Index Page oscltx_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 oscltx_c ( ConstSpiceDouble state [6],
                       SpiceDouble      et,
                       SpiceDouble      mu,
                       SpiceDouble      elts  [SPICE_OSCLTX_NELTS] )

#### Abstract

       Determine the set of osculating conic orbital elements that
       corresponds to the state (position, velocity) of a body at some
       epoch. In additional to the classical elements, return the true
       anomaly, semi-major axis, and period, if applicable.

#### Required_Reading

       None.

#### Keywords

       CONIC
       ELEMENTS
       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   Extended set of classical 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.
                      NU      True anomaly at epoch.
                      A       Semi-major axis. A is set to zero if
                              it is not computable.
                      TAU     Orbital period. Applicable only for
                              elliptical orbits. Set to zero otherwise.

                   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 orbits.

                   See the Parameters section for information on the
                   declaration of `elts'.

#### Parameters

       SPICE_OSCLTX_NELTS

                   is the length of the output array `elts'.

                   `elts' is intended to contain unused space to hold
                   additional elements that may be added in a later version
                   of this routine. In order to maintain forward
                   compatibility, user applications should declare `elts'
                   as follows:

                      SpiceDouble    elts[SPICE_OSCLTX_NELTS];

#### 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 eccentricity 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.

      11) The semi-major axis and period may not be computable for
          orbits having eccentricity too close to 1. If the semi-major
          axis is not computable, both it and the period are set to zero.
          If the period is not computable, it is set to zero.

#### Files

       None.

#### Particulars

       This routine returns in the first 8 elements of the array `elts'
       the outputs computed by oscelt_c, and in addition returns in
       elements 9-11 the quantities:

          elts[8]    true anomaly at `et', in radians.

          elts[9]   orbital semi-major axis at `et', in km. Valid
                    if and only if this value is non-zero.

                    The semi-major axis won't be computable if the
                    eccentricity of the orbit is too close to 1.
                    In this case A is set to zero.

          elts[10]  orbital period. If the period is not computable,
                    TAU is set to zero.

       The CSPICE routine conics_c is an approximate 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

          oscltx_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 1.0.0, 25-JAN-2017 (NJB) (KRG) (IMU) (EDW)

          Original version 11-NOV-2014 (NJB) (KRG) (IMU) (EDW)

#### Index_Entries

       extended conic elements from state
       extended osculating elements from state
       convert state to extended osculating elements

#### Link to routine oscltx_c source file oscltx_c.c

    Wed Apr  5 17:54:40 2017