprintf ( '      Z = %16.3f\n', pos(3) )
 
   %
   % Display the light time from target to observer.
   %
   fprintf ( [ '   One way light time between ExoMars-16 ', ...
               'TGO and the apparent\n',                    ...
               '      position of Earth (seconds): '        ...
               '%16.3f\n' ], ltime                            )
 
   %
   % Compute the apparent position of the Sun as seen
   % from Mars in the J2000 frame.
   %
   [pos, ltime] = cspice_spkpos ( 'SUN',   et,     ...
                                  'J2000', 'LT+S', 'MARS' );
 
   fprintf ( [ '   Apparent position of Sun as seen ', ...
               'from Mars in the \n',               ...
               '      J2000 frame (km):\n' ]              )
 
   fprintf ( '      X = %16.3f\n', pos(1) )
   fprintf ( '      Y = %16.3f\n', pos(2) )
   fprintf ( '      Z = %16.3f\n', pos(3) )
 
   %
   % 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.
   %
   [pos, ltime] = cspice_spkpos ( 'SUN',   et,     ...
                                  'J2000', 'NONE', 'MARS' );
 
   %
   % Compute the distance between the body centers in
   % kilometers.
   %
   dist = norm ( pos );
 
   %
   % Convert this value to AU using cspice_convrt.
   %
   dist_au = cspice_convrt ( dist, 'KM', 'AU' );
 
   fprintf ( [ '   Actual distance between Sun and Mars ' ...
               'body centers:\n' ]                         )
   fprintf ( '      (AU): %16.3f\n', dist_au               )
 
   %
   % Unload all kernels.
   %
   cspice_kclear;
 
   %
   % End of function getsta
   %


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Solution Sample Output



Execute the program: 

   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


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Extra Credit



In this ``extra credit'' section you will be presented with more complex tasks, aimed at improving your understanding of state computations, particularly the application of the different light time and stellar aberration corrections available in the cspice_spkezr 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.



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Task statements and questions



    1. Remove the Martian planetary ephemerides SPK (mar085.bsp) from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why?

    2. Remove the ExoMars-16 TGO frames definition kernel (em16_tgo_v07.tf) from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why?

    3. Extend your program to compute the geometric position of Jupiter as seen from Mars in the J2000 frame (J2000), in kilometers.

    4. 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.

    5. 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.

    6. Examine the ExoMars-16 TGO frames definition kernel to find the SPICE ID/name definitions.



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Solutions and answers



    1. When running the original program without the Martian planetary ephemerides SPK, an error is produced by cspice_spkezr: SPICE(SPKINSUFFDATA). 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 effect of the light time and stellar aberrations. The loaded SPK data is 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 is no longer loaded. Run ``brief'' on the SPKs used in the original task to find out what ephemeris objects are available from that kernel. 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''.

    2. When running the original program without the ExoMars-16 TGO frames definitions kernel, an error is produced by cspice_spkezr: SPICE(IDCODENOTFOUND). This error is generated because the observer 'TGO' is not a recognized name for an ephemeris object as TGO is not yet included in the official SPICE ID/name mappings and the mission specific mapping definitions, included in the FK, have not been loaded. In order to resolve this issue, two possibilities exist: load the SPICE ID/name mappings or use the NAIF IDs instead: 

         [state, ltime] = cspice_spkezr ( 'MARS',  et,    ...
                                          'J2000', 'LT+S', '-143' );
    3. If you run your extended program, with the original meta-kernel, the SPICE(SPKINSUFFDATA) error should be produced by the cspice_spkpos 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 is missing. SPKs with this data are available in the NAIF server at: 

      http://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/
    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 Jovian Satellite Ephemeris SPK jup310.bsp is: 

         Actual position of Jupiter as seen from Mars in the
            J2000 frame (km):
            X =   -536521483.296
            Y =   -384722940.462
            Z =   -145930841.439
    4. Once you have extended your program, download the required data from the official ExoMars-16 SPICE operational FTP site and update your meta-kernel. This is the solution for the input UTC time ``2018 JUN 11 19:32:00'' when using the following data for the EDM lander: 

