A planet moves around the Sun in an elliptical orbit.
(a) Show that the external torque acting on the planet about an axis through the Sun is zero?
(b) Since the torque is zero, the planet's angular momentum is constant. Write an expression for the planet's angular momentum in terms of its mass m, its distance r from the Sun, and its angular velocity (?
(c) Given r and w, how much area is swept out during a short time Δt? [Think of the area as a fraction of the area of a circle, like a slice of pie; if Δ t is short enough, the radius of the orbit during that time is nearly constant?
(d) Show that the area swept out per unit time is constant. You have just proved Kepler's second law!]?