Atlas of three body mean motion resonances in the Solar System

Abstract

We present a numerical method to estimate the strengths of arbitrary three body mean motion resonances between two planets in circular coplanar orbits and a massless particle in an arbitrary orbit. This method allows us to obtain an atlas of the three body resonances in the Solar System showing where are located and how strong are thousands of resonances involving all the planets from 0 to 1000au. This atlas confirms the dynamical relevance of the three body resonances involving Jupiter and Saturn in the asteroid belt but also shows the existence of a family of relatively strong three body resonances involving Uranus and Neptune in the far Trans-Neptunian region and relatively strong resonances involving terrestrial and jovian planets in the inner planetary system. We calculate the density of relevant resonances along the Solar System resulting that the main asteroid belt is located in a region of the planetary system with the lowest density of three body resonances. The method also allows the location of the equilibrium points showing the existence of asymmetric librations (σ≠0° or 180°). We obtain the functional dependence of the resonance’s strength with the order of the resonance and the eccentricity and inclination of the particle’s orbit. We identify some objects evolving in or very close to three body resonances with Earth–Jupiter, Saturn–Neptune and Uranus–Neptune apart from Jupiter–Saturn, in particular the NEA 2009 SJ18 is evolving in the resonance 1−1E−1J and the centaur 10199 Chariklo is evolving under the influence of the resonance 5−2S−2N.