 
         Additional kernels used in this task:
 
            a. EDM lander FK:
 
                  em16_emd_v00.tf
 
            b. EDM landing site SPK:
 
                  em16_edm_sot_landing_site_20161020_21000101_v01.bsp
 
            c. Generic PCK, where the Mars orientation constants are
               provided:
 
                  pck00010.tpc
 
 
         Apparent position of EDM Landing Site (EDM_LANDING_SITE, NAIF
         ID -117900) as seen from ExoMars-16 TGO in the J2000 frame
         (km):
            X =         -131.716
            Y =        -2168.989
            Z =          208.792
    5. When using 'NONE' aberration corrections, cspice_spkpos returns the geometric position of the target body relative to the observer. If 'LT' is used, the returned vector corresponds to the position of the target at the moment it emitted photons arriving at the observer at `et'. If 'LT+S' is used instead, the returned vector takes into account the observer's velocity relative to the solar system barycenter. The solution for the input UTC time ``2018 JUN 11 19:32:00'' is: 

         Actual (geometric) position of Sun as seen from Mars in the
            J2000 frame (km):
            X =    -24730875.201
            Y =    194558449.560
            Z =     89906170.855
         Light-time corrected position of Sun as seen from Mars in the
            J2000 frame (km):
            X =    -24730866.489
            Y =    194558445.246
            Z =     89906168.754
         Apparent position of Sun as seen from Mars in the
            J2000 frame (km):
            X =    -24712734.289
            Y =    194560532.943
            Z =     89906636.789


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Spacecraft Orientation and Reference Frames (xform)






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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.



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Learning Goals



Familiarity with the different types of kernels involved in chaining reference frames together, both inertial and non-inertial. Discover some of the vector math functions. Understand the difference between cspice_pxform and cspice_sxform.



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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 using Mice functions with which you are already familiar. The ``long-way'' presented above is intended to facilitate the introduction of the functions cspice_pxform and cspice_sxform.

You may find it useful to consult the permuted index, the headers of various source modules, and the following toolkit documentation:

    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.



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Solution





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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.
 
   \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


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Solution Source Code



A sample solution to the problem follows: 

   %
   % Remote sensing lesson:  Spacecraft Orientation and Reference Frames
   %
   function xform()
 
   %
   % Local Parameters
   %
   METAKR = 'xform.tm';
 
   %
   % Load the kernels that this program requires.  We
   % will need:
   %
   %      A leapseconds kernel
   %      A spacecraft clock kernel for ExoMars-16 TGO
   %      The necessary ephemerides
   %      A planetary constants file (PCK)
   %      A spacecraft orientation kernel for ExoMars-16 TGO (CK)
   %      A frame kernel (TF)
   %
   cspice_furnsh ( METAKR );
 
   %
   % Prompt the user for the input time string.
   %
   utctim = input ( 'Input UTC Time: ', 's' );
 
   fprintf ( 'Converting UTC Time: %s\n', utctim )
 
   %
   % Convert utctim to ET.
   %
   et = cspice_str2et ( utctim );
 
   fprintf ( '   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.
   %
   [state, ltime] = cspice_spkezr ( 'MARS',  et,     ...
                                    'J2000', 'LT+S', 'TGO' );
 
   %
   % Now obtain the transformation from the inertial
   % J2000 frame to the non-inertial body-fixed IAU_MARS
   % frame. Since we want the apparent state in the
   % (body-fixed) IAU_MARS reference frame, we
   % need to correct the orientation of this frame for
   % one-way light time; hence we subtract ltime from et
   % in the call below.
   %
   sxfmat = cspice_sxform ( 'J2000', 'IAU_MARS', et-ltime );
 
   %
   % Now rotate the apparent J2000 state into IAU_MARS
   % with the following matrix multiplication:
   %
   bfixst = sxfmat * state;
 
   %
   % Display the results.
   %
   fprintf ( [ '   Apparent state of Mars as seen ',  ...
               'from ExoMars-16 TGO in the IAU_MARS\n', ...
               '      body-fixed frame (km, km/s):\n' ] )
 
   fprintf ( '      X = %19.6f\n', bfixst(1) )
   fprintf ( '      Y = %19.6f\n', bfixst(2) )
   fprintf ( '      Z = %19.6f\n', bfixst(3) )
   fprintf ( '     VX = %19.6f\n', bfixst(4) )
   fprintf ( '     VY = %19.6f\n', bfixst(5) )
   fprintf ( '     VZ = %19.6f\n', bfixst(6) )
 
