Two small dense stars rotate about their common centre of mass as a binary system with the period 1 year for each. One star is of double the mass of the other and the mass of the lighter one is 1/3 of the mass of the sun. The distance between the stars is xR if distance between the earth & the sun is R, find x.
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Solution
Let, a be the distance
between stars and their masses are 2M3,M3. M is mass
of sun.
ωs=ωe=2π365×24×3600=(GMR3)0.5
consider the binary
star system, Gravitational force = centripetal force