Newton\'s Law of Gravitation states that two bodies having masses m1 and m2 attr
ID: 2188944 • Letter: N
Question
Newton's Law of Gravitation states that two bodies having masses m1 and m2 attract each other with a force F = G m1m2 r2 where G is the gravitational constant and r is the distance between the two bodies. Assume that the mass of the earth is 5.97 1024 kg and is concentrated at the center of the earth, the radius of the earth is 6.37 106 m, and G = 6.67 10-11 N-m2/kg2. Find the work required to launch a rocket of mass 500,000 kg vertically upwards to a height of 10,500 km from the center of the Earth. (Round your answer to three significant figures.)Explanation / Answer
Work to be done to place a satellite in an orbit of 10500 km = Potential energy of the satellite in its orbit - potential energy of the satellite on earth. = - G(m1m2)/(r + h) + G(m1m2)/r, where r = radius of the earth and h = height of the satellite above the surface of the earth = G(m1m2) * [1/r - 1/(r+h)] = G h (m1m2) / r(r+h)