Consider a universe where gravity is proportional to the distance between two masses. That is to say, any mass attracts any other mass with a force given by
with .
Here and are the positions of the masses and . In this odd universe, an isolated star with mass explodes into many fragments. It turns out that after some time all the fragments coalesce, that is, they meet at a single point even if the explosion is anisotropic. Find the time in seconds. Assume that Newton's law holds true in this universe and that the star was initially at rest.