A Second-Order Closed-Form J2 Model for the Draper Semi-Analytical Satellite Theory

Abstract

A second-order closed-form semi-analytical solution of the main problem of the artificial satellite theory (J2 contribution) consistent with the Draper Semi-analytic Satellite Theory (DSST) is presented. This paper aims to improve the computational speed of the numerical-based approach, which is only available in the GTDS-DSST version. The short-period terms are removed by means of an extension of the Lie-Deprit method using Delaunay variables. The averaged equations of motion are given explicitly and transformed to the non-singular equinoctial elements. Finally, the second-order terms in the equations of motion are included in the C/C++ version of the DSST orbit propagator.