 
Remote Sensing Hands-On Lesson (C)
===========================================================================
 
   February 8, 2010
 
 
Overview
--------------------------------------------------------
 
   In this lesson you will develop a series of simple programs that
   demonstrate the usage of CSPICE to compute a variety of different
   geometric quantities applicable to experiments carried out by a remote
   sensing instrument flown on an interplanetary spacecraft. This
   particular lesson focuses on a framing camera flying on the Cassini
   spacecraft, but many of the concepts are easily extended and generalized
   to other scenarios.
 
 
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.
 
 
References
--------------------------------------------------------
 
 
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
 
 
Required Readings
 
   The Required Reading documents are provided with the Toolkit and are
   located under the ``cspice/doc'' directory in the C 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
 
 
The Permuted Index
 
   Another useful document distributed with the Toolkit is the permuted
   index. This is located under the ``cspice/doc'' directory in the C
   installation tree.
 
   This text document provides a simple mechanism to discover what CSPICE
   functions perform a particular function of interest as well as the name
   of the source module that contains the function.
 
 
Source Code Header Comments
 
   The most detailed specification of a given SPICE FORTRAN or C routine is
   contained in the header section of its source code. The source code is
   distributed with the Toolkit and is located under
   ``toolkit/src/spicelib'' in FORTRAN and under ``cspice/src/cspice'' in C
   Toolkits.
 
   For example the source code of the STR2ET/str2et_c routine is
 
      toolkit/src/spicelib/str2et.for
 
   in the FORTRAN Toolkit and in
 
      cspice/src/cspice/str2et_c.c
 
   in the C Toolkit.
 
   Since some of the FORTRAN routines are entry points they are usually
   part of a source file that has different name. The ``Permuted Index''
   document mentioned above can be used to locate the name of their source
   file.
 
 
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  cas_iss_v09.ti            IK    ISS Instrument Kernel
 
   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/
 
 
CSPICE 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     furnsh_c              1,2
                         prompt_c
                         str2et_c
                         etcal_c
                         timout_c
                         sce2c_c
                         sce2s_c
 
        2     getsta     furnsh_c   vnorm_c    1,3-5
                         prompt_c
                         str2et_c
                         spkezr_c
                         spkpos_c
                         convrt_c
 
        3     xform      furnsh_c   vsep_c     1-8
                         prompt_c
                         str2et_c
                         spkezr_c
                         sxform_c
                         mxvg_c
                         spkpos_c
                         pxform_c
                         mxv_c
                         convrt_c
 
        4     subpts     furnsh_c              1,3-5,8
                         prompt_c
                         str2et_c
                         subpt_c
                         subsol_c
 
        5     fovint     furnsh_c   dpr_c      1-9
                         prompt_c
                         str2et_c
                         bodn2c_c
                         getfov_c
                         sincpt_c
                         reclat_c
                         ilumin_c
                         et2lst_c
 
 
   Refer to the headers of the various functions listed above, as detailed
   interface specifications are provided with the source code.
 
 
Time Conversion (convtm)
===========================================================================
 
 
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.
 
 
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.
 
 
Approach
--------------------------------------------------------
 
   The solution to the problem can be broken down into a series of simple
   steps:
 
       --   Decide which SPICE kernels are necessary. Prepare a meta-kernel
            listing the kernels and load it into the program.
 
       --   Prompt the user for an input UTC time string.
 
       --   Convert the input time string into ephemeris time expressed as
            seconds past J2000 TDB. Display the result.
 
       --   Convert ephemeris time into a calendar format. Display the
            result.
 
       --   Convert ephemeris time into a spacecraft clock string. Display
            the result.
 
   You may find it useful to consult the permuted index, the headers of
   various source modules, and the ``Time Required Reading'' (time.req) and
   ``SCLK Required Reading'' (sclk.req) documents.
 
   When completing the ``calendar format'' step above, consider using one
   of two possible methods: etcal_c or timout_c.
 
