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Advanced PhysicsQ&A LibraryA binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x105 ms-1 and a mass of m1 =5Ms ,where Ms= 1.98x1030kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.(a) What is the radius r1 of the orbit of the visible star?(b) Calculate the mass m2 of the black hole in terms of MS . [Hint: One root of the equation x3 = 20a(5a+x)2 , where a is a constant, is x = 28a .]Question

Asked Dec 16, 2019

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A binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x10^{5} ms^{-1} and a mass of m1 =5M_{s} ,where M_{s}= 1.98x10^{30}kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.

(a) What is the radius r1 of the orbit of the visible star?

(b) Calculate the mass m2 of the black hole in terms of M_{S} . [Hint: One root of the equation x^{3} = 20a(5a+x)^{2} , where a is a constant, is x = 28a .]

Step 1

A binary star system is represented by the figure given below.

Step 2

a)

As the visible star is executing circular motion about the center of mass, its radius *r*_{1 }is calculated as,

Step 3

Substitute 5.36(105) ms-1 for *v*1 and 30 hr for *T* and solve for *...*

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