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
  • 5
    $\begingroup$ I got a combined mass of 125 too, care to show your working? $\endgroup$ – James K Mar 22 '20 at 10:53
  • 1
    $\begingroup$ 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 :) $\endgroup$ – Je Qin Chooi Mar 24 '20 at 0:51

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