Long term evolution of planetary systems with a terrestrial planet and a giant planet

Abstract

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion. Finally, we briefly discuss possible applications of the analytical estimates in astrophysical problems.

Accepted for publication in MNRAS

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• Dynamics and habitability in circumstellar planetary systems of known binary stars
• Giant planets: good neighbors for habitable worlds?
• Aquaplanet Models on Eccentric Orbits: Effects of Rotation Rate on Observables
• Long-term dynamical survival of deep Earth coorbitals
• Exploring Climate with Obliquity in a Variable-eccentricity Earth-like World
• Dynamics and habitability of the TESS circumbinary systems TOI-1338 and TIC-172900988
• Testing the third body hypothesis in the Cataclysmic Variables LU Camelopardalis, QZSerpentis, V1007 Herculis and BK Lyncis