Stability criteria for hierarchical triple systems

Abstract

In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the concept of zero velocity surfaces of the restricted three body problem, to the general case. We also present criteria that have to do with escape of one of the bodies. Then, we talk about the criteria that have been derived using data from numerical integrations. Finally, we report on criteria that involve the concept of chaos. In all cases, wherever possible, we discuss advantages and disadvantages of the criteria and the methods their derivation was based on, and some comparison is made in several cases.

This is a preprint of a review article published in 'Celestial Mechanics and Dynamical Astronomy' in 2008

References in corpus (4)

• Long-Term Stability of Planets in Binary Systems
• Statistical properties of exoplanets III. Planet properties and stellar multiplicity
• Resonance Overlap is Responsible for Ejecting Planets in Binary Systems
• The Dynamics of Two Massive Planets on Inclined Orbits

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