Calculating Energy, Angular Momentum & Period for Binary Stars in ZMF

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Homework Statement



Two individual stars in a binary system (m1=mo, m2=2mo) are in circular orbit about their common centre of mass and are separated by a distance ro. At some stage, the more massive star explodes - resulting in the two stars having equal mass after the explosion

(a)Calculate the total energy, angular momentum and period of the binary star as viewed in the ZMF before the collision.

Homework Equations





The Attempt at a Solution



Not sure how to do this...For energy, do I find the energy of each inidividually and add? How about for angular momentum? Surely that is just zero in total because the two are equal and opposite?
thanks
 
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The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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