A small spacecraft of mass m is in a circular orbit of radius r above Earth’s surface. Assume the spacecraft’s mass is negligible compared with Earth’s mass ME, and ignore atmospheric drag.
(a) Describe two different choices of system that could be used to analyze the spacecraft’s motion: (i) the spacecraft alone and (ii) the spacecraft plus Earth. For each choice, list the interactions (gravitational or otherwise) that cross the system boundary.
(b) For the purpose of predicting the spacecraft’s orbital period, explain which of the two system choices in part (a) is more advantageous and why.
(c) Suppose the spacecraft briefly fires its onboard thrusters, delivering an impulse that changes its speed but not its altitude. For this maneuver, explain why the alternative system choice from part (a) becomes more convenient for analyzing the motion.
(d) Discuss how redefining the system boundary between parts (b) and (c) affects which forces are treated as internal or external and how this, in turn, changes the form of the conservation laws that can be applied.