Consider a planet orbiting the fixed sun. take the plane of the planet's orbit to be the xy plane, with the sun at the origin, and label the planet's position by polar coordinates (r, (a) show that the problems for chapter 3 103 planet's angular momentum has magnitude = mr2w, where co = 4 is the planet's angular velocity about the sun. (b) show that the rate at which the planet "sweeps out area" (as in kepler's second law) is d a idt = 4r2w, and hence that d a idt = £/2m. deduce kepler's second law.