Exact Separation of Long- and Short-Period Effects in the Computation of Mean Elements of Artificial Satellite Theory

EasyChair Preprint 15632

Abstract

It is well known that mean elements obtained by canonical perturbation theory only agree with the average dynamics of the osculating orbit up to first order effects. While this fact does not necessarily compromise the accuracy of corresponding perturbation solutions, the loose use of the terminology “mean elements” in artificial satellite theory may obscure the understanding of the variety of available solutions in the literature, and thus make the implementation of additional patches to increase their performance ambiguous. After briefly reviewing the topic, the purely periodic, non-canonical, mean to osculating transformation that yields the exact separation between short- and long-period variations is computed for the main problem of artificial satellite theory up to the second order of the zonal harmonic of the second degree. It is also shown that this kind of non-canonical solution confines the long-period oscillations of the semimajor axis in the mean variation equations.

Keyphrases: Artificial satellite theory, General perturbations, The method of Lie transforms, perturbation theory

@booklet{EasyChair:15632,
  author    = {Martin Lara},
  title     = {Exact Separation of Long- and Short-Period Effects in the Computation of Mean Elements of Artificial Satellite Theory},
  howpublished = {EasyChair Preprint 15632},
  year      = {EasyChair, 2024}}