A numerical study of fourth- and fifth-order retrograde mean motion resonances in planetary systems

Abstract

We present a numerical study on the stability of all fourth and fifth order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted problem) or masses corresponding to either Neptune, Saturn or Jupiter (planetary problem). The fixed point families exist in all cases and are identified through libration of all resonant angles simultaneously. In addition, configurations with libration of a single resonant angle were also observed. Our results for the elliptic restricted 3-body problem are in agreement with previous studies of retrograde periodic orbits, but we also observe new families not previously reported. Our results regarding stable resonant retrograde configurations in the planetary 3-body problem could be applicable to extra-solar systems.