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Remote Sensing Hands-On Lesson, using CASSINI (Python)

Table of Contents


   Remote Sensing Hands-On Lesson, using CASSINI (Python)
      Overview
      Note About HTML Links
      References
         Tutorials
         Required Readings
         The Permuted Index
         SpiceyPy API Documentation
      Kernels Used
      SpiceyPy Modules Used

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

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

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

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

   Intersecting Vectors with an Ellipsoid and a DSK (fovint)
      Task Statement
      Learning Goals
      Approach
      Solution
         Solution Meta-Kernel
         Solution Source Code
         Solution Sample Output
      Extra Credit




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Remote Sensing Hands-On Lesson, using CASSINI (Python)





March 01, 2023



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Overview




In this lesson you will develop a series of simple programs that demonstrate the usage of SpiceyPy to compute a variety of different geometric quantities applicable to experiments carried out by a remote sensing instrument flown on an interplanetary spacecraft. This particular lesson focuses on a framing camera flying on the Cassini 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, 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.



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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.



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Tutorials



The following SPICE tutorials serve as references for the discussions in this lesson:

   Name              Lesson steps/functions it describes
   ----------------  -----------------------------------------------
   Time              Time Conversion
   SCLK and LSK      Time Conversion
   SPK               Obtaining Ephemeris Data
   Frames            Reference Frames
   Using Frames      Reference Frames
   PCK               Planetary Constants Data
   CK                Spacecraft Orientation Data
   DSK               Detailed Target Shape (Topography) Data
These tutorials are available from the NAIF server at JPL:

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


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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


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The Permuted Index



Another useful document distributed with the Toolkit is the permuted index. It is located under the ``cspice/doc'' directory in the C installation tree.

This text document provides a simple mechanism by which users can discover which SpiceyPy functions perform functions of interest, as well as the names of the source files that contain these functions.




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SpiceyPy API Documentation



A SpiceyPy function's parameters specification is available using the built-in Python help system. A more detailed specification of the API can be found in the CSPICE HTML API documentation page located under ``cspice/doc/html/cspice''.

For example, the Python help function

   >>> import spiceypy
   >>> help(spiceypy.str2et)
describes of the str2et function's parameters, while the document

   cspice/doc/html/cspice/str2et_c.html
describes extensively the str2et functionality.



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Kernels Used




The following kernels are used in examples provided in this lesson:

   #  FILE NAME                 TYPE DESCRIPTION
   -- ------------------------- ---- -----------------------------------
   1  naif0008.tls              LSK  Generic LSK
   2  cas00084.tsc              SCLK Cassini SCLK
   3  981005_PLTEPH-DE405S.bsp  SPK  Solar System Ephemeris
   4  020514_SE_SAT105.bsp      SPK  Saturnian Satellite Ephemeris
   5  030201AP_SK_SM546_T45.bsp SPK  Cassini Spacecraft SPK
   6  cas_v37.tf                FK   Cassini FK
   7  04135_04171pc_psiv2.bc    CK   Cassini Spacecraft CK
   8  cpck05Mar2004.tpc         PCK  Cassini Project PCK
   9  phoebe_64q.bds            DSK  Phoebe DSK
   10 cas_iss_v09.ti            IK   ISS Instrument Kernel
These SPICE kernels are included in the lesson package.

In addition to these kernels, the extra credit exercises require the following kernels:

   #  FILE NAME       TYPE DESCRIPTION
   -- --------------- ---- ---------------------------------------------
   11 jup310_2004.bsp SPK  Generic Jovian Satellite Ephemeris
These SPICE kernels are available from the NAIF server at JPL:

   https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/


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SpiceyPy Modules Used




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

   CHAPTER EXERCISE   FUNCTIONS        NON-VOID         KERNELS
   ------- ---------  ---------------  ---------------  ----------
      1    convtm     spiceypy.furnsh  spiceypy.str2et  1,2
                      spiceypy.unload  spiceypy.etcal
                                       spiceypy.timout
                                       spiceypy.sce2s
 
           extra (*)                   spiceypy.unitim  1,2
                                       spiceypy.sct2e
                                       spiceypy.et2utc
                                       spiceypy.scs2e
 
      2    getsta     spiceypy.furnsh  spiceypy.str2et  1,3-5
                      spiceypy.unload  spiceypy.spkezr
                                       spiceypy.spkpos
                                       spiceypy.vnorm
                                       spiceypy.convrt
 
           extra (*)  spiceypy.kclear                   1,3-5,11
 
      3    xform      spiceypy.furnsh  spiceypy.str2et  1-8
                      spiceypy.unload  spiceypy.spkezr
                                       spiceypy.sxform
                                       spiceypy.mxvg
                                       spiceypy.spkpos
                                       spiceypy.pxform
                                       spiceypy.mxv
                                       spiceypy.convrt
                                       spiceypy.vsep
 
           extra (*)  spiceypy.kclear                   1-8
 
      4    subpts     spiceypy.furnsh  spiceypy.str2et  1,3-5,8,9
                      spiceypy.unload  spiceypy.subpnt
                                       spiceypy.vnorm
                                       spiceypy.subslr
 
           extra (*)  spiceypy.kclear  spiceypy.reclat  1,3-5,8
                                       spiceypy.dpr
                                       spiceypy.bodvrd
                                       spiceypy.recpgr
 
      5    fovint     spiceypy.furnsh  spiceypy.str2et  1-10
                      spiceypy.no_found_check  spiceypy.getfvn
                      spiceypy.unload  spiceypy.bodn2c
                                       spiceypy.sincpt
                                       spiceypy.reclat
                                       spiceypy.dpr
                                       spiceypy.illumf
                                       spiceypy.et2lst
 
 
      (*) Additional APIs and kernels used in Extra Credit tasks.
Use the Python built-in help system on the various functions listed above for the API parameters' description, and refer to the headers of their corresponding CSPICE versions for detailed interface specifications.



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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 "2004 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: spiceypy.etcal or spiceypy.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.
 
      The names and contents of the kernels referenced by this
      meta-kernel are as follows:
 
      File name                   Contents
      --------------------------  -----------------------------
      naif0008.tls                Generic LSK
      cas00084.tsc                Cassini SCLK
 
 
      \begindata
      KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls',
                          'kernels/sclk/cas00084.tsc' )
      \begintext


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Solution Source Code



A sample solution to the problem follows:

   #
   # Solution convtm
   #
   from __future__ import print_function
   from builtins import input
 
   import spiceypy
 
   def convtm():
       #
       # Local Parameters
       #
       METAKR = 'convtm.tm'
       SCLKID = -82
 
       spiceypy.furnsh( METAKR )
 
       #
       # Prompt the user for the input time string.
       #
       utctim = input( 'Input UTC Time: ' )
 
       print( 'Converting UTC Time: {:s}'.format( utctim ) )
 
       #
       # Convert utctim to ET.
       #
       et = spiceypy.str2et( utctim )
 
       print( '   ET Seconds Past J2000: {:16.3f}'.format( et ) )
 
       #
       # Now convert ET to a calendar time string.
       # This can be accomplished in two ways.
       #
       calet = spiceypy.etcal( et )
 
       print( '   Calendar ET (etcal):   {:s}'.format( calet ) )
 
       #
       # Or use timout for finer control over the
       # output format. The picture below was built
       # by examining the header of timout.
       #
       calet = spiceypy.timout( et, 'YYYY-MON-DDTHR:MN:SC ::TDB' )
 
       print( '   Calendar ET (timout):  {:s}'.format( calet ) )
 
       #
       # Convert ET to spacecraft clock time.
       #
       sclkst = spiceypy.sce2s( SCLKID, et )
 
       print( '   Spacecraft Clock Time: {:s}'.format( sclkst ) )
 
       spiceypy.unload( METAKR )
 
   if __name__ == '__main__':
       convtm()
 


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Solution Sample Output



Execute the program:

   Input UTC Time: 2004 jun 11 19:32:00
   Converting UTC Time: 2004 jun 11 19:32:00
      ET Seconds Past J2000:    140254384.185
      Calendar ET (etcal):   2004 JUN 11 19:33:04.184
      Calendar ET (timout):  2004-JUN-11T19:33:04
      Spacecraft Clock Time: 1/1465674964.105


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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 "2004 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 CASSINI ISS NAC camera. Convert "2004 jun 11 19:32:00" UTC.

