# Computing period, semi-major axis of binary

I have mass, $g$, and luminosity of each of the stars in a binary system, extracted from a model. I calculated the individual radii from $g$ and the mass. I am trying to compute $a$, but I seem to be stuck or I'm just missing something obvious. I can't think any method that does not involve the period.

How do I get the semi-major axis?

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If you only have mass, surface gravity, and luminosity, it's impossible to get either period or semi-major axis. Is there another datum to which you have access, that you might have overlooked? – Andrew Sep 15 '11 at 11:01
I was afraid of that. I decided to just sample periods from kepler data. That's the best I could come up with. Thank you! – McEnroe Sep 15 '11 at 16:50

To continue my discussion from my comment, what and how detailed is the model? If your model is detailed enough to include tidal distortion or hotspots (the illustration is for a neutron star, but regular binary stars can exhibit hot spots too) or other interaction details, you could have enough data to determine semi-major axis using this as a guide.

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If you know the specific angular momentum $h$, the eccentricity $e$, and the masses, you can determine the semi-major axis $a$.

$a = \frac{h^2}{G(m+n)(1-e^2)}$

Of course, if you knew all those things you could also calculate the orbital period:

$t = \frac{2\pi}{\frac{G^2(m+n)^2}{h^3}(1-e^2)^\frac{3}{2}}$

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