Halliday, Resnick & Walker — Gravitation: Problem 50

50 What are (a) the speed and (b) the period of a 400 kg satellite in an approximately circular orbit 900 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of $1.4 \times 10^5 \text{ J}$ per orbital revolution. Adopting the reasonable approximation that the satellite’s orbit becomes a “circle of slowly diminishing radius,” determine the satellite’s (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth’s center conserved for (g) the satellite and (h) the satellite–Earth system (assuming that system is isolated)?