 
Solution
--------------------------------------------------------
 
 
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/naif0008.tls',
                             'kernels/sclk/cas00084.tsc' )
         \begintext
 
 
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
         #include <stdio.h>
 
         /*
         Standard CSPICE User Include File
         */
         #include "SpiceUsr.h"
 
         /*
         Local Parameters
         */
 
         #define METAKR "convtm.tm"
         #define SCLKID -82
         #define STRLEN 50
 
         int main (void)
         {
 
            /*
            Local Variables
            */
            SpiceChar               calet  [STRLEN];
            SpiceChar               sclkst [STRLEN];
            SpiceChar               utctim [STRLEN];
 
            SpiceDouble             et;
 
            /*
            Load the kernels this program requires.
            Both the spacecraft clock kernel and a
            leapseconds kernel should be listed in
            the meta-kernel.
            */
            furnsh_c ( METAKR );
 
            /*
            Prompt the user for the input time string.
            */
            prompt_c ( "Input UTC Time: ", STRLEN, utctim );
 
            printf ( "Converting UTC Time: %s\n", utctim );
 
            /*
            Convert utctim to ET.
            */
            str2et_c ( utctim, &et );
 
            printf ( "   ET Seconds Past J2000: %16.3f\n", et );
 
            /*
            Now convert ET to a calendar time
            string.  This can be accomplished in two
            ways.
            */
            etcal_c ( et, STRLEN, calet );
 
            printf ( "   Calendar ET (etcal_c): %s\n", calet );
 
            /*
            Or use timout_c for finer control over the
            output format.  The picture below was built
            by examining the header of timout_c.
            */
            timout_c ( et,     "YYYY-MON-DDTHR:MN:SC ::TDB",
                       STRLEN, calet                         );
 
            printf ( "   Calendar ET (timout_c): %s\n", calet );
 
            /*
            Convert ET to spacecraft clock time.
            */
            sce2s_c ( SCLKID, et, STRLEN, sclkst );
 
            printf ( "   Spacecraft Clock Time: %s\n", sclkst );
 
            return(0);
         }
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Converting UTC Time: 2004 jun 11 19:32:00
         ET Seconds Past J2000:    140254384.185
         Calendar ET (etcal_c): 2004 JUN 11 19:33:04.184
         Calendar ET (timout_c): 2004-JUN-11T19:33:04
         Spacecraft Clock Time: 1/1465674964.105
 
 
Obtaining Target States and Positions (getsta)
===========================================================================
 
 
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.
 
 
Learning Goals
--------------------------------------------------------
 
   Understand the anatomy of an spkezr_c call. Discover the difference
   between spkezr_c and spkpos_c. Familiarity with the Toolkit utility
   ``brief''. Exposure to unit conversion with CSPICE.
 
 
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.
 
 
Solution
--------------------------------------------------------
 
 
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/naif0008.tls',
                             'kernels/spk/981005_PLTEPH-DE405S.bsp',
                             'kernels/spk/020514_SE_SAT105.bsp',
                             'kernels/spk/030201AP_SK_SM546_T45.bsp' )
         \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
      #include <stdio.h>
 
      /*
      Standard CSPICE User Include File
      */
      #include "SpiceUsr.h"
 
      /*
      Local Parameters
      */
 
      #define METAKR "getsta.tm"
      #define STRLEN 50
 
      int main (void)
      {
         /*
         Local Variables
         */
         SpiceChar               utctim [STRLEN];
 
         SpiceDouble             dist;
         SpiceDouble             et;
         SpiceDouble             ltime;
         SpiceDouble             pos   [3];
         SpiceDouble             state [6];
 
         /*
         Load the kernels that this program requires.  We
         will need a leapseconds kernel to convert input
         UTC time strings into ET.  We also will need the
         necessary SPK files with coverage for the bodies
         in which we are interested.
         */
         furnsh_c ( METAKR );
 
         /*
         Prompt the user for the input time string.
         */
         prompt_c (  "Input UTC Time: ", STRLEN, utctim );
 
         printf ( "Converting UTC Time: %s\n", utctim  );
 
         /*
         Convert utctim to ET.
         */
         str2et_c ( utctim, &et );
 
         printf ( "   ET seconds past J2000: %16.3f\n", et );
 
