Is the Solar System stable?

The search for the Solar System's stability is a fascinating adventure that started with Newton's discovery of the law of gravitation. While this question has been the source of major discoveries both in mathematics and in physics for about three centuries, it is still not fully answered. In the past 30 years, a breakthrough occurred with the numerical discovery that the Solar System is chaotic with a Lyapunov time of about 10 billion years. In particular, it has been shown that planetary collisions are possible between the four smallest terrestrial planets. Chaotic motion thus prevent any long-term accurate prediction of planetary positions, and requires us to invent new techniques to predict the state of the Solar System on a timescale comparable to its lifetime. In the present talk, I will show how the methods issued from statistical physics can be used to study the long-term stability of the Solar System. I will explain how the probability of fast destabilizations can be predicted using large deviation theory.