Two stars orbit their common center of mass on circular orbits.Star A is four times more massive than star B.How do their orbital periods compare to each other?
A) Star A has a longer orbital period than star B.
B) Star B has a longer orbital period than star A.
C) They are the same.
D) The orbital periods cannot be determined without knowing their initial velocities.

Question

Quizplus · Accepted Answer

The orbital period is directly proportional to the radius of the orbit, and inversely proportional to the square root of the mass of the star. Since star A is four times more massive than star B, its radius must be two times smaller than the radius of star B's orbit, so that both stars can have the same center of mass. Therefore, using Kepler's third law, their orbital periods must be the same.

Two Stars Orbit Their Common Center of Mass on Circular