structural:reformatting, stylistic:style_transfer, structural:scholar_edition
Stability of the Solar System

Sir Isaac Newton had published his Philosophiæ Naturalis Principia Mathematica in 1687 in which he gave a derivation of Kepler's laws, which describe the motion of the planets, from his laws of motion and his law of universal gravitation. However, though Newton had privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to account for the more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of the Solar System. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life. It is now generally regarded that Laplace's methods on their own, though vital to the development of the theory, are not sufficiently precise to demonstrate the stability of the Solar System; today the Solar System is understood to be generally chaotic at fine scales, although currently fairly stable on coarse scale.

One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn was expanding. The problem had been tackled by Leonhard Euler in 1748, and Joseph Louis Lagrange in 1763, but without success. In 1776, Laplace published a memoir in which he first explored the possible influences of a purported luminiferous ether or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtonian gravity. Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion. Laplace noted that though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis into the higher-order terms, up to and including the cubic. Using this more exact analysis, Laplace concluded that any two planets and the Sun must be in mutual equilibrium and thereby launched his work on the stability of the Solar System. Gerald James Whitrow described the achievement as "the most important advance in physical astronomy since Newton".

Laplace had a wide knowledge of all sciences and dominated all discussions in the Académie. Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.