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oscelt_c

 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

```   oscelt_c ( Determine conic elements from state )

void oscelt_c ( ConstSpiceDouble   state,
SpiceDouble        et,
SpiceDouble        mu,
SpiceDouble        elts   )

```

#### Abstract

```   Determine the set of osculating conic orbital elements that
corresponds to the state (position, velocity) of a body at
some epoch.
```

```   None.
```

#### Keywords

```   CONIC
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   Equivalent 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.

The epoch of the elements is the epoch of the input
are used to describe all three types (elliptic,
hyperbolic, and parabolic) of conic orbit.
```

#### Parameters

```   None.
```

#### 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.
```

#### Files

```   None.
```

#### Particulars

```   The CSPICE routine conics_c is the 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 elements of Phobos with respect to
Mars at some arbitrary time in the J2000 inertial reference
frame.

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

KPL/MK

File name: oscelt_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

'gm_de431.tpc',
'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program oscelt_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{
/.
Local variables.
./
SpiceDouble          elts   ;
SpiceDouble          et;
SpiceDouble          lt;
SpiceDouble          mu     ;
SpiceDouble          state  ;

SpiceInt             dim;

/.
Load the meta kernel listing the needed SPK, LSK and
PCK with gravitational parameters kernels.
./
furnsh_c ( "oscelt_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: the
bodvrd_c returns data as arrays, so to access the gravitational
parameter (the only value in the array), we use mu.
./
oscelt_c ( state, et, mu, elts );

/.
Output the elts vector.
./
printf( "Perifocal distance          (km): %21.10f\n", elts );
printf( "Eccentricity                    : %21.10f\n", elts );
printf( "Inclination                (deg): %21.10f\n",
elts * dpr_c() );
printf( "Lon of ascending node      (deg): %21.10f\n",
elts * dpr_c() );
printf( "Argument of periapsis      (deg): %21.10f\n",
elts * dpr_c() );
printf( "Mean anomaly at epoch      (deg): %21.10f\n",
elts * dpr_c() );
printf( "Epoch                        (s): %21.10f\n", elts );
printf( "Gravitational parameter (km3/s2): %21.10f\n", elts );

return ( 0 );
}

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

Perifocal distance          (km):       9232.5746716211
Eccentricity                    :          0.0156113904
Inclination                (deg):         38.1225231660
Lon of ascending node      (deg):         47.0384055902
Argument of periapsis      (deg):        214.1546430017
Mean anomaly at epoch      (deg):        340.5048466068
Epoch                        (s):  251812865.1837092042
Gravitational parameter (km3/s2):      42828.3736206991

2) Calculate the history of Phobos's orbit plane inclination
with respect to Mars in the J2000 frame 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 oscelt_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{
/.
Local parameters.
./
#define TIMLEN       41
/.
Local variables.
./
SpiceChar            utcstr [TIMLEN];

SpiceDouble          elts   ;
SpiceDouble          et;
SpiceDouble          lt;
SpiceDouble          mu     ;
SpiceDouble          state  ;
SpiceDouble          step;

SpiceInt             dim;
SpiceInt             i;

/.
Load the meta kernel listing the needed SPK, LSK and
PCK with gravitational parameters kernels.
./
furnsh_c ( "oscelt_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          Inclination\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                         );
oscelt_c ( state, et, mu, elts );

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

printf( "%s %12.6f\n", utcstr, elts * dpr_c( ) );

et += step;

}

return ( 0 );
}

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

UCT Time          Inclination
------------------------  -----------
2000 JAN 01 12:00:00.000    36.055248
2000 JUN 29 12:00:00.000    37.112144
2000 DEC 26 12:00:00.000    38.152129
2001 JUN 24 12:00:00.000    37.552071
2001 DEC 21 12:00:00.000    36.242049
2002 JUN 19 11:59:59.999    36.330470
2002 DEC 16 12:00:00.000    37.674595
2003 JUN 14 11:59:59.999    38.121191
2003 DEC 11 12:00:00.001    36.973204
2004 JUN 08 11:59:59.999    36.033732
2004 DEC 05 12:00:00.001    36.844542
2005 JUN 03 11:59:59.999    38.077365
2005 NOV 30 12:00:00.001    37.786106
2006 MAY 29 11:59:58.999    36.413540
2006 NOV 25 11:59:59.001    36.171050
2007 MAY 24 11:59:58.999    37.448015
2007 NOV 20 11:59:59.001    38.189118
2008 MAY 18 11:59:58.999    37.223573
2008 NOV 14 11:59:59.001    36.084745
2009 MAY 13 11:59:57.999    36.608971
```

#### 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

```     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)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.0.3, 10-AUG-2021 (JDR)

examples to -Examples section.

-CSPICE Version 1.0.2, 27-DEC-2007 (NJB)

Updated -Index_Entries header section to use keywords
"osculating" and "convert." Updated -Particulars header
section to refer to conics_c.

-CSPICE Version 1.0.1, 17-NOV-2005 (NJB)

The -Exceptions and -Restrictions header sections were filled in.
Some corrections were made to the code example.

-CSPICE Version 1.0.0, 16-APR-1999 (EDW)
```

#### Index_Entries

```   conic elements from state
osculating elements from state
convert state to osculating elements
```
`Fri Dec 31 18:41:10 2021`