You are asked to verify Kepler's Laws of Planetary Motion. For these exercises, assume that each planet moves in an orbit given by the vector- valued function r. Let r = ||r||, let G represent the universal gravitational constant, let M represent the mass of the sun, and let m represent the mass of the planet.

Prove Kepler’s Second Law: Each ray from the sun to a planet sweeps out equal areas of the ellipse in equal times.