Question

How much work would be needed to raise the payload from the surface of the moon (i.e., x = r) to the "end of the universe"?

Answer 1

moon was rotation Earth or sun
it's own orbit . universe is not end

Answer 2

W(3R) - W(2R) = -PR² (1/(3R) - 1/(2R)) = PR/6

Step-by-step explanation:

"Assume the weight move up at constant speed. With no net acceleration, the force applied is -(weight). Since the weight at height R is -P(R/x)² (minusbecause it's directed downward) the applied lifting force is P(R/x)², and the work done moving from x to x+dx is dW = P(R/x)² dx. Intetgrate this:"

W(x) = ?PR²/x² dx = -PR²/x + C

The work done moving from x=R to x=2R is:

W(2R) - W(R) = -PR²(1/(2R) - 1/R) = PR/2

(b) The work done moving from 2R to 3R is:

W(3R) - W(2R) = -PR² (1/(3R) - 1/(2R)) = PR/6