Laplace, in his weighty Theory of Jupiter and Saturn, explains the peculiarities of the motions of the two planets. Comparing data from Ptolemy to Brahe, he finds that Jupiter has systematically accelerated compared to predictions, and Saturn has systematically slowed down. Laplace realizes that the anomaly is dictated by the fact that the ratio between the planetary years of Saturn (29.48 years) and Jupiter (11.87 years) is almost equal to 5/2, which is a rational number. This means that every 10 years the two planets find themselves in the same mutual position, and their mutual perturbations can be amplified by resonance, thus preventing Jupiter from falling into the Sun and Saturn from escaping infinitely, abandoning the Solar System. Laplace isolates the issue in a numerical problem called the Problem of Small Divisors. Laplace will also identify several other quasi-rational ratios between the periods of the planets.
