A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket is given by
F(x) = - GMm/x2
Where M is the mass of the earth, m is the mass of the rocket, G is a universal, constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x ≥ 4000 miles.
Find the work, w1, done against gravity when the rocket rises 1400 miles.
Next, find the limit of the work, w2, as the rocket rises infinitely far from the earth.