How did Jean Le Rond d’Alembert study the orbital perturbations of planets?

Jean Le Rond d’Alembert studied the orbital perturbations of planets by applying advanced analytical methods to the problem of celestial motion. He presented his initial findings on these variations of orbit to the Academy of Sciences and later perfected his solutions in his work titled Recherches sur différents points importants du système du monde, published between 1754 and 1756.1

His approach was part of a broader effort to mathematize mechanics, transforming it from a branch of physics into an axiomatic system that relied on rigorous mathematical manipulation. By utilizing his developments in partial differential equations and his principles of dynamics, d’Alembert contributed to the foundational work in celestial mechanics that eventually allowed later scientists, such as Pierre-Simon, marquis de Laplace, to demonstrate the long-term stability of the solar system.21