Procedure

     CONICS ( Determine state from conic elements )

     SUBROUTINE CONICS ( ELTS, ET, STATE )

Abstract

     Determine the state (position, velocity) of an orbiting body
     from a set of elliptic, hyperbolic, or parabolic orbital
     elements.

Required_Reading

     None.

Keywords

     CONIC
     EPHEMERIS

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      ELTS    ( 8 )
     DOUBLE PRECISION      ET
     DOUBLE PRECISION      STATE   ( 6 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     ELTS       I   Conic elements.
     ET         I   Input time.
     STATE      O   State of orbiting body at ET.

Detailed_Input

     ELTS     are conic elements describing the orbit of a body
              around a primary. The elements are, in order:

                 RP      Perifocal distance.
                 ECC     Eccentricity.
                 INC     Inclination.
                 LNODE   Longitude of the ascending node.
                 ARGP    Argument of periapse.
                 M0      Mean anomaly at epoch.
                 T0      Epoch.
                 MU      Gravitational parameter.

              Units are km, rad, rad/sec, km**3/sec**2. The epoch
              is given in ephemeris seconds past J2000. The same
              elements are used to describe all three types
              (elliptic, hyperbolic, and parabolic) of conic orbit.

     ET       is the time at which the state of the orbiting body
              is to be determined, in ephemeris seconds J2000.

Detailed_Output

     STATE    is the state (position and velocity) of the body at
              time ET. Components are x, y, z, dx/dt, dy/dt, dz/dt.

Parameters

     None.

Exceptions

     1)  If the eccentricity supplied is less than 0, the error
         SPICE(BADECCENTRICITY) is signaled.

     2)  If a non-positive periapse distance is supplied, the error
         SPICE(BADPERIAPSEVALUE) is signaled.

     3)  If a non-positive value for the attracting mass is supplied,
         the error SPICE(BADGM) is signaled.

     4)  If ELTS is such that the resulting orbit at periapsis has
         either its position or velocity equal to zero, or the square
         of the resulting specific angular momentum's magnitude is
         zero, an error is signaled by a routine in the call tree of
         this routine. This is an indication of invalid ELTS elements.

     5)  If ET is such that the offset in time from periapsis, at which
         the state is to be determined, is so large that there is a
         danger of floating point overflow during computation, an error
         is signaled by a routine in the call tree of this routine.

Files

     None.

Particulars

     None.

Examples

     Let VINIT contain the initial state of a spacecraft relative to
     the center of a planet at epoch ET, and let GM be the gravitation
     parameter of the planet. The call

        CALL OSCELT ( VINIT, ET, GM, ELTS )

     produces a set of osculating elements describing the nominal
     orbit that the spacecraft would follow in the absence of all
     other bodies in the solar system and non-gravitational forces
     on the spacecraft.

     Now let STATE contain the state of the same spacecraft at some
     other epoch, LATER. The difference between this state and the
     state predicted by the nominal orbit at the same epoch can be
     computed as follows.

        CALL CONICS ( ELTS, LATER, NOMINAL )
        CALL VSUBG  ( NOMINAL, STATE, 6, DIFF )

        WRITE (*,*) 'Perturbation in x, dx/dt = ', DIFF(1), DIFF(4)
        WRITE (*,*) '                y, dy/dt = ', DIFF(2), DIFF(5)
        WRITE (*,*) '                z, dz/dt = ', DIFF(3), DIFF(6)

Restrictions

     None.

Literature_References

     [1]  R. Bate, D. Mueller, and J. White, "Fundamentals of
          Astrodynamics," Dover Publications Inc., 1971.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)
     I.M. Underwood     (JPL)

Version

    SPICELIB Version 4.1.0, 13-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Removed
        unnecessary entries in $Revisions section.

        Added entry #4 and updated entry #5 in $Exceptions section.

    SPICELIB Version 4.0.0, 26-MAR-1998 (WLT)

        There was a coding error in the computation of the mean
        anomaly in the parabolic case. This problem has been
        corrected.

    SPICELIB Version 3.0.1, 15-OCT-1996 (WLT)

        Corrected a typo in the description of the units associated
        with the input elements.

    SPICELIB Version 3.0.0, 12-NOV-1992 (WLT)

        The routine was re-written to make use of NAIF's universal
        variables formulation for state propagation (PROP2B). As
        a result, several problems were simultaneously corrected.

        A major bug was fixed that caused improper state evaluations
        for ET's that precede the epoch of the elements in the
        elliptic case.

        A danger of non-convergence in the solution of Kepler's
        equation has been eliminated.

        In addition to this reformulation of CONICS checks were
        installed that ensure the elements supplied are physically
        meaningful. Eccentricity must be non-negative. The
        distance at periapse and central mass must be positive. If
        not errors are signaled.

    SPICELIB Version 2.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 2.0.0, 19-APR-1991 (WLT)

        An error in the hyperbolic state generation was corrected.

    SPICELIB Version 1.0.0, 31-JAN-1990 (IMU)