         /*
         Compute the apparent state of Phoebe as seen from
         CASSINI in the J2000 frame.  All of the ephemeris
         readers return states in units of kilometers and
         kilometers per second.
         */
         spkezr_c ( "PHOEBE", et,    "J2000", "LT+S",
                    "CASSINI",  state, &ltime          );
 
         printf ( "   Apparent state of Phoebe as seen "
                  "from CASSINI in the J2000\n"        );
         printf ( "      frame (km, km/s):\n"          );
         printf ( "      X = %16.3f\n", state[0]       );
         printf ( "      Y = %16.3f\n", state[1]       );
         printf ( "      Z = %16.3f\n", state[2]       );
         printf ( "     VX = %16.3f\n", state[3]       );
         printf ( "     VY = %16.3f\n", state[4]       );
         printf ( "     VZ = %16.3f\n", state[5]       );
 
         /*
         Compute the apparent position of Earth as seen from
         CASSINI in the J2000 frame.  Note: We could have
         continued using spkezr_c and simply ignored the
         velocity components.
         */
         spkpos_c ( "EARTH", et,  "J2000", "LT+S",
                    "CASSINI",   pos, &ltime             );
 
         printf ( "   Apparent position of Earth as "
                  "seen from CASSINI in the J2000\n"     );
         printf ( "      frame (km): \n"                 );
         printf ( "      X = %16.3f\n", pos[0]           );
         printf ( "      Y = %16.3f\n", pos[1]           );
         printf ( "      Z = %16.3f\n", pos[2]           );
 
 
         /*
         We need only display LTIME, as it is precisely the
         light time in which we are interested.
         */
         printf ( "   One way light time between CASSINI and "
                  "the apparent position\n"                    );
         printf ( "      of Earth (seconds): %16.3f\n", ltime  );
 
         /*
         Compute the apparent position of the Sun as seen
         from Phoebe in the J2000 frame.
         */
         spkpos_c ( "SUN",  et,  "J2000", "LT+S",
                    "PHOEBE", pos, &ltime                );
 
         printf ( "   Apparent position of Sun as seen "
                  "from Phoebe in the\n"                 );
         printf ( "      J2000 frame (km): \n"           );
         printf ( "      X = %16.3f\n", pos[0]           );
         printf ( "      Y = %16.3f\n", pos[1]           );
         printf ( "      Z = %16.3f\n", pos[2]           );
 
         /*
         Now we need to compute the actual distance between
         the Sun and Phoebe.  The above SPKPOS call gives us
         the apparent distance, so we need to adjust our
         aberration correction appropriately.
         */
         spkpos_c ( "SUN",  et,  "J2000", "NONE",
                    "PHOEBE", pos, &ltime                );
 
         /*
         Compute the distance between the body centers in
         kilometers.
         */
         dist = vnorm_c ( pos );
 
         /*
         Convert this value to AU using convrt_c.
         */
         convrt_c ( dist, "KM", "AU", &dist );
 
         printf ( "   Actual distance between Sun and "
                  "Phoebe body centers:\n"               );
         printf ( "      (AU): %16.3f\n", dist           );
 
         return(0);
      }
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      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
 
 
Spacecraft Orientation and Reference Frames (xform)
===========================================================================
 
 
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.
 
 
Learning Goals
--------------------------------------------------------
 
   Familiarity with the different types of kernels involved in chaining
   reference frames together, both inertial and non-inertial. Discover some
   of the matrix and vector math functions. Understand the difference
   between pxform_c and sxform_c.
 
 
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 using
   CSPICE functions with which you are already familiar. The ``long-way''
   presented above is intended to facilitate the introduction of the
   functions pxform_c and sxform_c.
 
   You may find it useful to consult the permuted index, the headers of
   various source modules, and the following toolkit documentation:
 
       1.   Frames Required Reading (frames.req)
 
       2.   PCK Required Reading (pck.req)
 
       3.   SPK Required Reading (spk.req)
 
       4.   CK Required Reading (ck.req)
 
   This particular example makes use of many of the different types of
   SPICE kernels. You should spend a few moments thinking about which
   kernels you will need and what data they provide.
 
