Actually, real orbits are only approximately elliptical.
It was Kepler who first found that planetary orbits can be decribed very well with ellipses. Newton was the first to explain why. If one assumes that space and time have the simple structure which we ordinarily experience, and that the Sun and a lone planet are rigid spheres, obeying Newtonís law of gravity, then the elliptical orbits can be derived mathematically. Newton was the first to do so. Probably the simplest derivation which Iíve seen was in a lecture by Feynman, but even that derivation is much too lengthy for one of our little Web answers.
In real life the following effects make the orbits slightly non-elliptical.
1. Each planet is affected by the gravity of other planets, not just the Sun. Of course, Newton knew this. Such effects were actually used to discover the planet Neptune, due to its gravitational effects.
2a. The Sun isnít perfectly spherical. That has a noticable effect on inner planets.
2b. The Sun and planets arenít perfectly rigid.
3. However, our intuitive picture of Newtonian space and time is not quite exact. There are very small effects on the orbit of Mercury which are only explained by General Relativity.
(published on 10/22/2007)