The combined mass of a binary system is three solar masses. Star A is 1 AU and Star B is 2 AU from the center of mass. What are the masses of Star A and Star B, respectively
A)2.5, 0.5
B)1, 2
C)2, 1
D)0.5, 2.5

Question

Quizplus · Accepted Answer

According to Kepler's laws, the ratio of the squares of the periods of two orbiting bodies is equal to the ratio of their masses. Assuming the distance of Star A from the center of mass to be d, we have (1/d)^2 proportional to M_A and (2/(3-d))^2 proportional to M_B. Since the sum of their masses is 3 solar masses, we can write:
M_A = 3[(1/d)^2]/[1/d)^2 + (2/(3-d))^2]
M_B = 3[(2/(3-d))^2]/[1/d)^2 + (2/(3-d))^2]
By substituting d=1 and d=2, we can see that only choice C satisfies a total mass of 3 solar masses. Therefore, the masses of Star A and Star B, respectively, are 2 and 1 solar masses.

The Combined Mass of a Binary System Is Three Solar