Main-sequence systems: orbital stability around single star hosts

Stability is one of the most fundamental aspects regarding planetary systems. It plays an important role in our understanding on the formation channel of the planetary systems, as well as their habitability. Many approaches have been adopted to determine the stability of these systems, including brute-force N-body simulations, semi-analytical calculations, and more recently machine learning methods. This allows significant advances in our understanding of planetary system dynamics, as well as providing tools to constrain unknown parameters of exoplanetary systems (assuming these systems are stable). In the following, we focus on planets around single star hosts, and we provide an overview of the studies of planetary system stability for compact multi-planet systems and hierarchical multi-planet systems.
Comment: Preprint of a chapter for the 'Encyclopedia of Astrophysics' (Editor-in-Chief Ilya Mandel, Section Editor Dimitri Veras) to be published by Elsevier as a Reference Module. The number of references was capped