My friends and I have a problem that seems simple enough, but has proven to be pretty hard. We need some help. Suppose you have an object in space with no initial velocity relative to the Earth. Now, due to the Earth's gravity, the object will begin to accelerate towards the Earth instantly. We need to find the velocity of the object after any given time; so, we need an equation for the velocity of the object in terms of time t and the original distance r. Please note: Acceleration due to gravity does NOT equal -9.81m/s^2 for this problem. acceleration due to gravity is -GM/r^2 and r is decreasing as t increases because the object is accelerating towards the Earth at a faster and faster rate. Now, we realize this will probably take some differential equations to solve, but we can't find what differential equations we need to solve. Any help at all is appreciated. Thank you!