1. A comet of mass m is in an elliptical orbit around a star of mass M. At the closest point of its orbit, point P, the comet is a distance D from the center of the star, and at the farthest point, point A, the distance is 3D. You may disregard the presence of all other celestial bodies. Derive an expression for the change in the comet’s kinetic energy as it moves from point P to point A, in terms of system parameters and constants. Does the comet have its greatest speed at point A or point P?