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Geometric Event Finding Hands-On Lesson (FORTRAN)

Table of Contents

   Geometric Event Finding Hands-On Lesson (FORTRAN)
      Overview
      Note About HTML Links
      References
         Tutorials
         Required Readings
         The Permuted Index
         Source Code Header Comments
      Kernels Used
      SPICE Routines Used
   Find View Periods
      Task Statement
      Learning Goals
      Approach
         Solution steps
      Solution
         Solution Meta-Kernel
         Solution Code
         Solution Sample Output
   Find Times when Target is Visible
      Task Statement
      Learning Goals
      Approach
         Solution steps
      Solution
         Solution Code
         Solution Sample Output
   Extra Credit
      Task statements
      Solutions




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Geometric Event Finding Hands-On Lesson (FORTRAN)





August 31, 2016



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Overview




This lesson illustrates how the Geometry Finder (GF) subsystem of the SPICE Toolkit can be used to find time intervals when specified geometric conditions are satisfied.

In this lesson the student is asked to construct a program that finds the time intervals, within a specified time range, when the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's deep space station in New Norcia. Possible occultation of the spacecraft by Mars is to be considered.



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Note About HTML Links




The HTML version of this lesson contains links pointing to various HTML documents provided with the Toolkit. All of these links are relative and, in order to function, require this document to be in a certain location in the Toolkit HTML documentation directory tree.

In order for the links to be resolved, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the ``toolkit/'' tree and copy this document to that subdirectory before loading it into a Web browser.



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References






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Tutorials



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

 
   Name             Lesson steps/routines it describes
   ---------------  -----------------------------------------
   Time             Time Conversion
   SCLK and LSK     Time Conversion
   SPK              Obtaining Ephemeris Data
   Frames           Reference Frames
   Using Frames     Reference Frames
   PCK              Planetary Constants Data
   Lunar-Earth PCK  Lunar and Earth Orientation Data
   GF               The SPICE Geometry Ginder (GF) subsystem
These tutorials are available from the NAIF ftp server at JPL:

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


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Required Readings



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

   Name             Lesson steps/routines that it describes
   ---------------  -----------------------------------------
   cells.req        Cell/window initialization
   frames.req       Using reference frames
   gf.req           The SPICE geometry finder (GF) subsystem
   kernel.req       Loading SPICE kernels
   naif_ids.req     Body and reference frame names
   pck.req          Obtaining planetary constants data
   spk.req          Computing positions and velocities
   time.req         UTC to ET time conversion
   windows.req      The SPICE window data type


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The Permuted Index



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

This text document provides a simple mechanism by which users can discover which SPICE routines perform functions of interest, as well as the names of the source files that contain these routines. This is particularly useful for FORTRAN programmers because some of the routines are entry points; the names of these routines do not translate directly into the name of the respective source files that contain them.



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Source Code Header Comments



The most detailed specification of a given SPICE FORTRAN routine is contained in the header section of its source code. The source code is distributed with the Toolkit and is located under the ``toolkit/src/spicelib'' path.

For example path of the source code of the STR2ET routine is

   toolkit/src/spicelib/str2et.for


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Kernels Used




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

    1.  Solar System Ephemeris SPK, subsetted to cover only the time
        range of interest:
 
           de430.bsp
 
    2.  Martian Satellite Ephemeris SPK, subsetted to cover only the
        time range of interest:
 
           mar085.bsp
 
    3.  ESA stations SPK:
 
           estrack_v01.bsp
 
    4.  ESA stations frame definitions:
 
           estrack_v01.tf
 
    5.  EARTH_FIXED/ITRF93 frame connection:
 
           earthfixeditrf93.tf
 
    6.  Binary PCK for Earth:
 
           earth_070425_370426_predict.bpc
 
    7.  ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted to cover
        only the time range of interest:
 
           em16_tgo_mlt_20171205_20230115_v01.bsp
 
    8.  Generic LSK:
 
           naif0012.tls
 
    9.  Generic PCK:
 
           pck00010.tpc
 
   10.  ExoMars-16 TGO FK, containing the SPICE ID/name mappings for
        the TGO spacecraft:
 
           em16_tgo_v07.tf
These SPICE kernels are included in the lesson package available from the NAIF server at JPL:

   ftp://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Lessons/


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SPICE Routines Used




This section provides a summary of the routines 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.)

   Name        Function that it performs
   ----------  ---------------------------------------------------
   FURNSH      Loads kernels, individually or listed in meta-kernel
   GFOCLT      Solve for times of occultation or transit
   GFPOSC      Solve for times when a position vector coordinate
               constraint is met
   REPMC       Substitute a substring for a marker in a string
   REPMF       Substitute double precision value for marker in string
   RPD         Return number of radians per degree
   SSIZED      Set the size of a d.p. cell
   STR2ET      Converts a time string to ET seconds past J2000
   TIMOUT      Format a time string for output
   TOSTDO      Write a string to standard output
   WNCARD      Return cardinality of a SPICE window
   WNDIFD      Find the difference of two d.p. windows
   WNFETD      Fetch a specified interval from a d.p. window
   WNINSD      Insert an interval into a d.p. window
Refer to the headers of the various routines listed above, as detailed interface specifications are provided with the source code.



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Find View Periods







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Task Statement




Write a program that finds the set of time intervals, within the time range

   2018 JUN 10 TDB
   2018 JUN 14 TDB
when the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's New Norcia station. These time intervals are frequently called ``view periods.''

The spacecraft is considered visible if its apparent position (that is, its position corrected for light time and stellar aberration) has elevation of at least 6 degrees in the topocentric reference frame NEW_NORCIA_TOPO. In this exercise, we ignore the possibility of occultation of the spacecraft by Mars.

Use a search step size that ensures that no view periods of duration 5 minutes or longer will be missed by the search.

Display the start and stop times of these intervals using TDB calendar dates and millisecond precision.



