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 one orbit?
A) 320 days
B) 160 days
C) 20 days
D) 80 days

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. In this case, moon B has an orbital radius of 4r, which is 4 times the orbital radius of moon A. Therefore, the orbital period of moon B will be 4^3 = 64 times the orbital period of moon A. Since moon A takes 20 days to complete one orbit, moon B will take 20 * 64 = 1280 days to complete one orbit.

Two Moons Orbit a Planet in Nearly Circular Orbits