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 _____.

Question

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 _____.

Aicharya · Accepted Answer

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 . !

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…

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