oscelt_c

Index Page oscelt_c
A B C D E F G H I J K L M N O P Q R S T U V W X
Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries
#### Procedure
       void oscelt_c ( ConstSpiceDouble   state[6],
                       SpiceDouble        et,
                       SpiceDouble        mu,
                       SpiceDouble        elts[8]   )
#### Abstract
       Determine the set of osculating conic orbital elements that
       corresponds to the state (position, velocity) of a body at
       some epoch.
#### Required_Reading
       None.
#### Keywords
       CONIC
       EPHEMERIS
#### Brief_I/O
       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       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
#### Detailed_Input
       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.
#### Detailed_Output
       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.
#### Parameters
       None
#### Exceptions
       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
          determined.

       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.
#### Files
       None.
#### Particulars
       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
       vector.
#### 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

          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] );
#### Restrictions
       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.
#### Literature_References
       [1] Roger Bate, Fundamentals of Astrodynamics, Dover, 1971.
#### Author_and_Institution
       N.J. Bachman    (JPL)
       K.R. Gehringer  (JPL)
       I.M. Underwood  (JPL)
       E.D. Wright     (JPL)
#### Version
       -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)
#### Index_Entries
       conic elements from state
       osculating elements from state
       convert state to osculating elements
#### Link to routine oscelt_c source file oscelt_c.c

    Thu Apr 16 08:58:46 2009