A binary star consists of two stars A (mass 2.2 MS) and B (mass 11 MS), where MS is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of a star B about the centre of mass is

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A binary star consists of two stars A (mass 2.2 M_S) and B (mass 11 M_S), where M_S is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of a star B about the centre of mass is

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$\frac{m_{1} v_{1}^{2}}{r_{1}} = \frac{{Gm}_{1} m_{2}}{d^{2}}$

$\frac{v_{1}^{2}}{r_{1}} = \frac{{Gm}_{2}}{d^{2}}$

$v_{1} = \sqrt{\frac{{Gm}_{2} r}{d^{2}}} = \sqrt{\frac{{Gm}_{2}}{d} (\frac{5}{6})}$

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