 
Solution
--------------------------------------------------------
 
 
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/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
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
      #include <stdio.h>
 
      /*
      Standard CSPICE User Include File
      */
      #include "SpiceUsr.h"
 
      /*
      Local Parameters
      */
 
      #define METAKR "xform.tm"
      #define STRLEN 50
 
      int main (void)
      {
 
         /*
         Local Variables
         */
         SpiceChar               utctim [STRLEN];
 
         SpiceDouble             et;
         SpiceDouble             ltime;
         SpiceDouble             state  [6];
         SpiceDouble             bfixst [6];
         SpiceDouble             pos    [3];
         SpiceDouble             sform  [6][6];
         SpiceDouble             pform  [3][3];
         SpiceDouble             bsight [3];
         SpiceDouble             sep;
 
 
         /*
         Load the kernels that this program requires.  We
         will need:
 
            A leapseconds kernel
            A spacecraft clock kernel for CASSINI
            The necessary ephemerides
            A planetary constants file (PCK)
            A spacecraft orientation kernel for CASSINI (CK)
            A frame kernel (TF)
         */
         furnsh_c ( METAKR );
 
         /*
         Prompt the user for the input time string.
         */
         prompt_c ( "Input UTC Time: ", STRLEN, utctim );
 
         printf ( "Converting UTC Time: %s\n", utctim );
 
         /*
         Convert utctim to ET.
         */
         str2et_c ( utctim, &et );
 
         printf ( "   ET seconds past J2000: %16.3f\n", et );
 
         /*
         Compute the apparent state of Phoebe as seen from
         CASSINI in the J2000 reference frame.
         */
         spkezr_c ( "PHOEBE", et,    "J2000", "LT+S",
                    "CASSINI",  state, &ltime              );
 
         /*
         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.
         */
         sxform_c ( "J2000", "IAU_PHOEBE", et-ltime, sform );
 
         /*
         Now rotate the apparent J2000 state into IAU_PHOEBE
         with the following matrix multiplication:
         */
         mxvg_c ( sform, state, 6, 6, bfixst );
 
         /*
         Display the results.
         */
         printf ( "   Apparent state of Phoebe as seen "
                  "from CASSINI in the IAU_PHOEBE\n"    );
         printf ( "      body-fixed frame (km, km/s):\n");
         printf ( "      X = %19.6f\n", bfixst[0]       );
         printf ( "      Y = %19.6f\n", bfixst[1]       );
         printf ( "      Z = %19.6f\n", bfixst[2]       );
         printf ( "     VX = %19.6f\n", bfixst[3]       );
         printf ( "     VY = %19.6f\n", bfixst[4]       );
         printf ( "     VZ = %19.6f\n", bfixst[5]       );
 
         /*
         It is worth pointing out, all of the above could
         have been done with a single use of spkezr_c:
         */
         spkezr_c ( "PHOEBE", et,    "IAU_PHOEBE", "LT+S",
                    "CASSINI",  state, &ltime           );
 
         /*
         Display the results.
         */
         printf ( "   Apparent state of Phoebe as seen "
                  "from CASSINI in the IAU_PHOEBE\n"    );
         printf ( "       body-fixed frame (km, km/s) "
                  "obtained using spkezr_c directly:\n" );
         printf ( "      X = %19.6f\n", state[0]        );
         printf ( "      Y = %19.6f\n", state[1]        );
         printf ( "      Z = %19.6f\n", state[2]        );
         printf ( "     VX = %19.6f\n", state[3]        );
         printf ( "     VY = %19.6f\n", state[4]        );
         printf ( "     VZ = %19.6f\n", state[5]        );
 
         /*
         Note that the velocity found by using spkezr_c
         to compute the state in the IAU_PHOEBE frame differs
         at the few mm/second level from that found previously
         by calling spkezr_c and then sxform_c. Computing
         velocity via a single call to spkezr_c as we've
         done immediately above is slightly more accurate because
         it accounts for the effect of the rate of change of
         light time on the apparent angular velocity of the
         target's body-fixed reference frame.
 
