An analytical state transition matrix for an orbit perturbed by oblateness
Abstract
A new analytical state transition matrix is presented. This transition matrix contains the twobody terms and the secular and short periodic terms due to the J2 oblateness perturbation. The matrix is derived from a satellite theory which uses a set of 8 canonical elements with the true anomaly as the independent variable. This theory was chosen because of its accuracy and concise formulation. It presents no problems concerning the accuracy of the mean motion, which is typical for classical satellite theories. Numerical experiments show the J2 transition matrix to be superior to the simple twobody matrix.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1976
 Bibcode:
 1976aiaa.meetT....M
 Keywords:

 Canonical Forms;
 Matrices (Mathematics);
 Orbit Perturbation;
 Perturbation Theory;
 Satellite Perturbation;
 Two Body Problem;
 Differential Equations;
 Position Errors;
 State Vectors;
 Astrodynamics