| oscltx_c |
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Table of contents
Procedure
oscltx_c ( Extended osculating elements from state )
void oscltx_c ( ConstSpiceDouble state [6],
SpiceDouble et,
SpiceDouble mu,
SpiceDouble elts [SPICE_OSCLTX_NELTS] )
AbstractDetermine 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_ReadingNone. KeywordsCONIC ELEMENTS EPHEMERIS Brief_I/OVARIABLE 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.
FilesNone. ParticularsThis 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, < );
/.
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, < );
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_InstitutionN.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_Entriesextended conic elements from state extended osculating elements from state convert state to extended osculating elements |
Fri Dec 31 18:41:10 2021