         Now we are to compute the angular separation between
         the apparent position of 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.
         */
         spkpos_c ( "EARTH", et,  "J2000", "LT+S",
                    "CASSINI",   pos, &ltime            );
 
         /*
         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;
         bsight[1] = 0.0;
         bsight[2] = 1.0;
 
         /*
         Now compute the rotation matrix from CASSINI_HGA into
         J2000.
         */
         pxform_c ( "CASSINI_HGA", "J2000", et, pform  );
 
         /*
         And multiply the result to obtain the nominal
         antenna boresight in the J2000 reference frame.
         */
         mxv_c ( pform, bsight, bsight );
 
         /*
         Lastly compute the angular separation.
         */
         convrt_c ( vsep_c(bsight, pos), "RADIANS",
                    "DEGREES",           &sep          );
 
         printf ( "   Angular separation between the "
                  "apparent position of\n"             );
         printf ( "      Earth and the CASSINI high "
                  "gain antenna boresight (degrees):\n");
         printf ( "      %16.3f\n", sep                );
 
         /*
         Or alternatively we can work in the antenna
         frame directly.
         */
         spkpos_c ( "EARTH", et,  "CASSINI_HGA", "LT+S",
                    "CASSINI",   pos, &ltime              );
 
         /*
         The antenna boresight is the Z-axis in the
         CASSINI_HGA frame.
         */
         bsight[0] = 0.0;
         bsight[1] = 0.0;
         bsight[2] = 1.0;
 
         /*
         Lastly compute the angular separation.
         */
         convrt_c ( vsep_c(bsight, pos), "RADIANS",
                    "DEGREES",           &sep          );
 
         printf ( "   Angular separation between the "
                  "apparent position of\n"             );
         printf ( "      Earth and the CASSINI high "
                  "gain antenna boresight computed\n"  );
         printf ( "      using vectors in the CASSINI_HGA "
                  "frame (degrees):\n"                 );
         printf ( "      %16.3f\n", sep                );
 
         return(0);
      }
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      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_c 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
 
 
Computing Sub-spacecraft and Sub-solar Points (subpts)
===========================================================================
 
 
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 CASSINI on Phoebe in the
            body fixed frame IAU_PHOEBE in kilometers.
 
       2.   The apparent sub-solar point on Phoebe as seen from CASSINI in
            the body fixed frame IAU_PHOEBE in kilometers.
 
   and displays the results. Use the program to compute these quantities at
   "2004 jun 11 19:32:00" UTC.
 
 
Learning Goals
--------------------------------------------------------
 
   Discover higher level geometry calculation functions in CSPICE and their
   usage as it relates to CASSINI.
 
 
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?
 
 
Solution
--------------------------------------------------------
 
 
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/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' )
         \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
      #include <stdio.h>
 
      /*
      Standard CSPICE User Include File
      */
      #include "SpiceUsr.h"
 
      /*
      Local Parameters
      */
 
      #define METAKR "subpts.tm"
      #define STRLEN 50
 
      int main (void)
      {
         /*
         Local Variables
         */
         SpiceChar               utctim [STRLEN];
 
         SpiceDouble             et;
         SpiceDouble             spoint [3];
         SpiceDouble             srfvec [3];
         SpiceDouble             trgepc;
 
         /*
         Load the kernels that this program requires.  We
         will need:
 
            A leapseconds kernel
            The necessary ephemerides
            A planetary constants file (PCK)
         */
         furnsh_c ( METAKR );
 
         /*
         Prompt the user for the input time string.
         */
         prompt_c ( "Input UTC Time: ", STRLEN, utctim );
 
         printf ( "Converting UTC Time: %s\n", utctim );
 
         /*
         Convert utctim to ET.
         */
         str2et_c ( utctim, &et );
 
         printf ( "   ET seconds past J2000: %16.3f\n", et );
 
         /*
         Compute the apparent sub-observer point of CASSINI
         on Phoebe.
         */
         subpnt_c ( "NEAR POINT: ELLIPSOID",
                    "PHOEBE",  et,     "IAU_PHOEBE", "LT+S",
                    "CASSINI", spoint, &trgepc,      srfvec );
 
         printf ( "   Apparent sub-observer point of CASSINI "
                  "on Phoebe in the\n"                     );
         printf ( "   IAU_PHOEBE frame (km):\n"            );
         printf ( "      X = %16.3f\n", spoint[0]          );
         printf ( "      Y = %16.3f\n", spoint[1]          );
         printf ( "      Z = %16.3f\n", spoint[2]          );
         printf ( "    ALT = %16.3f\n", vnorm_c(srfvec)    );
 
