Stability of the Solar System

Remarks

In the queries of the Opticks Newton suggested that the mutual perturbations of the planets might grow until the system needs a reformation. Laplace and Lagrange showed that, to first order in the masses, the semi-major axes of the planets have no secular drift. The Kolmogorov–Arnold–Moser theorem shows that, for small enough masses, many initial conditions lead to quasi-periodic motions that last forever. But the real masses are far too large for the known estimates. Laskar showed in 1989, by integrating averaged equations over 200 million years, that the motion of the inner planets is chaotic in the sense of chaos theory. So the positions of the planets cannot be predicted more than some tens of millions of years ahead. Laskar and Gastineau computed 2501 orbits with very close initial conditions over 5 billion years. In about one percent of them the eccentricity of Mercury grew enough to allow a collision with Venus or the Sun. The question in its mathematical form is open.