Why does the earth rotate on an ellipse and not in a circle around the sun?
The Earth does not rotate in an ellipse. Rotation is the motion of turning around its axis. I assume you mean the Earth’s revolution (orbit) around the sun. All the planets, comets, and asteroids orbits are ellipses. Kepler was the first to propose that the planets’ orbits were ellipses with the sun at one focus. In kinetics (the study of motion), an elliptical orbit is more stable over time than a circular orbit – an elliptical orbit can be perturbed a bit without the orbit becoming completely unstable – not so with a circular orbit. Plus, a circular orbit is difficult to form from a rotating disk of material since the disk that formed the solar system was not symmetrical – there were density fluctuations that would have precluded circular orbits.