   %
   % It is worth pointing out, all of the above could
   % have been done with a single use of cspice_spkezr:
   %
   %
   [state, ltime] = cspice_spkezr ( 'MARS',     et,     ...
                                    'IAU_MARS', 'LT+S', ...
                                    'TGO'                  );
   %
   % Display the results.
   %
   fprintf ( [ '   Apparent state of Mars as seen ',    ...
               'from ExoMars-16 TGO in the IAU_MARS\n', ...
               '      body-fixed frame (km, km/s) ',    ...
               'obtained using cspice_spkezr\n',        ...
               '      directly:\n'                 ]   )
 
   fprintf ( '      X = %19.6f\n', state(1) )
   fprintf ( '      Y = %19.6f\n', state(2) )
   fprintf ( '      Z = %19.6f\n', state(3) )
   fprintf ( '     VX = %19.6f\n', state(4) )
   fprintf ( '     VY = %19.6f\n', state(5) )
   fprintf ( '     VZ = %19.6f\n', state(6) )
 
   %
   % Note that the velocity found by using cspice_spkezr
   % to compute the state in the IAU_MARS frame differs
   % at the few mm/second level from that found previously
   % by calling cspice_spkezr and then cspice_sxform.
   % Computing velocity via a single call to cspice_spkezr
   % as we've done immediately above is slightly more
   % accurate than the previous method because the latter
   % 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.
   %
   [pos, ltime] = cspice_spkpos ( 'MARS',  et,     ...
                                  'J2000', 'LT+S', 'TGO' );
 
   %
   % Now compute the location of the nominal instrument view
   % direction.  From reading the frame kernel we know that
   % the instrument view direction is nominally the -Y axis
   % of the TGO_SPACECRAFT frame defined there.
   %
   bsight = [ 0.D0; -1.D0; 0.D0 ];
 
   %
   % Now compute the rotation matrix from TGO_SPACECRAFT into
   % J2000.
   %
   pform = cspice_pxform ( 'TGO_SPACECRAFT', 'J2000', et );
 
   %
   % And multiply the result to obtain the nominal instrument
   % view direction in the J2000 reference frame.
   %
   bsight = pform * bsight;
 
   %
   % Lastly compute the angular separation.
   %
   sep = cspice_convrt ( cspice_vsep(bsight, pos), ...
                         'RADIANS', 'DEGREES'         );
 
   fprintf ( [ '   Angular separation between the ',      ...
               'apparent position of Mars and the\n',     ...
               '      ExoMars-16 TGO nominal instrument ' ...
               'view direction (degrees):\n'              ...
               '      %16.3f\n' ],                        ...
               sep                                           );
 
   %
   % Or alternatively we can work in the spacecraft
   % frame directly.
   %
   [pos, ltime] = cspice_spkpos ( 'MARS', et, 'TGO_SPACECRAFT', ...
                                  'LT+S', 'TGO'                  );
 
   %
   % The nominal instrument view direction is the -Y-axis
   % in the TGO_SPACECRAFT frame.
   %
   bsight = [ 0.D0; -1.D0; 0.D0 ];
 
   %
   % Lastly compute the angular separation.
   %
   sep = cspice_convrt ( cspice_vsep(bsight, pos), ...
                         'RADIANS', 'DEGREES'         );
 
   fprintf ( [ '   Angular separation between the ',      ...
               'apparent position of Mars and the\n'      ...
               '      ExoMars-16 TGO nominal instrument ' ...
               'view direction computed\n'                ...
               '      using vectors in the '              ...
               'TGO_SPACECRAFT frame (degrees):\n'        ...
               '      %16.3f\n' ],                        ...
             sep                                             );
 
   %
   % Unload all kernels.
   %
   cspice_kclear;
 
   %
   % End of function xform
   %


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Solution Sample Output



Execute the program: 

   Converting UTC Time: 2018 JUN 11 19:32:00
      ET seconds past J2000:    582017589.185
      Apparent state of Mars as seen from ExoMars-16 TGO in the IAU_MARS
         body-fixed frame (km, km/s):
         X =        -2843.464125
         Y =         2235.459544
         Z =         1095.894969
        VX =            0.311443
        VY =           -1.151929
        VZ =            3.082123
      Apparent state of Mars as seen from ExoMars-16 TGO in the IAU_MARS
         body-fixed frame (km, km/s) obtained using cspice_spkezr
         directly:
         X =        -2843.464125
         Y =         2235.459544
         Z =         1095.894969
        VX =            0.311443
        VY =           -1.151929
        VZ =            3.082123
      Angular separation between the apparent position of Mars and the
         ExoMars-16 TGO nominal instrument view direction (degrees):
                    5.438
      Angular separation between the apparent position of Mars and the
         ExoMars-16 TGO nominal instrument view direction computed
         using vectors in the TGO_SPACECRAFT frame (degrees):
                    5.438


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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.



