 
Preface - Other Stuff (The Red Shirt topics) (FORTRAN)
===========================================================================
 
     March 28, 2005
 
     The extensive scope of the SPICE system's functionality includes
     features the average user may not expect or appreciate, features NAIF
     refers to as "Other Stuff." This workbook includes a set of lessons to
     introduce the beginning to moderate user to a several such features.
 
     The lessons provide a brief description to several related sets of
     routines, associated reference documents, a programming task designed
     to teach the use of the routines, and an example solution to the
     programming problem.
 
 
Coding and Use Lessons
===========================================================================
 
     This workbook includes several lessons to demonstrate use of the less
     celebrated SPICE routines.
 
         1.   Kernel Management with the Kernel Subsystem
 
         2.   The Kernel Pool
 
         3.   Coordinate Conversions
 
         4.   Advanced Time Manipulation Routines
 
         5.   Error Handling
 
         6.   Windows, Sets, and Cells
 
         7.   Utility and Constants Routines
 
 
NAIF Documentation
--------------------------------------------------------
 
     The technical complexity of the various SPICE subsystems mandates an
     extensive, user-friendly documentation set. The set differs somewhat
     depending on your choice of development language, FORTRAN, C, or IDL,
     but provides the same information with regards to SPICE operation.
 
     The sources for a user needing information concerning the SPICE System
     or other NAIF product:
 
         --   Required Readings and Users Guides
 
         --   Source Code Documentation
 
         --   API Documentation
 
         --   Tutorials
 
 
Required Reading and Users Guides
 
     NAIF Required Reading (*.req) documents introduce the functionality of
     particular SPICE subsystems:
 
 
           cells.req       ek.req          intrdctn.req    problems.req
           ck.req          ellipses.req    kernel.req      rotation.req
           cspice.req      error.req       naif_ids.req    scanning.req
           daf.req         frames.req      pck.req         sclk.req
           das.req         icy.req         planes.req      sets.req
 
           spc.req
           spk.req
           symbols.req
           time.req
           windows.req
 
 
     NAIF Users Guides (*.ug) describe the proper use of particular SPICE
     tools:
 
 
           brief.ug        convert.ug      spacit.ug       tictoc.ug
           chronos.ug      inspekt.ug      spkmerge.ug     tobin.ug
           ckbrief.ug      mkspk.ug        states.ug       toxfr.ug
           commnt.ug       simple.ug       subpt.ug        version.ug
 
 
     These text documents exist in the 'doc' directory of the main Toolkit
     directory:
 
           ../toolkit/doc/
 
     HTML format documentation
 
     As of delivery N57, the SPICE distributions include HTML versions of
     Required Readings and Users Guides, accessible from the HTML
     documentation directory:
 
           ../toolkit/doc/html/index.html
 
 
Source Code
 
     All SPICELIB and CSPICE source files include usage and design
     information incorporated in a comment block known as the "header."
 
     A header consists of several marked sections:
 
         --   Procedure: Routine name and one line expansion of the
              routine's name.
 
         --   Abstract: A tersely worded explanation describing the
              routine.
 
         --   Copyright: An identification of the copyright holder for the
              routine.
 
         --   Required_Reading: A list of SPICE required reading documents
              relating to the routine.
 
         --   Brief_I/O: A table of arguments, identifying each as either
              input, output, or both, with a very brief description of the
              variable.
 
         --   Detailed_Input & Detailed_Output: An elaboration of the
              Brief_I/O section providing comprehensive information on
              argument use.
 
         --   Parameters: Description and declaration of any parameters
              (constants) specific to the routine.
 
         --   Exceptions: A list of error conditions the routine detects
              and signals plus a discussion of any other exceptional
              conditions the routine may encounter.
 
         --   Files: A list of other files needed for the routine to
              operate.
 
         --   Particulars: A discussion of the routine's function (if
              needed). This section may also include information relating
              to "how" and "why" the routine performs an operation and to
              explain functionality of routines that operate by side
              effects.
 
         --   Examples: Descriptions and code snippets concerning usage of
              the routine.
 
         --   Restrictions: Restrictions or warnings concerning use.
 
         --   Literature_References: A list of sources required to
              understand the algorithms or data used in the routine.
 
         --   Author_and_Institution: The names and affiliations for
              authors of the routine.
 
         --   Version: A list of edits and the authors of those edits made
              to the routine since initial delivery to the SPICE system.
 
     The source code for SPICE products is stored in 'src' sub-directory of
     the main SPICE directory:
 
           ../toolkit/src/
 
     Find the SPICELIB library source code in:
 
           ../toolkit/src/spicelib/
 
 
API Documentation
 
     The source file headers contain all API documentation for the SPICELIB
     package.
 
 
Tutorials
 
     A set of Microsoft PowerPoint presentations provide a general overview
     of the complete SPICE toolkit. Download the set at:
 
           http://naif.jpl.nasa.gov/naif/tutorials.html
 
     Access individual files in the 'office/individual_docs/' directory; an
     archive of all tutorial files is available in the 'office/packages/'
     directory.
 
 
Text kernels
--------------------------------------------------------
 
     Several workbooks use SPICE text kernels. SPICE identifies a text
     kernel as an ASCII text file containing the mark-up tags the kernel
     subsystem requires to identify data assignments in that file, and
     "name=value" data assignments.
 
     The subsystem uses two tags:
 
        \begintext
 
     and
 
        \begindata
 
     to mark information blocks within the text kernel. The \begintext tag
     specifies all text following the tag as comment information to be
     ignored by the subsystem.
 
     Things to know:
 
         1.   The \begindata tag marks the start of a data definition
              block. The subsystem processes all text following this marker
              as SPICE kernel data assignments until finding a \begintext
              marker.
 
         2.   The kernel subsystem defaults to the \begintext mode until
              the parser encounters a \begindata tag. Once in \begindata
              mode the subsystem processes all text as variable assignments
              until the next \begintext tag.
 
         3.   Enter the tags as the only text on a line, i.e.:
 
 
           \begintext
 
              ... commentary information on the data assignments ...
 
           \begindata
 
              ... data assignments ...
 
 
         4.   A text kernel containing non-native line terminators causes a
              no-op when read by the kernel subsystem, i.e. the state of
              the kernel pool does not change. To reduce the aggravations
              cause by this situation, as of N57 the FURNSH call includes a
              line terminator check, signaling an error on non-native text
              files.
 
 
Text kernel format
 
     Scalar assignments.
 
           VAR_NAME_DP  = 1.234
           VAR_NAME_INT = 1234
           VAR_NAME_STR = 'FORBIN'
 
     Please note the use of a single quote in string assignments.
 
     Vector assignments. Vectors must contain the same type data.
 
           VEC_NAME_DP  = ( 1.234   , 45.678  , 901234.5 )
           VEC_NAME_INT = ( 1234    , 456     , 789      )
           VEC_NAME_STR = ( 'FORBIN', 'FALKEN', 'ROBUR'  )
 
           also
 
           VEC_NAME_DP  = ( 1.234,
                           45.678,
                           901234.5 )
 
           VEC_NAME_STR = ( 'FORBIN',
                            'FALKEN',
                            'ROBUR' )
 
     Time assignments.
 
           TIME_VAL = @31-JAN-2003-12:34:56.798
           TIME_VEC = ( @01-DEC-2004, @15-MAR-2004 )
 
     The at-sign character '@' indicates a time string. The pool subsystem
     converts the strings to double precision TDB (a numeric value). Please
     note, the time strings must not contain embedded blanks. WARNING - a
     TDB string is not the same as a UTC string.
 
     The above examples depict direct assignments via the '=' operator. The
     kernel pool also permits incremental assignments via the '+='
     operator.
 
     Please refer to the kernels required reading, kernel.req, for
     additional information.
 
 
Kernels for lessons
--------------------------------------------------------
 
 
Input kernel files
 
     The lessons may include kernels a program must load to operate. For
     this workbook, a user can download all kernels from the NAIF anonymous
     ftp site:
 
           ftp://naif.jpl.nasa.gov/pub/naif/generic_kernels
 
           FILE NAME                TYPE  DESCRIPTION
           -----------------------  ----  ----------------------
           naif0007.tls             LSK   Generic LSK
           leapseconds.tls          LSK   The current leapseconds
                                          kernel (naif0007.tls as
                                          of May 2004)
           de405s.bsp               SPK   Planet Ephemeris SPK
           pck00007.tpc             PCK   Generic PCK
 
 
Output
 
     The code examples listed in this workbook include corresponding
     outputs for the described inputs. The output of a given example on a
     particular platform may not exactly match that shown since compilers
     and math libraries differ between platform architectures.
 
 
Lesson 1: Kernel Management with the Kernel Subsystem
===========================================================================
 
     Lesson Goals:
 
     This lesson demonstrates us of the kernel subsystem to load, unload,
     and list loaded kernels. Comprehension of kernel file data access
     precedence. Data loaded last (later) has precedence over similar data
     loaded first (earlier).
 
     This lesson requires creation of a SPICE meta kernel.
 
 
Relevant Routines
--------------------------------------------------------
 
         --   FURNSH loads the meta kernel and the SPICE kernels listed
              within that kernel.
 
         --   KTOTAL retrieves the number of SPICE kernels loaded by the
              kernel subsystem.
 
         --   KDATA returns information about each loaded kernel.
 
         --   UNLOAD removes a kernel from the kernel subsystem.
 
