A history of the stability problem in celestial mechanics, from Newton to Laplace (1642-1787)
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Abstract
Newton'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.
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