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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?



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Solutions and answers



    1. When running the original software using as input the UTC time string ``2018 jun 12 18:25:00'' cspice_pxform returns the SPICE(NOFRAMECONNECT) error, which indicates that there is 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: 

            Segment No.: 1
 
            Object:  -143000
              Interval Begin ET        Interval End ET          AV
              ------------------------ ------------------------ ---
              2018-JUN-11 00:01:09.184 2018-JUN-12 06:28:03.102 Y
              2018-JUN-12 06:58:03.102 2018-JUN-12 18:15:43.102 Y
              2018-JUN-12 18:45:43.102 2018-JUN-13 04:03:23.102 Y
              2018-JUN-13 04:33:23.102 2018-JUN-13 07:59:43.102 Y
              2018-JUN-13 08:29:43.102 2018-JUN-13 12:01:09.184 Y
    whereas if you had used ckbrief without -dump you would have gotten the following information (only CK segment begin/end times): 

            Object:  -143000
              Interval Begin ET        Interval End ET          AV
              ------------------------ ------------------------ ---
              2018-JUN-11 00:01:09.184 2018-JUN-13 12:01:09.184 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 out that the science deck is NOT illuminated, since the angular separation -- 130.543 degrees -- is greater than 90 degrees.



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Computing Sub-spacecraft and Sub-solar Points (subpts)






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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 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.

and displays the results. Use the program to compute these quantities at "2018 jun 11 19:32:00" UTC.



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Learning Goals



Discover higher level geometry calculation functions in Mice and their usage as it relates to ExoMars-16 TGO.



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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: Which method do you want to use to compute the sub-solar (or sub-observer) point?



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Solution





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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-spacecraft and Sub-solar Points'' task
      in the Remote Sensing Hands On Lesson.
 
   \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/fk/em16_tgo_v07.tf',
    'kernels/pck/pck00010.tpc'
 
                      )
 
   \begintext


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Solution Source Code



A sample solution to the problem follows: 

   %
   % Remote sensing lesson:  Computing Sub-spacecraft
   % and Sub-solar Points
   %
   function subpts()
 
   %
   % Local parameters
   %
   METAKR = 'subpts.tm';
 
   %
   % Load the kernels that this program requires.  We
   % will need:
   %
   %      A leapseconds kernel
   %      The necessary ephemerides
   %      A planetary constants file (PCK)
   %      A frames kernel (TF) with the TGO ID/name mapping
   %
   cspice_furnsh ( METAKR );
 
   %
   % Prompt the user for the input time string.
   %
   utctim = input ( 'Input UTC Time: ', 's' );
 
   fprintf ( 'Converting UTC Time: %s\n', utctim )
 
   %
   % Convert utctim to ET.
   %
   et = cspice_str2et ( utctim );
 
   fprintf ( '   ET seconds past J2000: %16.3f\n', et )
 
   %
   % Compute the apparent sub-observer point of ExoMars-16 TGO
   % on Mars.
   %
   [spoint, trgepc, srfvec ] = ...
         cspice_subpnt ( 'NEAR POINT: ELLIPSOID', 'MARS', ...
                         et, 'IAU_MARS', 'LT+S',  'TGO'     );
 
   fprintf ( [ '   Apparent sub-observer point of ',      ...
               'ExoMars-16 TGO on Mars in the\n',         ...
               '   IAU_MARS frame (km):\n' ]                )
 
   fprintf ( '      X = %16.3f\n', spoint(1) )
   fprintf ( '      Y = %16.3f\n', spoint(2) )
   fprintf ( '      Z = %16.3f\n', spoint(3) )
   fprintf ( '    ALT = %16.3f\n', norm(srfvec) )
 