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Learning Goals




Exposure to SPICE GF event finding routines. Familiarity with SPICE windows and routines that manipulate them. Exposure to SPICE time parsing and output formatting routines.



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Approach






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Solution steps



A possible solution could consist of the following steps:

Preparation:

    1. Review the SPICELIB cell and window Required Reading.

    2. Decide what SPICE kernels are necessary. Use the SPICE summary tool BRIEF to examine the coverage of the binary kernels and verify the availability of required data.

    3. Create a meta-kernel listing the SPICE kernels to be loaded. (Hint: consult a programming example tutorial, or the Introduction to Kernels tutorial, for a reminder of how to do this.)

    Name the meta-kernel 'viewpr.tm'.

Next, write a program that performs the following steps:

    1. Use FURNSH to load the meta-kernel.

    2. Declare a SPICELIB window ``CNFINE'' to hold the time period within which the search is to be conducted, and a SPICELIB window RISWIN ("rise/set window") to hold the view periods found by the search. Initialize the confinement and result windows using SSIZED.

    3. Insert the given time bounds into the confinement window using WNINSD.

    4. Select a step size for searching for visibility state transitions: in this case, each target rise or set event is a state transition.

    The step size must be large enough so the search proceeds with reasonable speed, but small enough so that no visibility transition events---that is, target rise or set events---are missed.

    5. Use the GF routine GFPOSC to find the window of times, within the confinement window CNFINE, during which the ExoMars-16 TGO spacecraft is above the elevation limit as seen from ESA's New Norcia station, in the the reference frame NEW_NORCIA_TOPO.

    Use light time and stellar aberration corrections for the apparent position of the spacecraft as seen from the station.

    6. Fetch and display the contents of the result window. Use WNFETD to extract from the result window the start and stop times of each time interval. Display each of the intervals in the result window as a pair of start and stop times. Express each time as a TDB calendar date using the routine TIMOUT.

    The SPICELIB ``replace marker'' routines REPxxx are useful for substituting values into output strings. Consult, for example, the header of REPMC.

You may find it useful to consult the references listed above. In particular, the header of the SPICE GF routine GFPOSC contains pertinent documentation.



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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 'viewpr.tm'. Its contents follow:

 
   KPL/MK
 
      This is the meta-kernel used in the solution of the tasks in the
      Geometric Event Finding Hands On Lesson.
 
 
   \begindata
 
      KERNELS_TO_LOAD = (
 
         'kernels/spk/de430.bsp'
         'kernels/spk/mar085.bsp',
         'kernels/spk/estrack_v01.bsp'
         'kernels/fk/estrack_v01.tf'
         'kernels/fk/earthfixeditrf93.tf'
         'kernels/pck/earth_070425_370426_predict.bpc'
         'kernels/lsk/naif0012.tls'
         'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp'
         'kernels/pck/pck00010.tpc'
         'kernels/fk/em16_tgo_v07.tf'
 
                        )
 
   \begintext
 


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Solution Code



The example program below shows one possible solution.

 
         PROGRAM VIEWPR
         IMPLICIT NONE
   C
   C     Find and display the window of times when the ExoMars-16
   C     TGO spacecraft is above a specified elevation limit in the
   C     topocentric reference frame of ESA's New Norcia station.
   C
 
   C
   C     SPICELIB functions
   C
         DOUBLE PRECISION      RPD
         INTEGER               WNCARD
 
   C
   C     Global GF parameters: we import from this file
   C     the definition of the GF workspace size parameter
   C
   C        NWMAX
   C
         INCLUDE 'gf.inc'
 
   C
   C     Local parameters
   C
   C     Format string for time output:
   C
         CHARACTER*(*)         TDBFMT
         PARAMETER           ( TDBFMT =
        .                    'YYYY MON DD HR:MN:SC.### (TDB) ::TDB' )
 
   C
   C     The meta-kernel:
   C
         CHARACTER*(*)         METAKR
         PARAMETER           ( METAKR = 'viewpr.tm' )
 
 
   C
   C     Maximum number of intervals in any window:
   C
         INTEGER               MAXIVL
         PARAMETER           ( MAXIVL = 1000 )
 
   C
   C     Maximum result window size:
   C
         INTEGER               MAXWIN
         PARAMETER           ( MAXWIN = 2 * MAXIVL )
 
   C
   C     SPICELIB cell bound:
   C
         INTEGER               LBCELL
         PARAMETER           ( LBCELL = -5 )
 
   C
   C     String length parameters:
   C
         INTEGER               CORLEN
         PARAMETER           ( CORLEN = 10 )
 
         INTEGER               FRNMLN
         PARAMETER           ( FRNMLN = 32 )
 
         INTEGER               LNSIZE
         PARAMETER           ( LNSIZE = 200 )
 
         INTEGER               NAMLEN
         PARAMETER           ( NAMLEN = 32 )
 
         INTEGER               OPLEN
         PARAMETER           ( OPLEN  = 50 )
 
         INTEGER               TIMLEN
         PARAMETER           ( TIMLEN = 50 )
 
   C
   C     Local variables
   C
         CHARACTER*(CORLEN)    ABCORR
         CHARACTER*(NAMLEN)    CRDSYS
         CHARACTER*(NAMLEN)    COORD
         CHARACTER*(LNSIZE)    LINE
         CHARACTER*(FRNMLN)    OBSFRM
         CHARACTER*(OPLEN)     RELATE
         CHARACTER*(NAMLEN)    SRFPT
         CHARACTER*(TIMLEN)    START
         CHARACTER*(TIMLEN)    STOP
         CHARACTER*(NAMLEN)    TARGET
         CHARACTER*(TIMLEN)    TIMSTR
         CHARACTER*(LNSIZE)    TITLE
 
