Chapter 6: The Stability of the Solar System

Urbain Jean-Joseph Le Verrier repeated Laplace’s calculations on planetary motions taking into account higher order terms. As far as Le Verrier was concerned, Laplace had shown that Newtonian mechanics is basically correct; he was not interested in testing whether the gravitation law was exact but rather was interested in constructing as precise a theory as possible. For this reason he took account of the perturbations due to all the planets and expanded perturbing functions between planet pairs up to sixth order with respect to inclinations, and up to seventh order with respect to eccentricities…