Is the Solar System stable?

Abstract

Since the formulation of the problem by Newton, and during three centuries, astronomers and mathematicians have sought to demonstrate the stability of the Solar System. As mentioned by Poincaré, several demonstrations of the stability of the Solar System have been published. By Laplace and Lagrange in the first place, then by Poisson, and more recently by Arnold. Others came after again. Were the old demonstrations insufficient, or are the new ones unnecessary? These rigorous demonstrations are in fact various approximations of idealized systems, but thanks to the numerical experiments of the last two decades, we know now that the motion of the planets in the Solar System is chaotic. This prohibits any accurate prediction of the planetary trajectories beyond a few tens of millions of years. The recent simulations even show that planetary collisions or ejections are possible on a period of less than 5 billion years, before the end of the life of the Sun. © 2013 Springer Basel.