A semi-empirical stability criterion for real planetary systems with eccentric orbits

Abstract

We test a crossing orbit stability criterion for eccentric planetary systems, based onWisdom's criterion of first-order mean motion resonance overlap. We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocentre distance of the inner orbit is larger than the pericentre distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multiplanetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.