The motion of the inner planets (Mercury, Venus, Earth and Mars) is chaotic. Numerical evidence was given by Jacques Laskar, who showed in 1994 that the orbits of the inner planets exhibited resonances in some periodic motions. Because of the sensitivity to initial conditions, numerical errors grow exponentially, so it is impossible to control the positions of the planets over long periods of time (hundreds of millions of years) using the standard equations of planetary motion. Laskar derived an *averaged system* of equations and showed that the orbit of Mercury could at some time cross that of Venus.

Another way to study chaotic systems is to use numerous simulations in parallel, using an ensemble of initial conditions and derive probabilities of future behaviors. The shadowing lemma guarantees that a simulated trajectory for a close initial condition resembles a real trajectory. In 2009, Laskar announced in *Nature* the results of an ambitious program of 2000 parallel simulations of the solar system over periods of the order of 5 billions years. The new model of the solar system was much more sophisticated and included some relativistic effects. The simulations showed a 1% chance that Mercury could be destabilized and encounter a collision with the Sun or Venus. A much smaller number of simulations showed that all the inner planets could be destabilized, with a potential collision between the Earth and either Venus or Mars likely in approximately 3.3 billion years.