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Newton's Law of Gravitation

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1. 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/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 between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x greater or equal to 4000 miles.

a). Find the work W done against gravity when the rocket rises 1000 miles. Express your answers in terms of G, M, and m.
b). Find the work W done against gravity when the rocket rises d miles.
c). Find the limit of the work found in part (b) as d-all real numbers, and determine whether it is possible, with a finite amount of work, to send the rocket arbitrarily far away.

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