         DOUBLE PRECISION      ADJUST
 
   C
   C     Confinement window used to store interval to be searched:
   C
         DOUBLE PRECISION      CNFINE ( LBCELL : MAXWIN )
         DOUBLE PRECISION      ELVLIM
         DOUBLE PRECISION      ETBEG
         DOUBLE PRECISION      ETEND
         DOUBLE PRECISION      INTBEG
         DOUBLE PRECISION      INTEND
         DOUBLE PRECISION      REVLIM
 
   C
   C     STEPSZ is the step size, measured in seconds, used to search
   C     for times bracketing a state transition.
   C
         DOUBLE PRECISION      STEPSZ
 
   C
   C     Result window used to store rise/set times:
   C
         DOUBLE PRECISION      RISWIN ( LBCELL : MAXWIN )
 
   C
   C     Workspace array:
   C
         DOUBLE PRECISION      WORK   ( LBCELL : MAXWIN,  NWMAX )
 
 
         INTEGER               I
         INTEGER               WINSIZ
 
   C
   C     Load the meta-kernel.
   C
         CALL FURNSH ( METAKR )
 
   C
   C     Assign the inputs for our search.
   C
   C     Since we're interested in the apparent location of the
   C     target, we use light time and stellar aberration
   C     corrections.  We use the "converged Newtonian" form
   C     of the light time correction because this choice may
   C     increase the accuracy of the occultation times we'll
   C     compute using GFOCLT.
   C
         SRFPT  = 'NEW_NORCIA'
         OBSFRM = 'NEW_NORCIA_TOPO'
         TARGET = 'TGO'
         ABCORR = 'CN+S'
         START  = '2018 JUN 10 TDB'
         STOP   = '2018 JUN 14 TDB'
         ELVLIM =  6.0D0
   C
   C     The elevation limit above has units of degrees; we convert
   C     this value to radians for computation using SPICE routines.
   C     We'll store the equivalent value in radians in REVLIM.
   C
         REVLIM = RPD() * ELVLIM
 
   C
   C     Since SPICE doesn't directly support the AZ/EL coordinate
   C     system, we use the equivalent constraint
   C
   C        latitude > REVLIM
   C
   C     in the latitudinal coordinate system, where the reference
   C     frame is topocentric and is centered at the viewing location.
   C
         CRDSYS = 'LATITUDINAL'
         COORD  = 'LATITUDE'
         RELATE = '>'
 
   C
   C     The adjustment value only applies to absolute extrema
   C     searches; simply give it an initial value of zero
   C     for this inequality search.
   C
         ADJUST = 0.D0
 
   C
   C     STEPSZ is the step size, measured in seconds, used to search
   C     for times bracketing a state transition. Since we don't expect
   C     any events of interest to be shorter than five minutes, and
   C     since the separation between events is well over 5 minutes,
   C     we'll use this value as our step size. Units are seconds.
   C
         STEPSZ = 300.D0
 
   C
   C     Display a banner for the output report:
   C
         TITLE  = 'Inputs for target visibility search:'
         CALL TOSTDO ( ' '   )
         CALL TOSTDO ( TITLE )
         CALL TOSTDO ( ' '   )
 
         LINE   = '   Target                       = #'
         CALL REPMC  ( LINE, '#', TARGET, LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Observation surface location = #'
         CALL REPMC  ( LINE, '#', SRFPT,  LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Observer''s reference frame   = #'
         CALL REPMC  ( LINE, '#', OBSFRM,  LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Elevation limit (degrees)    = #'
         CALL REPMF ( LINE, '#', ELVLIM, 7, 'F', LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Aberration correction        = #'
         CALL REPMC  ( LINE, '#', ABCORR, LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Step size (seconds)          = #'
         CALL REPMF ( LINE, '#', STEPSZ, 9, 'F', LINE )
         CALL TOSTDO ( LINE )
 
   C
   C     Convert the start and stop times to ET.
   C
         CALL STR2ET ( START, ETBEG )
         CALL STR2ET ( STOP,  ETEND )
 
   C
   C     Display the search interval start and stop times
   C     using the format shown below.
   C
   C        2004 MAY 06 20:15:00.000 (TDB)
   C
         CALL TIMOUT ( ETBEG, TDBFMT, TIMSTR )
         LINE = '   Start time                   = '//TIMSTR
         CALL TOSTDO ( LINE )
 
         CALL TIMOUT ( ETEND, TDBFMT, TIMSTR )
         LINE = '   Stop time                    = '//TIMSTR
         CALL TOSTDO ( LINE )
 
         CALL TOSTDO ( ' ' )
 
   C
   C     Every SPICELIB window must have its size initialized.
   C
   C     Initialize the "confinement" window with the interval
   C     over which we'll conduct the search.
   C
         CALL SSIZED ( MAXWIN, CNFINE )
 
         CALL WNINSD ( ETBEG,  ETEND, CNFINE )
 
   C
   C     Initialize the result window; this window will contain
   C     the rise/set times found by our search.
   C
         CALL SSIZED ( MAXWIN, RISWIN )
 
   C
   C     In the call below, the workspace dimensions are
   C
   C        ( MAXWIN, NWMAX )
   C
   C     Now search for the time period, within our confinement
   C     window, during which the apparent target has elevation
   C     at least equal to the elevation limit.
   C
         CALL GFPOSC ( TARGET, OBSFRM, ABCORR, SRFPT,
        .              CRDSYS, COORD,  RELATE, REVLIM,
        .              ADJUST, STEPSZ, CNFINE, MAXWIN,
        .              NWMAX,  WORK,   RISWIN         )
 
   C
   C     The function WNCARD returns the number of intervals
   C     in a SPICE window.
   C
         WINSIZ = WNCARD( RISWIN )
 
         IF ( WINSIZ .EQ. 0 ) THEN
 
            WRITE (*,*) 'No events were found.'
 