    5. Find the earliest UTC time that can be converted to CASSINI 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 CASSINI 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: spiceypy.unitim and spiceypy.timout. The difference between them is the type of output produced by each method. spiceypy.unitim returns the double precision value of an input epoch, while spiceypy.timout returns the string representation of the ephemeris time in Julian Date format (when picture input is set to 'JULIAND.######### ::TDB'). Refer to the function header for further details. The solution for the requested input UTC string is:

      Julian Date TDB:   2453168.3146318
    2. When running the original program without the LSK kernel, an error is produced:

   Traceback (most recent call last):
     File "convtm.py", line 67, in <module>
       convtm()
     File "convtm.py", line 30, in convtm
       et = spiceypy.str2et( utctim )
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 139, in with_errcheck
       check_for_spice_error(f)
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 122, in check_for_spice_error
       raise dynamically_instantiate_spiceyerror(
   spiceypy.utils.exceptions.SpiceNOLEAPSECONDS:
   =====================================================================
   ===========
 
   Toolkit version: CSPICE_N0067
 
   SPICE(NOLEAPSECONDS) --
 
   The variable that points to the leapseconds (DELTET/DELTA_AT) could n
   ot be located in the kernel pool.  It is likely that the leapseconds
   kernel has not been loaded.
 
   str2et_c --> STR2ET --> TTRANS
 
   =====================================================================
   ===========
    This error is triggered by spiceypy.str2et because the variable that points to the leapseconds is not present in the kernel pool and therefore the program lacks data required to perform the requested UTC to ephemeris time conversion.

    By default, SPICE will report, as a minimum, a short descriptive message and a expanded form of this short message where more details about the error are provided. If this error message is not sufficient for you to understand what has happened, you could go to the ``Exceptions'' section in the SPICELIB or CSPICE headers of the function that has triggered the error and find out more information about the possible causes.

    3. When running the original program without the SCLK kernel, an error is produced:

   Traceback (most recent call last):
     File "convtm.py", line 67, in <module>
       convtm()
     File "convtm.py", line 58, in convtm
       sclkst = spiceypy.sce2s( SCLKID, et )
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 139, in with_errcheck
       check_for_spice_error(f)
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 122, in check_for_spice_error
       raise dynamically_instantiate_spiceyerror(
   spiceypy.utils.exceptions.SpiceKERNELVARNOTFOUND:
   =====================================================================
   ===========
 
   Toolkit version: CSPICE_N0067
 
   SPICE(KERNELVARNOTFOUND) --
   The Variable Was not Found in the Kernel Pool.
   Kernel variable SCLK_DATA_TYPE_82 was not found in the kernel pool.
 
   sce2s_c --> SCE2S --> SCE2T --> SCTYPE --> SCTY01
 
   =====================================================================
   ===========
    This error is triggered by spiceypy.sce2s. In this case the error message may not give you enough information to understand what has actually happened. Nevertheless, the expanded form of this short message clearly indicates that the SCLK kernel for the spacecraft ID -82 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 CASSINI ISS NAC camera. In order to do so, examine the ISS instrument kernel listed above and look for the ``NAIF ID Code to Name Mapping'' and there, for the NAIF ID given to CASSINI_ISS_NAC (which is -82360). Then replace in your code the SCLK ID -82 with -82360. After executing the program using the original meta-kernel, you will be getting the same error as in the previous task. Despite the error being exactly the same, this case is different. Generally, spacecraft clocks are associated with the spacecraft ID and not with its payload, sensors or structures IDs. Therefore, in order to do conversions from/to spacecraft clock for payload, sensors or spacecraft structures, the spacecraft ID must be used.

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

    5. Use spiceypy.sct2e with the encoding of the Cassini spacecraft clock time set to 0.0 ticks and convert the resulting ephemeris time to UTC using either spiceypy.timout or spiceypy.et2utc. The solution for the requested SCLK string is:

      Earliest UTC convertible to SCLK: 1980-01-01T00:00:00.000
    6. Use spiceypy.scs2e with the SCLK string obtained in the computations performed in the regular tasks and convert the resulting ephemeris time to UTC using either spiceypy.et2utc, with 'ISOC' format and 3 digits precision, or using spiceypy.timout using the time picture 'YYYY-MM-DDTHR:MN:SC.### ::RND'. The solution of the requested conversion is:

      Spacecraft Clock Time:          1/1465674964.105
      UTC time from spacecraft clock: 2004-06-11T19:31:59.999


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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 Phoebe as seen from CASSINI 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 CASSINI in the J2000 frame, in kilometers.

    3. The one-way light time between CASSINI and the apparent position of Earth, in seconds.

    4. The apparent position of the Sun as seen from Phoebe in the J2000 frame (J2000), in kilometers.

    5. The actual (geometric) distance between the Sun and Phoebe, in astronomical units.

and displays the results. Use the program to compute these quantities at "2004 jun 11 19:32:00" UTC.



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Learning Goals




Understand the anatomy of an spiceypy.spkezr call. Discover the difference between spiceypy.spkezr and spiceypy.spkpos. Familiarity with the Toolkit utility ``brief''. Exposure to unit conversion with SpiceyPy.



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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 Phoebe relative to CASSINI in the J2000 reference frame, corrected for aberrations.

    -- Compute the position of Earth relative to CASSINI in the J2000 reference frame, corrected for aberrations. (The function in the library that computes this also returns the one-way light time between CASSINI and Earth.)

    -- Compute the position of the Sun relative to Phoebe in the J2000 reference frame, corrected for aberrations.

    -- Compute the position of the Sun relative to Phoebe 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.



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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.
 
      The names and contents of the kernels referenced by this
      meta-kernel are as follows:
 
      File name                   Contents
      --------------------------  -----------------------------
      naif0008.tls                Generic LSK
      981005_PLTEPH-DE405S.bsp    Solar System Ephemeris
      020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris
      030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK
 
 
      \begindata
      KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls',
                          'kernels/spk/981005_PLTEPH-DE405S.bsp',
                          'kernels/spk/020514_SE_SAT105.bsp',
                          'kernels/spk/030201AP_SK_SM546_T45.bsp' )
      \begintext


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Solution Source Code



A sample solution to the problem follows:

   #
   # Solution getsta.py
   #
   from __future__ import print_function
   from builtins import input
 
   import spiceypy
 
   def getsta():
       #
       # Local parameters
       #
       METAKR = 'getsta.tm'
 
       #
       # Load the kernels that this program requires.  We
       # will need a leapseconds kernel to convert input
       # UTC time strings into ET.  We also will need the
       # necessary SPK files with coverage for the bodies
       # in which we are interested.
       #
       spiceypy.furnsh( METAKR )
 
       #
       #Prompt the user for the input time string.
       #
       utctim = input( 'Input UTC Time: ' )
 
       print( 'Converting UTC Time: {:s}'.format(utctim)  )
 
