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 circular-planar 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 bi-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.

Preprint

Subjects: Astrophysics - Earth and Planetary Astrophysics; Mathematical Physics