         ELSE
   C
   C        Display the view periods.
   C
            LINE = 'Visibility times of # as seen from #:'
            CALL REPMC ( LINE, '#', TARGET, LINE )
            CALL REPMC ( LINE, '#', SRFPT,  LINE )
 
            CALL TOSTDO ( LINE )
            CALL TOSTDO ( ' '  )
 
            DO I = 1, WINSIZ
   C
   C           Fetch the start and stop times of the Ith interval
   C           from the search result window VISWIN.
   C
               CALL WNFETD ( RISWIN, I, INTBEG, INTEND )
 
   C
   C           Convert the rise time to a TDB calendar string.
   C
               CALL TIMOUT ( INTBEG, TDBFMT, TIMSTR )
 
   C
   C           Write the string to standard output.
   C
               IF ( I .EQ. 1 ) THEN
                  LINE = 'Visibility or window start time:  #'
               ELSE
                  LINE = 'Visibility start time:            #'
               END IF
 
               CALL REPMC ( LINE, '#', TIMSTR, LINE )
               CALL TOSTDO ( LINE )
 
   C
   C           Convert the set time to a TDB calendar string.
   C
               CALL TIMOUT ( INTEND, TDBFMT, TIMSTR )
   C
   C           Write the string to standard output.
   C
               IF ( I .EQ. WINSIZ ) THEN
                  LINE = 'Visibility or window stop time:   #'
               ELSE
                  LINE = 'Visibility stop time:             #'
               END IF
 
               CALL REPMC ( LINE, '#', TIMSTR, LINE )
               CALL TOSTDO ( LINE )
 
               CALL TOSTDO ( ' ' )
 
            END DO
 
         END IF
 
         END


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Solution Sample Output



Numerical results shown for this example may differ across platforms since the results depend on the SPICE kernels used as input and on the host platform's arithmetic implementation.

After compiling the program, execute it. The output is:

 
 
   Inputs for target visibility search:
 
      Target                       = TGO
      Observation surface location = NEW_NORCIA
      Observer's reference frame   = NEW_NORCIA_TOPO
      Elevation limit (degrees)    = 6.000000
      Aberration correction        = CN+S
      Step size (seconds)          = 300.000000
      Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
      Stop time                    = 2018 JUN 14 00:00:00.000 (TDB)
 
   Visibility times of TGO as seen from NEW_NORCIA:
 
   Visibility or window start time:  2018 JUN 10 00:00:00.000 (TDB)
   Visibility stop time:             2018 JUN 10 02:11:17.355 (TDB)
 
   Visibility start time:            2018 JUN 10 13:19:58.777 (TDB)
   Visibility stop time:             2018 JUN 11 02:08:16.008 (TDB)
 
   Visibility start time:            2018 JUN 11 13:16:50.542 (TDB)
   Visibility stop time:             2018 JUN 12 02:05:12.548 (TDB)
 
   Visibility start time:            2018 JUN 12 13:13:38.573 (TDB)
   Visibility stop time:             2018 JUN 13 02:02:06.618 (TDB)
 
   Visibility start time:            2018 JUN 13 13:10:23.432 (TDB)
   Visibility or window stop time:   2018 JUN 14 00:00:00.000 (TDB)
 


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Find Times when Target is Visible







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Task Statement




Extend the program of the previous chapter to find times when the ExoMars-16 TGO orbiter is:

    -- Above the elevation limit in the NEW_NORCIA_TOPO topocentric reference frame.

    -- and is not occulted by Mars

Store the set of time intervals when the spacecraft is visible in a SPICELIB window. We'll call this the ``result window.''

Display each of the intervals in the result window as a pair of start and stop times. Express each time as a TDB calendar date using the same format as in the previous program.



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Learning Goals




Familiarity with the GF occultation finding routine GFOCLT. Further experience with the SPICELIB window routines.



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Approach






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Solution steps



A possible solution would consist of the following steps:

    1. Use the meta-kernel of the previous lesson.

    2. Include the code from the program of the previous chapter in a new source file; modify this code to create the new program.

    3. Declare a SPICELIB window OCCWIN to hold the results of the occultation search. Also declare a second SPICELIB window VISWIN to hold the final result. Initialize OCCWIN and VISWIN using SSIZED.

    4. Search for occultations of the ExoMars-16 TGO orbiter as seen from New Norcia station using GFOCLT. Use as the confinement window for this search the result window from the elevation search performed by GFPOSC.

    Since occultations occur when the apparent ExoMars-16 TGO spacecraft position is behind the apparent figure of Mars, light time correction must be performed for the occultation search. To improve accuracy of the occultation state determination, use ``converged Newtonian'' light time correction.

    5. Use the SPICELIB window subtraction routine WNDIFD to subtract the window of times when the spacecraft is occulted from the window of times when the spacecraft is above the elevation limit. The difference window VISWIN is the final result.

    6. Modify the code to display the contents of the window VISWIN.

This completes the assignment.



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Solution






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Solution Code



 
         PROGRAM VISIBL
         IMPLICIT NONE
   C
   C     Find and display the window of times when the ExoMars-16
   C     TGO spacecraft is above a specified elevation limit in the
   C     topocentric reference frame of ESA's New Norcia station
   C     and is not occulted by Mars.
   C
 
   C
   C     SPICELIB functions
   C
         DOUBLE PRECISION      RPD
         INTEGER               WNCARD
 
   C
   C     Global GF parameters: we import from this file
   C     the definition of the GF workspace size parameter
   C
   C        NWMAX
   C
   C     and the occultation parameters
   C
   C        OCCLN
   C        SHPLEN
   C
         INCLUDE 'gf.inc'
 
   C
   C     Local parameters
   C
   C     Format string for time output:
   C
         CHARACTER*(*)         TDBFMT
         PARAMETER           ( TDBFMT =
        .                    'YYYY MON DD HR:MN:SC.### (TDB) ::TDB' )
 
   C
   C     The meta-kernel:
   C
         CHARACTER*(*)         METAKR
         PARAMETER           ( METAKR = 'viewpr.tm' )
 
