What is the distance between two objects in space as a function of time, considering only the force of gravity? To be specific, there are no other objects to be considered and the objects in question are not rotating.
For instance, say you have two objects that are 6 million miles apart. One is 50,000 kg and the other is 200 kg. Say I want to know how much time has passed when they are 3 million miles apart. How would I go about doing that?
EDIT: Looking at the other question I am having trouble following David Z's steps in his answer. Intermediate steps would be helpful. In particular I don't see how the integration step works. I also don't understand why the initial r value, ri remains as a variable after it's derivative has been set to 0, wouldn't the integral of that derivative (i.e. the function ri) be 0 + C? I also don't see how you wind up with a term that includes 2 under a square root sign.
I can not ask for the intermediate steps on the question itself because I do not have the reputation points.
I think it probably answers my question or will once I understand it, but I am not sure.
EDIT: I can sort of understand the integration step. But it seems like he is integrating with respect to two different variables on both sides, the variables being r on the left and the derivative of r on the right. There must be something I'm missing here.