1) The problem statement : For this problem, We use Newtonian Mechanics. We are placed in a geocentric frame of reference. An object (of which the mass is irrelevant for this problem) is released into the earth's gravitational field at an altitude p(0) with no velocity whatsoever. The question is how do you describe the motion of this object ? In other words, how to find the function p(t) which associates position p to any instant t of the free fall considering that the acceleration is given as a function of position a(p) = (G*M)/(p^2) where G is the gravitational constant and M the mass of the earth. 2) Relevant equations : a(p) = (G*M)/(p^2) 3) Attempted solution : I realized i was confronted with a differential equation and that its solution would be the function I'm looking for. However, I'm new to differential equations and I could only go this far : a(p) = (G*M)/(p^2) means that p''(t) = (G*M)/(p(t))^2 So I would have to solve this : y'' = k/(y)^2 ( with k = G*M ) This where I need your help. Many thanks for considering my request.