Solving Binary Star Problems: Tips & Strategies

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The discussion focuses on solving binary star problems, specifically regarding orbital mechanics and the relationship between velocity, radius, and semi-major axes. The user expresses confusion about calculating the observed maximum velocity shift and the implications of the angle of inclination. Key points include the clarification that the semi-major axis relates to the distance between the stars, not the sum of their radii. Additionally, it is noted that Kepler's third law is essential for determining the semi-major axis in these scenarios. Understanding these concepts is crucial for accurately solving binary star problems.
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Homework Statement


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Homework Equations


For circular orbit, r = Pv / 2 pi , Where P = orbital period and v=orbital velocity

r' = r sini , where i is unknown angle to plane of sky.

The Attempt at a Solution


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I'm really not getting these binary problems at all.

I would start by finding v, but how is this from them "the observed maximum velocity shift of 26.1 km/s" ?
Then I would use r = Pv / 2 pi , and the separation would just be 2r as they are identical stars, is this right?
I don't know where to start with the angle of inclination part.

Also, in my notes, talking about binaries in general, it says that r1 + r2 = a
I think that's r1= radius of star 1, r2 = radius of star 2, a = true semi-major orbital axis, but I don't understand this, how could the 2 radii total the semi-major axis? Surely it would be 2a if anything?
And talking about the semi-major axis, does the system actually have a semi-major axis? I thought there was just one for each star.

Really lost here, any help would be appreicated, thanks!
 

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You'll have to consider the masses of the stars to get the orbital velocity. The period and the radial velocity alone are not sufficient.

You can consider the semi-major axis of each star, or the semi-major axis of the distance between the stars. But for a circular orbit with identical masses, you can just take the radius of the circle as semi-major axis of each star. This is NOT the distance between the stars!
 
Try using Kepler's third law to find ##a##.
 
Thanks guys, it was Kepler's 3rd that I needed.
 
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