For a long time I've wondered how you derive the equations of orbital motion from the law of universal gravitation. Recently I've been feeling like my mathematics knowledge has caught up to the point where I can attempt to do this myself, but I keep getting stuck at the same point and I was hoping someone could point me in the right direction in terms of where to proceed. I've tried the problem from about half a dozen different angles so I won't list step-by-step my work unless someone asks me to, but the problem is that I am trying to work out the parametric equations for the orbital path of objects and I get stuck in a recursive loop. I am trying to describe the radial distance of an object from a gravitational source but the acceleration that this object is feeling is dependent on radial distance, so I get a equation for the radial distance that depends on the radial distance. Can anyone point me towards a way to get around this? Or to clarify what I'm doing?