 
Requirements and References
--------------------------------------------------------
 
     Knowledge of information in the kernels.req document, the mk.ppt and
     intro_to_kernels.ppt tutorial files.
 
 
Programming Task
--------------------------------------------------------
 
     Write a program to load a meta kernel, interrogate the SPICE system
     for the names and types of all loaded kernels, then demonstrate the
     unload functionality and the resulting effects.
 
 
Code Solution
--------------------------------------------------------
 
 
First, create a meta text kernel:
 
     You can use two versions of a meta kernel with code examples
     (meta.ker) in this lesson. Either a kernel with explicit path
     information:
 
 
        \begindata
 
           KERNELS_TO_LOAD = ( 'kernels/spk/de405s.bsp',
                               'kernels/pck/pck00007.tpc',
                               'kernels/lsk/leapseconds.tls')
 
        \begintext
 
 
     ... or a more generic meta kernel using the PATH_VALUES/PATH_SYMBOLS
     functionality to declare path names as variables:
 
 
        \begintext
 
        Define the paths to the kernel directory. Use the PATH_SYMBOLS
        as aliases to the paths.
 
        \begindata
 
           PATH_VALUES     = ( 'kernels/lsk',
                               'kernels/spk',
                               'kernels/pck' )
 
           PATH_SYMBOLS    = ( 'LSK', 'SPK', 'PCK' )
 
           KERNELS_TO_LOAD = ( '$LSK/naif0007.tls',
                               '$SPK/de405s.bsp',
                               '$PCK/pck00007.tpc' )
 
        \begintext
 
 
 
Now the solution source code:
 
 
              PROGRAM KERNEL
              IMPLICIT NONE
 
        C
        C     Declare the needed variables:
        C
              CHARACTER*(32) META
              CHARACTER*(32) FILE
              CHARACTER*(32) TYPE
              CHARACTER*(32) SOURCE
 
              INTEGER        COUNT
              INTEGER        I
              INTEGER        HANDLE
 
              LOGICAL        FOUND
 
        C
        C     Assign the path name of the meta kernel to META.
        C
              META = 'meta.ker'
 
        C
        C     Load the meta kernel then use KTOTAL to interrogate the
        C     SPICE kernel subsystem for the total number of loaded kernel
        C     files. KTOTAL accepts as input values:
        C
        C                   SPK  --- all SPK files are counted in the total
        C                   CK   --- all CK files are counted in the total.
        C                   PCK  --- all binary PCK files are counted in
        C                            the total.
        C                   EK   --- all EK files are counted in the total.
        C                   TEXT --- all text kernels that are not
        C                            meta-text kernels are included in the
        C                            total.
        C                   META --- all meta-text kernels are counted in
        C                            the total.
        C                   ALL  --- every type of kernel is counted in the
        C                            total.
        C
        C     We want the count of all kernels, so use 'ALL'.
        C
              CALL FURNSH ( META )
              CALL KTOTAL ( 'ALL', COUNT )
 
              WRITE(*,*) 'Kernel count after load: ', COUNT
 
        C
        C     Loop over the number of files; interrogate the SPICE system
        C     with KDATA for the kernel names, kernel source,
        C     and the type. 'FOUND' returns a boolean indicating whether
        C     any kernel files of the specified type were loaded by
        C     the kernel subsystem. This example ignores checking 'FOUND'
        C     as kernels are known to be loaded.
        C
              DO I=1, COUNT
 
                 CALL KDATA ( I, 'ALL', FILE, TYPE, SOURCE, HANDLE,
             .                FOUND )
 
                 WRITE(*,*) 'File   ', FILE
                 WRITE(*,*) 'Type   ', TYPE
                 WRITE(*,*) 'Source ', SOURCE
                 WRITE(*,*) ' '
 
              END DO
 
        C
        C     Unload one kernel then check the count.
        C
              CALL UNLOAD ( 'kernels/spk/de405s.bsp' )
              CALL KTOTAL ( 'ALL', COUNT )
 
        C
        C     The subsystem should report one less kernel.
        C
              WRITE(*,*) 'Kernel count after one unload: ', COUNT
 
        C
        C     Now unload the meta kernel. This action unloads all
        C     files listed in the meta kernel.
        C
              CALL UNLOAD ( META )
 
        C
        C     Check the count. SPICE should return a count of zero.
        C
              CALL KTOTAL ( 'ALL', COUNT )
              WRITE(*,*) 'Kernel count after meta unload: ', COUNT
 
              END
 
 
 
Run the code example
 
     First we see the number of all loaded kernels returned from the KTOTAL
     call:
 
 
         Kernel count after load:   4
 
 
     Now the KDATA loop returns the name of each loaded kernel, the type of
     kernel (SPK, CK, TEXT, etc.) and the source of the kernel - the
     mechanism that loaded the kernel. The source either identifies a meta
     kernel, or contains an empty string. An empty source string indicates
     a direct load of the kernel with a FURNSH call.
 
 
        File   meta.ker
        Type   META
        Source
 
        File   kernels/spk/de405s.bsp
        Type   SPK
        Source meta.ker
 
        File   kernels/pck/pck00007.tpc
        Type   TEXT
        Source meta.ker
 
        File   kernels/lsk/naif0007.tls
        Type   TEXT
        Source meta.ker
 
        Kernel count after one unload:   3
        Kernel count after meta unload:   0
 
 
 
Lesson 2: The Kernel Pool
===========================================================================
 
     Lesson Goals:
 
     The lesson demonstrates the SPICE system's facility to retrieve
     different types of data (string, numeric, scalar, array) from the
     kernel pool.
 
     For the code examples, use this generic text kernel (cassini.ker)
     containing PCK-type data, kernels to load, and example time strings:
 
        \begintext
 
        Ring model data.
 
        \begindata
 
           BODY699_RING1_NAME     = 'A Ring'
           BODY699_RING1          = (122170.0 136780.0 0.1 0.1 0.5)
 
           BODY699_RING1_1_NAME   = 'Encke Gap'
           BODY699_RING1_1        = (133405.0 133730.0 0.0 0.0 0.0)
 
           BODY699_RING2_NAME     = 'Cassini Division'
           BODY699_RING2          = (117580.0 122170.0 0.0 0.0 0.0)
 
        \begintext
 
        The kernel pool recognizes values preceded by '@' as time
        values. When read, the kernel subsystem converts these
        representations into double precision ephemeris time.
 
        Caution: The kernel subsystem interprets the time strings
        identified by '@' as TDB. The same string passed as input
        to @STR2ET is processed as UTC.
 
        The three expressions stored in the EXAMPLE_TIMES array represent
        the same epoch.
 
        \begindata
 
           EXAMPLE_TIMES       = ( @APRIL-1-2004-12:34:56.789,
                                   @4/1/2004-12:34:56.789,
                                   @JD2453097.0242684
                                  )
 
        \begintext
 
        Name the kernels to load. Use path symbols.
 
        \begindata
 
           PATH_VALUES     = ('kernels/spk',
                              'kernels/pck',
                              'kernels/lsk')
 
           PATH_SYMBOLS    = ('SPK' , 'PCK' , 'LSK' )
 
           KERNELS_TO_LOAD = ( '$SPK/de405s.bsp',
                               '$PCK/pck00007.tpc',
                               '$LSK/leapseconds.tls')
 
        \begintext
 
 
Relevant Routines
--------------------------------------------------------
 
         --   GIPOOL retrieves integer values from the kernel subsystem.
 
         --   GDPOOL retrieves double precision values from the kernel
              subsystem
 
         --   GCPOOL retrieves character values from the kernel subsystem
 
         --   DTPOOL returns data (name, type, size) describing a kernel
              pool variable.
 
         --   GNPOOL retrieves the names of kernel pool variables matching
              a given template.
 
 
Requirements and References
--------------------------------------------------------
 
     Knowledge of the material in the kernels.req document and the
     intro_to_kernels.ppt tutorial file.
 
     The main references for pool routines are found in the source file
     pool.f. Most pool routines exist in pool.f as entry points.
 
 
Programming Task
--------------------------------------------------------
 
     Write a program to retrieve particular string and numeric text kernel
     variables, both scalars and arrays. Interrogate the kernel pool for
     assigned variable names.
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM KERVAR
              IMPLICIT NONE
 
        C
        C     Note, the pool routines return a boolean to 'FOUND'
        C     signaling whether the requested variable name exists
        C     in the kernel pool. The code solutions do not check the
        C     boolean value since the solutions use variables known to
        C     exist. In general, code should always check the boolean
        C     value to ensure return of valid data.
        C
 
        C
        C     Define the max number of kernel variables
        C     of concern for this examples.
        C
              INTEGER                     N_ITEMS
              PARAMETER                  (N_ITEMS = 20 )
 
        C
        C     Define the maximum length for any string.
        C
              INTEGER                     STRLEN
              PARAMETER                  (STRLEN = 80 )
 
        C
        C     As usual, type our variables...
        C
              INTEGER                     I
              INTEGER                     J
              INTEGER                     DIM
              INTEGER                     N_VAR
              INTEGER                     N_VAL
              INTEGER                     START
 
              LOGICAL                     FOUND
 
              DOUBLE PRECISION            DVARS    (N_ITEMS)
 
              CHARACTER* (STRLEN)         CVALS    (N_ITEMS)
              CHARACTER* (STRLEN)         CVARS    (N_ITEMS)
              CHARACTER* (12)             TYPE
              CHARACTER* (12)             TMPLATE
 