   %
   % Compute the apparent sub-solar point on Mars
   % as seen from ExoMars-16 TGO.
   %
   [spoint, trgepc, srfvec ] = ...
         cspice_subslr ( 'NEAR POINT: ELLIPSOID', 'MARS', ...
                         et, 'IAU_MARS', 'LT+S',  'TGO'     );
 
   fprintf ( [ '   Apparent sub-solar point on Mars ',    ...
               'as seen from ExoMars-16 TGO in\n',        ...
               '   the IAU_MARS frame (km):\n' ]            )
 
   fprintf ( '      X = %16.3f\n', spoint(1) )
   fprintf ( '      Y = %16.3f\n', spoint(2) )
   fprintf ( '      Z = %16.3f\n', spoint(3) )
 
   %
   % Unload all kernels.
   %
   cspice_kclear;
 
   %
   % End of function subpts
   %


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Solution Sample Output



Execute the program: 

   Converting UTC Time: 2018 JUN 11 19:32:00
      ET seconds past J2000:    582017589.185
      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


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Extra Credit



In this ``extra credit'' section you will be presented with more complex tasks, aimed at improving your understanding of cspice_subpnt and cspice_subslr 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.



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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 apparent 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 use Phobos' radii(1) as its 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.



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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 apparent 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: 

         Apparent 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 =           -0.675
    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 sub-spacecraft point on
         Phobos (degrees, km):
            LAT =           -3.030
            LON =           19.088
            R   =           12.779
 
         Planetographic coordinates of the sub-spacecraft point on
         Phobos (degrees, km):
            LAT =           -6.267
            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 -- -0.202 km -- because it was computed using a different and incorrect Phobos surface model, a spheroid with equal equatorial radii, for the surface point computed by cspice_subpnt on the Phobos surface modeled 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.



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Intersecting Vectors with a Triaxial Ellipsoid (fovint)






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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. 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 vector, if an intersection is found, the program displays the results of the above computations, otherwise it indicates no intersection has occurred.

At each point of intersection compute the following:

    3. Phase angle

    4. Solar incidence angle

    5. Emission angle

Additionally compute the local solar time at the intercept of the spectrometer aperture boresight with the surface of Mars.

Use this program to compute values at the epoch:

    2018 jun 11 19:32:00 UTC



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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 triaxial ellipsoidal target bodies. Discover another high level geometry function and another time conversion function in Mice.



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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.

    -- 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.



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Solution





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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 a Triaxial Ellipsoid'' task
      in the Remote Sensing Hands On Lesson.
 
   \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'
 
                      )
 
   \begintext


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Solution Source Code



A sample solution to the problem follows: 

   %
   % Remote sensing lesson:  Intersecting Vectors
   % with a Triaxial Ellipsoid
   %
 
   function fovint()
 
   %
   % Local Parameters
   %
   METAKR    = 'fovint.tm';
   BCVLEN    = 5;
 
   %
   % We use a cell array to store our vector names, which
   % have unequal lengths.
   %
   vecnam = { 'Boundary Corner 1',
              'Boundary Corner 2',
              'Boundary Corner 3',
              'Boundary Corner 4',
              'ExoMars-16 TGO NOMAD LNO Nadir Boresight' };
 
   %
   % Load the kernels that this program requires.  We will need:
   %
   %    A leapseconds kernel.
   %    A SCLK kernel for ExoMars-16 TGO.
   %    Any necessary ephemerides.
   %    The ExoMars-16 TGO frame kernel.
   %    An ExoMars-16 TGO C-kernel.
   %    A PCK file with Mars constants.
   %    The ExoMars-16 TGO NOMAD I-kernel.
   %
   cspice_furnsh ( METAKR );
 
   %
   % Prompt the user for the input time string.
   %
   utctim = input ( 'Input UTC Time: ', 's' );
 
   fprintf ( 'Converting UTC Time: %s\n', utctim )
 
   %
   % Convert utctim to ET.
   %
   et = cspice_str2et ( utctim );
 
   fprintf ( '  ET seconds past J2000: %16.3f\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.
   %
   [ lnonid, found ] = cspice_bodn2c ( 'TGO_NOMAD_LNO_NAD' );
 
   %
   % Stop the program if the code was not found.
   %
   if  ~found
 
      fprintf ( [ 'Unable to locate the ID code for ', ...
                  'TGO_NOMAD_LNO_NAD\n' ]                  );
      return;
 
   end
 
   %
   % Now retrieve the field of view parameters.
   %
   [shape, insfrm, bsight, bounds] =  ...
      cspice_getfov ( lnonid, BCVLEN );
 
 
   %
   % Rather than treat 'bsight' as a separate vector,
   % copy it and 'bounds' to 'scan_vecs'.
   %
   scan_vecs = [ bounds, bsight ];
 
