Stability over exponentially long times in the planetary problem

Publisher Website
Google Scholar
Abstract
Using a scheme given by Lochak, we derive constructively a Nekhorochev-like result of stability in the planetary n-body problem. This allows us to give bounds on the variation of the semi-major axes of the planets over very long times. In this attempt, we first extend the theorems of stability over exponentially long times in the case of nearly integrable degenerate systems. Then, a refined study of the planetary Hamiltonian is needed to carry out the application. More specifically, we give accurate estimates of the complex analyticity widths for the considered Hamiltonian.