The stability of our solar system

Most investigations of the stability of the solar system have been concerned with the question as to whether the very long term effect of the gravitational attractions of the planets on each other will be to alter the nearly coplanar, nearly circular nature of the orbits in which they move. Analytical investigations in the traditions of Laplace, Lagrange, Poisson and Poincaré strongly indicate stability, though rely on asymptotic expansions with difficult analytical properties. The question is related to the existence of invariant tori, which have been proved to exist in certain motions. Numerical integration experiments have thrown considerable light on possible types of motions, especially in fictitious solar systems in which the planetary masses have been increased to enhance the perturbations, and in testing how critical are stability boundary estimates given by Hill surface type methods.