        C
        C     ...and two SPICELIB routines we use.
        C
              INTEGER                     LASTNB
              LOGICAL                     EQSTR
 
        C
        C     Load the example kernel containing the kernel variables.
        C     The kernels defined in KERNELS_TO_LOAD load into the
        C     kernel pool with this call.
        C
              CALL FURNSH ('cassini.ker' )
 
        C
        C     Initialize the START value. This values indicates
        C     index of the first element to return if a kernel
        C     variable is an array. START = 1 mean return everything.
        C     START = 2 mean return everything but the first element.
        C
              START = 1
 
        C
        C     Set the template for the variable names to find. Let's
        C     look for all variables containing  the string RING.
        C     Define this with the wildcard template '*RING*'. Note:
        C     the template '*RING' would match any variable name
        C     ending with the RING string.
        C
              TMPLATE =  '*RING*'
 
        C
        C     We're ready to interrogate the kernel pool for
        C     the variables matching the template. GNPOOL tells us:
        C
        C        1. Does the kernel pool contain any variables that
        C           match the template (value of FOUND).
        C        2. If so, how many variables? (value of N_VAL)
        C        3. The variable names. (CVALS, an array of strings)
        C
              CALL GNPOOL ( TMPLATE, START, STRLEN, N_VAL, CVALS, FOUND )
 
              IF ( FOUND ) THEN
                 WRITE(*,*) 'No. variables matching template: ', N_VAL
                 WRITE(*,*)
              ELSE
                  WRITE(*,*) 'No kernel variables matched template'
                  STOP
              ENDIF
 
        C
        C     Okay, now we know something about the kernel pool
        C     variables of interest to us. Let's find out more...
        C
              DO I=1, N_VAL
 
        C
        C        Use DTPOOL to return the dimension and TYPE,
        C        C (character) or N (numeric), of each pool
        C        variable name in the CVALS array.
        C
        C        The SPICE function LASTNB returns the index of
        C        the last non-blank character in the CVALS string.
        C        This is convenient to trim the trailing whitespace
        C        of a string.
        C
                 CALL DTPOOL ( CVALS(I), FOUND, DIM, TYPE )
                 WRITE(*,*) CVALS(I)(1:LASTNB(CVALS(I)) )
                 WRITE(*,*) ' No. items: ', DIM, '   Of type: ', TYPE
 
        C
        C        Use the EQSTR routine to test character equality,
        C        'N' (numeric) or 'C' (character).
        C
                 IF ( EQSTR( 'N', TYPE ) ) THEN
 
        C
        C           If TYPE equals 'N', we found a numeric array.
        C           In this case any numeric array will be an array
        C           of double precision numbers ("doubles"). GDPOOL
        C           retrieves doubles from the kernel pool. DVARS
        C           contains the array of N_VAR values.
        C
                    CALL GDPOOL ( CVALS(I), START, N_ITEMS,
             .                                     N_VAR  , DVARS, FOUND )
                    DO J=1 ,N_VAR
                       WRITE(*,*) '  Numeric value: ', DVARS(J)
                    END DO
 
                 ELSE IF ( EQSTR( 'C', TYPE ) ) THEN
 
        C
        C           If TYPE equals 'C', we found a string array.
        C           GCPOOL retrieves string values from the
        C           kernel pool. CVARS contains the array of N_VAR
        C           values.
        C
                    CALL GCPOOL ( CVALS(I), START, N_ITEMS,
             .                                     N_VAR, CVARS, FOUND )
                    DO J=1 ,N_VAR
                       WRITE(*,*) '  String value: ',
             .                    CVARS(J)(1:LASTNB(CVARS(J)) )
                    END DO
 
                 END IF
 
                 WRITE(*,*)
 
              END DO
 
        C
        C     Now look at the time variable EXAMPLE_TIMES. Extract this
        C     value as an array of doubles.
        C
              CALL GDPOOL ( 'EXAMPLE_TIMES', START, N_ITEMS,
             .                               N_VAR  , DVARS, FOUND )
 
              WRITE(*,*) 'EXAMPLE_TIMES'
 
              DO J=1 ,N_VAR
                 WRITE(*,*) '  Time value (ET): ', DVARS(J)
              END DO
 
              END
 
 
 
Run the code example
 
     The program runs and first reports the number of kernel pool variables
     matching the template, 6.
 
 
        No. variables matching template:   6
 
 
     The program then loops over the DTPOOL 6 times, reporting the name of
     each pool variable, the number of data items assigned to that
     variable, and the variable type. Within the DTPOOL loop, a second loop
     outputs the contents of the data variable using GCPOOL or GDPOOL.
 
 
         BODY699_RING1
          No. items:   5   Of type: N
           Numeric value:     122170.00000000
           Numeric value:     136780.00000000
           Numeric value:     1.0000000000000D-01
           Numeric value:     1.0000000000000D-01
           Numeric value:    0.50000000000000
 
         BODY699_RING2
          No. items:   5   Of type: N
           Numeric value:     117580.00000000
           Numeric value:     122170.00000000
           Numeric value:   0.
           Numeric value:   0.
           Numeric value:   0.
 
         BODY699_RING1_1_NAME
          No. items:   1   Of type: C
           String value: Encke Gap
 
         BODY699_RING2_NAME
          No. items:   1   Of type: C
           String value: Cassini Division
 
         BODY699_RING1_NAME
          No. items:   1   Of type: C
           String value: A Ring
 
         BODY699_RING1_1
          No. items:   5   Of type: N
           Numeric value:     133405.00000000
           Numeric value:     133730.00000000
           Numeric value:   0.
           Numeric value:   0.
           Numeric value:   0.
 
 
     Note the final time value differs from the previous values in the
     final two decimal places despite the intention that all three strings
     represent the same time. This results from round-off when converting a
     decimal Julian day representation to the seconds past J2000 ET
     representation.
 
 
        EXAMPLE_TIMES
          Time value:          134094896.78900
          Time value:          134094896.78900
          Time value:          134094896.78975
 
 
 
Lesson 3: Coordinate Conversions
===========================================================================
 
     Lesson Goals:
 
     The SPICE system provides functions to convert coordinate tuples
     between Cartesian and various non Cartesian coordinate systems
     including conversion between geodetic and rectangular coordinates.
 
     This lesson presents these coordinate transform routines for
     rectangular, cylindrical, and spherical systems.
 
 
Relevant Routines
--------------------------------------------------------
 
         --   LATREC, latitudinal to rectangular
 
         --   LATCYL, latitudinal to cylindrical
 
         --   LATSPH, latitudinal to spherical
 
         --   RECCYL, rectangular to cylindrical
 
         --   RECGEO, rectangular to geodetic
 
         --   RECLAT, rectangular to latitudinal
 
         --   RECSPH, rectangular to spherical
 
         --   RECRAD, rectangular to right ascension - declination
 
         --   SPHREC, spherical to rectangular
 
         --   SPHCYL, spherical to cylindrical
 
         --   SPHLAT, spherical to latitudinal
 
         --   CYLLAT, cylindrical to latitudinal
 
         --   CYLSPH, cylindrical to spherical
 
         --   CYLREC, cylindrical to rectangular
 
         --   GEOREC, geodetic to rectangular
 
 
Requirements and References
--------------------------------------------------------
 
     Basic knowledge of the standard coordinate systems used in celestial
     mechanics. The contents of concepts.ppt and derived_quant.ppt tutorial
     files.
 
 
Programming Task
--------------------------------------------------------
 
     Write a program to convert a Cartesian 3-vector representing some
     location to the other coordinate representations. Use the position of
     the Moon with respect to Earth in an inertial and non-inertial
     reference frame as the example vector.
 
 
Code Solution
--------------------------------------------------------
 
              PROGRAM COORD
              IMPLICIT NONE
 
        C
        C     Type the variables.
        C
              INTEGER              DIM
 
              CHARACTER*(32)       INRFRM
              CHARACTER*(32)       NONFRM
              CHARACTER*(32)       TIMSTR
 
              DOUBLE PRECISION     ET
              DOUBLE PRECISION     RANGE
              DOUBLE PRECISION     RA
              DOUBLE PRECISION     DEC
              DOUBLE PRECISION     LAT
              DOUBLE PRECISION     COLAT
              DOUBLE PRECISION     LON
              DOUBLE PRECISION     LTIME
              DOUBLE PRECISION     FLAT
              DOUBLE PRECISION     RAD   (3)
              DOUBLE PRECISION     POS   (3)
 
        C
        C    Declare the SPICELIB function to scale radians to degrees.
        C
              DOUBLE PRECISION     DPR
 
              INRFRM = 'J2000'
              NONFRM = 'IAU_EARTH'
 
        C
        C     Load the needed kernels using a FURNSH call on a
        C     meta kernel.
        C
              CALL FURNSH ( 'meta.ker' )
 
        C
        C     Prompt the user for a time string. Convert the
        C     time string to ephemeris time J2000 (ET).
        C
              CALL PROMPT ( 'Time of interest: ', TIMSTR )
              CALL STR2ET ( TIMSTR, ET )
 
        C
        C     Access the kernel pool data for the triaxial radii of the
        C     Earth. RAD(1) holds the equatorial radius, RAD(2)
        C     the polar radius.
        C
              CALL BODVRD ( 'EARTH', 'RADII', 3, DIM, RAD)
 
