A trinary star system which is a system of three stars orbiting around centre of mass of system has time period of 3 years, while the distance between any two stars of the system is 2 astronomical uni

Question

A trinary star system which is a system of three stars orbiting around centre of mass of system has time period of 3 years, while the distance between any two stars of the system is 2 astronomical unit. All the three stars are identical and mass of the sun is M and total mass of this multiple star system is $\frac{a}{b} \times M$ . Then find $\frac{b}{3}$ ? (a and b are lowest possible integers) (1 astronomical unit is equal to distance between sun and earth, time period of rotation of earth around sun is 1year)

$\frac{a}{b}$

TestHub · Accepted Answer

T 0 2 ​ = GM s ​ 4 π 2 R 3 ​ ​ 2 a 2 2 Gm 2 3 ​ ​ = 3 ​ mw 2 a ​ w 2 = a 3 3 Gm ​ T 2 = w 2 4 π 2 ​ = 3 Gm 4 π 2 a 3 ​ ​ Given T = 3 T 0 ​ a = 2 R ​ 9 T 0 2 ​ = 3 Gm 4 π 2 ​ × 8 R 3 GM s ​ 9 × 4 π 2 R 3 ​ = 3 8 ​ × Gm 4 π 2 R 3 ​ m = 27 8 M s ​ ​ ​ Total mass = 3 m = 9 8 ​ M s ​

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