On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects

The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the planar circular case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple two-dimensional map, that is invariant with respect to the mass parameter of the planet, and turns out to be a remarkable tool to investigate the distribution of the co-orbitals objects of interest. The study is based on the data corresponding to the ephemerides computed by the JPL Horizons system for asteroids with a sufficient low orbital inclination with respect to the Sun–planet orbital plane. These objects are cataloged according to their current dynamics, together with the transitions that occur in the given time frame from a given type of co-orbital motion to another. The results provide a general catalog of co-orbital asteroids in the solar system, the first one to our knowledge, and an efficient mean to study transitions.