Subject: Finding a formula for the period of orbital motion in terms of the orbital

Hello --

Three identical stars, at the vertices of an equilateral triangle, 
orbit about their common center of mass.  Find the period of this 
orbital motion in terms of the orbital radius, R, and the mass of 
each star, M.

         vector v  
         <------- M
               *  @  *
          *      / \      *
                /   \     
               /     \
       *      /       \       *
             /         \
            /     @.    \
      *    /     CM  .R  \     *   /
          /            .  \       /vector v
     M @   -----------------     /
      \*                     *@M
       \
vector v\ *               *
              *      *

(v denotes velocity, CM denotes center of mass, M = mass of each 
star, R denotes orbital radius)

[Difficulty]
The answer given by the book is 2pi*sqrt[(sqrt(3)*R^3)/(GM)].

[Thoughts]
The centripetal acceleration is v^2/R, and v = 2pi/T, where T is the 
period or time for one revolution, 2pi.  F = ma = M*(v^2/R) = M*
[(2pi/T)^2]/R.  Do I have to use Newton's Law of Universal 
Gravitation F = G * m_1 * m_2/r^2, and set it equal to my above 
equation (I don't think so, since CM, or center of mass, is not a 
point mass and thus there is no attraction between each star and the 
CM)?  If setting it equal to my above equation is the correct way, 
then m_1 = M and M_2 = CM, and the term M is eliminated, which I 
don't think is the correct way of solving this problem.  Please help 
me, please!  Any hint will be appreciated.  Thank you in advance!
(I think the sqrt(3)in the book's answer has to do with the 3 stars, 
since there are 3 of them.)

Thank you so much.  By the way, I am only 14 and am studying physics and 
calculus on my own.

Re: Finding a formula for the period of orbital motion in terms of the orbital