Help on how to find stellar radius with an eclipsing binary system

[arella]

Homework Statement

I won't post the problem yet, as I do want to try this on my own, but I really am stuck on how to approach this.

I'm given two images of an eclipsing binary, one labeled primary and one labeled secondary (even at this point, I'm not entire sure what that means). One star remains in the middle, why a notably smaller star orbits around it in positions 1-4 in the secondary example, and 1'-4' in the primary example. I'm given:

- a value for a in kilometers
- P=3.0^d
- t1, t2, t3, and t4 in hours, all corresponding to different positions of the smaller star as it passes/goes behind the larger one.

I'm asked to find the radii of both stars, but I don't know where to start.

Relevant Equations

I know that we have

r = sqrt[L/(4*pi*sigma*T^4)]

but I have no way of getting L or T as far as I know.

I'm also unsure as to why I was given the value for a, as the only equation I can think of to use is Newton's version of Kepler's 3rd.

My best guess right now is use Newton's version of Kepler's 3rd Law to maybe find a combined mass, as I'm under the impression that the smaller star's mass would still be too large to ignore, but I'm not confident. And I wouldn't be sure as where t go from their, either. Any guidance would be greatly appreciated!

 

[haruspex]

I think a little too much has been lost in your attempt to precis the question. I'm not even sure whether primary and secondary are referring to two different binary systems or aspects of the same binary system, or two minor stars and one major in a triple star system.
And how is 'a' defined?

 

[arella]

I think a little too much has been lost in your attempt to precis the question. I'm not even sure whether primary and secondary are referring to two different binary systems or aspects of the same binary system, or two minor stars and one major in a triple star system.
And how is 'a' defined?

I'm sorry! The primary and secondary are referring to the same system, with the smaller start show crossing in front of the bigger star in the secondary case and crossing behind in the primary. the value a is given as 7 x 10^6 km.

 

[haruspex]

I'm sorry! The primary and secondary are referring to the same system, with the smaller start show crossing in front of the bigger star in the secondary case and crossing behind in the primary. the value a is given as 7 x 10^6 km.

I don't care about the value of a, I need to know what it represents.