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A binary (double) star system consists of two stars of masses m and 2m revolving about their common centre of mass under their mutual gravitational attraction. If the separation between the two stars is r, then their period of revolution about the centre of mass is proportional to:
- r^(3/2)
- r
- m^(1/2)
- m^(-1/2)
Correct answer: r^(3/2)
Solution
For two stars orbiting their centre of mass, the gravitational force G*m*(2m)/r² equals the centripetal requirement. The standard result is T² = 4*pi²*r³/(G*(m1 + m2)) = 4*pi²*r³/(G*3m). So T proportional to r^(3/2). It is also proportional to m^(-1/2) (since T = 2*pi*sqrt(r³/(3Gm))), but the question's primary intended answer is the dependence on r: T proportional to r^(3/2).
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