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CornerCase

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## Homework Statement

Consider only two asteroids, both of uniform mass m

_{a}, r=10km radius, separated by s=10m. What are the equations for velocity and orbital period for a stable circular orbit?

## Homework Equations

If the asteroids are considered point masses then the distance between them, R, is 2r+s.

Planetary orbital period equation: T = [tex]\stackrel{2\piR^{\stackrel{3}{2}}}{\sqrt{Gm_{a}}}[/tex]

Planetary orbital velocity equation: v = [tex]\sqrt{\stackrel{Gm_{a}}{R}}[/tex]

The barycenter is always .5R

_{Sorry, I don't know how to put the division bar in between yet}

## The Attempt at a Solution

The problem is that the planetary equations are based upon m

_{1}>> m

_{2}. The barycenter is always within m

_{1}(and wobble occurs). But with m

_{1}= m

_{2}they each orbit a common center. Is the answer to assume point masses and use the above equations assuming R=2r+s? Then calculate T and v but know that they circle at a point halfway between the two?