   %
   % Now perform the same set of calculations for each
   % vector listed in the 'bounds' array.
   %
   for vi = 1:5
 
      %
      % Call sincpt to determine coordinates of the
      % intersection of this vector with the surface
      % of Mars.
      %
      [ point, trgepc, srfvec, found ] =               ...
         cspice_sincpt ( 'Ellipsoid', 'MARS',   et,    ...
                         'IAU_MARS',  'LT+S',   'TGO', ...
                         insfrm,      scan_vecs(:,vi)      );
 
      %
      % Check the found flag.  Display a message if
      % the point of intersection was not found,
      % otherwise continue with the calculations.
      %
      fprintf ( 'Vector: %s\n', vecnam{vi} )
 
      if  ~found
 
          fprintf ( 'No intersection point found at this epoch.' );
 
      else
 
         %
         % Now, we have discovered a point of intersection.
         % Start by displaying the position vector in the
         % IAU_MARS frame of the intersection.
         %
         fprintf ( [ '  Position vector of surface intercept ', ...
                     'in the IAU_MARS frame (km):\n' ] );
 
         fprintf ( '     X   = %16.3f\n', point(1) )
         fprintf ( '     Y   = %16.3f\n', point(2) )
         fprintf ( '     Z   = %16.3f\n', point(3) )
 
         %
         % Display the planetocentric latitude and longitude
         % of the intercept.
         %
         [ radius, lon, lat ] = cspice_reclat ( point );
 
         fprintf ( [ '  Planetocentric coordinates of the ', ...
                     'intercept (degrees):\n' ]                   );
 
         fprintf ( '     LAT = %16.3f\n', lat * cspice_dpr );
         fprintf ( '     LON = %16.3f\n', lon * cspice_dpr );
 
         %
         % Compute the illumination angles at this point.
         %
         [ trgepc, srfvec, phase, solar, emissn ] =        ...
            cspice_ilumin ( 'Ellipsoid', 'MARS', et,       ...
                            'IAU_MARS',  'LT+S', 'TGO ',   ...
                            point                              );
 
         fprintf ( [ '  Phase angle (degrees):',           ...
                     '             %14.3f\n'   ],          ...
                   phase  * cspice_dpr                         );
 
         fprintf ( [ '  Solar incidence angle (degrees):', ...
                     '   %14.3f\n'   ],                    ...
                   solar  * cspice_dpr                         );
 
         fprintf ( [ '  Emission angle (degrees):',        ...
                     '          %14.3f\n'   ],             ...
                     emissn * cspice_dpr                       );
 
      end
 
      fprintf ( '\n' );
 
   end
 
   %
   % Lastly compute the local solar time at the boresight
   % intersection.
   %
   if  found
 
      %
      % Get Mars ID.
      %
      [ marsid, found ] = cspice_bodn2c ( 'MARS' );
 
      %
      % 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
 
         fprintf ( 'Unable to locate the ID code for Mars.' )
         return
 
      end
 
      %
      % Compute local solar time corresponding to the TDB light
      % time corrected epoch at the intercept.
      %
      [ hr, min, sc, time, ampm ] = ...
         cspice_et2lst ( trgepc, marsid, lon, 'PLANETOCENTRIC' );
 
      fprintf ( [ '  Local Solar Time at boresight ', ...
                  'intercept (24 Hour Clock):\n',     ...
                   '     %s\n' ],                     ...
                time                                       )
 
   else
 
      fprintf ( [ '  No boresight intercept to compute ', ...
                  'local solar time.' ]                        )
   end
 
 
   %
   % Unload kernels we loaded at the start of the function.
   %
   cspice_unload ( METAKR );
 
   %
   % End of function fovint
   %


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Solution Sample Output



Execute the program: 

   Converting UTC Time: 2018 JUN 11 19:32:00
     ET seconds past J2000:    582017589.185
   Vector: Boundary Corner 1
     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
 
   Vector: Boundary Corner 2
     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
 
   Vector: Boundary Corner 3
     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
 
   Vector: Boundary Corner 4
     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
 
   Vector: ExoMars-16 TGO NOMAD LNO Nadir Boresight
     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
 
     Local Solar Time at boresight intercept (24 Hour Clock):
        14:51:36


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Extra Credit



There are no ``extra credit'' tasks for this step of the lesson.