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ev2lin

Table of contents
Procedure
Abstract
Required_Reading
Keywords
Declarations
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version

Procedure

     EV2LIN ( Evaluate "two-line" element data, near-earth )

     SUBROUTINE EV2LIN ( ET, GEOPHS, ELEMS, STATE )

Abstract

     Deprecated: This routine has been superseded by the SPICELIB
     routine EVSGP4. *ALL* TLE evaluations should use that routine.
     NAIF supports EV2LIN only for backward compatibility.

     Evaluate NORAD two-line element data for near-earth, earth
     orbiting spacecraft (that is spacecraft with orbital periods
     less-than 225 minutes). This evaluator uses algorithms as
     described in Hoots 1980 [1].

Required_Reading

     None.

Keywords

     EPHEMERIS

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      ET
     DOUBLE PRECISION      GEOPHS ( * )
     DOUBLE PRECISION      ELEMS  ( * )
     DOUBLE PRECISION      STATE  ( * )

     INTEGER               NMODL
     PARAMETER           ( NMODL = 6 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ET         I   Epoch in seconds past ephemeris epoch J2000.
     GEOPHS     I   Geophysical constants
     ELEMS      I   Two-line element data
     STATE      O   Evaluated state
     NMODL      P   Parameter controlling number of buffered elements.

Detailed_Input

     ET       is the epoch in TDB seconds past ephemeris epoch J2000
              at which a state should be produced from the
              input elements.

     GEOPHS   is a collection of 8 geophysical constants needed
              for computing a state. The order of these
              constants must be:

                 GEOPHS(1) = J2 gravitational harmonic for Earth.
                 GEOPHS(2) = J3 gravitational harmonic for Earth.
                 GEOPHS(3) = J4 gravitational harmonic for Earth.

              These first three constants are dimensionless.

                 GEOPHS(4) = KE: Square root of the GM for Earth where
                             GM is expressed in Earth radii cubed per
                             minutes squared.

                 GEOPHS(5) = QO: High altitude bound for atmospheric
                             model in km.

                 GEOPHS(6) = SO: Low altitude bound for atmospheric
                             model in km.

                 GEOPHS(7) = RE: Equatorial radius of the earth in km.

                 GEOPHS(8) = AE: Distance units/earth radius
                             (normally 1)

              Below are currently recommended values for these
              items:

                 J2 =    1.082616D-3
                 J3 =   -2.53881D-6
                 J4 =   -1.65597D-6

              The next item is the square root of GM for the Earth
              given in units of earth-radii**1.5/Minute

                 KE =    7.43669161D-2

              The next two items define the top and bottom of the
              atmospheric drag model used by the type 10 ephemeris
              type. Don't adjust these unless you understand the full
              implications of such changes.

                 QO =  120.0D0
                 SO =   78.0D0

              The ER value is the equatorial radius in km of the Earth
              as used by NORAD.

                 ER = 6378.135D0

              The value of AE is the number of distance units per
              Earth radii used by the NORAD state propagation
              software. The value should be 1 unless you've got a very
              good understanding of the NORAD routine SGP4 and the
              affect of changing this value.

                 AE =    1.0D0

     ELEMS    is an array containing two-line element data
              as prescribed below. The elements NDD6O and BSTAR
              must already be scaled by the proper exponent stored
              in the two line elements set. Moreover, the
              various items must be converted to the units shown
              here.

                 ELEMS (  1 ) = NDT20 in radians/minute**2
                 ELEMS (  2 ) = NDD60 in radians/minute**3
                 ELEMS (  3 ) = BSTAR
                 ELEMS (  4 ) = INCL  in radians
                 ELEMS (  5 ) = NODE0 in radians
                 ELEMS (  6 ) = ECC
                 ELEMS (  7 ) = OMEGA in radians
                 ELEMS (  8 ) = M0    in radians
                 ELEMS (  9 ) = N0    in radians/minute
                 ELEMS ( 10 ) = EPOCH of the elements in seconds
                                past ephemeris epoch J2000.

Detailed_Output

     STATE    is the state produced by evaluating the input elements
              at the input epoch ET. Units are km and km/sec relative
              to the TEME reference frame.