         /*
         Compute the apparent sub-solar point on Phoebe
         as seen from CASSINI.
         */
         subslr_c ( "NEAR POINT: ELLIPSOID",
                    "PHOEBE",  et,     "IAU_PHOEBE", "LT+S",
                    "CASSINI", spoint, &trgepc,      srfvec );
 
         printf ( "   Apparent sub-solar point on Phoebe "
                  "as seen from CASSINI in\n"                );
         printf ( "   the IAU_PHOEBE frame (km):\n"        );
         printf ( "      X = %16.3f\n", spoint[0]            );
         printf ( "      Y = %16.3f\n", spoint[1]            );
         printf ( "      Z = %16.3f\n", spoint[2]            );
 
         return(0);
      }
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Converting UTC Time: 2004 JUN 11 19:32:00
         ET seconds past J2000:    140254384.185
         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
 
 
Intersecting Vectors with a Triaxial Ellipsoid (fovint)
===========================================================================
 
 
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. 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 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 camera
   boresight with the surface of Phoebe.
 
   Use this program to compute values at the epoch:
 
            2004 jun 11 19:32:00 UTC
 
 
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
   CSPICE.
 
 
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.
 
       --   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.
 
 
Solution
--------------------------------------------------------
 
 
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/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' )
         \begintext
 
 
Solution Source Code
 
   A sample solution to the problem follows:
 
      #include <stdio.h>
 
      /*
      Standard CSPICE User Include File
      */
      #include "SpiceUsr.h"
      #include <stdlib.h>
 
      /*
      Local Parameters
      */
      #define METAKR "fovint.tm"
      #define STRLEN 50
      #define BCVLEN 5
 
      int main (void)
      {
         /*
         Local Variables
         */
         SpiceChar               ampm   [STRLEN];
         SpiceChar               insfrm [STRLEN];
         SpiceChar               shape  [STRLEN];
         SpiceChar               time   [STRLEN];
         SpiceChar               utctim [STRLEN];
         SpiceChar               *vecnam[] = {
                                   "Boundary Corner 1",
                                   "Boundary Corner 2",
                                   "Boundary Corner 3",
                                   "Boundary Corner 4",
                                   "Cassini NAC Boresight"
         };
 
         SpiceDouble             bounds [BCVLEN][3];
         SpiceDouble             bsight [3];
         SpiceDouble             emissn;
         SpiceDouble             et;
         SpiceDouble             lat;
         SpiceDouble             lon;
         SpiceDouble             phase;
         SpiceDouble             point  [3];
         SpiceDouble             radius;
         SpiceDouble             solar;
         SpiceDouble             srfvec [3];
         SpiceDouble             trgepc;
 
         SpiceInt                hr;
         SpiceInt                i;
         SpiceInt                mn;
         SpiceInt                n;
         SpiceInt                nacid;
         SpiceInt                phoeid;
         SpiceInt                sc;
 
         SpiceBoolean            found;
 
         /*
         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.
         */
         furnsh_c ( METAKR );
 
         /*
         Prompt the user for the input time string.
         */
         prompt_c ( "Input UTC Time: ", STRLEN, utctim );
 
         printf ( "Converting UTC Time: %s\n", utctim );
 
         /*
         Convert utctim to ET.
         */
         str2et_c ( utctim, &et );
 
         printf ( "  ET seconds past J2000: %16.3f\n", et );
 
         /*
         Now we need to obtain the FOV configuration of
         the ISS NAC camera.  To do this we will need the
         ID code for CASSINI_ISS_NAC.
         */
         bodn2c_c ( "CASSINI_ISS_NAC", &nacid, &found );
 
         /*
         Stop the program if the code was not found.
         */
         if ( !found )
         {
            printf ( "Unable to locate the ID code for "
                     "CASSINI_ISS_NAC\n"                   );
            exit   ( EXIT_FAILURE );
         }
 
         /*
         Now retrieve the field of view parameters.
         */
         getfov_c ( nacid, BCVLEN, STRLEN, STRLEN,
                    shape, insfrm, bsight, &n,      bounds );
 
         /*
         Rather than treat BSIGHT as a separate vector,
         copy it into the last slot of BOUNDS.
         */
         for ( i=0; i<3; i++ )
         {
            bounds[4][i] = bsight[i];
         }
 
