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.
Levine, A method of orbital navigation using optical sightings to unknown land- marks, AIAA Journal, 4 (1966) pp
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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.