An analytical state transition matrix for orbits perturbed by an oblate spheroid
Abstract
An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1977
 Bibcode:
 1977STIN...7815137M
 Keywords:

 Orbit Perturbation;
 Orbital Mechanics;
 Orbital Position Estimation;
 Satellite Perturbation;
 Algorithms;
 Matrices (Mathematics);
 Orbital Elements;
 Perturbation Theory;
 Satellite Orbits;
 Astrodynamics