Solving Binary Star Problems: Tips & Strategies

[tarkin]

Homework Statement

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Image attached

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

[/B]
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!

 

[mfb]

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!

 

[vela]

Try using Kepler's third law to find $a$.

 

[tarkin]

Thanks guys, it was Kepler's 3rd that I needed.