Question

A "double star" is a composite system of two stars rotating about their centre of mass under their mutual gravitational attraction. Let us consider such
a double star which has two stars of masses m each at separation I. If T is the time period of rotation about their centre of mass then find T.​

Answer 1

Answer:

π√(8l/Gm).

Explanation:

From the question we get that the masses are placed at a given aligned position. So, the two star's gravitational force and the centrifugal force of attraction will be same.

For the center of the two body's to be symmetrical we get that the distacne must be 2mx=ml. So, the distance will be x=l/2. So, the force of the centrifugal will be mω^2x or mω^2(l/2). The gravitational force will be Gmm/^2. So, on equating the two equation we will get that mω^2(l/2)=Gmm/^2. Since, ω=2π/T. So, on substituting we will get that (4π^2/T^2)*1/2=Gm/l. Or the value of the time period will be T^2=8π^2*l/Gm. So, the time period T will be π√(8l/Gm).

Answer 2

Answer:

see the attached image

Explanation:

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