        C
        C     Calculate the flattening factor for the Earth.
        C
        C              equatorial_radius - polar_radius
        C     flat =   ________________________________
        C
        C                    equatorial_radius
        C
              FLAT = (RAD(1) - RAD(3))/RAD(1)
 
        C
        C     Make the SPKPOS call to determine the apparent position
        C     of the Moon w.r.t. to the Earth at ET in the inertial frame.
        C
              CALL SPKPOS ( 'MOON', ET, INRFRM, 'LT+S','EARTH',
             .               POS  , LTIME)
 
        C
        C     Show the current frame and time.
        C
              WRITE(*,*) 'Time : ', TIMSTR
              WRITE(*,*) ' Inertial Frame: ', INRFRM
 
 
        C
        C     First, convert the position vector
        C     X = POS(1), Y = POS(2), Z = POS(3), to RA/DEC.
        C
              CALL RECRAD ( POS, RANGE, RA, DEC )
              WRITE(*,*) '  Range/Ra/Dec'
              WRITE(*,*) '   Range: ', RANGE
              WRITE(*,*) '   RA   : ', RA * DPR()
              WRITE(*,*) '   DEC  : ', DEC* DPR()
 
        C
        C     ...latitudinal coordinates...
        C
              CALL RECLAT ( POS, RANGE, LON, LAT )
              WRITE(*,*) '  Latitudinal'
              WRITE(*,*) '   Rad  : ', RANGE
              WRITE(*,*) '   Lon  : ', LON * DPR()
              WRITE(*,*) '   Lat  : ', LAT * DPR()
 
        C
        C     ...spherical coordinates use the colatitude,
        C     the angle from the Z axis.
        C
              CALL RECSPH ( POS, RANGE, COLAT, LON )
              WRITE(*,*) '  Spherical'
              WRITE(*,*) '   Rad  : ', RANGE
              WRITE(*,*) '   Lon  : ', LON   * DPR()
              WRITE(*,*) '   Colat: ', COLAT * DPR()
 
        C
        C     Make the SPKPOS call to determine the apparent position
        C     of the Moon w.r.t. to the Earth at ET in the non-inertial,
        C     body fixed, frame.
        C
              CALL SPKPOS ( 'MOON', ET, NONFRM, 'LT+S','EARTH',
             .               POS, LTIME)
 
              WRITE(*,*)
              WRITE(*,*) ' Non-inertial Frame: ', NONFRM
 
        C
        C     ...latitudinal coordinates...
        C
              CALL RECLAT ( POS, RANGE, LON, LAT )
              WRITE(*,*) '  Latitudinal'
              WRITE(*,*) '   Rad  : ', RANGE
              WRITE(*,*) '   Lon  : ', LON * DPR()
              WRITE(*,*) '   Lat  : ', LAT * DPR()
 
        C
        C     ...spherical coordinates...
        C
              CALL RECSPH ( POS, RANGE, COLAT, LON )
              WRITE(*,*) '  Spherical'
              WRITE(*,*) '   Rad  : ', RANGE
              WRITE(*,*) '   Lon  : ', LON   * DPR()
              WRITE(*,*) '   Colat: ', COLAT * DPR()
 
        C
        C     ...finally, convert the position to geodetic
        C     coordinates.
        C
              CALL RECGEO ( POS, RAD(1), FLAT, LON, LAT, RANGE )
              WRITE(*,*) '  Geodetic'
              WRITE(*,*) '   Rad  : ', RANGE
              WRITE(*,*) '   Lon  : ', LON * DPR()
              WRITE(*,*) '   Lat  : ', LAT * DPR()
 
              WRITE(*,*)
 
              END
 
 
 
Run the code example
 
     Input a time/date at which to calculate the Moon's position. (the
     'TDB' tag indicates a Barycentric Dynamical Time value).
 
 
        Time of interest: Feb 3 2002 TDB
 
 
     Examine the Moon position in the J2000 inertial frame, display the
     time and frame:
 
 
         Time : Feb 3 2002 TDB
          Inertial Frame: J2000
 
 
     Convert the Moon Cartesian coordinates to right ascension declination.
 
 
           Range/Ra/Dec
            Range:   369340.815
            RA   :   203.643686
            DEC  :  -4.97901037
 
 
     Latitudinal. Note the difference in the expressions for longitude and
     right ascension though they represent a measure of the same quantity.
     The RA/DEC system measures RA in the interval [0,2Pi). Latitudinal
     coordinates measures longitude in the interval (-Pi,Pi].
 
 
           Latitudinal
            Rad  :   369340.815
            Lon  :  -156.356314
            Lat  :  -4.97901037
 
 
     Spherical. Note the difference between the expression of latitude in
     the Latitudinal system and the corresponding Spherical colatitude. The
     spherical coordinate system uses the colatitude, the angle measure
     away from the positive Z axis. Latitude is the angle between the
     position vector and the x-y (equatorial) plane with positive angle
     defined as toward the positive Z direction
 
 
           Spherical
            Rad  :   369340.815
            Lon  :  -156.356314
            Colat:   94.9790104
 
 
     The same position look-up in a body fixed (non-inertial) frame,
     IAU_EARTH.
 
          Non-inertial Frame: IAU_EARTH
 
     Latitudinal coordinates return the geocentric latitude.
 
 
        Latitudinal
            Rad  :   369340.815
            Lon  :   70.97395
            Lat  :  -4.98967514
 
 
     Spherical.
 
 
           Spherical
            Rad  :   369340.815
            Lon  :   70.97395
            Colat:   94.9896751
 
 
     Geodetic. The cartographic lat/lon.
 
 
           Geodetic
            Rad  :   362962.837
            Lon  :   70.97395
            Lat  :  -4.99024929
 
 
 
Lesson 4: Advanced Time Manipulation Routines
===========================================================================
 
     Lesson Goals:
 
     Introduce the routines used for advanced manipulation of time strings.
     Understand the concept of ephemeris time (ET) as used in SPICE.
 
 
Relevant Routines
--------------------------------------------------------
 
         --   STR2ET converts time strings to ephemeris time (ET).
 
         --   TIMOUT formats a time string output.
 
         --   TPICTR creates a format template for use in TIMOUT.
 
         --   TSETYR sets the reference century/year for two digit
              representation of the year.
 
 
Requirements and References
--------------------------------------------------------
 
     Knowledge of the time.req document, the time.ppt, lsk_and_sclk.ppt,
     and other_functions.ppt tutorial files.
 
     Also, examine the header of TIMOUT for a list of the string markers
     used by TIMOUT and TPICTR to describe time string format. Always keep
     in mind STR2ET assumes 'UTC' unless indicated otherwise.
 
 
Programming Task
--------------------------------------------------------
 
     Demonstrate the advanced functions of the time utilities with regard
     to formatting of time strings for output. Formatting options include
     altering calendar representations of the time strings. Convert
     time-date strings between different SPICE-supported formats.
 
 
Code Solution
--------------------------------------------------------
 
     Caution: Be sure to assign sufficient string lengths for time
     formats/pictures.
 
 
              PROGRAM TIC
              IMPLICIT NONE
 
        C
        C     Declare the needed variables:
        C
              CHARACTER*(64)      ERROR
              CHARACTER*(50)      PICTR1
              CHARACTER*(50)      PICTR2
              CHARACTER*(50)      PICTR3
              CHARACTER*(50)      TIMSTR
              CHARACTER*(32)      LSK
 
              DOUBLE PRECISION    ET
              DOUBLE PRECISION    ET1
              DOUBLE PRECISION    ET2
              DOUBLE PRECISION    JYEAR
 
              LOGICAL             OK
 
        C
        C     Assign the LSK variable to the name of the leapsecond,
        C     kernel and create an arbitrary time string.
        C
              LSK    = 'kernels/lsk/leapseconds.tls'
              TIMSTR = 'Mar 15, 2003 12:34:56.789 AM PST'
 
        C
        C     Load the leapseconds kernel.
        C
              CALL FURNSH ( LSK )
 
              WRITE(*,*) 'Original time string       : ', TIMSTR
 
        C
        C     Convert the time string to the number of ephemeris
        C     seconds past the J2000 epoch. This is the most common
        C     internal time representation used by the SPICE
        C     system; SPICE refers to this as ephemeris time (ET).
        C
              CALL STR2ET ( TIMSTR, ET )
              WRITE(*,*) 'Corresponding ET           : ', ET
 
        C
        C     Make a picture of an output format. Describe a Unix-like
        C     time string then send the picture and the ET value through
        C     TIMOUT to format and convert the ET representation of
        C     the time string into the form described by PICTR1. The
        C     '::UTC-7' token indicates the time zone for the TIMSTR
        C     output - PDT. 'PDT' is part of the output, but not a time
        C     system token.
        C
              PICTR1 = 'Wkd Mon DD HR:MN:SC PDT YYYY ::UTC-7'
              CALL TIMOUT ( ET, PICTR1, TIMSTR )
              WRITE(*,*) 'Time in string format 1    : ', TIMSTR
 
        C
        C     Create another picture. This time combine a calendar,
        C     2 digit year, with a Julian Day format.
        C
              PICTR2 = 'Wkd Mon DD HR:MN ::UTC-7 YR (JULIAND.##### JDUTC)'
              CALL TIMOUT ( ET, PICTR2, TIMSTR )
              WRITE(*,*) 'Time in string format 2    : ', TIMSTR
 