       #
       #Convert utctim to ET.
       #
       et = spiceypy.str2et( utctim )
 
       print( '   ET seconds past J2000: {:16.3f}'.format(et) )
 
       #
       # Compute the apparent state of Phoebe as seen from
       # CASSINI in the J2000 frame.  All of the ephemeris
       # readers return states in units of kilometers and
       # kilometers per second.
       #
       [state, ltime] = spiceypy.spkezr( 'PHOEBE', et,      'J2000',
                                         'LT+S',   'CASSINI'       )
 
       print( '   Apparent state of Phoebe as seen '
              'from CASSINI in the J2000\n'
              '      frame (km, km/s):'              )
 
       print( '      X = {:16.3f}'.format(state[0])       )
       print( '      Y = {:16.3f}'.format(state[1])       )
       print( '      Z = {:16.3f}'.format(state[2])       )
       print( '     VX = {:16.3f}'.format(state[3])       )
       print( '     VY = {:16.3f}'.format(state[4])       )
       print( '     VZ = {:16.3f}'.format(state[5])       )
 
       #
       # Compute the apparent position of Earth as seen from
       # CASSINI in the J2000 frame.  Note: We could have
       # continued using spkezr and simply ignored the
       # velocity components.
       #
       [pos, ltime] = spiceypy.spkpos( 'EARTH', et,        'J2000',
                                       'LT+S',  'CASSINI',         )
 
       print( '   Apparent position of Earth as '
              'seen from CASSINI in the J2000\n'
              '      frame (km):'                )
       print( '      X = {:16.3f}'.format(pos[0])  )
       print( '      Y = {:16.3f}'.format(pos[1])  )
       print( '      Z = {:16.3f}'.format(pos[2])  )
 
       #
       # We need only display LTIME, as it is precisely the
       # light time in which we are interested.
       #
       print( '   One way light time between CASSINI and '
              'the apparent position\n'
              '      of Earth (seconds):'
              ' {:16.3f}'.format(ltime) )
 
       #
       # Compute the apparent position of the Sun as seen from
       # PHOEBE in the J2000 frame.
       #
       [pos, ltime] = spiceypy.spkpos( 'SUN',  et,       'J2000',
                                       'LT+S', 'PHOEBE',         )
 
       print( '   Apparent position of Sun as '
              'seen from Phoebe in the\n'
              '       J2000 frame (km):'           )
       print( '      X = {:16.3f}'.format(pos[0])  )
       print( '      Y = {:16.3f}'.format(pos[1])  )
       print( '      Z = {:16.3f}'.format(pos[2])  )
 
       #
       # Now we need to compute the actual distance between
       # the Sun and Phoebe.  The above spkpos call gives us
       # the apparent distance, so we need to adjust our
       # aberration correction appropriately.
       #
       [pos, ltime] = spiceypy.spkpos( 'SUN',  et,      'J2000',
                                       'NONE', 'PHOEBE'         )
 
       #
       # Compute the distance between the body centers in
       # kilometers.
       #
       dist = spiceypy.vnorm( pos )
 
       #
       # Convert this value to AU using convrt.
       #
       dist = spiceypy.convrt( dist, 'KM', 'AU' )
 
       print( '   Actual distance between Sun and '
              'Phoebe body centers:\n'
              '      (AU): {:16.3f}'.format(dist) )
 
       spiceypy.unload( METAKR )
 
   if __name__ == '__main__':
       getsta()
 


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Solution Sample Output



Execute the program:

   Input UTC Time: 2004 jun 11 19:32:00
   Converting UTC Time: 2004 jun 11 19:32:00
      ET seconds past J2000:    140254384.185
      Apparent state of Phoebe as seen from CASSINI in the J2000
         frame (km, km/s):
         X =         -119.921
         Y =         2194.139
         Z =          -57.639
        VX =           -5.980
        VY =           -2.119
        VZ =           -0.295
      Apparent position of Earth as seen from CASSINI in the J2000
         frame (km):
         X =    353019393.123
         Y =  -1328180352.140
         Z =   -568134171.697
      One way light time between CASSINI and the apparent position
         of Earth (seconds):         4960.427
      Apparent position of Sun as seen from Phoebe in the
          J2000 frame (km):
         X =    376551465.272
         Y =  -1190495630.303
         Z =   -508438699.110
      Actual distance between Sun and Phoebe body centers:
         (AU):            9.012


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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 spiceypy.spkezr function, and some common errors that may happen when computing these states.

These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks.



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Task statements and questions



    1. Remove the Solar System 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 Saturn in the J2000 frame (J2000), in kilometers.

    3. Extend, or modify, your program to compute the position of the Sun as seen from Saturn in the J2000 frame (J2000), in kilometers, using the following light time and aberration corrections: NONE, LT and LT+S. Explain the differences.

    4. Examine the CASSINI frames definition kernel and the ISS instrument kernel to find the SPICE ID/name definitions.



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Solutions and answers



    1. When running the original program without the Solar System ephemerides SPK, an error is produced by spiceypy.spkezr:

   Traceback (most recent call last):
     File "getsta.py", line 128, in <module>
       getsta()
     File "getsta.py", line 46, in getsta
       [state, ltime] = spiceypy.spkezr( 'PHOEBE', et,      'J2000',
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 139, in with_errcheck
       check_for_spice_error(f)
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 122, in check_for_spice_error
       raise dynamically_instantiate_spiceyerror(
   spiceypy.utils.exceptions.SpiceSPKINSUFFDATA:
   =====================================================================
   ===========
 
   Toolkit version: CSPICE_N0067
 
   SPICE(SPKINSUFFDATA) --
 
   Insufficient ephemeris data has been loaded to compute the state of -
   82 (CASSINI) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris
    epoch 2004 JUN 11 19:33:04.184.
 
   spkezr_c --> SPKEZR --> SPKEZ --> SPKACS --> SPKGEO
 
   =====================================================================
   ===========
    This error is generated when trying to compute the apparent state of Phoebe as seen from CASSINI in the J2000 frame because despite both Phoebe and CASSINI ephemeris data being relative to the Saturn Barycenter, 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 CASSINI with respect to the Saturn Barycenter, and geometric states of Phoebe with respect to the Saturn 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 Saturn Barycenter relative to the Solar System barycenter are no longer loaded. Run ``brief'' on the SPKs used in the original task to find out which ephemeris objects are available from those kernels. If you want to find out what is the 'center of motion' for the ephemeris object(s) included in an SPK, use the -c option when running ``brief'':

 
   BRIEF -- Version 4.1.0, September 17, 2021 -- Toolkit Version N0067
 
 
   Summary for: kernels/spk/981005_PLTEPH-DE405S.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)
           MARS (499) w.r.t. MARS BARYCENTER (4)
           Start of Interval (UTC)             End of Interval (UTC)
           -----------------------------       -------------------------
   ----
           2004-JUN-11 05:00:00.000            2004-JUN-12 12:00:00.000
 
 
   Summary for: kernels/spk/020514_SE_SAT105.bsp
 
   Bodies: MIMAS (601) w.r.t. SATURN BARYCENTER (6)
           ENCELADUS (602) w.r.t. SATURN BARYCENTER (6)
           TETHYS (603) w.r.t. SATURN BARYCENTER (6)
           DIONE (604) w.r.t. SATURN BARYCENTER (6)
           RHEA (605) w.r.t. SATURN BARYCENTER (6)
           TITAN (606) w.r.t. SATURN BARYCENTER (6)
           HYPERION (607) w.r.t. SATURN BARYCENTER (6)
           IAPETUS (608) w.r.t. SATURN BARYCENTER (6)
           PHOEBE (609) w.r.t. SATURN BARYCENTER (6)
           SATURN (699) w.r.t. SATURN BARYCENTER (6)
           Start of Interval (UTC)             End of Interval (UTC)
           -----------------------------       -------------------------
   ----
           2004-JUN-11 05:00:00.000            2004-JUN-12 12:00:00.000
 
