eqncpv_c |

Table of contents## Procedureeqncpv_c (Equinoctial Elements to position and velocity) void eqncpv_c ( SpiceDouble et, SpiceDouble epoch, ConstSpiceDouble eqel[9], SpiceDouble rapol, SpiceDouble decpol, SpiceDouble state[6] ) ## AbstractCompute the state (position and velocity) of an object whose trajectory is described via equinoctial elements relative to some fixed plane (usually the equatorial plane of some planet). ## Required_ReadingSPK ## KeywordsEPHEMERIS ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- et I Epoch in seconds past J2000 to find state epoch I Epoch of elements in seconds past J2000 eqel I Array of equinoctial elements rapol I Right Ascension of the pole of the reference plane decpol I Declination of the pole of the reference plane state O State of the object described by `eqel'. ## Detailed_Inputet is the epoch (ephemeris time) at which the state of the target body is to be computed. `et' is measured in seconds past the J2000 epoch. epoch is the epoch of the equinoctial elements in seconds past the J2000 epoch. eqel is an array of 9 double precision numbers that are the equinoctial elements for some orbit expressed relative to the equatorial frame of the central body defined as - The Z-axis of the equatorial frame is the direction of the pole of the central body relative to some inertial frame; - The X-axis is given by the cross product of the Z-axis of the inertial frame with the direction of the pole of the central body; and - The Y-axis completes a right handed frame. If the X-axis of the equatorial frame is aligned with the X-axis of the inertial frame, then the X-axis of the equatorial frame will be located at 90 degrees + rapol in the inertial frame. The specific arrangement of the elements is spelled out below: eqel[0] is the semi-major axis (A) of the orbit in km. eqel[1] is the value of H at the specified epoch. ( E*sin(argp+node) ). eqel[2] is the value of K at the specified epoch ( E*cos(argp+node) ). eqel[3] is the mean longitude (mean0+argp+node) at the epoch of the elements measured in radians. eqel[4] is the value of P (tan(inc/2)*sin(node))at the specified epoch. eqel[5] is the value of Q (tan(inc/2)*cos(node))at the specified epoch. eqel[6] is the rate of the longitude of periapse (dargp/dt + dnode/dt ) at the epoch of the elements. This rate is assumed to hold for all time. The rate is measured in radians per second. eqel[7] is the derivative of the mean longitude ( dm/dt + dargp/dt + dnode/dt ). This rate is assumed to be constant and is measured in radians/second. eqel[8] is the rate of the longitude of the ascending node ( dnode/dt). This rate is measured in radians per second. where inc is the inclination of the orbit, argp is the argument of periapse, node is longitude of the ascending node, and E is eccentricity of the orbit. rapol is the Right Ascension of the pole of the reference plane with respect to some inertial frame (measured in radians). decpol is the Declination of the pole of the reference plane with respect to some inertial frame (measured in radians). ## Detailed_Outputstate is the state of the object described by `eqel' relative to the inertial frame used to define `rapol' and `decpol'. Units are in km and km/sec. ## ParametersNone. ## Exceptions1) If the eccentricity corresponding to the input elements is greater than 0.9, the error SPICE(ECCOUTOFRANGE) is signaled by a routine in the call tree of this routine. 2) If the semi-major axis of the elements is non-positive, the error SPICE(BADSEMIAXIS) is signaled by a routine in the call tree of this routine. ## FilesNone. ## ParticularsThis routine evaluates the input equinoctial elements for the specified epoch and return the corresponding state. This routine was adapted from a routine provided by Bob Jacobson of the Planetary Dynamics Group of the Navigation and Flight Mechanics Section at JPL. ## ExamplesThe numerical results shown for this example 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) Compute a state vector from a set of equinoctial elements. Suppose you have classical elements and rates of change of the ascending node and argument of periapse for some satellite of the Earth. By transforming the classical elements this routine computes the state of the object at an arbitrary epoch. The code below illustrates how to do this. The table below illustrates the meanings of the various variables used in the discussion below. Variable Meaning -------- ---------------------------------- a Semi-major axis in km. ecc Eccentricity of orbit. inc Inclination of orbit. node Longitude of the ascending node at epoch. omega Argument of periapse at epoch. m Mean anomaly at epoch. dmdt Mean anomaly rate in radians/second. dnode Rate of change of longitude of ascending node in radians/second. domega Rate of change of argument of periapse in radians/second. epoch is the epoch of the elements in seconds past the J2000 epoch. Example code begins here. /. Program eqncpv_ex1 ./ #include <stdio.h> #include <math.h> #include "SpiceUsr.h" int main() { /. Local variables. ./ SpiceInt i; SpiceDouble a; SpiceDouble argp; SpiceDouble decpol; SpiceDouble ecc; SpiceDouble eqel [9]; SpiceDouble et; SpiceDouble gm; SpiceDouble inc; SpiceDouble m0; SpiceDouble n; SpiceDouble node; SpiceDouble p; SpiceDouble rapol; SpiceDouble t0; SpiceDouble state [6]; p = 1.0e4; gm = 398600.436; ecc = 0.1; a = p/( 1. - ecc ); n = sqrt ( gm / a ) / a; argp = 30. * rpd_c(); node = 15. * rpd_c(); inc = 10. * rpd_c(); m0 = 45. * rpd_c(); t0 = -100000000.; /. Define the input equinoctial elements. eqel[0] = a eqel[1] = ecc * sin( omega + node ) eqel[2] = ecc * cos( omega + node ) eqel[3] = m + omega + node eqel[4] = tan(inc/2.0) * sin(node) eqel[5] = tan(inc/2.0) * cos(node) eqel[6] = domega eqel[7] = domega + dmdt + dnode eqel[8] = dnode In this case, the rates of node and argument of periapse are zero and the pole of the central frame is aligned with the pole of an inertial frame. ./ eqel[0] = a; eqel[1] = ecc*sin(argp+node); eqel[2] = ecc*cos(argp+node); eqel[3] = m0 + argp + node; eqel[4] = tan(inc/2.)*sin(node); eqel[5] = tan(inc/2.)*cos(node); eqel[6] = 0.; eqel[7] = n; eqel[8] = 0.; rapol = -halfpi_c(); decpol = halfpi_c(); et = t0 - 10000.0; for ( i = 0; i < 10; i++) { et = et + 250.; ## Restrictions1) The equinoctial elements used by this routine are taken from "Tangent" formulation of equinoctial elements P = tan(inclination/2) * sin(R.A. of ascending node) Q = tan(inclination/2) * cos(R.A. of ascending node) Other formulations use Sine instead of Tangent. We shall call these the "Sine" formulations. P = sin(inclination/2) * sin(R.A. of ascending node) Q = sin(inclination/2) * cos(R.A. of ascending node) If you have equinoctial elements from this alternative formulation you should replace P and Q by the expressions below. P = P / sqrt( 1.0 - P*P - Q*Q ) Q = Q / sqrt( 1.0 - P*P - Q*Q ) This will convert the Sine formulation to the Tangent formulation. ## Literature_References[1] W. Owen and R. Vaughan, "Optical Navigation Program Mathematical Models," JPL Engineering Memorandum 314-513, August 9, 1991. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) E.D. Wright (JPL) ## Version-CSPICE Version 1.0.1, 02-AUG-2021 (JDR) Edited the header to comply with NAIF standard. Added example's problem statement. Removed unused variable from code example. Added SPK required reading and -Exceptions section. Removed unnecessary comments from the code. -CSPICE Version 1.0.0, 20-MAR-2012 (EDW) ## Index_EntriesCompute a state from equinoctial elements |

Fri Dec 31 18:41:06 2021