Newton\'s Law of Gravitation states that two bodies with masses m1 and m2 attrac
ID: 2851602 • Letter: N
Question
Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant. F = G(m_1m_2)/r^2 Use Newton's Law of Gravitation to compute the work W required to propel a 1100 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.981024 kg and is concentrated at its center. Take the radius of the earth to be 6.37106 m and G = 6.6710-11 Nm2/kg2. (Round your answer to three significant digits.)
Explanation / Answer
Work=integral[R to infinity] Gm1m2/r2 dr
=integral[6.37106to infinity] 6.6710-115.9810241100/r2 dr
=l[6.37106to infinity] 6.6710-115.9810241100(-1/r)
=6.6710-115.9810241100(-1/infinity) -6.6710-115.9810241100(-1/6.37106)
=0+ 6.6710-115.9810241100(1/6.37106)
=6.888*1010 J
Work =6.888*1010 J