 
   Summary for: kernels/spk/030201AP_SK_SM546_T45.bsp
 
   Body: CASSINI (-82) w.r.t. SATURN BARYCENTER (6)
         Start of Interval (UTC)             End of Interval (UTC)
         -----------------------------       ---------------------------
   --
         2004-JUN-11 05:00:00.000            2004-JUN-12 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 spiceypy.spkpos function because you have not loaded enough ephemeris data to compute the position of Jupiter with respect to Saturn. The loaded SPKs contain data for Saturn 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:
 
      File name                Contents
      -----------------------  ----------------------------------
      jup310_2004.bsp          Generic Jovian Satellite Ephemeris
 
 
      available in the NAIF server at:
 
   https://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 "2004 jun 11 19:32:00" when using the downloaded Jovian Satellite Ephemeris SPK:

      Actual position of Jupiter as seen from Saturn in the
         J2000 frame (km):
         X =   -436016583.291
         Y =  -1094176737.323
         Z =   -446585337.431
    3. When using 'NONE' aberration corrections, spiceypy.spkpos returns the geometric position of the target body relative to the observer. If 'LT' is used, the returned vector corresponds to the position of the target at the moment it emitted photons arriving at the observer at `et'. If 'LT+S' is used instead, the returned vector takes into account the observer's velocity relative to the solar system barycenter. The solution for the input UTC time "2004 jun 11 19:32:00" is:

 
      Actual (geometric) position of Sun as seen from Saturn in the
         J2000 frame (km):
         X =    367770592.367
         Y =  -1197330367.359
         Z =   -510369088.677
      Light-time corrected position of Sun as seen from Saturn in the
         J2000 frame (km):
         X =    367770572.921
         Y =  -1197330417.733
         Z =   -510369109.509
      Apparent position of Sun as seen from Saturn in the
         J2000 frame (km):
         X =    367726456.168
         Y =  -1197342627.879
         Z =   -510372252.747
 


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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, computes and displays the following at the epoch of interest:

    1. The apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE 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 Earth as seen from CASSINI and the nominal boresight of the CASSINI high gain antenna (HGA).

    The HGA boresight direction is provided by the kernel variable TKFRAME_-82101_BORESIGHT, which is defined in the Cassini frame kernel cited above in the section ``Kernels Used.'' In this kernel, the HGA boresight vector is expressed relative to the CASSINI_HGA reference frame.

Use the program to compute these quantities at the epoch "2004 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 matrix and vector math functions. Understand the difference between spiceypy.pxform and spiceypy.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 Phoebe relative to CASSINI in the J2000 reference frame, corrected for aberrations.

    -- Compute the state transformation matrix from J2000 to IAU_PHOEBE at the epoch, adjusted for light time.

    -- Multiply the state of Phoebe relative to CASSINI in the J2000 reference frame by the state transformation matrix computed in the previous step.

    -- Compute the position of Earth relative to CASSINI in the J2000 reference frame, corrected for aberrations.

    -- Determine what the nominal boresight of the CASSINI high gain antenna is by examining the frame kernel's content.

    -- Compute the rotation matrix from the CASSINI high gain antenna frame to J2000.

    -- Multiply the nominal boresight expressed in the CASSINI high gain antenna frame by the rotation matrix from the previous step.

    -- Compute the separation between the result of the previous step and the apparent position of the Earth relative to CASSINI in the J2000 frame.

HINT: Several of the steps above may be compressed into a single step using SpiceyPy functions with which you are already familiar. The ``long way'' presented above is intended to facilitate the introduction of the functions spiceypy.pxform and spiceypy.sxform.

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

    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.
 
      The names and contents of the kernels referenced by this
      meta-kernel are as follows:
 
      File name                   Contents
      --------------------------  -----------------------------
      naif0008.tls                Generic LSK
      cas00084.tsc                Cassini SCLK
      981005_PLTEPH-DE405S.bsp    Solar System Ephemeris
      020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris
      030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK
      cas_v37.tf                  Cassini FK
      04135_04171pc_psiv2.bc      Cassini Spacecraft CK
      cpck05Mar2004.tpc           Cassini Project PCK
 
 
      \begindata
      KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls',
                          'kernels/sclk/cas00084.tsc',
                          'kernels/spk/981005_PLTEPH-DE405S.bsp',
                          'kernels/spk/020514_SE_SAT105.bsp',
                          'kernels/spk/030201AP_SK_SM546_T45.bsp',
                          'kernels/fk/cas_v37.tf',
                          'kernels/ck/04135_04171pc_psiv2.bc',
                          'kernels/pck/cpck05Mar2004.tpc' )
      \begintext


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Solution Source Code



A sample solution to the problem follows:

   #
   # Solution xform.py
   #
   from __future__ import print_function
   from builtins import input
 
   import spiceypy
 
   def xform():
       #
       # Local parameters
       #
       METAKR = 'xform.tm'
 
       #
       # Load the kernels that this program requires.  We
       # will need:
       #
       #    A leapseconds kernel
       #    A spacecraft clock kernel for CASSINI
       #    The necessary ephemerides
       #    A planetary constants file (PCK)
       #    A spacecraft orientation kernel for CASSINI (CK)
       #    A frame kernel (TF)
       #
       spiceypy.furnsh( METAKR )
 
       #
       #  Prompt the user for the input time string.
       #
       utctim = input( 'Input UTC Time: ' )
 
       print( 'Converting UTC Time: {:s}'.format(utctim)  )
 
       #
       #Convert utctim to ET.
       #
       et = spiceypy.str2et( utctim )
 
       print( '   ET seconds past J2000: {:16.3f}'.format(et) )
 
       #
       # Compute the apparent state of Phoebe as seen from
       # CASSINI in the J2000 frame.
       #
       [state, ltime] = spiceypy.spkezr( 'PHOEBE', et,      'J2000',
                                         'LT+S',   'CASSINI'       )
       #
       # Now obtain the transformation from the inertial
       # J2000 frame to the non-inertial body-fixed IAU_PHOEBE
       # frame.  Since we want the apparent position, we
       # need to subtract ltime from et.
       #
       sform = spiceypy.sxform( 'J2000', 'IAU_PHOEBE', et-ltime )
 
       #
       # Now rotate the apparent J2000 state into IAU_PHOEBE
       # with the following matrix multiplication:
       #
       bfixst = spiceypy.mxvg ( sform, state )
 
       #
       # Display the results.
       #
       print( '   Apparent state of Phoebe as seen '
              'from CASSINI in the IAU_PHOEBE\n'
              '      body-fixed frame (km, km/s):'      )
       print( '      X = {:19.6f}'.format(bfixst[0])    )
       print( '      Y = {:19.6f}'.format(bfixst[1])    )
       print( '      Z = {:19.6f}'.format(bfixst[2])    )
       print( '     VX = {:19.6f}'.format(bfixst[3])    )
       print( '     VY = {:19.6f}'.format(bfixst[4])    )
       print( '     VZ = {:19.6f}'.format(bfixst[5])    )
 
