Kepler's laws: Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?
A) 20 d
B) 40 d
C) 80 d
D) 160 d
E) 320 d

Question

Quizplus · Accepted Answer

According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. If moon B has an orbital radius 4 times that of moon A, then the period of moon B is (4^1.5) times that of moon A. Therefore, the period of moon B is 8 times 20 days, which is 160 days.

Kepler's Laws: Two Moons Orbit a Planet in Nearly Circular