An elementary derivation of Newtonian gravity from Kepler's laws is presented together with a homogeneous-function generalization of Keplerian orbits that preserves convexity and yields generalized hodographs.
Graves, On the Motion of a Point upon the Surface of a Sphere , Proceedings of the Royal Irish Academy, volume II, No
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Does Newtonian dynamics need Euclidean space?
An elementary derivation of Newtonian gravity from Kepler's laws is presented together with a homogeneous-function generalization of Keplerian orbits that preserves convexity and yields generalized hodographs.