A paradox of Newtonian gravitation and Laplace’s solution

Abstract

Newton’s theory of gravitation solvedmany problems of celestialmechanics but led to some major problems, one of which was that it gave rise to a serious paradox discussed in this article. The paradox has a number of manifestations one of which is presented here. It should be remembered that the root cause of all these paradoxes is fundamentally the same. Laplace attempted an ad hoc solution. However, it could not be mathematically demonstrated that his proposal solves the difficulty. In this article, it is shown that his suggestion removes the problem. A physical phenomenon that can justify Laplace’s suggestion is also mentioned briefly. This article also poses an interesting mathematical problem that can be attempted by interested readers. The computational solution is presented here.