Secular perturbations in Jupter and Saturn orbits

Abstract

The mutual gravitational attraction between the planets of the Solar System causes changes in their orbits that would be perfectly elliptical if the planets were subject only to the gravitational action of the Sun. These changes in orbits can be relatively short periods (a few years) at the end of which the planets return to their previous state. They can also have a cumulative effect by gradually changing orbits over years or centuries in a row, completely modifying the original orbit, or returning to the initial state after several centuries. These are the most interesting to analyze and are called secular disturbances.
This text analyzes the most apparent case of this phenomenon: the gravitational interaction between Jupiter and Saturn. Significant alterations were detected by the astronomer Halley in 1695, and at that time no reasonable justification in light of the law of universal gravitation was found, leading to doubts on the validity of this law. The problem was solved almost 100 years later by Laplace. This text is an analysis of Laplace's article Mémoire sur les inégalités séculaires des planètes et des satellites, from 1787, and its later developments.