Putting a satellite in orbit The strength of Earth’s

Chapter 6, Problem 31E

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Putting a satellite in orbit The strength of Earth’s gravitational field varies with the distance r from Earth’s center, and the magnitude of the gravitational force experienced by a satellite of mass m during and after launch is Here, is Earth’s mass, is the universal gravitational constant, and r is measured in meters. The work it takes to lift a 1000-kg satellite from Earth’s surface to a circular orbit 35,780 km above Earth’s center is therefore given by the integral Evaluate the integral. The lower limit of integration is Earth’s radius in meters at the launch site. (This calculation does not take into account energy spent lifting the launch vehicle or energy spent bringing the satellite to orbit velocity.)