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, M = 5.975 * 10²⁴ kg is Earth’s mass, G = 6.6720 * 10^-11 N · m² kg^-2 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. 

Transcribed Image Text:

F(r) = mMG p²