The work done by gravitational force on a planet revolving around the sun in one revolution is

0

We know that orbits are elliptical. Since the gravitational force acts along the line joining the sun and planet. It cannot produce any torque about the sun. That means the angular momentum of the planet remains constant. Consequently the speed of the planet changes from time to time. When it comes nearer to the sun its speed increases and vice versa. In one complete revolution, the kinetic energy of the planet increases first and then decreases until it reaches the same value. Thus the work done by gravitational force is zero.