(a) Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force
F = G m1m2 / r2
Where r is the distance between the bodies and G is the gravitational constant. If one of the bodies is fixed, find the work needed to move the other from r = a to r = b.
(b) Compute the work required to launch a 1000-kg satellite vertically to a height of 1000 km. You may assume that the earth's mass is 5.98 × 1024 kg and is concentrated at its center. Take the radius of the earth to be 6.37 × 106 m and G = 6.67 × 10-11 N ∙ m2/kg2.