An application fo the Nekhoroshev theorem to the restricted three-body problem
The stability of motion in the planar circular restricted three-body problem is considered. The Hamiltonian of the perturbed motion is expresed in the canonical Delaunay variables and developed in the Fourier series taking into account a small parameter. The Nekhoroshev theorem which gives an exponentional estimate of the time of stability of nearly integrable Hamiltonian systems is applied. As a concrete application the Sun-Ceres-Jupiter case was considered. It is found that a stability of motion is possible for a time comparable to the age of the solar system and for a mass ratio of the primaries less or equal than \(10^{-6}\).
scientific article; zbMATH DE number 1077167