Newton’s theory of gravitation solvedmany problemsof celestial mechanics but led to some majorproblems, one of which was that it gave rise toa serious paradox discussed in this article. Theparadox has a number of manifestations one ofwhich is presented here. It should be rememberedthat the root cause of all these paradoxes isfundamentally the same. Laplace attempted anad hoc solution. However, it could not be mathematicallydemonstrated that his proposal solvesthe difficulty. In this article, it is shown that hissuggestion removes the problem. A physical phenomenonthat can justify Laplace’s suggestion isalso mentioned briefly. This article also posesan interesting mathematical problem that can beattempted by interested readers. The computationalsolution is presented here.