(a) A binary star system consists of two stars of masses m₁ and m₂ orbiting about one another.

Suppose that the orbits of the two stars are circles of radii \(r_{1}\) and \(r_{2}\), centered on their center of mass. Show that the period of the orbital motion is given by

(b) The binary system Cygnus X-1 consists of two stars orbiting about their common center of mass with orbital period 5.6 days. One of the stars is a supergiant with a mass 25 times that of the sun. The other star is believed to be a black hole with a mass of about 10 times the mass of the sun. From the information given, determine the distance between these stars, assuming that the orbits are circular.

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4 T = = (11 +12). G(m + m2)