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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?

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# Binary stars

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