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JEE Advanced2021PhysicsGravitationActual

The distance between two stars of masses 3 M S and 6 M S is 9 R . Here R is the mean distance between the centres of the Earth and the Sun, and M S is the mass of the Sun. Two stars orbit around their common centre of mass in circular orbits with period n T , where T is the period of Earth's revolution around the Sun. The value of n is _____.

Correct answer

0

Step-by-step solution

T = 2 π R 3 / 2 G M S For binary stars, T ' = 2 π r 3 / 2 G M 1 + M 2 Put M 1 = 3 M S , M 2 = 6 M S and r = 9 R T ' = 2 π × 9 3 / 2 × R 3 / 2 G 3 M S + 6 M S = 2 π × 9 3 / 2 × R 3 / 2 9 1 / 2 G M S = 9 2 π R 3 / 2 G M S ∴    T ' = 9 T Value of n = 9 .

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