        C
        C     Why create a picture by hand when SPICE can do it for you?
        C     Input a string to TPICTR with the format of interest.
        C     'OK' returns a boolean indicating whether an error
        C     occurred while parsing the picture string, if so,
        C     an error diagnostic message returns in 'ERROR'. In this
        C     example, no need exists to check the error flag since
        C     the picture string is known as correct.
        C
              CALL TPICTR ( '12:34:56.789 P.M. PDT January 1, 2006',
             .              PICTR3, OK, ERROR )
 
              CALL TIMOUT ( ET, PICTR3, TIMSTR )
              WRITE(*,*) 'Time in string format 3    : ', TIMSTR
 
        C
        C     Two digit year representations often cause problems due to
        C     the ambiguity of the century. The routine TSETYR gives the
        C     user the ability to set a default range for 2 digit year
        C     representation. SPICE uses 1969AD as the default start
        C     year so the numbers inclusive of 69 to 99 represent
        C     years 1969AD to 1999AD, the numbers inclusive of 00 to 68
        C     represent years 2000AD to 2068AD.
        C
        C     Define a time string with  a two-digit year. Since
        C     the SPICE base year is 1969, the time subsystem interprets
        C     the string as 1979.
        C
              TIMSTR = 'Mar 15, 79 12:34:56'
              CALL STR2ET ( TIMSTR, ET1 )
 
        C
        C     Setting 1980 as the base year causes SPICE to interpret the
        C     year values 80 to 99 as 1980AD to 1999AD; the year values
        C     00 to 79 as 2000AD to 2079AD.
        C
              CALL TSETYR ( 1980 )
              CALL STR2ET ( TIMSTR, ET2 )
 
        C
        C     Calculate the number of years between the two ET
        C     representations, ~100.
        C
              WRITE(*,*) 'Years between evaluations: ',(ET2 - ET1)/JYEAR()
 
              END
 
 
 
Run the code example
 
 
        Original time string     : Mar 15, 2003 12:34:56.789 AM PST
        Corresponding ET         :   100989361.
        Time in string format 1  : Sat Mar 15 01:34:56 PDT 2003
        Time in string format 2  : Sat Mar 15 01:34 03(2452713.85760 JDUTC)
        Time in string format 3  : 01:34:56.789 A.M. PDT March 15, 2003
        Years between evaluations:   100.
 
 
 
Lesson 5: Error Handling
===========================================================================
 
     Lesson Goal:
 
     This lesson introduces the basics of the error subsystem and its
     various the response modes: DEFAULT, RETURN, ABORT, RETURN, IGNORE,
     the error output modes: SHORT, LONG, EXPLAIN TRACEBACK, DEFAULT, ALL,
     NONE, and the error traceback message.
 
 
Relevant Routines:
--------------------------------------------------------
 
         --   FAILED returns TRUE if a SPICE error signaled.
 
         --   RESET resets the error subsystem to the state prior to an
              error signal - WARNING, this call resets only the error
              subsystem, the rest of the SPICE system is unchanged.
 
         --   ERRACT sets the reaction of the error subsystem to an error.
 
         --   ERRCH inserts a character/string into an error message.
 
         --   ERRDP inserts a double precision value into an error message.
 
         --   ERRINT inserts an integer value into an error message.
 
         --   ERRDEV sets the device for error output.
 
         --   ERRPRT sets the error message items for output on an error
              signal.
 
         --   SIGERR signals a SPICE error with a given short message.
 
         --   SETMSG sets the long message corresponding to SIGERR.
 
         --   RETURN returns TRUE if a routine should return to caller on
              entry.
 
 
Requirements and References
--------------------------------------------------------
 
     Knowledge of material in the error.req document and the exceptions.ppt
     tutorial file. Comprehension of the catch/throw concept.
 
 
Programming Task
--------------------------------------------------------
 
     Show the behavior of the various error modes by writing a program to
     signal an error, check for an error signal, set the long and short
     error strings, set error behavior (DEFAULT, RETURN, ABORT, RETURN).
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM ERRSYS
              IMPLICIT NONE
 
        C
        C     Define needed variables.
        C
              CHARACTER*(32)    ERRCON
 
              LOGICAL           DOLOOP
              LOGICAL           FAILED
 
              DOLOOP         = .TRUE.
 
        C
        C     Check into the error subsystem to create a traceback
        C     showing the call tree. A CHKOUT must balance every
        C     CHKIN.
        C
              CALL CHKIN( 'ERRSYSF' )
 
        C
        C     Before we start, what's the initial (default)
        C     error state? ERRACT both sets the state and
        C     reports the state.
        C
              CALL ERRACT ( 'GET', ERRCON )
              WRITE(*,*) 'Default error state: ', ERRCON
 
 
        C
        C     Now start an input loop so we can try different
        C     settings for error modes.
        C
              DO WHILE ( DOLOOP )
 
        C
        C        Again use ERRACT to retrieve the current error mode.
        C
                 CALL ERRACT ( 'GET', ERRCON )
                 WRITE(*,*) 'Current error state: ', ERRCON
 
        C
        C        Okay, input one of the response settings strings
        C        then set the error subsystem mode to that value.
        C
                 CALL PROMPT ( 'Set error condition (DEFAULT, REPORT, '
             .              // 'ABORT, RETURN, IGNORE) :', ERRCON )
                 CALL ERRACT ( 'SET', ERRCON )
 
        C
        C        Cause an error signal.
        C
                 CALL DOERR
 
        C
        C        Check for an error signal via a call to FAILED.
        C        At this point we see an important difference
        C        between the error mode's responses to an error
        C        signal.
        C
                 IF ( .NOT. FAILED() ) THEN
 
                    WRITE(*,*) 'No error signal noted.'
 
                 ELSE
 
                    WRITE(*,*) 'Error signal noted.'
 
                 END IF
 
              END DO
 
        C
        C     Check out of the error subsystem tho' we'll
        C     never hit this call.
        C
              CALL CHKOUT ( 'ERRSYSF' )
 
              STOP
              END
 
 
 
        C
        C     This subroutine initiates a SPICE error signal.
        C
              SUBROUTINE DOERR
 
        C
        C     Check into the error subsystem as before.
        C
              CALL CHKIN( 'DOERR' )
 
        C
        C     Let's signal an error. The string passed by SETMSG
        C     is the long error message. You may place markers in the
        C     long message string then later substitute other data
        C     items for those markers.
        C
              CALL SETMSG ( 'A truly horrendous event occurred '
             .          //  'during execution of this program. '
             .          //  'Data added to long error message string: '
             .          //  'A double #, an int #, and a string #.' )
 
        C
        C     Now substitute other data into the long message string.
        C     Note the substitutions work on the first found marker.
        C
              CALL ERRDP ( '#', 186282.397D0 )
              CALL ERRINT( '#', 666          )
              CALL ERRCH ( '#', 'A STRING'   )
 
        C
        C     SIGERR causes the error signal with the string passed
        C     from SETMSG. Set the error flag in the SPICE error
        C     subsystem and execute the proper error response.
        C
              CALL SIGERR ( 'OOPS(SOMETHINGBAD)' )
 
              CALL CHKOUT( 'DOERR' )
 
              RETURN
              END
 
 
 
Run the code example
 
     o- Demo the DEFAULT mode:
 
        Default error state: DEFAULT
        Current error state: DEFAULT
 
     The subsystem is in error state DEFAULT. Let the subsystem run to the
     error signal in DEFAULT mode:
 
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE):default
 
     What subsystem reaction occurs in this state?
 
 
        ===================================================================
 
        Toolkit version: N0057
 
        OOPS(SOMETHINGBAD) --
 
        A truly horrendous event occurred during execution of this program.
        Data added to long error message string: A double
        1.8628239700000E+05, an int 666, and a string A STRING.
 
        A traceback follows. The name of the highest level module is first.
        ERRSYSF --> DOERR
 
        Oh, by the way:  The SPICELIB error handling actions are
        USER-TAILORABLE.  You can choose whether the Toolkit aborts or
        continues when errors occur, which error messages to output, and
        where to send the output.  Please read the ERROR "Required Reading"
        file, or see the routines ERRACT, ERRDEV, and ERRPRT.
 
        ===================================================================
 
 
     Notice we see no error signal status line. The program quit when it
     signaled an error. The program output the error messages, an
     additional information blurb ("Oh by the way"), the Toolkit version,
     and the traceback list.
 
     o- Rerun the program in REPORT mode:
 
        Default error state: DEFAULT
        Current error state: DEFAULT
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :report
 
     How does the REPORT reaction differ from DEFAULT? A demo to
     illustrate...
 
 
 
        ===================================================================
 
        Toolkit version: N0057
 
        OOPS(SOMETHINGBAD) --
 
        A truly horrendous event occurred during execution of this program.
        Data added to long error message string: A double
        1.8628239700000E+05, an int 666, and a string A STRING.
 
        A traceback follows. The name of the highest level module is first.
        ERRSYSF --> DOERR
 
        ===================================================================
        Error signal noted.
 
        Current error state: REPORT
        Set error condition (DEFAULT, REPORT, ABORT, RETURN, IGNORE) :
 
 
 
     The error output ceases after the traceback then returns into the
     calling routine. Note the error signal marker indicates detection of
     the signal. The subsystem in REPORT mode does not print the
     information blurb. The SPICE system can continue to run after an error
     signal with the error state set to REPORT - this mode flags an error
     then allows the program to continue the run. It may happen that the
     cause of the error condition causes instability in the SPICE system.
 
     o- Rerun to test ABORT mode:
 
 
        Default error state: DEFAULT
        Current error state: DEFAULT
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :abort
 
 
     How does the subsystem respond in ABORT mode?
 
