Chapter 6.6, Problem 26ES

(a) The formula $\omega \left(x\right)=k/x^2$ in Exercise $25$ is applicable to all celestial bodies. Assuming that the Moon is a sphere of radius $1080\text{ mi}$ , find the force that the Moon exerts on an astronaut who is x mi from the surface of the Moon if her weight on the Moon’s surface is $20\text{ lb}$ .

(b) How much work is required to lift the astronaut to a point that is $10.8\text{ mi}$ above the Moon’s surface?