Binary stars
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Consider two stars S1 and S2 of masses M1 and M2 respectively, revolving around a common centre of mass O. Clearly the two stars constitute a binary system.
Let a1 and a2 be the radii of revolution. Then, by definition of centre of mass,
Let v1 and v2 be the speeds of revolution of the S1 and S2 respectively and T be the common period of revolution about the centre of mass O.
The centripetal force 
required for circular motion of S2 is provided by the gravitational attraction between S1 and S2, 
From here, M1 + M2 can be calculated
Clearly, the masses M1 and M2 of stars S1 and S2 respectively, can be calculated.
Earth-moon system
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The method used in the binary star system can be also used for planet-satellite binary system.
This is possible because the planet and the satellite also revolve around a common centre of mass.
Let us now consider the Earth-moon system. Both move in circles about their centre of mass, always being on opposite sides of it. The centre of mass moves along an elliptical path around the sun. The forces of attraction between the Earth and the moon are internal to the Earth-Moon system. On the other hand, the sun's attraction of both earth and moon are external forces.