 
 
        ===================================================================
 
        Toolkit version: N0057
 
        OOPS(SOMETHINGBAD) --
 
        A truly horrendous event occurred during execution of this program.
        Data added to long error message string: A double
        1.8628239700000E+05, an int 666, and a string A STRING.
 
        A traceback follows. The name of the highest level module is first.
        ERRSYSF --> DOERR
 
        ===================================================================
 
 
 
     ABORT responds quite like DEFAULT except the error output does not
     include the information blurb shown in the DEFAULT output. All
     execution stops when the error signals.
 
     o- Run the program to demo the RETURN mode:
 
 
        Default error state: DEFAULT
        Current error state: DEFAULT
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :return
 
 
     RETURN mode provides the highest measure of flexibility to deal with
     error signals. On output:
 
 
 
        ===================================================================
 
        Toolkit version: N0057
 
        OOPS(SOMETHINGBAD) --
 
        A truly horrendous event occurred during execution of this program.
        Data added to long error message string: A double
        1.8628239700000E+05, an int 666, and a string A STRING.
 
        A traceback follows. The name of the highest level module is first.
        ERRSYSF --> DOERR
 
        ===================================================================
         Error signal noted.
         Current error state: RETURN
 
 
 
     The subroutine signals an error then returns similar to REPORT mode.
     However, this mode includes another property. If we make another pass
     through the command loop:
 
 
        Set error condition (DEFAULT, REPORT, ABORT, RETURN, IGNORE):return
        Error signal noted.
        Current error state: RETURN
 
 
     We see no error output. The main property of the RETURN mode is to
     allow program execution to continue but immediately return from all
     SPICE routines that check the state of the RETURN function. This mode
     restricts program flow after an error signal.
 
     o- And the final mode to test, IGNORE:
 
 
        Default error state: DEFAULT
        Current error state: DEFAULT
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :ignore
        No error signal noted.
        Current error state: IGNORE
        Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :
 
 
     No error output, no error signal. IGNORE mode prevents expression of
     all error subsystem functions; the subsystem does not set RETURN or
     FAILED. While using IGNORE mode the user cannot identify an error
     signal. Carefully consider program requirements before any use of
     IGNORE mode.
 
 
Programming Task
--------------------------------------------------------
 
     Write an interactive program to return a state vector based on a
     user's input. Code the program with the capability to recover from
     user input mistakes, inform the user of the mistake, then continue to
     run.
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM ADERR
              IMPLICIT NONE
 
        C
        C     Declare our variables.
        C
              CHARACTER*( 32 )    TARG
 
              LOGICAL             DOLOOP
              LOGICAL             EQSTR
              LOGICAL             FAILED
 
              DOUBLE PRECISION    STATE(6)
              DOUBLE PRECISION    LTIME
 
 
        C
        C     First important action. The DEFAULT error setting
        C     in the SPICE system displays an error message when
        C     an error signals then quits the program. We want the
        C     error message, but no 'quit.'
        C
        C     The RETURN mode signals an error then returns to the
        C     caller. Just what we need. REPORT mode performs almost
        C     the same function as RETURN, however RETURN mode
        C     sets the RETURN() value to TRUE and so the program does
        C     not execute those SPICE routines that check the RETURN()
        C     value. Consider REPORT mode useful for debugging.
        C
              CALL ERRACT( 'SET', 'RETURN'  )
 
        C
        C     Load the data we need for state evaluation.
        C
              CALL FURNSH( 'meta.ker' )
 
        C
        C     Set a flag to start/stop and continue the
        C     inquiry loop.
        C
              DOLOOP     = .TRUE.
 
        C
        C     Start our input query loop to the user.
        C
              DO WHILE ( DOLOOP )
 
        C
        C        For simplicity, we request only one input.
        C        The program calculates the state vector from
        C        Earth to the user specified target (TARG) in the
        C        J2000 frame, at ephemeris time zero, using
        C        aberration correction LT+S (light time plus
        C        stellar aberration).
        C
                 CALL PROMPT ( 'Target: ', TARG )
 
                 IF (  EQSTR( TARG, 'NONE' ) ) THEN
 
        C
        C           An exit condition. If the user inputs NONE
        C           for a target name, set the loop to stop...
        C
                    DOLOOP = .FALSE.
 
                 ELSE
 
        C
        C           ...otherwise evaluate the state between the Earth
        C           and the target.
        C
                    CALL SPKEZR ( TARG, 0.D0, 'J2000', 'LT+S', 'EARTH',
             .                    STATE, LTIME )
 
        C
        C           What if the program can't perform the evaluation?
        C           Since we set the error subsystem to RETURN we know
        C           a failed SPKEZR call sets the FAILED flag to
        C           TRUE then returns control to the calling routine.
        C           The SPICE system also outputs an error message
        C           informing the user of the problem's cause.
        C
        C           Examine the state of FAILED() to determine if we
        C           output a state vector or not.
        C
                    IF ( .NOT. FAILED() ) THEN
                       WRITE(*,*) 'R : ', STATE(1), STATE(2), STATE(3)
                       WRITE(*,*) 'V : ', STATE(4), STATE(5), STATE(6)
                       WRITE(*,*) 'LT: ', LTIME
 
                    ELSE
 
        C
        C              Problem. The FAILED() routine returned a TRUE.
        C              Reset the error subsystem for another pass.
        C
                       CALL RESET()
 
                    END IF
 
                 END IF
 
              END DO
 
              END
 
 
 
Run the code example
 
     Now run the code with various inputs to observe behavior. Begin the
     run using known astronomical bodies. Recall the SPICE default units
     are kilometers, kilometers per second, kilograms, and seconds. The 'R'
     marker identifies the (X,Y,Z) position of the body in kilometers, the
     'V' marker identifies the velocity of the body in kilometers per
     second, and the 'LT' marker identifies the one-way light time between
     the bodies at the requested evaluation time.
 
 
        Target: Moon
         R :  -291584.617  -266693.402  -76095.6476
         V :   0.643527473 -0.666082437 -0.3013231
         LT:   1.34231061
 
        Target: Mars
         R :   234536077. -132584384. -63102685.7
         V :   30.9597591  28.9364647  13.1144902
         LT:   923.00108
 
        Target: Pluto barycenter
         R :  -1.45130474E+09 -4.31817414E+09 -918251434.
         V :   35.0383793      3.06559507     -0.0151397628
         LT:   15501.2583
 
        Target: Puck
 
        ===================================================================
 
        Toolkit version: N0057
 
        SPICE(SPKINSUFFDATA) --
 
        Insufficient ephemeris data has been loaded to compute the state of
        715 (PUCK) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris
        epoch 2000 JAN 01 12:00:00.000.
 
        A traceback follows.  The name of the highest level module is
        first.
        SPKEZR --> SPKEZ --> SPKAPP --> SPKSSB --> SPKGEO
 
        ===================================================================
 
 
     Perplexing. What happened?
 
     The kernel files named in meta.ker did not include ephemeris data for
     Puck. When the SPK subsystem tried to evaluate Puck's position, the
     evaluation failed due to lack of data, so an error signaled.
 
     The above error signifies an absence of state information at ephemeris
     time 2000 JAN 01 12:00:00.000 (the requested time, ephemeris time
     zero). Since the program set the error mode to RETURN, program
     execution continues.
 
     Try another look-up.
 
        Target: Casper
 
        ===================================================================
 
        Toolkit version: N0057
 
        SPICE(IDCODENOTFOUND) --
 
        The target, 'Casper', is not a recognized name for an ephemeris
        object. The cause of this problem may be that you need an updated
        version of the SPICE Toolkit. Alternatively you may call SPKEZ
        directly if you know the SPICE ID codes for both 'Casper' and
        'EARTH'
 
        A traceback follows.  The name of the highest level module is
        first.
        SPKEZR
 
        ===================================================================
 
 
     An easy to understand error. The SPICE system does not contain
     information on a body named 'Casper.'
 
     Another look-up, this time, something easy.
 
 
        Target: Venus
         R :  -80970027.5  -139655773.  -53860126.
         V :   31.1696929  -27.0001826  -12.3162193
         LT:   567.655074
 
 
     The look-up succeeded despite two errors in our run. The SPICE system
     can respond to error conditions (not system errors) in much the same
     fashion as languages with catch/throw instructions.
 
 
Lesson 6: Windows, Sets, and Cells
===========================================================================
 
     Lesson Goal:
 
     This lesson introduces the concepts of the SPICE data types 'cell' and
     'window. A 'cell' is as the basis for set calculations in SPICE. A
     'window' permits a user to manipulate continuous intervals of the real
     line. A 'window' is nothing more than an ordered, double precision
     cell that contains zero or more intervals
 
     An interval being an ordered pair of numbers,
 
           [ a(i), b(i) ]
 
     where
 
           a(i)  <  b(i)
                 -
 
     The intervals within a window are both ordered and disjoint. That is,
     the beginning of each interval is greater than the end of the previous
     interval
 
           b(i)  <  a(i+1)
 
     A common use of a window is to calculate when the time intervals
     covering known events, eclipses, occultation, right ascension within a
     certain value, etc intersect.
 
 
Relevant Routines
--------------------------------------------------------
 
         --   WNCOMD determines the compliment of a window with respect to
              a defined interval.
 