       #
       # It is worth pointing out, all of the above could
       #  have been done with a single use of spkezr:
       #
       [state, ltime] = spiceypy.spkezr(
                           'PHOEBE', et,      'IAU_PHOEBE',
                           'LT+S',   'CASSINI'              )
       #
       # Display the results.
       #
       print( '   Apparent state of Phoebe as seen '
              'from CASSINI in the IAU_PHOEBE\n'
              '      body-fixed frame (km, km/s) '
              'obtained using spkezr directly:'        )
       print( '      X = {:19.6f}'.format(state[0])    )
       print( '      Y = {:19.6f}'.format(state[1])    )
       print( '      Z = {:19.6f}'.format(state[2])    )
       print( '     VX = {:19.6f}'.format(state[3])    )
       print( '     VY = {:19.6f}'.format(state[4])    )
       print( '     VZ = {:19.6f}'.format(state[5])    )
 
       #
       # Note that the velocity found by using spkezr
       # to compute the state in the IAU_PHOEBE frame differs
       # at the few mm/second level from that found previously
       # by calling spkezr and then sxform. Computing
       # velocity via a single call to spkezr as we've
       # done immediately above is slightly more accurate because
       # it accounts for the effect of the rate of change of
       # light time on the apparent angular velocity of the
       # target's body-fixed reference frame.
       #
       # Now we are to compute the angular separation between
       # the apparent position of the Earth as seen from the
       # orbiter and the nominal boresight of the high gain
       # antenna.  First, compute the apparent position of
       # the Earth as seen from CASSINI in the J2000 frame.
       #
       [pos, ltime] = spiceypy.spkpos( 'EARTH', et,      'J2000',
                                       'LT+S',  'CASSINI'        )
 
       #
       # Now compute the location of the antenna boresight
       # at this same epoch.  From reading the frame kernel
       # we know that the antenna boresight is nominally the
       # +Z axis of the CASSINI_HGA frame defined there.
       #
       bsight = [ 0.0, 0.0, 1.0]
 
       #
       # Now compute the rotation matrix from CASSINI_HGA into
       # J2000.
       #
       pform = spiceypy.pxform( 'CASSINI_HGA', 'J2000', et )
 
       #
       # And multiply the result to obtain the nominal
       # antenna boresight in the J2000 reference frame.
       #
       bsight = spiceypy.mxv( pform, bsight )
 
       #
       # Lastly compute the angular separation.
       #
       sep =  spiceypy.convrt( spiceypy.vsep(bsight, pos),
                               'RADIANS', 'DEGREES'       )
 
       print( '   Angular separation between the '
              'apparent position of\n'
              '      Earth and the CASSINI high '
              'gain antenna boresight (degrees):\n'
              '      {:16.3f}'.format(sep)        )
 
       #
       # Or alternatively we can work in the antenna
       # frame directly.
       #
       [pos, ltime] = spiceypy.spkpos(
                         'EARTH', et,      'CASSINI_HGA',
                         'LT+S',  'CASSINI'               )
 
       #
       # The antenna boresight is the Z-axis in the
       # CASSINI_HGA frame.
       #
       bsight = [ 0.0, 0.0, 1.0 ]
 
       #
       # Lastly compute the angular separation.
       #
       sep =  spiceypy.convrt( spiceypy.vsep(bsight, pos),
                               'RADIANS', 'DEGREES'       )
 
       print( '   Angular separation between the '
              'apparent position of\n'
              '      Earth and the CASSINI high '
              'gain antenna boresight computed\n'
              '      using vectors in the CASSINI_HGA '
              'frame (degrees):\n'
              '      {:16.3f}'.format(sep)            )
 
       spiceypy.unload( METAKR )
 
   if __name__ == '__main__':
       xform()
 


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Solution Sample Output



Execute the program:

   Input UTC Time: 2004 jun 11 19:32:00
   Converting UTC Time: 2004 jun 11 19:32:00
      ET seconds past J2000:    140254384.185
      Apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE
         body-fixed frame (km, km/s):
         X =        -1982.639762
         Y =         -934.530471
         Z =         -166.562595
        VX =            3.970833
        VY =           -3.812498
        VZ =           -2.371663
      Apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE
         body-fixed frame (km, km/s) obtained using spkezr directly:
         X =        -1982.639762
         Y =         -934.530471
         Z =         -166.562595
        VX =            3.970832
        VY =           -3.812496
        VZ =           -2.371663
      Angular separation between the apparent position of
         Earth and the CASSINI high gain antenna boresight (degrees):
                   71.924
      Angular separation between the apparent position of
         Earth and the CASSINI high gain antenna boresight computed
         using vectors in the CASSINI_HGA frame (degrees):
                   71.924


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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 ``2004 jun 11 18:25:00''. Explain what happens.

    2. Compute the angular separation between the apparent position of the Sun as seen from CASSINI and the nominal boresight of the CASSINI high gain antenna (HGA). Is the HGA illuminated?



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Solutions and answers



    1. When running the original software using as input the UTC time string "2004 jun 11 18:25:00":

   Traceback (most recent call last):
     File "xform.py", line 183, in <module>
       xform()
     File "xform.py", line 130, in xform
       pform = spiceypy.pxform( 'CASSINI_HGA', 'J2000', et )
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 139, in with_errcheck
       check_for_spice_error(f)
     File "/home/bsemenov/virtenvs/ndt_3.8/lib/python3.8/site-packages/s
   piceypy/spiceypy.py", line 122, in check_for_spice_error
       raise dynamically_instantiate_spiceyerror(
   spiceypy.utils.exceptions.SpiceNOFRAMECONNECT:
   =====================================================================
   ===========
 
   Toolkit version: CSPICE_N0067
 
   SPICE(NOFRAMECONNECT) --
 
   At epoch 1.4025036418463E+08 TDB (2004 JUN 11 18:26:04.184 TDB), ther
   e is insufficient information available to transform from reference f
   rame -82101 (CASSINI_HGA) to reference frame 1 (J2000). Frame CASSINI
   _HGA could be transformed to frame -82000 (CASSINI_SC_COORD). The lat
   ter is a CK frame; a CK file containing data for instrument or struct
   ure -82000 at the epoch shown above, as well as a corresponding SCLK
   kernel, must be loaded in order to use this frame. Failure to find re
   quired CK data could be due to one or more CK files not having been l
   oaded, or to the epoch shown above lying within a coverage gap or bey
   ond the coverage bounds of the loaded CK files. It is also possible t
   hat no loaded CK file has required angular velocity data for the inpu
   t epoch, even if a loaded CK does have attitude data for that epoch.
   You can use CKBRIEF with the -dump option to display coverage interva
   ls of a CK file.
 
   pxform_c --> PXFORM --> REFCHG
 
   =====================================================================
   ===========
    spiceypy.pxform returns the SPICE(NOFRAMECONNECT) error, which indicates that there are not sufficient data to perform the transformation from the CASSINI_HGA frame to J2000 at the requested epoch. If you summarize the CASSINI spacecraft CK using the ``ckbrief'' utility program with the -dump option (display interpolation intervals boundaries) you will find that the CK contains gaps within its segment:

 
   CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067
 
 
   Summary for: kernels/ck/04135_04171pc_psiv2.bc
 
   Segment No.: 1
 
   Object:  -82000
     Interval Begin UTC       Interval End UTC         AV
     ------------------------ ------------------------ ---
     2004-JUN-11 05:00:00.000 2004-JUN-11 09:25:02.019 Y
     2004-JUN-11 09:26:14.019 2004-JUN-11 18:24:37.152 Y
     2004-JUN-11 18:26:13.152 2004-JUN-12 05:53:26.012 Y
     2004-JUN-12 05:54:56.012 2004-JUN-12 10:32:08.016 Y
     2004-JUN-12 10:33:26.016 2004-JUN-12 11:59:59.998 Y
 
 
    whereas if you had used ckbrief without -dump you would have gotten the following information (only CK segment begin/end times):

 
   CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067
 
 
   Summary for: kernels/ck/04135_04171pc_psiv2.bc
 
   Object:  -82000
     Interval Begin UTC       Interval End UTC         AV
     ------------------------ ------------------------ ---
     2004-JUN-11 05:00:00.000 2004-JUN-12 11:59:59.998 Y
 
 
    which has insufficient detail to reveal the problem.