 
   C
   C     Maximum number of events we can handle in our event set:
   C
         INTEGER               MAXEVT
         PARAMETER           ( MAXEVT = 1000 )
 
   C
   C     Maximum result window size:
   C
         INTEGER               MAXWIN
         PARAMETER           ( MAXWIN = 2 * MAXEVT )
 
   C
   C     SPICELIB cell bound:
   C
         INTEGER               LBCELL
         PARAMETER           ( LBCELL = -5 )
 
   C
   C     String length parameters:
   C
         INTEGER               BDNMLN
         PARAMETER           ( BDNMLN = 36 )
 
         INTEGER               CORLEN
         PARAMETER           ( CORLEN = 10 )
 
         INTEGER               FRNMLN
         PARAMETER           ( FRNMLN = 32 )
 
         INTEGER               LNSIZE
         PARAMETER           ( LNSIZE = 200 )
 
         INTEGER               NAMLEN
         PARAMETER           ( NAMLEN = 32 )
 
         INTEGER               OPLEN
         PARAMETER           ( OPLEN  = 50 )
 
         INTEGER               TIMLEN
         PARAMETER           ( TIMLEN = 50 )
 
   C
   C     Local variables
   C
         CHARACTER*(CORLEN)    ABCORR
         CHARACTER*(BDNMLN)    BACK
         CHARACTER*(FRNMLN)    BFRAME
         CHARACTER*(BDNMLN)    BSHAPE
         CHARACTER*(NAMLEN)    CRDSYS
         CHARACTER*(NAMLEN)    COORD
         CHARACTER*(FRNMLN)    FFRAME
         CHARACTER*(FRNMLN)    FRAME
         CHARACTER*(BDNMLN)    FRONT
         CHARACTER*(SHPLEN)    FSHAPE
         CHARACTER*(LNSIZE)    LINE
         CHARACTER*(OCLLN)     OCCTYP
         CHARACTER*(OPLEN)     RELATE
         CHARACTER*(NAMLEN)    SRFPT
         CHARACTER*(TIMLEN)    START
         CHARACTER*(TIMLEN)    STOP
         CHARACTER*(NAMLEN)    TARGET
         CHARACTER*(TIMLEN)    TIMSTR
         CHARACTER*(LNSIZE)    TITLE
 
         DOUBLE PRECISION      ADJUST
 
   C
   C     Confinement window used to store interval to be searched:
   C
         DOUBLE PRECISION      CNFINE ( LBCELL : MAXEVT )
         DOUBLE PRECISION      ELVLIM
         DOUBLE PRECISION      ETBEG
         DOUBLE PRECISION      ETEND
         DOUBLE PRECISION      INTBEG
         DOUBLE PRECISION      INTEND
         DOUBLE PRECISION      REVLIM
 
   C
   C     STEPSZ is the step size, measured in seconds, used to search
   C     for times bracketing a state transition.
   C
         DOUBLE PRECISION      STEPSZ
 
   C
   C     Result window used to store occultation times:
   C
         DOUBLE PRECISION      OCCWIN ( LBCELL : MAXWIN )
 
   C
   C     Result window used to store rise/set times:
   C
         DOUBLE PRECISION      RISWIN ( LBCELL : MAXWIN )
 
   C
   C     Result window used to store visibility periods:
   C
         DOUBLE PRECISION      VISWIN ( LBCELL : MAXWIN )
 
   C
   C     Workspace array:
   C
         DOUBLE PRECISION      WORK   ( LBCELL : MAXWIN,  NWMAX )
 
 
         INTEGER               I
         INTEGER               WINSIZ
 
   C
   C     Load the meta-kernel.
   C
         CALL FURNSH ( METAKR )
 
   C
   C     Assign the inputs for our search.
   C
         SRFPT  = 'NEW_NORCIA'
         FRAME  = 'NEW_NORCIA_TOPO'
         TARGET = 'TGO'
         ABCORR = 'CN+S'
         START  = '2018 JUN 10 TDB'
         STOP   = '2018 JUN 14 TDB'
         ELVLIM =  6.0D0
   C
   C     The elevation limit above has units of degrees; we convert
   C     this value to radians for computation using SPICE routines.
   C     We'll store the equivalent value in radians in REVLIM.
   C
         REVLIM = RPD() * ELVLIM
 
   C     Since we're interested in the apparent location of the
   C     target, we use light time and stellar aberration
   C     corrections.
   C
   C     Since SPICE doesn't directly support the AZ/EL coordinate
   C     system, we use the equivalent constraint
   C
   C        latitude > REVLIM
   C
   C     in the latitudinal coordinate system, where the reference
   C     frame is topocentric and is centered at the viewing location.
   C
         CRDSYS = 'LATITUDINAL'
         COORD  = 'LATITUDE'
         RELATE = '>'
 
   C
   C     STEPSZ is the step size, measured in seconds, used to search
   C     for times bracketing a state transition. Since we don't expect
   C     any events of interest to be shorter than five minutes, and
   C     since the separation between events is well over 5 minutes,
   C     we'll use this value as our step size. Units are seconds.
   C
         STEPSZ = 300.D0
 
   C
   C     We model the target shape as a point and the blocking body's
   C     shape as an ellipsoid. No body-fixed reference frame is
   C     required for the target since its orientation is not used.
   C
         BACK   = TARGET
         BSHAPE = 'POINT'
         BFRAME = ' '
         FRONT  = 'MARS'
         FSHAPE = 'ELLIPSOID'
         FFRAME = 'IAU_MARS'
 
   C
   C     The occultation type should be set to 'ANY' for a point
   C     target.
   C
         OCCTYP = 'ANY'
 
   C
   C     Display a banner for the output report:
   C
         TITLE  = 'Inputs for target visibility search:'
         CALL TOSTDO ( ' '   )
         CALL TOSTDO ( TITLE )
         CALL TOSTDO ( ' '   )
 
