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If we equate Kepler's Third Law with Newton's Law of Gravity we derive what is called The Mass Function: f(M) = PK2^3/2.pi.G = M1(sin(i))^3/(1+Q)^2 On the left hand side we have P and K2, binary parameters which we can measure from data. This gives the minimum mass of M1. Question: Why? (Hint: sin(i) has values between 0 and 1). On the right hand side we have i, M1 and the mass ratio, Q = M2/M1. If we can determine P, K2, i and Q we can determine the mass of the unseen star. If it is greater than 3 solar masses we can say with great certainty that it is a black hole. It is impractical, however, to go and observe every single binary we know of in the Milky Way. There is not enough time or resources to embark upon such a project. What we need is another clue to tell us where to look. |