## 'Relativistic' Phenomena in a Non-Relativistic Arena

We have discussed *repulsive* gravity within the context of the conformal equivalence between the squares of Hookean ellipses and the orbits in a gravitational field. In particular attractive oscillators corresponds to attractive gravity while a negative Hookean law is equivalent to repulsive gravity. Here, we show that oscillators and gravitational forces lead to non-Euclidean geometries. This has been discussed before by Milnor, "On the geometry of the Kepler problem" in *Not. Am Math Soc*. **90** (1983) 353-365.