Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 31?

Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 310 million kilometers and take 8.0 Earth years to orbit about a point midway between them. What is the mass of each?Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 31?The velocity is v=2pi r/T where T=8yr is the period and r=155 million km. From the Universal Law of Gravitation and Newton's 2nd Law we have GM^2/r^2=Mv^2/r. Substitute in for v and simplify to get

M=4pi^2 r^3/(G T^2).

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