# Orbital Angular Momentum of a Binary Star System

Let's say you have a binary star system, consider the orbital motion of that binary star consisting of two solar-like stars separated by 20 stellar radii. How would one calculate the angular momentum for this system? The angular momentum we want is defined by the equation:

$$L = I\Omega = Mk^2 R^2 \Omega$$

Where $$M$$ is the Mass, $$R$$ is the radii of the orbit, $$k$$ the gyradius, and $$\Omega$$ the angular velocity.

$$M$$ and $$R$$ are easy enough. I'm confused on how to get $$k$$ and $$\Omega$$? Would the gyradius $$k$$ be what was given to me in an earlier part of the question (0.25) for when I had to calculate the Angular momentum of the Sun or would I have to calculate it separately for this case? What about $$\Omega$$? Would it simply be $$\frac{2\pi}{28 days \cdot 24 hours \cdot 60 mins \cdot 60 secs}$$ where the period of rotation comes from the Sun?

Clarification/help is appreciated. Thanks

• Seems like your getting your homework done? May 3 at 8:24