Orbits stability under the influence of Mücket-Treder potential

Abstract

The Mucket-Treder-type potential was initially introduced to explain the discrepancy between Mercury’s observed perihelion advance and the computed value based on Newton’s law, but it can also be used for many astronomical situations as, for instance, the study of the very eccentric cometary orbits in the neighborhood of the Sun. In this paper we tackle the two-body problem in the Mucket-Treder post-Newtonian field from the particular standpoint of orbits stability. Starting from the equations of motion and first integrals written in standard polar coordinates, we apply McGehee-type transformations of the second kind. Then we depict the phase-space structure considering the foliations by the energy constant and the angular momentum constant. Various stability regions are found for each case.