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

<blockquote>
  <p>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. </p>
  
  <ul>
  <li>a. 0.5</li>
  <li>b. 1</li>
  <li>c. 2</li>
  <li>d. 4</li>
  <li>e. 8</li>
  </ul>
</blockquote>

<p>What I got so far:</p>

<ul>
<li>Distance to system: 2pc (6.171e16 m)</li>
<li>Minimum separation: 5.98e11 m</li>
<li>Maximum separation: 5.38e12 m</li>
<li>Relative semimajor axis: 2.99e12 m (20AU)</li>
<li>Combined mass: 125 solar masses</li>
</ul>

CC BY-SA 4.0
2020-03-22T10:53:21.740Z
I got a combined mass of 125 too,  care to show your working?
James K
CC BY-SA 4.0
2020-03-24T00:51:36.917Z
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 :)
Chooi Je Qin
<astrophysics><orbital-mechanics><binary-star>
Combined mass of binary stars
Chooi Je Qin
# Combined mass of binary stars

(Asked by: username_0 on 2020-03-22)

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

**Tags:** astrophysics, orbital-mechanics, binary-star

> **Comments:**
> **username_1**: I got a combined mass of 125 too,  care to show your working?  
> **username_0**: username_1, 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 :)  

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## 0 answers

