On the averaging principle for one-frequency systems. An application to satellite motions

TL;DR

This paper applies an advanced averaging error estimation method to satellite motion in polar orbits, demonstrating efficient and accurate error bounds compared to direct numerical solutions for multiple satellite data sets.

Contribution

It extends previous averaging error estimation techniques to satellite dynamics, providing a practical and less costly way to estimate errors in orbital simulations.

Findings

Averaging errors are accurately estimated for satellite orbits.

The method reduces computational costs compared to direct numerical integration.

Estimates are validated on real satellite data.

Abstract

This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been introduced to obtain precise, fully quantitative estimates on the averaging error. Here, this procedure is applied to the motion of a satellite in a polar orbit around an oblate planet, retaining only the J_2 term in the multipole expansion of the gravitational potential. To exemplify the method, the averaging errors are estimated for the data corresponding to two Earth satellites; for a very large number of orbits, computation of our estimators is much less expensive than the direct numerical solution of the equations of motion.