    2. By computing the apparent position of the Sun as seen from CASSINI in the CASSINI_HGA frame, and the angular separation between this vector and the nominal boresight of the CASSINI high gain antenna (+Z-axis of the CASSINI_HGA frame), you will find whether the HGA is illuminated. The solution for the input UTC time "2004 jun 11 19:32:00" is:

   Angular separation between the apparent position of the Sun and the
   nominal boresight of the CASSINI high gain antenna (degrees):
        73.130
 
   HGA illumination:
      CASSINI high gain antenna IS illuminated.
    since the angular separation is smaller than 90 degrees.



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Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts)







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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 CASSINI on Phoebe, in the body fixed frame IAU_PHOEBE, in kilometers, and the spacecraft altitude as the distance between the spacecraft and this point, in kilometers.

    2. The apparent sub-solar point on Phoebe, as seen from CASSINI in the body fixed frame IAU_PHOEBE, 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 "2004 jun 11 19:32:00" UTC.



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Learning Goals




Discover higher level geometry calculation functions in SpiceyPy and their usage as it relates to CASSINI.



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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: 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?



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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.
 
      The names and contents of the kernels referenced by this
      meta-kernel are as follows:
 
      File name                   Contents
      --------------------------  -----------------------------
      naif0008.tls                Generic LSK
      981005_PLTEPH-DE405S.bsp    Solar System Ephemeris
      020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris
      030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK
      cpck05Mar2004.tpc           Cassini Project PCK
      phoebe_64q.bds              Phoebe DSK
 
 
      \begindata
      KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls',
                          'kernels/spk/981005_PLTEPH-DE405S.bsp',
                          'kernels/spk/020514_SE_SAT105.bsp',
                          'kernels/spk/030201AP_SK_SM546_T45.bsp',
                          'kernels/pck/cpck05Mar2004.tpc'
                          'kernels/dsk/phoebe_64q.bds' )
 
      \begintext


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Solution Source Code



A sample solution to the problem follows:

   #
   # Solution subpts.py
   #
   from __future__ import print_function
   from builtins import input
 
   #
   # SpiceyPy package:
   #
   import spiceypy
 
   def subpts():
       #
       # Local parameters
       #
       METAKR = 'subpts.tm'
 
       #
       # Load the kernels that this program requires.  We
       # will need:
       #
       #    A leapseconds kernel
       #    The necessary ephemerides
       #    A planetary constants file (PCK)
       #    A DSK file containing Phoebe shape data
       #
       spiceypy.furnsh( METAKR )
 
       #
       #Prompt the user for the input time string.
       #
       utctim = input( 'Input UTC Time: ' )
 
       print( ' Converting UTC Time: {:s}'.format(utctim)  )
 
       #
       #Convert utctim to ET.
       #
       et = spiceypy.str2et( utctim )
 
       print( '   ET seconds past J2000: {:16.3f}'.format(et) )
 
       for  i  in range(2):
 
           if  i  == 0:
               #
               # Use the "near point" sub-point definition
               # and an ellipsoidal model.
               #
               method = 'NEAR POINT/Ellipsoid'
 
           else:
               #
               # Use the "nadir" sub-point definition
               # and a DSK model.
               #
               method = 'NADIR/DSK/Unprioritized'
 
           print( '\n Sub-point/target shape model: {:s}\n'.format(
               method )  )
 
           #
           # Compute the apparent sub-observer point of CASSINI
           # on Phoebe.
           #
           [spoint, trgepc, srfvec] = spiceypy.subpnt(
                                   method,       'PHOEBE',  et,
                                   'IAU_PHOEBE', 'LT+S', 'CASSINI' )
 
           print( '   Apparent sub-observer point of CASSINI '
                  'on Phoebe in the\n'
                  '   IAU_PHOEBE frame (km):' )
           print( '      X = {:16.3f}'.format(spoint[0])              )
           print( '      Y = {:16.3f}'.format(spoint[1])              )
           print( '      Z = {:16.3f}'.format(spoint[2])              )
           print( '    ALT = {:16.3f}'.format(spiceypy.vnorm(srfvec)) )
 
           #
           # Compute the apparent sub-solar point on Phoebe
           # as seen from CASSINI.
           #
           [spoint, trgepc, srfvec] = spiceypy.subslr(
                           method,       'PHOEBE',  et,
                           'IAU_PHOEBE', 'LT+S', 'CASSINI' )
 
           print( '   Apparent sub-solar point on Phoebe '
                  'as seen from CASSINI in\n'
                  '   the IAU_PHOEBE frame (km):'  )
           print( '      X = {:16.3f}'.format(spoint[0])   )
           print( '      Y = {:16.3f}'.format(spoint[1])   )
           print( '      Z = {:16.3f}'.format(spoint[2])   )
 
       #
       # End of computation block for "method"
       #
       print( '' )
 
       spiceypy.unload( METAKR )
 
   if __name__ == '__main__':
       subpts()


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Solution Sample Output



Execute the program:

   Input UTC Time: 2004 jun 11 19:32:00
    Converting UTC Time: 2004 jun 11 19:32:00
      ET seconds past J2000:    140254384.185
 
    Sub-point/target shape model: NEAR POINT/Ellipsoid
 
      Apparent sub-observer point of CASSINI on Phoebe in the
      IAU_PHOEBE frame (km):
         X =          104.498
         Y =           45.269
         Z =            7.383
       ALT =         2084.116
      Apparent sub-solar point on Phoebe as seen from CASSINI in
      the IAU_PHOEBE frame (km):
         X =           78.681
         Y =           76.879
         Z =          -21.885
 
    Sub-point/target shape model: NADIR/DSK/Unprioritized
 
      Apparent sub-observer point of CASSINI on Phoebe in the
      IAU_PHOEBE frame (km):
         X =           95.373
         Y =           40.948
         Z =            6.610
       ALT =         2094.242
      Apparent sub-solar point on Phoebe as seen from CASSINI in
      the IAU_PHOEBE frame (km):
         X =           79.111
         Y =           77.338
         Z =          -22.028
 


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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 spiceypy.subpnt and spiceypy.subslr functions.

These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks.



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Task statements and questions



    1. Recompute the apparent sub-solar point on Phoebe as seen from CASSINI in the body fixed frame IAU_PHOEBE in kilometers using the 'Intercept/ellipsoid' method at ``2004 jun 11 19:32:00''. Explain the differences.

