On mean elements in artificial-satellite theory

Abstract

The merits of a perturbation theory based on a mean-to-osculating transformation that is purely periodic in the fast angle are investigated. The exact separation of the perturbed Keplerian dynamics into purely short-period effects and long-period mean frequencies is achieved by a non-canonical transformation, which, therefore, cannot be obtained by Hamiltonian methods. For this case, the evolution of the mean elements strictly adheres to the average behavior of the osculating orbit. However, due to the unavoidable truncation of perturbation solutions, the fact that this kind of theory confines in the mean variations the long-period terms of the semimajor axis, how tiny they may be, can have adverse effects in the accuracy of long-term semi-analytic propagations based on it.