Earth satellite dynamics by Picard iterations

TL;DR

This paper applies Picard's iterative method to Earth's satellite dynamics, providing a new solution that improves orbit propagation accuracy by correcting mean motion and initial conditions.

Contribution

It introduces a Picard iteration-based approach to satellite motion under Earth's oblateness, yielding more accurate mean dynamics and in-track error reduction.

Findings

Improved mean motion value enhances orbit propagation accuracy.

Secular terms correction improves initial condition accuracy.

Method recovers known linear trends in orbital elements.

Abstract

The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their solution under the strict mathematical assumptions of Picard's iterative method. Our approach recovers the known linear trends of the right ascension of the ascending node and the argument of the perigee, but differs from the accepted solution in the value of the mean motion. This amended rate radically improves the in-track errors of typical orbit propagations. In addition, our truncation of the Picard iterations solution to its secular terms includes the corrections that must be applied to the osculating initial conditions in the right propagation of the mean dynamics.