Why do planets move along elliptical paths and not circular orbits?
Planets move along elliptical orbits because planets move in a gravitational force field which falls off as one over the square of the distance between the sun and the planet ( Force = GMm/r^2 from Newton’s Law of Gravity). The planet is also subject to the conservation of momentum and energy, and the only ‘solution’ to this combination of requirements is an elliptical orbit. Intuitively, if a planet were in a circular orbit, but the orientation of this orbit were perturbed very slightly, because the strength of the gravitational force depends on separation, there will be some parts of the new orbit where the planet would feel a slightly stronger gravitational pull than at other parts. The speed of the planet would speed up slightly, and so the instantaneous shape of the new orbit would change. In a circular orbit, a planet would have the same orbital speed everywhere. This is not possible in a gravitational field unless, like a pencil balanced on its edge, the planet were orbiting at