         LINE   = '   Target                       = #'
         CALL REPMC  ( LINE, '#', TARGET, LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Observation surface location = #'
         CALL REPMC  ( LINE, '#', SRFPT,  LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Observer''s reference frame   = #'
         CALL REPMC  ( LINE, '#', FRAME,  LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Blocking body                = #'
         CALL REPMC  ( LINE, '#', FRONT, LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Blocker''s reference frame    = #'
         CALL REPMC  ( LINE, '#', FFRAME,  LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Elevation limit (degrees)    = #'
         CALL REPMF ( LINE, '#', ELVLIM, 7, 'F', LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Aberration correction        = #'
         CALL REPMC  ( LINE, '#', ABCORR, LINE )
         CALL TOSTDO ( LINE )
 
         LINE   = '   Step size (seconds)          = #'
         CALL REPMF ( LINE, '#', STEPSZ, 9, 'F', LINE )
         CALL TOSTDO ( LINE )
 
   C
   C     Convert the start and stop times to ET.
   C
         CALL STR2ET ( START, ETBEG )
         CALL STR2ET ( STOP,  ETEND )
 
   C
   C     Display the search interval start and stop times
   C     using the format shown below.
   C
   C        2004 MAY 06 20:15:00.000 (TDB)
   C
         CALL TIMOUT ( ETBEG, TDBFMT, TIMSTR )
         LINE = '   Start time                   = '//TIMSTR
         CALL TOSTDO ( LINE )
 
         CALL TIMOUT ( ETEND, TDBFMT, TIMSTR )
         LINE = '   Stop time                    = '//TIMSTR
         CALL TOSTDO ( LINE )
 
         CALL TOSTDO ( ' ' )
 
   C
   C     Every SPICELIB window must have its size initialized.
   C
   C     Initialize the "confinement" window with the interval
   C     over which we'll conduct the search.
   C
         CALL SSIZED ( MAXWIN, CNFINE )
 
         CALL WNINSD ( ETBEG,  ETEND, CNFINE )
 
   C
   C     Initialize the result window; this window will contain
   C     the rise/set times found by our search.
   C
         CALL SSIZED ( MAXWIN, RISWIN )
 
   C
   C     Initialize the occultation and visibility windows.
   C
         CALL SSIZED ( MAXWIN, OCCWIN )
         CALL SSIZED ( MAXWIN, VISWIN )
 
   C
   C     The adjustment value only applies to absolute extrema
   C     searches;  simply give it an initial value of zero
   C     for this inequality search.
   C
         ADJUST = 0.D0
 
   C
   C     Note that the workspace dimensions are ( MAXWIN, NWMAX ).
   C
   C     Now search for the time period, within our confinement
   C     window, during which the apparent target has elevation
   C     at least equal to the elevation limit.
   C
         CALL GFPOSC ( TARGET, FRAME,  ABCORR, SRFPT,
        .              CRDSYS, COORD,  RELATE, REVLIM,
        .              ADJUST, STEPSZ, CNFINE, MAXWIN,
        .              NWMAX,  WORK,   RISWIN         )
 
   C
   C     Now find the times when the apparent target is above
   C     the elevation limit and is not occulted by the
   C     blocking body (Mars). We'll find the times when the target
   C     is above the elevation limit and *is* occulted, then subtract
   C     that window from the view period window RISWIN found above.
   C
   C     For this occultation search, we can use RISWIN as
   C     the confinement window because we're not interested in
   C     occultations that occur when the target is below the
   C     elevation limit.
   C
   C     Find occultations within the view period window.
   C
         CALL GFOCLT ( OCCTYP, FRONT,  FSHAPE, FFRAME,
        .              BACK,   BSHAPE, BFRAME, ABCORR,
        .              SRFPT,  STEPSZ, RISWIN, OCCWIN )
 
   C
   C     Subtract the occultation window from the view period
   C     window: this yields the time periods when the target
   C     is visible.
   C
         CALL WNDIFD ( RISWIN, OCCWIN, VISWIN )
 
   C
   C     The function WNCARD returns the number of intervals
   C     in a SPICE window.
   C
         WINSIZ = WNCARD( VISWIN )
 
         IF ( WINSIZ .EQ. 0 ) THEN
 
            WRITE (*,*) 'No events were found.'
 
         ELSE
   C
   C        Display the visibility time periods.
   C
            LINE = 'Visibility times of # as seen from #:'
            CALL REPMC ( LINE, '#', TARGET, LINE )
            CALL REPMC ( LINE, '#', SRFPT,  LINE )
 
            CALL TOSTDO ( LINE )
            CALL TOSTDO ( ' '  )
 
 
            DO I = 1, WINSIZ
   C
   C           Fetch the start and stop times of the Ith interval
   C           from the search result window VISWIN.
   C
               CALL WNFETD ( VISWIN, I, INTBEG, INTEND )
 
   C
   C           Convert the rise time to a TDB calendar string.
   C
               CALL TIMOUT ( INTBEG, TDBFMT, TIMSTR )
 
   C
   C           Write the string to standard output.
   C
               IF ( I .EQ. 1 ) THEN
                  LINE = 'Visibility or window start time:  #'
               ELSE
                  LINE = 'Visibility start time:            #'
               END IF
 
               CALL REPMC ( LINE, '#', TIMSTR, LINE )
               CALL TOSTDO ( LINE )
 
 
               CALL TIMOUT ( INTEND, TDBFMT, TIMSTR )
   C
   C           Write the string to standard output.
   C
               IF ( I .EQ. WINSIZ ) THEN
                  LINE = 'Visibility or window stop time:   #'
               ELSE
                  LINE = 'Visibility stop time:             #'
               END IF
 
               CALL REPMC ( LINE, '#', TIMSTR, LINE )
               CALL TOSTDO ( LINE )
 
               CALL TOSTDO ( ' ' )
 
            END DO
 
         END IF
 
         END
 


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Solution Sample Output



Numerical results shown for this example may differ across platforms since the results depend on the SPICE kernels used as input and on the host platform's arithmetic implementation.

