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Index Page oscltx_c

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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

       oscltx_c ( Extended osculating elements from state )

       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.

       mu          is the gravitational parameter (GM, km^3/sec^2) 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 by a routine in the call tree of this routine.

       2)  If the specific angular momentum vector derived from `state'
           is the zero vector, the error SPICE(DEGENERATECASE)
           is signaled by a routine in the call tree of this routine.

       3)  If the position or velocity vectors derived from `state'
           is the zero vector, the error SPICE(DEGENERATECASE)
           is signaled by a routine in the call tree of this routine.

       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

       The numerical results shown for these examples 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) Determine the osculating conic orbital elements of Phobos
          with respect to Mars at some arbitrary time in the J2000
          inertial reference frame, including true anomaly, semi-major
          axis and period.

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

             KPL/MK

             File name: oscltx_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
                ---------                     --------
                mar097.bsp                    Mars satellite ephemeris
                gm_de431.tpc                  Gravitational constants
                naif0012.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'mar097.bsp',
                                    'gm_de431.tpc',
                                    'naif0012.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program oscltx_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables.
             ./
             SpiceDouble          elts   [SPICE_OSCLTX_NELTS];
             SpiceDouble          et;
             SpiceDouble          lt;
             SpiceDouble          mu     [1];
             SpiceDouble          state  [6];

             SpiceInt             dim;

             /.
             Load the meta kernel listing the needed SPK, LSK and
             PCK with gravitational parameters kernels.
             ./
             furnsh_c ( "oscltx_ex1.tm" );

             /.
             Convert the time string to ephemeris time
             ./
             str2et_c ( "Dec 25, 2007", &et );

             /.
             Retrieve the state of Phobos with respect to Mars in
             J2000.
             ./
             spkezr_c ( "PHOBOS", et, "J2000", "NONE", "MARS",
                         state,   &lt                         );

             /.
             Read the gravitational parameter for Mars.
             ./
             bodvrd_c ( "MARS", "GM", 1, &dim, mu );

             /.
             Convert the state 6-vector to the elts 8-vector. Note:
             bodvrd_c returns data as arrays, so to access the
             gravitational parameter (the only value in the array),
             we use mu[0]).
             ./
             oscltx_c ( state, et, mu[0], elts );

             /.
             Output the elts vector.
             ./
             printf( "Perifocal distance          (km):  %20.9f\n",
                      elts[0]                                      );
             printf( "Eccentricity                    :  %20.9f\n",
                      elts[1]                                      );
             printf( "Inclination                (deg):  %20.9f\n",
                      elts[2] * dpr_c ( )                          );
             printf( "Lon of ascending node      (deg):  %20.9f\n",
                      elts[3] * dpr_c ( )                          );
             printf( "Argument of periapsis      (deg):  %20.9f\n",
                      elts[4] * dpr_c ( )                          );
             printf( "Mean anomaly at epoch      (deg):  %20.9f\n",
                      elts[5] * dpr_c ( )                          );
             printf( "Epoch                        (s):  %20.9f\n",
                      elts[6]                                      );
             printf( "Gravitational parameter (km3/s2):  %20.9f\n",
                      elts[7]                                      );
             printf( "True anomaly at epoch      (deg):  %20.9f\n",
                      elts[8] * dpr_c ( )                          );
             printf( "Orbital semi-major axis     (km):  %20.9f\n",
                      elts[9]                                      );
             printf( "Orbital period               (s):  %20.9f\n",
                      elts[10]                                     );

             return ( 0 );
          }

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

          Perifocal distance          (km):        9232.574671621
          Eccentricity                    :           0.015611390
          Inclination                (deg):          38.122523166
          Lon of ascending node      (deg):          47.038405590
          Argument of periapsis      (deg):         214.154643002
          Mean anomaly at epoch      (deg):         340.504846607
          Epoch                        (s):   251812865.183709204
          Gravitational parameter (km3/s2):       42828.373620699
          True anomaly at epoch      (deg):         339.896662808
          Orbital semi-major axis     (km):        9378.993805149
          Orbital period               (s):       27577.090893061

       2) Calculate the history of Phobos's orbital period at intervals
          of six months for a time interval of 10 years.

          Use the meta-kernel from the first example.

          Example code begins here.

          /.
             Program oscltx_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define TIMLEN       24

             /.
             Local variables.
             ./
             SpiceChar            utcstr [TIMLEN];

             SpiceDouble          elts   [SPICE_OSCLTX_NELTS];
             SpiceDouble          et;
             SpiceDouble          lt;
             SpiceDouble          mu     [1];
             SpiceDouble          state  [6];
             SpiceDouble          step;

             SpiceInt             dim;
             SpiceInt             i;

             /.
             Load the meta kernel listing the needed SPK, LSK and
             PCK with gravitational parameters kernels.
             ./
             furnsh_c ( "oscltx_ex1.tm" );

             /.
             Read the gravitational parameter for Mars.
             ./
             bodvrd_c ( "MARS", "GM", 1, &dim, mu );

             /.
             Convert the time string to ephemeris time
             ./
             str2et_c ( "Jan 1, 2000 12:00:00", &et );

             /.
             A step of six months - in seconds.
             ./
             step = 180.0 * spd_c ( );

             /.
             10 years in steps of six months starting
             approximately Jan 1, 2000.
             ./
             printf( "        UCT Time             Period\n" );
             printf( "------------------------  ------------\n" );

             for ( i = 0; i < 20; i++ )
             {

                /.
                Retrieve the state; convert to osculating elements.
                ./
                spkezr_c ( "PHOBOS", et, "J2000", "NONE", "MARS",
                            state,  &lt                          );
                oscltx_c ( state, et, mu[0], elts );

                /.
                Convert the ephemeris time to calendar UTC.
                ./
                et2utc_c ( et, "C", 3, TIMLEN, utcstr );

                printf( "%s  %11.5f\n", utcstr, elts[10] );

                et = et + step;

             }

             return ( 0 );
          }

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

                  UCT Time             Period
          ------------------------  ------------
          2000 JAN 01 12:00:00.00  27575.41925
          2000 JUN 29 12:00:00.00  27575.12405
          2000 DEC 26 12:00:00.00  27574.98775
          2001 JUN 24 12:00:00.00  27574.27316
          2001 DEC 21 12:00:00.00  27573.09614
          2002 JUN 19 11:59:59.99  27572.26206
          2002 DEC 16 12:00:00.00  27572.33639
          2003 JUN 14 11:59:59.99  27572.57699
          2003 DEC 11 12:00:00.00  27572.44191
          2004 JUN 08 11:59:59.99  27572.33853
          2004 DEC 05 12:00:00.00  27572.96474
          2005 JUN 03 11:59:59.99  27574.45044
          2005 NOV 30 12:00:00.00  27575.62760
          2006 MAY 29 11:59:58.99  27576.17410
          2006 NOV 25 11:59:59.00  27576.70212
          2007 MAY 24 11:59:58.99  27577.62501
          2007 NOV 20 11:59:59.00  27578.95916
          2008 MAY 18 11:59:58.99  27579.54508
          2008 NOV 14 11:59:59.00  27578.92061
          2009 MAY 13 11:59:57.99  27577.80062

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

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       K.R. Gehringer      (JPL)
       I.M. Underwood      (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 1.0.1, 10-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Reformatted
           -Detailed_Input and -Parameters sections.

           Added complete code examples to -Examples section.

       -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

    Fri Dec 31 18:41:10 2021