Dynamics of two planets in co-orbital motion

TL;DR

This paper investigates the stability, periodic orbits, and new asymmetric solutions of two planets in co-orbital motion, considering various mass ratios and eccentricities, and examines the effects of slow mass variation.

Contribution

It identifies a new regime of asymmetric periodic solutions in co-orbital planetary systems and analyzes their stability across different parameters.

Findings

Discovery of asymmetric periodic solutions at specific angular configurations.

Stable co-orbital configurations persist under adiabatic mass changes.

Mapping of stability regions for different mass ratios and eccentricities.

Abstract

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, where \sigma is the difference in mean longitudes and \Delta\omega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.