After compiling the program, execute it. The output is:

 
   Inputs for target visibility search:
 
      Target                       = TGO
      Observation surface location = NEW_NORCIA
      Observer's reference frame   = NEW_NORCIA_TOPO
      Blocking body                = MARS
      Blocker's reference frame    = IAU_MARS
      Elevation limit (degrees)    = 6.000000
      Aberration correction        = CN+S
      Step size (seconds)          = 300.000000
      Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
      Stop time                    = 2018 JUN 14 00:00:00.000 (TDB)
 
   Visibility times of TGO as seen from NEW_NORCIA:
 
   Visibility or window start time:  2018 JUN 10 00:00:00.000 (TDB)
   Visibility stop time:             2018 JUN 10 01:00:30.640 (TDB)
 
   Visibility start time:            2018 JUN 10 01:41:03.610 (TDB)
   Visibility stop time:             2018 JUN 10 02:11:17.355 (TDB)
 
   Visibility start time:            2018 JUN 10 13:28:28.785 (TDB)
   Visibility stop time:             2018 JUN 10 14:45:38.197 (TDB)
 
   Visibility start time:            2018 JUN 10 15:26:21.981 (TDB)
   Visibility stop time:             2018 JUN 10 16:43:32.192 (TDB)
 
   Visibility start time:            2018 JUN 10 17:24:17.290 (TDB)
   Visibility stop time:             2018 JUN 10 18:41:27.535 (TDB)
 
   Visibility start time:            2018 JUN 10 19:22:13.628 (TDB)
   Visibility stop time:             2018 JUN 10 20:39:21.785 (TDB)
 
   Visibility start time:            2018 JUN 10 21:20:08.856 (TDB)
   Visibility stop time:             2018 JUN 10 22:37:12.445 (TDB)
 
   Visibility start time:            2018 JUN 10 23:18:00.834 (TDB)
   Visibility stop time:             2018 JUN 11 00:35:01.034 (TDB)
 
   Visibility start time:            2018 JUN 11 01:15:50.883 (TDB)
   Visibility stop time:             2018 JUN 11 02:08:16.008 (TDB)
 
   Visibility start time:            2018 JUN 11 13:16:50.542 (TDB)
   Visibility stop time:             2018 JUN 11 14:20:09.789 (TDB)
 
   Visibility start time:            2018 JUN 11 15:01:08.370 (TDB)
   Visibility stop time:             2018 JUN 11 16:18:03.385 (TDB)
 
   Visibility start time:            2018 JUN 11 16:59:03.014 (TDB)
   Visibility stop time:             2018 JUN 11 18:15:58.739 (TDB)
 
   Visibility start time:            2018 JUN 11 18:56:59.199 (TDB)
   Visibility stop time:             2018 JUN 11 20:13:54.308 (TDB)
 
   Visibility start time:            2018 JUN 11 20:54:55.301 (TDB)
   Visibility stop time:             2018 JUN 11 22:11:47.045 (TDB)
 
   Visibility start time:            2018 JUN 11 22:52:48.925 (TDB)
   Visibility stop time:             2018 JUN 12 00:09:35.868 (TDB)
 
   Visibility start time:            2018 JUN 12 00:50:39.046 (TDB)
   Visibility stop time:             2018 JUN 12 02:05:12.548 (TDB)
 
   Visibility start time:            2018 JUN 12 13:13:38.573 (TDB)
   Visibility stop time:             2018 JUN 12 13:54:43.524 (TDB)
 
   Visibility start time:            2018 JUN 12 14:35:54.054 (TDB)
   Visibility stop time:             2018 JUN 12 15:52:36.256 (TDB)
 
   Visibility start time:            2018 JUN 12 16:33:47.502 (TDB)
   Visibility stop time:             2018 JUN 12 17:50:30.988 (TDB)
 
   Visibility start time:            2018 JUN 12 18:31:42.896 (TDB)
   Visibility stop time:             2018 JUN 12 19:48:26.827 (TDB)
 
   Visibility start time:            2018 JUN 12 20:29:39.039 (TDB)
   Visibility stop time:             2018 JUN 12 21:46:20.933 (TDB)
 
   Visibility start time:            2018 JUN 12 22:27:33.596 (TDB)
   Visibility stop time:             2018 JUN 12 23:44:11.473 (TDB)
 
   Visibility start time:            2018 JUN 13 00:25:24.992 (TDB)
   Visibility stop time:             2018 JUN 13 01:42:00.777 (TDB)
 
   Visibility start time:            2018 JUN 13 13:10:23.432 (TDB)
   Visibility stop time:             2018 JUN 13 13:29:19.789 (TDB)
 
   Visibility start time:            2018 JUN 13 14:10:38.985 (TDB)
   Visibility stop time:             2018 JUN 13 15:27:11.882 (TDB)
 
   Visibility start time:            2018 JUN 13 16:08:31.566 (TDB)
   Visibility stop time:             2018 JUN 13 17:25:06.068 (TDB)
 
   Visibility start time:            2018 JUN 13 18:06:26.219 (TDB)
   Visibility stop time:             2018 JUN 13 19:23:01.820 (TDB)
 
   Visibility start time:            2018 JUN 13 20:04:22.175 (TDB)
   Visibility stop time:             2018 JUN 13 21:20:57.296 (TDB)
 
   Visibility start time:            2018 JUN 13 22:02:17.650 (TDB)
   Visibility or window stop time:   2018 JUN 13 23:18:49.624 (TDB)
 


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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 the geometry event finding subsystem and particularly the GFPOSC and GFDIST routines.

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 to the questions asked in these tasks.



