Classical Gravitational Period After Newton
The main aim of Newton's successors, from Leonhard Euler, Alexis Clairaut and Jean d'Alembert in the mid-eighteenth century, down to E W Brown in the late nineteenth and early twentieth century, was to account completely and much more precisely for the moon's motions on the basis of Newton's laws, i.e. the laws of motion and of universal gravitation by attractions inversely proportional to the squares of the distances between the attracting bodies. They also wished to put the inverse-square law of gravitation to the test, and for a time in the 1740s it was seriously doubted, on account of what was then thought to be a large discrepancy between the Newton-theoretical and the observed rates in the motion of the lunar apogee. However Clairaut showed shortly afterwards (1749–50) that at least the major cause of the discrepancy lay not in the lunar theory based on Newton's laws, but in excessive approximations that he and others had relied on to evaluate it.
Most of the improvements in theory after Newton were made in algebraic form: they involved voluminous and highly laborious amounts of infinitesimal calculus and trigonometry. It also remained necessary, for completing the theories of this period, to refer to observational measurements.
Read more about this topic: Lunar Theory
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