         --   WNCOND contracts a window's intervals.
 
         --   WNDIFD : Calculate the difference between two windows; i.e.
              every point existing in the first but not the second.
 
         --   WNELMD returns TRUE or FALSE if a value exists in a window.
 
         --   WNEXPD expands the size of the intervals in a window.
 
         --   WNEXTD extracts a window's endpoints .
 
         --   WNFETD retrieves a specified interval from a window.
 
         --   WNFILD fills gaps between intervals in a window.
 
         --   WNFLTD filter/removes small intervals from a window.
 
         --   WNINCD determines if an interval exists within a window.
 
         --   WNINSD inserts an interval into a window.
 
         --   WNINTD calculates the intersection of two windows.
 
         --   WNRELD compares two windows. Comparison operations available,
              equality '=', inequality '<>', subset '<=' and '>=', proper
              subset '<' and '>'.
 
         --   WNSUMD creates a window summary.
 
         --   WNUNID calculates the union of two windows.
 
         --   WNVALD validates/creates a window from a cell array.
 
 
Requirements and References
--------------------------------------------------------
 
     Knowledge of cells.req, sets.req, and windows.req documents, as well
     as the other_functions.ppt tutorial file.
 
 
Programming task:
--------------------------------------------------------
 
     Given the times of line-of-sight for a vehicle from a ground station
     and the times for an acceptable Sun-station-vehicle phase angle, write
     a program to determine the time intervals common to both
     configurations.
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM WIN
              IMPLICIT NONE
 
        C
        C     Define our variable types.
        C
              INTEGER           LBCELL
              PARAMETER        (LBCELL = -5 )
 
              INTEGER           MAXSIZ
              PARAMETER        (MAXSIZ = 8 )
 
              INTEGER           I
              INTEGER           SMALL
              INTEGER           LARGE
 
 
              CHARACTER * 32    LOS   ( MAXSIZ )
              CHARACTER * 32    PHASE ( MAXSIZ )
              CHARACTER * 26    UTCSTR( 2 )
 
        C
        C     Define the cells to use as windows.
        C     The windows can hold 8 data values i.e.
        C     four intervals.
        C
              DOUBLE PRECISION  LOSWIN(LBCELL:MAXSIZ)
              DOUBLE PRECISION  PHSWIN(LBCELL:MAXSIZ)
              DOUBLE PRECISION  SCHED (LBCELL:MAXSIZ)
 
              DOUBLE PRECISION  LEFT
              DOUBLE PRECISION  RIGHT
              DOUBLE PRECISION  MEAS
              DOUBLE PRECISION  AVG
              DOUBLE PRECISION  STDDEV
 
        C
        C     SPICELIB functions associated with windows.
        C
              INTEGER           CARDD
              INTEGER           SIZED
 
        C
        C    Define sets of time intervals. For the purposes of this
        C    tutorial program, define time intervals representing
        C    an unobscured line of sight between a ground station
        C    and some  body.
        C
              DATA     LOS / 'Jan 1, 2003 22:15:02', 'Jan 2, 2003 4:43:29'
             .               'Jan 4, 2003 9:55:30' , 'Jan 4, 2003 11:26:52'
             .               'Jan 5, 2003 11:09:17', 'Jan 5, 2003 13:00:41'
             .               'Jan 6, 2003 00:08:13', 'Jan 6, 2003 2:18:01'
             .             /
 
        C
        C    A second set of intervals representing the times for which
        C    an acceptable phase angle exits between the ground station,
        C    the body and the Sun.
        C
              DATA   PHASE / 'Jan 2, 2003 00:03:30', 'Jan 2, 2003 19:00:00'
             .               'Jan 3, 2003 8:00:00' , 'Jan 3, 2003 9:50:00'
             .               'Jan 5, 2003 12:00:00', 'Jan 5, 2003 12:45:00'
             .               'Jan 6, 2003 00:30:00', 'Jan 6, 2003 23:00:00'
             .             /
 
 
        C
        C     Load our meta kernel for the leapseconds data.
        C
              CALL FURNSH ( 'meta.ker' )
 
        C
        C     Windows consist of double precision values, convert the
        C     time tags defined in the LOS and PHASE arrays to
        C     double precision ET. Store the double values in the
        C     LOSWIN and PHSWIN arrays. Null out SCHED before attempting
        C     to validate - this removes any garbage values.
        C
              DO I = 1, 8
                 CALL STR2ET( LOS(I)  , LOSWIN(I) )
                 CALL STR2ET( PHASE(I), PHSWIN(I) )
                 SCHED(I) = 0.d0
              END DO
 
 
        C
        C     Validate the windows from the double precision cells.
        C     Since we use 4 intervals, the set the window to accept 8
        C     data values ( 4 * 2 = 8 ). Since we require no more than
        C     8 data values, assign a window size of 8.
        C
              CALL WNVALD ( 8, 8, LOSWIN )
              CALL WNVALD ( 8, 8, PHSWIN )
              CALL WNVALD ( 8, 8, SCHED  )
 
        C
        C     The issue for consideration, at what times do line of
        C     sight events coincide with acceptable phase angles?
        C     Perform the set operation AND on LOSWIN, PHSWIN,
        C     place the results in the window SCHED.
        C
              CALL WNINTD( LOSWIN, PHSWIN, SCHED )
 
              CALL TOSTDO ( ' ' )
              WRITE(*,*) 'No. data values in SCHED            : ',
             .                                                CARDD(SCHED)
              WRITE(*,*) 'Space available for values in SCHED : ',
             .                                                SIZED(SCHED)
 
        C
        C     Output the results. The number of intervals in SCHED
        C     is half the number of data points (the cardinality).
        C     Use a call to CARDD to retrieve the window's cardinality.
        C
              CALL TOSTDO ( ' ' )
              CALL TOSTDO ( 'Time intervals meeting defined criterion.')
 
              DO I = 1, CARDD( SCHED )/2
 
        C
        C        Extract from the derived SCHED the values defining the
        C        time intervals, [LEFT, RIGHT].
        C
                 CALL WNFETD ( SCHED, I, LEFT, RIGHT )
 
        C
        C        Convert the ET values to UTC for human comprehension.
        C
                 CALL ET2UTC ( LEFT , 'C', 3, UTCSTR(1) )
                 CALL ET2UTC ( RIGHT, 'C', 3, UTCSTR(2) )
 
        C
        C        Output the UTC string and the corresponding index
        C        for the interval.
        C
                 WRITE(*,*)  I, '  ', UTCSTR(1), ' ',UTCSTR(2)
 
              END DO
 
        C
        C     Summarize the SCHED window.
        C
              CALL TOSTDO ( ' ' )
              CALL TOSTDO ( 'Summary of SCHED window' )
              CALL WNSUMD ( SCHED, MEAS, AVG, STDDEV, SMALL, LARGE )
 
              WRITE(*,*) 'o Total measure of SCHED    : ', MEAS
              WRITE(*,*) 'o Average measure of SCHED  : ', AVG
              WRITE(*,*) 'o Standard deviation of '
              WRITE(*,*) '  the measures in SCHED     : ', STDDEV
 
        C
        C     The values for SMALL and LARGE refer to the indexes of the
        C     values in the array (SCHED). The shortest interval
        C     is [ SCHED(SMALL), SCHED(SMALL+1)]; the longest is
        C     [ SCHED(LARGE), SCHED(LARGE+1)]. Output the indexes for
        C     the shortest and longest intervals.
        C
        C
              WRITE(*,*) 'o Index of shortest interval: ', (SMALL+1)/2
              WRITE(*,*) 'o Index of longest interval : ', (LARGE+1)/2
 
              END
 
 
 
Run the code example
 
     The output window has the name SCHED (schedule).
 
     Output the amount of data held in SCHED compared to the maximum
     possible amount.
 
         No. data values in SCHED            :   6
         Space available for values in SCHED :   8
 
     List the time intervals for which a line of sight exists during the
     time of a proper phase angle.
 
 
        Time intervals meeting defined criterion.
           1  2003 JAN 02 00:03:30.000   2003 JAN 02 04:43:29.000
           2  2003 JAN 05 12:00:00.000   2003 JAN 05 12:45:00.000
           3  2003 JAN 06 00:30:00.000   2003 JAN 06 02:18:01.000
 
 
     Finally, an analysis of the SCHED data. The measure of an interval
     [a,b] (a <= b) equals b-a. Real values output in units of seconds.
 
 
        Summary of SCHED window
         o Total measure of SCHED    :     25980.
         o Average measure of SCHED  :     8660.
         o Standard deviation of
           the measures in SCHED     :     5958.55022
         o Index of shortest interval:   2
         o Index of longest interval :   1
 
 
 
Lesson 7: Utility and Constants Routines
===========================================================================
 
     Lesson Goals:
 
     SPICE provides several routines to perform commonly needed tasks.
     Among these include calls to convert values between unit expressions,
     determine the equality of strings, and indicate whether a file exists.
 
     SPICE also includes a set of functions that return constant values
     often used in astrodynamics, time calculations, and geometry.
 
 
Relevant Routines
--------------------------------------------------------
 
         --   CONVRT converts between measurements units
 
         --   TKVRSN returns the current version of the toolkit
 
         --   EQSTR returns a boolean describing the equality of two
              strings. The comparison is case insensitive and ignores
              spaces.
 
         --   EXISTS returns a boolean indicating the existence of a file.
 
