Chapter 6.4, Problem 33E

(a) Newton’s Law of Gravitation states that two bodies with masses m₁, and m₂, attract each other with a force

$F=G\frac{m_1{m}_2}{r^2}$

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