A. consider a perfectly spherical planet of total mass m and radius r. divide the planet into shells of mass dm and thickness dr. each shell is a different radius r from the center of the planet. write and expression for the mass dm of the shell and radius r in terms of m, r, r, and dr.
b. each shell of mass dm is "peeled" off of the remaining mass left on the planet. it takes a certain amount of energy du to remove each shell to an infinite distance away. determine the energy du required to remove the shell of mass dm that is at radius r from the planet's surface to infinity.
c. determine the total energy u required to remove all of the planet's mass to infinity.