oscltx_c |

Table of contents## Procedureoscltx_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_Inputstate 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_Outputelts 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'. ## ParametersSPICE_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]; ## Exceptions1) 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. ## ExamplesThe 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]). ./ ## Restrictions1) 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