<Moderator's note: Moved from elsewhere and therefore no template.> I'm trying to calculate the distance of free fall for an object with zero tangential velocity but a given radial velocity at a given height over a given period of time. This calculation cannot assume that g is constant as it deals with orbital heights. These calculations are needed for an orbital ring that I'm designing. Here is my working out so far. 1.) F=ma 2.) F=GMm/R^2 Sub 1.) into 2.) ma=GMm/R^2 a=GM/R^2 v=da/dt v=d/dt(GM/R^2) v=GM d/dt(1/R^2) R=dv/dt R=GM d^2/dt^2(1/R^2) I can't figure out how to solve this second order differential equation. Is there a better way of doing it/where did I go wrong?