Table of contents
CSPICE_OSCLTX determines 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.
Given:
state the state (position and velocity) of the body at some epoch.
[6,1] = size(state); double = class(state)
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 the epoch of the input state, in ephemeris seconds past
J2000.
[1,1] = size(et); double = class(et)
mu the gravitational parameter (GM, km^3/sec^2) of the primary
body.
[1,1] = size(mu); double = class(mu)
the call:
[elts] = cspice_oscltx( state, et, mu )
returns:
elts equivalent conic elements describing the orbit of the body
around its primary.
[SPICE_OSCLTX_NELTS,1] = size(elts); double = class(elts)
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'.
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.
Any numerical results shown for these examples may differ between
platforms as the results depend on the SPICE kernels used as input
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.
function oscltx_ex1()
%
% Load the meta kernel listing the needed SPK, LSK and
% PCK with gravitational parameters kernels.
%
cspice_furnsh( 'oscltx_ex1.tm' );
%
% Convert the time string to ephemeris time
%
[et] = cspice_str2et( 'Dec 25, 2007' );
%
% Retrieve the state of Phobos with respect to Mars in
% J2000.
%
[state, lt] = cspice_spkezr( 'PHOBOS', et, 'J2000', ...
'NONE', 'MARS' );
%
% Read the gravitational parameter for Mars.
%
[mu] = cspice_bodvrd( 'MARS', 'GM', 1 );
%
% Convert the state 6-vector to the elts 8-vector. Note:
% cspice_bodvrd returns data as arrays, so to access the
% gravitational parameter (the only value in the array),
% we use mu(1)).
%
[elts] = cspice_oscltx( state, et, mu(1) );
%
% Output the elts vector.
%
fprintf( 'Perifocal distance (km): %20.9f\n', elts(1) )
fprintf( 'Eccentricity : %20.9f\n', elts(2) )
fprintf( 'Inclination (deg): %20.9f\n', ...
elts(3) * cspice_dpr )
fprintf( 'Lon of ascending node (deg): %20.9f\n', ...
elts(4) * cspice_dpr )
fprintf( 'Argument of periapsis (deg): %20.9f\n', ...
elts(5) * cspice_dpr )
fprintf( 'Mean anomaly at epoch (deg): %20.9f\n', ...
elts(6) * cspice_dpr )
fprintf( 'Epoch (s): %20.9f\n', elts(7) )
fprintf( 'Gravitational parameter (km3/s2): %20.9f\n', elts(8) )
fprintf( 'True anomaly at epoch (deg): %20.9f\n', ...
elts(9) * cspice_dpr )
fprintf( 'Orbital semi-major axis (km): %20.9f\n', elts(10) )
fprintf( 'Orbital period (s): %20.9f\n', elts(11) )
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/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.
function oscltx_ex2()
%
% Load the meta kernel listing the needed SPK, LSK and
% PCK with gravitational parameters kernels.
%
cspice_furnsh( 'oscltx_ex1.tm' );
%
% Read the gravitational parameter for Mars.
%
[mu] = cspice_bodvrd( 'MARS', 'GM', 1 );
%
% Convert the time string to ephemeris time
%
[et] = cspice_str2et( 'Jan 1, 2000 12:00:00' );
%
% A step of six months - in seconds.
%
step = 180.0 * cspice_spd;
%
% 10 years in steps of six months starting
% approximately Jan 1, 2000.
%
fprintf( ' UCT Time Period\n' )
fprintf( '------------------------ ------------\n' )
for i=1:20
%
% Retrieve the state; convert to osculating elements.
%
[state, lt] = cspice_spkezr( 'PHOBOS', et, 'J2000', ...
'NONE', 'MARS' );
[elts] = cspice_oscltx( state, et, mu(1) );
%
% Convert the ephemeris time to calendar UTC.
%
[utcstr] = cspice_et2utc( et, 'C', 3 );
fprintf( '%s %11.5f\n', utcstr, elts(11) )
et = et + step;
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
UCT Time Period
------------------------ ------------
2000 JAN 01 12:00:00.000 27575.41925
2000 JUN 29 12:00:00.000 27575.12405
2000 DEC 26 12:00:00.000 27574.98775
2001 JUN 24 12:00:00.000 27574.27316
2001 DEC 21 12:00:00.000 27573.09614
2002 JUN 19 11:59:59.999 27572.26206
2002 DEC 16 12:00:00.000 27572.33639
2003 JUN 14 11:59:59.999 27572.57699
2003 DEC 11 12:00:00.001 27572.44191
2004 JUN 08 11:59:59.999 27572.33853
2004 DEC 05 12:00:00.001 27572.96474
2005 JUN 03 11:59:59.999 27574.45044
2005 NOV 30 12:00:00.001 27575.62760
2006 MAY 29 11:59:58.999 27576.17410
2006 NOV 25 11:59:59.001 27576.70212
2007 MAY 24 11:59:58.999 27577.62501
2007 NOV 20 11:59:59.001 27578.95916
2008 MAY 18 11:59:58.999 27579.54508
2008 NOV 14 11:59:59.001 27578.92061
2009 MAY 13 11:59:57.999 27577.80062
This routine returns in the first 8 elements of the array `elts'
the outputs computed by cspice_oscelt, and in addition returns in
elements 9-11 the quantities:
elts(9) true anomaly at `et', in radians.
elts(10) 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(11) orbital period. If the period is not computable,
TAU is set to zero.
The Mice routine cspice_conics is an approximate inverse of this
routine: cspice_conics maps a set of osculating elements and a time to a
state vector.
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.
12) If any of the input arguments, `state', `et' or `mu', is
undefined, an error is signaled by the Matlab error handling
system.
13) If any of the input arguments, `state', `et' or `mu', is not
of the expected type, or it does not have the expected
dimensions and size, an error is signaled by the Mice
interface.
None.
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
Mice routine cspice_conics and compare the resulting state
vector with the one supplied to this routine.
MICE.REQ
[1] R. Bate, D. Mueller, and J. White, "Fundamentals of
Astrodynamics," Dover Publications Inc., 1971.
J. Diaz del Rio (ODC Space)
-Mice Version 1.0.0, 10-AUG-2021 (JDR)
extended conic elements from state
extended osculating elements from state
convert state to extended osculating elements
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