(a) Assuming Earth to be a homogeneous sphere that has a

(a) Assuming Earth to be a homogeneous sphere that has a radius r and a mass m, show that the period T (time for one daily rotation) of Earths rotation about its axis is related to its radius by where Here L is the magnitude of the spin angular momentum of Earth. (b) Suppose that the radius r changes by a very small amount, due to some internal cause, such as thermal expansion. Show that the fractional change in the period is given approximately by (c) By how many kilometers would r need to increase for the period to change by (so that leap years would no longer be necessary)?