# Combined mass of binary stars

This is Question 17 from USAAAO Practice Round 2015. The answer is D. It would be best if someone can detail out the workings.

In a nearby star system, two stars are seen to orbit each other every 8 years. At their closest, the stars are 2” apart. At their furthest, they are 18” apart. If a parallax of 0.5” is observed for the star system, what is its combined mass in solar masses? Assume an inclination of 90 degrees.

• a. 0.5
• b. 1
• c. 2
• d. 4
• e. 8

What I got so far:

• Distance to system: 2pc (6.171e16 m)
• Minimum separation: 5.98e11 m
• Maximum separation: 5.38e12 m
• Relative semimajor axis: 2.99e12 m (20AU)
• Combined mass: 125 solar masses
• I got a combined mass of 125 too, care to show your working? – James K Mar 22 '20 at 10:53
• James K, after I have the semi major axis, I calculate the mass using Kepler’s Third Law. I think there must be some typo in the data given because we got the same answer. Thanks for your help :) – Je Qin Chooi Mar 24 '20 at 0:51