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Two binary stars (m1 and m2) orbit each other around their center of mass. They orbit in circles of radii r1 and r2. I am to show that the period is given by T

^{2}=4pi

^{2}(r

_{1}+r

_{2})

^{3}/(G(m

_{1}+m

_{2}))

The mutual force between m1 and m2 is F=Gm

_{1}m

_{2}/(r

_{1}+r

_{2})

^{2}

Considering m1, the acceleration of m1 is given by a

_{1}=Gm

_{2}/(r

_{1}+r

_{2})

^{2}=v

_{1}

^{2}/r

_{1}

Solving for v and using T

_{1}=2(pi)r

_{1}/v

_{1}=T

_{2}, I get T

^{2}=4pi

^{2}r

_{1}(r

_{1}+r

_{2})

^{2}/(Gm

_{2})

What did I do wrong?