    2. Compute the geometric sub-spacecraft point of CASSINI on Phoebe in the body fixed frame IAU_PHOEBE in kilometers using the 'Near point/ellipsoid' method at ``2004 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 Phoebe's radii by calling spiceypy.bodvrd and use the first element of the returned radii values as Phoebe's equatorial radius. Explain why planetocentric and planetographic latitudes and longitudes are different. Explain why the planetographic altitude for a point on the surface of Phoebe 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 Phoebe is not spherical, these two points are not the same:

      Apparent sub-solar point on Phoebe as seen from CASSINI in
      the IAU_PHOEBE frame using the 'Near Point: ellipsoid' method
      (km):
         X =           78.681
         Y =           76.879
         Z =          -21.885
 
      Apparent sub-solar point on Phoebe as seen from CASSINI in
      the IAU_PHOEBE frame using the 'Intercept: ellipsoid' method
      (km):
         X =           74.542
         Y =           79.607
         Z =          -24.871
    2. The geometric sub-spacecraft point of CASSINI on Phoebe in the body fixed frame IAU_PHOEBE in kilometers at ``2004 jun 11 19:32:00'' UTC epoch is:

      Geometric sub-spacecraft point of CASSINI on Phoebe in
      the IAU_PHOEBE frame using the 'Near Point: ellipsoid' method
      (km):
         X =          104.497
         Y =           45.270
         Z =            7.384
    3. The sub-spacecraft point of CASSINI on Phoebe in planetocentric and planetographic coordinates at ``2004 jun 11 19:32:00'' UTC epoch is:

      Planetocentric coordinates of the CASSINI
      sub-spacecraft point on Phoebe (degrees, km):
      LAT =            3.710
      LON =           23.423
      R   =          114.121
 
      Planetographic coordinates of the CASSINI
      sub-spacecraft point on Phoebe (degrees, km):
      LAT =            4.454
      LON =          336.577
      ALT =           -0.831
    The planetocentric and planetographic longitudes are different (``graphic'' = 360 - ``centric'') because planetographic longitudes on Phoebe are measured positive west as defined by Phoebe's 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 Phoebe surface model: a spheroid with equal equatorial radii. The surface point returned by spiceypy.subpnt was computed by treating Phoebe 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 an Ellipsoid and a DSK (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 CASSINI ISS NAC camera boresight and field of view (FOV) boundary vectors with the surface of Phoebe. Compute each intercept twice: once with Phoebe's shape modeled as an ellipsoid, and once with Phoebe's shape modeled by DSK data. The program presents each point of intersection as

    1. A Cartesian vector in the IAU_PHOEBE frame

    2. Planetocentric (latitudinal) coordinates in the IAU_PHOEBE 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 camera boresight with the surface of Phoebe, using both ellipsoidal and DSK shape models.

Use this program to compute values at the epoch:

    "2004 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 target bodies whose shapes are modeled as ellipsoids or provided by DSKs. Discover another high level geometry function and another time conversion function in SpiceyPy.



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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 CASSINI NAC camera.

    -- 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 CASSINI NAC camera.

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 Phoebe 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 CASSINI ISS instrument kernel to determine the name of the NAC camera 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.
 
      The names and contents of the kernels referenced by this
      meta-kernel are as follows:
 
      File name                   Contents
      --------------------------  -----------------------------
      naif0008.tls                Generic LSK
      cas00084.tsc                Cassini SCLK
      981005_PLTEPH-DE405S.bsp    Solar System Ephemeris
      020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris
      030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK
      cas_v37.tf                  Cassini FK
      04135_04171pc_psiv2.bc      Cassini Spacecraft CK
      cpck05Mar2004.tpc           Cassini Project PCK
      cas_iss_v09.ti              ISS Instrument Kernel
      phoebe_64q.bds              Phoebe DSK
 
 
      \begindata
      KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls',
                          'kernels/sclk/cas00084.tsc',
                          'kernels/spk/981005_PLTEPH-DE405S.bsp',
                          'kernels/spk/020514_SE_SAT105.bsp',
                          'kernels/spk/030201AP_SK_SM546_T45.bsp',
                          'kernels/fk/cas_v37.tf',
                          'kernels/ck/04135_04171pc_psiv2.bc',
                          'kernels/pck/cpck05Mar2004.tpc',
                          'kernels/ik/cas_iss_v09.ti'
                          'kernels/dsk/phoebe_64q.bds' )
      \begintext


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Solution Source Code



A sample solution to the problem follows:

 
   #
   # Solution fovint.py
   #
   from __future__ import print_function
   from builtins import input
 
   #
   # SpiceyPy package:
   #
   import spiceypy
   from spiceypy.utils.support_types import SpiceyError
 
   def fovint():
       #
       # Local parameters
       #
       METAKR = 'fovint.tm'
       ROOM   = 4
 
       #
       # Load the kernels that this program requires.  We
       # will need:
       #
       #    A leapseconds kernel.
       #    A SCLK kernel for CASSINI.
       #    Any necessary ephemerides.
       #    The CASSINI frame kernel.
       #    A CASSINI C-kernel.
       #    A PCK file with Phoebe constants.
       #    The CASSINI ISS I-kernel.
       #    A DSK file containing Phoebe shape data.
       #
       spiceypy.furnsh( METAKR )
 
       #
       # Prompt the user for the input time string.
       #
       utctim = input( 'Input UTC Time: ' )
 
       print( 'Converting UTC Time: {:s}'.format(utctim)  )
 
       #
       # Convert utctim to ET.
       #
       et = spiceypy.str2et( utctim )
 
       print( '  ET seconds past J2000: {:16.3f}\n'.format(et) )
 
       #
       # Now we need to obtain the FOV configuration of
       # the ISS NAC camera.
       #
       [ shape, insfrm, bsight,
         n, bounds ] = spiceypy.getfvn( 'CASSINI_ISS_NAC', ROOM )
 
       #
       # `bounds' is a numpy array. We'll convert it to a list.
       #
       # Rather than treat BSIGHT as a separate vector,
       # copy it into the last slot of BOUNDS.
       #
       bounds = bounds.tolist()
       bounds.append( bsight )
 
       #
       # Set vector names to be used for output.
       #
       vecnam = [ 'Boundary Corner 1',
                  'Boundary Corner 2',
                  'Boundary Corner 3',
                  'Boundary Corner 4',
                  'Cassini NAC Boresight' ]
 
       #
       # Set values of "method" string that specify use of
       # ellipsoidal and DSK (topographic) shape models.
       #
       # In this case, we can use the same methods for calls to both
       # spiceypy.sincpt and spiceypy.ilumin. Note that some SPICE
       # routines require different "method" inputs from those
       # shown here. See the API documentation of each routine
       # for details.
       #
       method = [ 'Ellipsoid', 'DSK/Unprioritized' ]
 
       #
       # Get ID code of Phoebe. We'll use this ID code later, when we
       # compute local solar time.
       #
       try:
           phoeid = spiceypy.bodn2c( 'PHOEBE' )
 
       except SpiceyError as exc:
           #
           # The ID code for PHOEBE is built-in to the library.
           # However, it is good programming practice to get
           # in the habit of handling exceptions that may
           # be thrown when a quantity is not found.
           #
           # Also see the call to spiceypy.sincpt below for an
           # example of handling a "not found" condition that is
           # not an error.
           #
           print( 'Exception message is: {:s}'.format( exc.message ) )
 
           raise
 
       #
       # Now perform the same set of calculations for each
       # vector listed in the BOUNDS array. Use both
       # ellipsoidal and detailed (DSK) shape models.
       #
       for i  in  range(5):
           #
           # Call sincpt to determine coordinates of the
           # intersection of this vector with the surface
           # of Phoebe.
           #
           print( 'Vector: {:s}\n'.format( vecnam[i] ) )
 
           for  j  in range(2):
 
               print ( ' Target shape model: {:s}\n'.format(
                                          method[j]      )  )
 
               #
               # Treat an "intercept not found" condition as a normal
               # case rather than as an exception. This way we
               # distinguish between this condition and other
               # exceptions, in particular, any other "not found"
               # exceptions.
               #
               with spiceypy.no_found_check():
 
