void oscltx_c ( ConstSpiceDouble state ,
SpiceDouble elts [SPICE_OSCLTX_NELTS] )
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.
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.
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
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,
RP Perifocal distance.
LNODE Longitude of the ascending node.
ARGP Argument of periapsis.
M0 Mean anomaly at 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'.
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'
1) If MU is not positive, the error SPICE(NONPOSITIVEMASS)
2) If the specific angular momentum vector derived from `state'
is the zero vector, the error SPICE(DEGENERATECASE)
3) If the position or velocity vectors derived from `state'
is the zero vector, the error SPICE(DEGENERATECASE)
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
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.
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 true anomaly at `et', in radians.
elts 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 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
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, diff );
printf( " y, dy/dt = %e %e\n", diff, diff );
printf( " z, dz/dt = %e %e\n", diff, diff );
1) The input state vector must be expressed relative to an
inertial reference frame.
2) Osculating elements are generally not useful for
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.
 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 1.0.0, 25-JAN-2017 (NJB) (KRG) (IMU) (EDW)
Original version 11-NOV-2014 (NJB) (KRG) (IMU) (EDW)
extended conic elements from state
extended osculating elements from state
convert state to extended osculating elements