Two identical satellites travel on the same elliptical orbit around Earth
PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two identical satellites travel on the same elliptical orbit around Earth. Satellite X is momentarily at apogee (distance rX), and Satellite Y is momentarily at perigee (distance rY), where rX>rY. Which of the following best explains why Satellite X moves more slowly than Satellite Y at those instants?
(a) The gravitational force is weaker at apogee, so the satellite requires a smaller centripetal force and therefore must slow down.
(b) According to Kepler’s third law, a larger orbital radius leads to a longer period, so the satellite must move more slowly when it is farther from Earth.
(c) Angular momentum of the satellite–Earth system is conserved; a greater distance from Earth’s center requires a lower speed to keep angular momentum constant.
(d) Because total mechanical energy is conserved, the gravitational potential energy increases at apogee, so the total energy rises and the satellite must slow down.