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## Homework Statement

Two asteroids (approximately the same size and mass) are orbiting each other at a given radius a. The center of mass is orbiting the sun at a distance (semimajor axis) b with an orbital period of P.

I would like to estimate the mass/size of each of the asteroids.

By analysing the motion of the orbit of the two asteroids around their center of mass I can determine what their mass is based on the period of this orbit.

However, I am stuck on trying to relate the period of the asteroids mutual orbit with the period of the center of mass's orbit around the sun.

I thought that conservation of angular momentum would play a roll, however I do not know the total momentum of the sun-asteroid-asteroid system.

Can anyone point me toward relating these two periods?

## Homework Equations

[tex] L = m\omega^{2}R [/tex]

[tex] \omega = \frac{2\pi}{T} [/tex]

[tex] F_{g} = \frac{GMm}{R^{2}} [/tex]