         /*
         Now perform the same set of calculations for each
         vector listed in the BOUNDS array.
         */
         for ( i=0; i<5; i++ )
         {
            /*
            Call sincpt_c to determine coordinates of the
            intersection of this vector with the surface
            of Phoebe.
            */
            sincpt_c ( "Ellipsoid", "PHOEBE",  et,     "IAU_PHOEBE",
                       "LT+S",      "CASSINI", insfrm, bounds[i],
                       point,       &trgepc,   srfvec, &found       );
 
            /*
            Check the found flag.  Display a message if
            the point of intersection was not found,
            otherwise continue with the calculations.
            */
            printf ( "Vector: %s\n", vecnam[i] );
 
            if ( !found )
            {
               printf ( "No intersection point found at "
                        "this epoch for this vector.\n"   );
            }
            else
            {
               /*
               Now, we have discovered a point of intersection.
               Start by displaying the position vector in the
               IAU_PHOEBE frame of the intersection.
               */
               printf ( "  Position vector of surface intercept "
                        "in the IAU_PHOEBE frame (km):\n" );
               printf ( "     X   = %16.3f\n", point[0] );
               printf ( "     Y   = %16.3f\n", point[1] );
               printf ( "     Z   = %16.3f\n", point[2] );
 
               /*
               Display the planetocentric latitude and longitude
               of the intercept.
               */
               reclat_c ( point, &radius, &lon, &lat );
 
               printf ( "  Planetocentric coordinates of "
                        "the intercept (degrees):\n"  );
               printf ( "     LAT = %16.3f\n", lat * dpr_c() );
               printf ( "     LON = %16.3f\n", lon * dpr_c() );
 
               /*
               Compute the illumination angles at this
               point.
               */
               ilumin_c ( "Ellipsoid", "PHOEBE",  et,     "IAU_PHOEBE",
                          "LT+S",      "CASSINI", point,  &trgepc,
                          srfvec,      &phase,    &solar, &emissn     );
 
               printf ( "  Phase angle (degrees):           "
                        "%16.3f\n", phase * dpr_c()          );
               printf ( "  Solar incidence angle (degrees): "
                        "%16.3f\n", solar * dpr_c()          );
               printf ( "  Emission angle (degrees):        "
                        "%16.3f\n", emissn * dpr_c()         );
 
            }
 
            printf ( "\n" );
 
         }
 
         /*
         Lastly compute the local solar time at the
         boresight intersection.
         */
         if ( found )
         {
            /*
            Get ID code of Phoebe.
            */
            bodn2c_c ( "PHOEBE", &phoeid, &found );
 
            /*
            The ID code for PHOEBE is built-in to the library.
            However, it is good programming practice to get
            in the habit of checking your found-flags.
            */
            if ( !found )
            {
               printf ( "Unable to locate the body ID code "
                        "for Phoebe.\n"                      );
               exit   ( EXIT_FAILURE );
            }
 
            /*
            Compute local solar time corresponding to the TDB light
            time corrected epoch at the intercept.
            */
            et2lst_c ( trgepc,
                       phoeid,
                       lon,
                       "PLANETOCENTRIC",
                       STRLEN,
                       STRLEN,
                       &hr,
                       &mn,
                       &sc,
                       time,
                       ampm             );
 
            printf ( "  Local Solar Time at boresight "
                     "intercept (24 Hour Clock):\n"      );
            printf ( "     %s\n", time                   );
         }
         else
         {
            printf ( "  No boresight intercept to "
                     "compute local solar time.\n"   );
         }
 
         return(0);
      }
 
 
Solution Sample Output
 
   After compiling the program, execute it:
 
      Converting UTC Time: 2004 JUN 11 19:32:00
        ET seconds past J2000:    140254384.185
      Vector: Boundary Corner 1
        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 =           36.433
        Phase angle (degrees):                     28.110
        Solar incidence angle (degrees):           16.121
        Emission angle (degrees):                  14.627
 
      Vector: Boundary Corner 2
        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
 
      Vector: Boundary Corner 3
        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
 
      Vector: Boundary Corner 4
        Position vector of surface intercept in the IAU_PHOEBE frame (km):
           X   =           81.997
           Y   =           77.106
           Z   =            1.699
        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
 
      Vector: Cassini NAC Boresight
        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
 
        Local Solar Time at boresight intercept (24 Hour Clock):
           11:31:50
 