         --   CLIGHT : velocity of light in a vacuum, kilometers per second
 
         --   DPR : number of degrees per radian (180/Pi)
 
         --   RPD : number radians per degree (Pi/180)
 
         --   SPD : number of seconds per day (60*60*24)
 
         --   B1900 : Julian Date of the epoch Besselian Date 1900.0
 
         --   B1950 : Julian date of the epoch Besselian Date 1950.0
 
         --   J1900 : Julian date of 1900 JAN 0.5 (1899 DEC 31 12:00:00)
 
         --   J1950 : Julian date of 1950 JAN 1.0 (1950 JAN 1 00:00:00)
 
         --   J2000 : Julian date of 2000 JAN 1.5 (2000 JAN 1 12:00:00)
 
         --   J2100 : Julian date of 2100 JAN 1.5 (2100 JAN 1 12:00:00)
 
         --   TWOPI : double precision value of 2 * Pi
 
         --   PI : double precision value of Pi
 
         --   HALFPI : double precision value of 0.5 * Pi
 
         --   JYEAR : seconds per Julian year (365.25 Julian days)
 
         --   TYEAR : seconds per tropical year (approximately the number
              of seconds from one spring equinox to the next)
 
 
Requirements and References
--------------------------------------------------------
 
     The references used to define or calculate the constants functions are
     found in the source code file and/or the API reference. Also reference
     the other_functions.ppt tutorial file.
 
 
Programming Task
--------------------------------------------------------
 
     Write an interactive program to convert values between various units.
     Demonstrate the flexibility of the unit conversion routine, the string
     equality function, and show the version ID function.
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM UNITS
              IMPLICIT NONE
 
        C
        C     Define the few variables
        C     needed for data input and output.
        C
              CHARACTER* (32)   FUNITS
              CHARACTER* (32)   TUNITS
 
              DOUBLE PRECISION  FVALUE
              DOUBLE PRECISION  TVALUE
 
        C
        C     Define the TKVRSN return value.
        C
              CHARACTER*(12)    VERS
 
        C
        C     Display the Toolkit version string with a
        C     TKVRSN call.
        C
              CALL TKVRSN( 'TOOLKIT', VERS )
              WRITE(*,*)
              WRITE(*,*) 'Convert demo program compiled against '
             .       //  'SPICE Toolkit ', VERS
              WRITE(*,*)
 
        C
        C     The user first inputs the name of a unit of measure.
        C     Send the name through TOSTAN for de-aliasing.
        C
              CALL PROMPT ( 'From Units : ', FUNITS )
              CALL TOSTAN ( FUNITS )
 
        C
        C     Input a double precision value to express in a new
        C     unit format.
        C
              WRITE(*,'(A13$)') 'From Value : '
              READ (*,*)         FVALUE
 
        C
        C     Now the user inputs the name of the output units.
        C     Again we send the units name through TOSTAN for
        C     de-aliasing.
        C
              CALL PROMPT ( 'To Units   : ', TUNITS )
              CALL TOSTAN ( TUNITS )
 
        C
        C     Call CONVRT to perform the conversion. CONVRT
        C     signals an error if:
        C        1. Either unit is unknown.
        C        2. The input and output units are not in the same
        C           class (length, angular measure, or time).
        C
              CALL CONVRT ( FVALUE, FUNITS, TUNITS, TVALUE )
 
        C
        C     Output the results.
        C
              WRITE(*,*) TVALUE, ' ' , TUNITS
 
              STOP
              END
 
 
        C
        C     As a convenience, let's alias a few common terms
        C     to their appropriate counterpart. Use EQSTR to
        C     compare strings. The comparison ignores letter
        C     case and trailing/leading spaces.
        C
              SUBROUTINE TOSTAN ( ALIAS )
              IMPLICIT NONE
 
              LOGICAL           EQSTR
              CHARACTER*(*)     ALIAS
 
        C
        C     Start de-aliasing. Check the input string
        C     against a set of defined (allowed) aliases.
        C
              IF ( EQSTR( ALIAS, 'meter' ) ) THEN
 
        C
        C        First, a 'meter' by any other name is a
        C        'METER' and smells as sweet ...
        C
                 ALIAS = 'METERS'
 
              ELSE IF ( EQSTR( ALIAS, 'clicks'     )   .OR.
             .          EQSTR( ALIAS, 'KILOMETERS' )   .OR.
             .          EQSTR( ALIAS, 'KILOMETER'  ) ) THEN
 
        C
        C        ... 'clicks', 'KILOMETERS' and
        C        'KILOMETER' identifies 'KM'....
        C
                 ALIAS = 'KM'
 
              ELSE IF ( EQSTR( ALIAS, 'secs' ) )THEN
 
        C
        C        ... 'secs' to 'SECONDS'.
        C
                 ALIAS = 'SECONDS'
 
              ELSE IF ( EQSTR( ALIAS, 'miles' ) )THEN
 
        C
        C        ... and finally 'miles' to 'STATUTE_MILES'.
        C        Normal people think in statute miles. Only
        C        sailors think in nautical miles - one
        C        minute of arc at the equator.
        C
                 ALIAS = 'STATUTE_MILES'
 
              END IF
 
        C
        C     Much better, so return. If the input matched
        C     none of the aliases, this routine did nothing.
        C
              RETURN
              END
 
 
 
Run the code example
 
     Run a few conversions through the application to ensure it works. The
     intro banner gives us the Toolkit version against which the
     application was linked:
 
 
        Convert demo program compiled against SPICE Toolkit N0057
        >From Units : clicks
        >From Value : 3
        To Units   : miles
             1.8641135767120 STATUTE_MILES
 
 
     Now we know. Three kilometers equals 1.864 miles.
 
     Pheidippides ran 26.2 miles from the Marathon Plain to Athens. How far
     in kilometers?
 
 
        >From Units : miles
        >From Value : 26.2
        To Units   : km
             42.164812800000 km
 
 
 
Programming Task
--------------------------------------------------------
 
     Write a program to output SPICE constants and use those constants to
     calculate some rudimentary values.
 
 
Code Solution
--------------------------------------------------------
 
 
              PROGRAM CONST
              IMPLICIT NONE
 
        C
        C     As required in FORTRAN define the (return) type for
        C     the functions. All the functions have the same calling
        C     sequence:
        C
        C        VALUE = function_name()
        C        CALL some_procedure( function_name() )
        C        WRITE(*,*) function_name()
        C
              DOUBLE PRECISION      CLIGHT
              DOUBLE PRECISION      DPR
              DOUBLE PRECISION      RPD
              DOUBLE PRECISION      SPD
              DOUBLE PRECISION      J2000
              DOUBLE PRECISION      HALFPI
              DOUBLE PRECISION      J2100
              DOUBLE PRECISION      TYEAR
 
        C
        C     First a simple example using the seconds per day
        C     constant...
        C
              WRITE(*,*) 'Number of (S)econds (P)er (D)ay         : ',
             .            SPD()
 
        C
        C     ...then show the value of degrees per radian, 180/Pi...
        C
              WRITE(*,*) 'Number of (D)egrees (P)er (R)adian      : ',
             .            DPR()
 
        C
        C     ...and the inverse, radians per degree, Pi/180.
        C     It is obvious DPR() equals 1.D/RPD(), or more simply
        C     DPR() * RPD() equals 1
        C
              WRITE(*,*) 'Number of (R)adians (P)er (D)egree      : ',
             .            RPD()
 
        C
        C     What's the value for the astrophysicist's favorite
        C     physical constant (in a vacuum)?
        C
              WRITE(*,*) 'Speed of light in KM per second         : ',
             .            CLIGHT()
 
        C
        C     How long (in Julian days) from the J2000 epoch to the
        C     J2100 epoch?
        C
              WRITE(*,*) 'Number of days between epochs J2000'
              WRITE(*,*) '  and J2100                             : ',
             .            J2100() - J2000()
 
        C
        C     Redo the calculation returning seconds...
        C
              WRITE(*,*) 'Number of seconds between epochs'
              WRITE(*,*) '  J2000 and J2100                       : ',
             .            SPD() * (J2100() - J2000() )
 
        C
        C     ...then tropical years.
        C
              WRITE(*,*) 'Number of tropical years between'
              WRITE(*,*) '  epochs J2000 and J2100                : ',
             .            ( SPD() / TYEAR() ) * (J2100() - J2000() )
 
        C
        C     Finally, how can I convert a radian value to degrees.
        C
              WRITE(*,*) 'Number of degrees in Pi/2 radians of arc: ',
             .            HALFPI() * DPR()
 
        C
        C     and degrees to radians.
        C
              WRITE(*,*) 'Number of radians in 250 degrees of arc : ',
             .            250.D0 * RPD()
 
              END
 
 
 
Run the code example
 
 
        Number of (S)econds (P)er (D)ay         :     86400.000000000
        Number of (D)egrees (P)er (R)adian      :     57.295779513082
        Number of (R)adians (P)er (D)egree      :     1.7453292519943D-02
        Speed of light in KM per second         :     299792.45800000
        Number of days between epochs J2000
          and J2100                             :     36525.000000000
        Number of seconds between epochs
          J2000 and J2100                       :     3155760000.0000
        Number of tropical years between
          epochs J2000 and J2100                :    100.002135902909
        Number of degrees in Pi/2 radians of arc:     90.000000000000
        Number of radians in 250 degrees of arc :     4.3633231299858
 
 
