Question

Note : Logical explanation needed.Just don't copy solution from another website.

Il Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0X 102 m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate, because otherwise the stars would crash together in the center What is the period of rotation?

Answer 1

For three to move in circle, for on eah star by other two must be equal to required centripetal dorce dor star to move in circle, that is mw^2r.

Where m is mass of star, w is angular velocity and r is radius of circle.

Masses maintain shape of equilateral triangle and move about the centroid of triangle. If side of triangle is a , radius of circle of each star is a/√3 , distance of vertices od equilateral triangle from centroid.

Force applied by each star on other two is Gm^2/a^2. Two such forces are acting on each star along ge sides of triangle, that is making an angle of 60 deg with each other. Hence resulting gravitational force on each star is √3 Gm^2/a^2, towards centroid. Hence

√3Gm^2/a^2 = mw^2 a/√3

w = √(3Gm/a^3)

Period of rotation = 2π/w = 2π√(a^3/3Gm)

Using mass of sun m = 2×10^30

G = 6.7×10^-11 and a = 1×10^12, we get time period

T = 3.1×10^8 sec = 9.9 yrs