Suzuki, Jeff A.2023-10-032023-10-031996https://hdl.handle.net/2144/46795Newton's system of universal gravitation did not provide for long-term stability of the solar system, and gave rise to two versions of the stability question. The first was instability through resistance. During the first half of the eighteenth century, neo-Cartesians and others suggested the existence of an interplanetary medium to eliminate Newton's "occult" action at a distance. Though Cartesian vortices were finally eliminated at mid-century by the success of the strictly Newtonian theories of Clairaut and Euler, the interplanetary medium remained, supported by the secular acceleration of the Moon and discrepancies in the motions of Jupiter and Saturn. This evidence was questionable, however, and led Lagrange to argue that the remaining discrepancies in the motions of the Moon and planets were due to gravitation alone. Lagrange first argued for the periodicity of the variations in the Moon's motion, then, in 1776, he demonstrated that gravitation could cause only periodic variations in the major axes of the planets. Laplace, using methods Lagrange pioneered, extended the proof to cover all the important orbital elements, providing the classical proof of the stability of the solar system.en-USThis work is being made available in OpenBU by permission of its author, and is available for research purposes only. All rights are reserved to the author.MathematicsThesis/Dissertation