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Task statements




    1. Write a program that finds the times, within the time range

         2018 JUN 10 TDB
         2018 JUN 11 TDB
    when the ExoMars-16 Trace Gas Orbiter (TGO) crosses Mars' equator. Display the results using TDB calendar dates and millisecond precision.

    2. Write a program that finds the times, within the time range

         2018 JUN 10 TDB
         2018 JUN 11 TDB
    when the ExoMars-16 Trace Gas Orbiter (TGO) is at periapsis. Display the results using TDB calendar dates and millisecond precision.

    3. Write a program that finds the times, within the time range

         2018 JUN 10 TDB
         2018 JUN 11 TDB
    when the ExoMars-16 Trace Gas Orbiter (TGO) is at apoapsis. Display the results using TDB calendar dates and millisecond precision.



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Solutions




   1. Inputs for the equator crossing search, using GFPOSC for
   the spacecraft latitude in the Mars body-fixed frame equal to 0:
 
         Target                       = TGO
         Observer                     = MARS
         Observer's reference frame   = IAU_MARS
         Elevation limit (degrees)    = 0.000000
         Aberration correction        = NONE
         Step size (seconds)          = 300.000000
         Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
         Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)
 
      TGO Mars' equator crossing times:
 
      Equator crossing time:            2018 JUN 10 00:14:08.836 (TDB)
      Equator crossing time:            2018 JUN 10 01:12:34.582 (TDB)
      Equator crossing time:            2018 JUN 10 02:12:00.375 (TDB)
      Equator crossing time:            2018 JUN 10 03:10:28.808 (TDB)
      Equator crossing time:            2018 JUN 10 04:09:53.955 (TDB)
      Equator crossing time:            2018 JUN 10 05:08:23.919 (TDB)
      Equator crossing time:            2018 JUN 10 06:07:48.630 (TDB)
      Equator crossing time:            2018 JUN 10 07:06:17.539 (TDB)
      Equator crossing time:            2018 JUN 10 08:05:42.659 (TDB)
      Equator crossing time:            2018 JUN 10 09:04:09.120 (TDB)
      Equator crossing time:            2018 JUN 10 10:03:34.270 (TDB)
      Equator crossing time:            2018 JUN 10 11:01:59.269 (TDB)
      Equator crossing time:            2018 JUN 10 12:01:22.866 (TDB)
      Equator crossing time:            2018 JUN 10 12:59:49.352 (TDB)
      Equator crossing time:            2018 JUN 10 13:59:13.289 (TDB)
      Equator crossing time:            2018 JUN 10 14:57:41.242 (TDB)
      Equator crossing time:            2018 JUN 10 15:57:07.576 (TDB)
      Equator crossing time:            2018 JUN 10 16:55:35.266 (TDB)
      Equator crossing time:            2018 JUN 10 17:55:02.773 (TDB)
      Equator crossing time:            2018 JUN 10 18:53:30.271 (TDB)
      Equator crossing time:            2018 JUN 10 19:52:56.383 (TDB)
      Equator crossing time:            2018 JUN 10 20:51:23.966 (TDB)
      Equator crossing time:            2018 JUN 10 21:50:47.729 (TDB)
      Equator crossing time:            2018 JUN 10 22:49:14.385 (TDB)
      Equator crossing time:            2018 JUN 10 23:48:37.583 (TDB)
 
 
 
   2. Inputs for the periapsis search, using GFDIST for the
   spacecraft distance from Mars at a local minimum:
 
         Target                       = TGO
         Observer                     = MARS
         Observer's reference frame   = J2000
         Aberration correction        = NONE
         Step size (seconds)          = 300.000000
         Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
         Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)
 
      TGO periapsis times:
 
      Periapsis time:                   2018 JUN 10 00:43:06.357 (TDB)
      Periapsis time:                   2018 JUN 10 02:40:47.168 (TDB)
      Periapsis time:                   2018 JUN 10 04:38:45.496 (TDB)
      Periapsis time:                   2018 JUN 10 06:36:32.706 (TDB)
      Periapsis time:                   2018 JUN 10 08:34:10.548 (TDB)
      Periapsis time:                   2018 JUN 10 10:31:49.108 (TDB)
      Periapsis time:                   2018 JUN 10 12:29:20.342 (TDB)
      Periapsis time:                   2018 JUN 10 14:27:07.089 (TDB)
      Periapsis time:                   2018 JUN 10 16:25:36.081 (TDB)
      Periapsis time:                   2018 JUN 10 18:24:02.653 (TDB)
      Periapsis time:                   2018 JUN 10 20:22:23.184 (TDB)
      Periapsis time:                   2018 JUN 10 22:20:12.453 (TDB)
 
 
   3. Inputs for the apoapsis search, using GFDIST for the
   spacecraft distance from Mars at a local maximum:
 
         Target                       = TGO
         Observer                     = MARS
         Observer's reference frame   = J2000
         Aberration correction        = NONE
         Step size (seconds)          = 300.000000
         Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
         Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)
 
      TGO apoapsis times:
 
      Apoapsis time:                    2018 JUN 10 01:41:44.632 (TDB)
      Apoapsis time:                    2018 JUN 10 03:39:31.106 (TDB)
      Apoapsis time:                    2018 JUN 10 05:37:22.115 (TDB)
      Apoapsis time:                    2018 JUN 10 07:34:59.674 (TDB)
      Apoapsis time:                    2018 JUN 10 09:32:25.708 (TDB)
      Apoapsis time:                    2018 JUN 10 11:29:47.945 (TDB)
      Apoapsis time:                    2018 JUN 10 13:27:30.200 (TDB)
      Apoapsis time:                    2018 JUN 10 15:26:02.524 (TDB)
      Apoapsis time:                    2018 JUN 10 17:24:37.842 (TDB)
      Apoapsis time:                    2018 JUN 10 19:23:11.265 (TDB)
      Apoapsis time:                    2018 JUN 10 21:21:13.530 (TDB)
      Apoapsis time:                    2018 JUN 10 23:18:56.796 (TDB)