Parameters

     NMODL    is a parameter that controls how many element sets
              can be buffered internally. Since there are a lot
              of computations that are independent of time these
              are buffered and only computed if an unbuffered
              model is supplied. This value should always
              be at least 2. Increasing it a great deal is not
              advised since the time needed to search the
              buffered elements for a match increases linearly
              with the NMODL. Empirically, 6 seems to be a good
              break even value for NMODL.

Exceptions

     1)  No checks are made on the reasonableness of the inputs.

     2)  If the number of iterations for the calculation exceeds the
         limit for this value, the error SPICE(ITERATIONEXCEEDED) is
         signaled. This error should signal only for bad (nonphysical)
         TLEs.

Files

     None.

Particulars

     This routine evaluates NORAD two-line element sets for
     near-earth orbiting satellites using the algorithms described in
     Hoots 1980 [1]. This code is an adaptation of
     the NORAD routine SGP4 to eliminate common blocks, allow
     buffering of models and intermediate parameters and double
     precision calculations.

     Near earth is as an orbital period of less than 225
     minutes.

Examples

     The numerical results shown for this example may differ across
     platforms. The results depend on the SPICE kernels used as
     input, the compiler and supporting libraries, and the machine
     specific arithmetic implementation.

     1) Suppose you have a set of two-line elements for the LUME 1
        cubesat. This example shows how you can use this routine
        together with the routine GETELM to propagate a state to an
        epoch of interest.

        Use the meta-kernel shown below to load the required SPICE
        kernels.


           KPL/MK

           File name: ev2lin_ex1.tm

           This meta-kernel is intended to support operation of SPICE
           example programs. The kernels shown here should not be
           assumed to contain adequate or correct versions of data
           required by SPICE-based user applications.

           In order for an application to use this meta-kernel, the
           kernels referenced here must be present in the user's
           current working directory.

           The names and contents of the kernels referenced
           by this meta-kernel are as follows:

              File name           Contents
              ---------           ------------------------------------
              naif0012.tls        Leapseconds
              geophysical.ker     geophysical constants for evaluation
                                  of two-line element sets.

           \begindata

              KERNELS_TO_LOAD = ( 'naif0012.tls',
                                  'geophysical.ker'  )

           \begintext

           End of meta-kernel


        Example code begins here.


              PROGRAM EV2LIN_EX1
              IMPLICIT NONE

        C
        C     Local parameters.
        C
              CHARACTER*(*)         TIMSTR
              PARAMETER           ( TIMSTR = '2020-05-26 02:25:00' )

              INTEGER               PNAMLN
              PARAMETER           ( PNAMLN = 2  )

              INTEGER               TLELLN
              PARAMETER           ( TLELLN = 69 )

        C
        C     The LUME-1 cubesat is an Earth orbiting object; set
        C     the center ID to the Earth ID.
        C
              INTEGER               CENTER
              PARAMETER           ( CENTER  = 399     )

        C
        C     Local variables.
        C
              CHARACTER*(PNAMLN)    NOADPN ( 8  )
              CHARACTER*(TLELLN)    TLE    ( 2  )

              DOUBLE PRECISION      ELEMS  ( 10 )
              DOUBLE PRECISION      EPOCH
              DOUBLE PRECISION      ET
              DOUBLE PRECISION      GEOPHS ( 8  )
              DOUBLE PRECISION      STATE  ( 6  )

              INTEGER               I
              INTEGER               N

        C
        C     These are the variables that will hold the constants
        C     required by EV2LIN. These constants are available from
        C     the loaded PCK file, which provides the actual values
        C     and units as used by NORAD propagation model.
        C
        C        Constant   Meaning
        C        --------   ------------------------------------------
        C        J2         J2 gravitational harmonic for Earth.
        C        J3         J3 gravitational harmonic for Earth.
        C        J4         J4 gravitational harmonic for Earth.
        C        KE         Square root of the GM for Earth.
        C        QO         High altitude bound for atmospheric model.
        C        SO         Low altitude bound for atmospheric model.
        C        ER         Equatorial radius of the Earth.
        C        AE         Distance units/earth radius.
        C
              DATA          NOADPN  /  'J2', 'J3', 'J4', 'KE',
             .                         'QO', 'SO', 'ER', 'AE'  /

