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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?