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

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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 _____.

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Correct answer: A. A

T = 2 &#960; R 3 / 2 G M S For binary stars, T ' = 2 &#960; 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 &#960; &#215; 9 3 / 2 &#215; R 3 / 2 G 3 M S + 6 M S = 2 &#960; &#215; 9 3 / 2 &#215; R 3 / 2 9 1 / 2 G M S = 9 2 &#960; R 3 / 2 G M S &#8756; &#160;&#160; T ' = 9 T Value of  n = 9 .

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