        C
        C     Define the Two-Line Element set for LUME-1.
        C
              TLE(1)  = '1 43908U 18111AJ  20146.60805006  .00000806'
             .      //                   '  00000-0  34965-4 0  9999'
              TLE(2)  = '2 43908  97.2676  47.2136 0020001 220.6050 '
             .      //                   '139.3698 15.24999521 78544'

        C
        C     Load the PCK file that provides the geophysical
        C     constants required for the evaluation of the two-line
        C     elements sets. Load also an LSK, as it is required by
        C     GETELM to perform time conversions. Use a meta-kernel for
        C     convenience.
        C
              CALL FURNSH ( 'ev2lin_ex1.tm' )

        C
        C     Retrieve the data from the kernel, and place it on
        C     the GEOPHS array.
        C
              DO I = 1, 8

                 CALL BODVCD ( CENTER, NOADPN(I), 1, N, GEOPHS(I) )

              END DO

        C
        C     Convert the Two Line Elements lines to the element sets.
        C     Set the lower bound for the years to be the beginning
        C     of the space age.
        C
              CALL GETELM ( 1957, TLE, EPOCH, ELEMS )

        C
        C     Now propagate the state using EV2LIN to the epoch of
        C     interest.
        C
              CALL STR2ET ( TIMSTR, ET )
              CALL EV2LIN ( ET, GEOPHS, ELEMS, STATE )

        C
        C     Display the results.
        C
              WRITE(*,'(2A)')       'Epoch   : ', TIMSTR
              WRITE(*,'(A,3F16.8)') 'Position:', (STATE(I), I=1,3)
              WRITE(*,'(A,3F16.8)') 'Velocity:', (STATE(I), I=4,6)


              END


        When this program was executed on a Mac/Intel/gfortran/64-bit
        platform, the output was:


        Epoch   : 2020-05-26 02:25:00
        Position:  -4644.60403398  -5038.95025540   -337.27141117
        Velocity:     -0.45719025      0.92884817     -7.55917355

Restrictions

     None.

Literature_References

     [1]  F. Hoots and R. Roehrich, "Spacetrack Report #3: Models for
          Propagation of the NORAD Element Sets," U.S. Air Force
          Aerospace Defense Command, Colorado Springs, CO, 1980.

     [2]  F. Hoots, "Spacetrack Report #6: Models for Propagation of
          Space Command Element Sets,"  U.S. Air Force Aerospace
          Defense Command, Colorado Springs, CO, 1986.

     [3]  F. Hoots, P. Schumacher and R. Glover, "History of Analytical
          Orbit Modeling in the U. S. Space Surveillance System,"
          Journal of Guidance, Control, and Dynamics. 27(2):174-185,
          2004.

     [4]  D. Vallado, P. Crawford, R. Hujsak and T. Kelso, "Revisiting
          Spacetrack Report #3," paper AIAA 2006-6753 presented at the
          AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO.,
          August 21-24, 2006.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)
     E.D. Wright        (JPL)

Version

    SPICELIB Version 1.1.1, 01-NOV-2021 (JDR) (EDW)

        Declared routine as deprecated.

        Corrected the description of QO and SO constants in the
        detailed description of the input argument GEOPHS and the input
        element names in ELEMS.

        Added Spacetrack Report #3 to literature references.

        Edited the header to comply with NAIF standard. Added complete
        code example based on existing fragments.

    SPICELIB Version 1.1.0, 15-SEP-2014 (EDW)

        Added error check to prevent infinite loop in
        calculation of EST.

    SPICELIB Version 1.0.3, 02-JAN-2008 (EDW)

        Corrected error in the calculation of the C4 term
        identified by Curtis Haase.

        Minor edit to the COEF1 declaration strictly
        identifying the constant as a double.

        From:

           COEF1  = COEF  / PSISQ**3.5

        To:

           COEF1  = COEF  / PSISQ**3.5D0

    SPICELIB Version 1.0.2, 08-JUL-2004 (EDW)

        Corrected error in the calculation of the C2 term.
        Reordered C1, C2 calculations to avoid division
        by BSTAR.

    SPICELIB Version 1.0.1, 10-MAR-1998 (EDW)

        Corrected error in header describing the GEOPHS array.

    SPICELIB Version 1.0.0, 14-JAN-1994 (WLT)
Fri Dec 31 18:36:21 2021