                   [ point, trgepc, srfvec, found ] = spiceypy.sincpt(
 
                       method[j],    'PHOEBE',  et,
                       'IAU_PHOEBE', 'LT+S',    'CASSINI',
                       insfrm,       bounds[i]             )
 
               if  found:
                   #
                   # Now, we have discovered a point of intersection.
                   # Start by displaying the position vector in the
                   # IAU_PHOEBE frame of the intersection.
                   #
                   print( '  Position vector of surface intercept '
                          'in the IAU_PHOEBE frame (km):'           )
                   print( '     X   = {:16.3f}'.format( point[0] )  )
                   print( '     Y   = {:16.3f}'.format( point[1] )  )
                   print( '     Z   = {:16.3f}'.format( point[2] )  )
 
                   #
                   # Display the planetocentric latitude and longitude
                   # of the intercept.
                   #
                   [ radius, lon, lat ] = spiceypy.reclat( point )
 
                   print( '  Planetocentric coordinates of '
                          'the intercept (degrees):'          )
                   print( '     LAT = {:16.3f}'.format(
                                      lat * spiceypy.dpr() )  )
                   print( '     LON = {:16.3f}'.format(
                                      lon * spiceypy.dpr() )  )
                   #
                   # Compute the illumination angles at this
                   # point.
                   #
                   [ trgepc, srfvec, phase, solar,
                     emissn, visibl, lit           ] = spiceypy.illumf(
                       method[j],    'PHOEBE', 'SUN',     et,
                       'IAU_PHOEBE', 'LT+S',   'CASSINI', point )
 
                   print( '  Phase angle (degrees):           '
                          '{:16.3f}'.format( phase*spiceypy.dpr() )  )
                   print( '  Solar incidence angle (degrees): '
                          '{:16.3f}'.format( solar*spiceypy.dpr() )  )
                   print( '  Emission angle (degrees):        '
                          '{:16.3f}'.format( emissn*spiceypy.dpr())  )
                   print( '  Observer visible:  {:s}'.format(
                       str(visibl) )  )
                   print( '  Sun visible:       {:s}'.format(
                       str(lit)    )  )
 
                   if  i  ==  4:
                       #
                       # Compute local solar time corresponding
                       # to the light time corrected TDB epoch
                       # at the boresight intercept.
                       #
                       [ hr, mn, sc, time, ampm ] = spiceypy.et2lst(
                           trgepc,
                           phoeid,
                           lon,
                           'PLANETOCENTRIC' )
 
                       print( '\n  Local Solar Time at boresight '
                              'intercept (24 Hour Clock):\n'
                              '     {:s}'.format( time )       )
                     #
                     # End of LST computation block.
                     #
 
               else:
                   #
                   # Display a message if no intercept was found.
                   # Otherwise, continue with the calculations.
                   #
                   print( 'No intersection point found at '
                          'this epoch for this vector.\n'  )
 
               #
               # End of spiceypy.sincpt intercept handling block.
               #
               print( '' )
           #
           # End of target shape model loop.
           #
       #
       # End of vector loop.
       #
 
       spiceypy.unload( METAKR )
 
   if __name__ == '__main__':
      fovint()


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Solution Sample Output



Execute the program:

   Input UTC Time: 2004 jun 11 19:32:00
   Converting UTC Time: 2004 jun 11 19:32:00
     ET seconds past J2000:    140254384.185
 
   Vector: Boundary Corner 1
 
    Target shape model: Ellipsoid
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           91.026
        Y   =           67.190
        Z   =            2.030
     Planetocentric coordinates of the intercept (degrees):
        LAT =            1.028
        LON =           36.432
     Phase angle (degrees):                     28.110
     Solar incidence angle (degrees):           16.121
     Emission angle (degrees):                  14.627
     Observer visible:  true
     Sun visible:       true
 
    Target shape model: DSK/Unprioritized
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           78.770
        Y   =           61.570
        Z   =            0.964
     Planetocentric coordinates of the intercept (degrees):
        LAT =            0.552
        LON =           38.013
     Phase angle (degrees):                     28.110
     Solar incidence angle (degrees):           31.132
     Emission angle (degrees):                  16.539
     Observer visible:  true
     Sun visible:       true
 
   Vector: Boundary Corner 2
 
    Target shape model: Ellipsoid
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           89.991
        Y   =           66.726
        Z   =           14.733
     Planetocentric coordinates of the intercept (degrees):
        LAT =            7.492
        LON =           36.556
     Phase angle (degrees):                     27.894
     Solar incidence angle (degrees):           22.894
     Emission angle (degrees):                  14.988
     Observer visible:  true
     Sun visible:       true
 
    Target shape model: DSK/Unprioritized
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           76.586
        Y   =           60.579
        Z   =           13.657
     Planetocentric coordinates of the intercept (degrees):
        LAT =            7.962
        LON =           38.344
     Phase angle (degrees):                     27.894
     Solar incidence angle (degrees):           32.013
     Emission angle (degrees):                  11.845
     Observer visible:  true
     Sun visible:       true
 
   Vector: Boundary Corner 3
 
    Target shape model: Ellipsoid
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           80.963
        Y   =           76.643
        Z   =           14.427
     Planetocentric coordinates of the intercept (degrees):
        LAT =            7.373
        LON =           43.430
     Phase angle (degrees):                     28.171
     Solar incidence angle (degrees):           21.315
     Emission angle (degrees):                  21.977
     Observer visible:  true
     Sun visible:       true
 
    Target shape model: DSK/Unprioritized
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           68.677
        Y   =           71.100
        Z   =           13.444
     Planetocentric coordinates of the intercept (degrees):
        LAT =            7.745
        LON =           45.993
     Phase angle (degrees):                     28.171
     Solar incidence angle (degrees):           36.039
     Emission angle (degrees):                  14.474
     Observer visible:  true
     Sun visible:       true
 
   Vector: Boundary Corner 4
 
    Target shape model: Ellipsoid
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           81.997
        Y   =           77.106
        Z   =            1.698
     Planetocentric coordinates of the intercept (degrees):
        LAT =            0.865
        LON =           43.239
     Phase angle (degrees):                     28.385
     Solar incidence angle (degrees):           13.882
     Emission angle (degrees):                  21.763
     Observer visible:  true
     Sun visible:       true
 
    Target shape model: DSK/Unprioritized
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           73.186
        Y   =           73.131
        Z   =            0.934
     Planetocentric coordinates of the intercept (degrees):
        LAT =            0.517
        LON =           44.978
     Phase angle (degrees):                     28.385
     Solar incidence angle (degrees):           41.268
     Emission angle (degrees):                  17.493
     Observer visible:  true
     Sun visible:       true
 
   Vector: Cassini NAC Boresight
 
    Target shape model: Ellipsoid
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           86.390
        Y   =           72.089
        Z   =            8.255
     Planetocentric coordinates of the intercept (degrees):
        LAT =            4.196
        LON =           39.844
     Phase angle (degrees):                     28.139
     Solar incidence angle (degrees):           18.247
     Emission angle (degrees):                  17.858
     Observer visible:  true
     Sun visible:       true
 
     Local Solar Time at boresight intercept (24 Hour Clock):
        11:31:50
 
    Target shape model: DSK/Unprioritized
 
     Position vector of surface intercept in the IAU_PHOEBE frame (km):
        X   =           74.326
        Y   =           66.602
        Z   =            7.247
     Planetocentric coordinates of the intercept (degrees):
        LAT =            4.153
        LON =           41.863
     Phase angle (degrees):                     28.139
     Solar incidence angle (degrees):           33.200
     Emission angle (degrees):                   9.230
     Observer visible:  true
     Sun visible:       true
 
     Local Solar Time at boresight intercept (24 Hour Clock):
        11:39:55
 


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Extra Credit




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