(a) Show that, by setting r=R+y in the right-hand member of Eq. (13.17′) and expanding that member in a power series iny/R, the expression in Eq. (13.16) for the potential energy Vg due to gravity is a first-order approximation for the expression given in Eq. (13.17′).

(b) Using the same expansion, derive a second-order approximation for Vg.