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

Question

F(x) = − (GMm/x^2)


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 1800 miles.

W1 =
GMm (mile-pounds)

Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth.

W2 =
GMm (mile-pounds)