Serway & Jewett — Universal Gravitation: Problem 40

Many people assume air resistance acting on a moving object will always make the object slow down. It can, however, actually be responsible for making the object speed up. Consider a 100-kg Earth satellite in a circular orbit at an altitude of 200 km. A small force of air resistance makes the satellite drop into a circular orbit with an altitude of 100 km. (a) Calculate the satellite's initial speed. (b) Calculate its final speed in this process. (c) Calculate the initial energy of the satellite–Earth system. (d) Calculate the final energy of the system. (e) Show that the mechanical energy of the system has decreased and find the amount of the decrease due to friction. (f) What force makes the satellite’s speed increase? Hint: You will find a free-body diagram useful in explaining your answer.