In polar coordinates the angular momentum of a moving body of mass in is defined to be...

In polar coordinates the angular momentum of a moving body of mass in is defined to be Assume that the coordinates of the body are respectively. If L is constant, show that the area A swept out by r is A = L (b - a)/2m. When the sun is taken to be at the origin, this proves Kepler's second law of planetary motion: The radius vector joining the sun sweeps out equal areas in equal intervals of time. See Figure 3.17.