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   void oscelt_c ( ConstSpiceDouble   state[6],
                   SpiceDouble        et,
                   SpiceDouble        mu,
                   SpiceDouble        elts[8]   )


   Determine the set of osculating conic orbital elements that
   corresponds to the state (position, velocity) of a body at
   some epoch.






   --------  ---  --------------------------------------------------
   state      I   State of body at epoch of elements.
   et         I   Epoch of elements.
   mu         I   Gravitational parameter (GM) of primary body.
   elts       O   Equivalent conic elements


   state      is the state (position and velocity) of the body
              at some epoch. Components are x, y, z, dx/dt, dy/dt,
              dz/dt. `state' must be expressed relative to an 
              inertial reference frame.  Units are km and km/sec.

   et         is the epoch of the input state, in ephemeris seconds
              past J2000.

                                                    3    2
   mu         is the gravitational parameter (GM, km /sec ) of
              the primary body.


   elts       are equivalent conic elements describing the orbit
              of the body around its primary. The elements are,
              in order:

                    rp      Perifocal distance.
                    ecc     Eccentricity.
                    inc     Inclination.
                    lnode   Longitude of the ascending node.
                    argp    Argument of periapsis.
                    m0      Mean anomaly at epoch.
                    t0      Epoch.
                    mu      Gravitational parameter.

              The epoch of the elements is the epoch of the input
              state. Units are km, rad, rad/sec. The same elements
              are used to describe all three types (elliptic,
              hyperbolic, and parabolic) of conic orbit.




   1) If `mu' is not positive, the error SPICE(NONPOSITIVEMASS)
      is signaled.

   2) If the specific angular momentum vector derived from STATE
      is the zero vector, the error SPICE(DEGENERATECASE)
      is signaled.

   3) If the position or velocity vectors derived from STATE
      is the zero vector, the error SPICE(DEGENERATECASE)
      is signaled.

   4) If the inclination is determined to be zero or 180 degrees,
      the longitude of the ascending node is set to zero.

   5) If the eccentricity is determined to be zero, the argument of
      periapse is set to zero.

   6) If the eccentricy of the orbit is very close to but not
      equal to zero, the argument of periapse may not be accurately

   7) For inclinations near but not equal to 0 or 180 degrees,
      the longitude of the ascending node may not be determined
      accurately.  The argument of periapse and mean anomaly may
      also be inaccurate.

   8) For eccentricities very close to but not equal to 1, the
      results of this routine are unreliable.

   9) If the specific angular momentum vector is non-zero but
      "close" to zero, the results of this routine are unreliable.

  10) If `state' is expressed relative to a non-inertial reference
      frame, the resulting elements are invalid.  No error checking
      is done to detect this problem.




   The CSPICE routine conics_c is the inverse of this routine:
   conics_c maps a set of osculating elements and a time to a state


   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

      oscelt_c ( 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.

   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.

      conics_c ( elts,    later, nominal );
      vsubg_c  ( nominal, state, 6, diff );

      printf( "Perturbation in x, dx/dt = %e %e\n", diff[0], diff[3] );
      printf( "                y, dy/dt = %e %e\n", diff[1], diff[4] );
      printf( "                z, dz/dt = %e %e\n", diff[2], diff[5] );


   1) The input state vector must be expressed relative to an
      inertial reference frame.

   2) Osculating elements are generally not useful for
      high-accuracy work.

   3) Accurate osculating elements may be difficult to derive for
      near-circular or near-equatorial orbits. Osculating elements
      for such orbits should be used with caution.

   4) Extracting osculating elements from a state vector is a
      mathematically simple but numerically challenging task.  The
      mapping from a state vector to equivalent elements is
      undefined for certain state vectors, and the mapping is
      difficult to implement with finite precision arithmetic for
      states near the subsets of R6 where singularities occur.

      In general, the elements found by this routine can have
      two kinds of problems:

         - The elements are not accurate but still represent
           the input state accurately.  The can happen in
           cases where the inclination is near zero or 180
           degrees, or for near-circular orbits.

         - The elements are garbage.  This can occur when
           the eccentricity of the orbit is close to but
           not equal to 1.   In general, any inputs that cause
           great loss of precision in the computation of the
           specific angular momentum vector or the eccentricity
           vector will result in invalid outputs.

      For further details, see the Exceptions section.

      Users of this routine should carefully consider whether
      it is suitable for their applications.  One recommended
      "sanity check" on the outputs is to supply them to the
      CSPICE routine conics_c and compare the resulting state
      vector with the one supplied to this routine.


   [1] Roger Bate, Fundamentals of Astrodynamics, Dover, 1971.


   N.J. Bachman    (JPL)
   K.R. Gehringer  (JPL)
   I.M. Underwood  (JPL)
   E.D. Wright     (JPL)


   -CSPICE Version 1.0.2, 27-DEC-2007 (NJB)
      Updated Index_Entries header section to use keywords
      "osculating" and "convert." Updated Particulars header
      section to refer to conics_c.

   -CSPICE Version 1.0.1, 17-NOV-2005 (NJB)

      The Exceptions and Restrictions header sections were filled in.
      Some corrections were made to the code example.

   -CSPICE Version 1.0.0, 16-APR-1999 (EDW)


   conic elements from state 
   osculating elements from state
   convert state to osculating elements
Wed Apr  5 17:54:40 2017