Question 452: Gravitation

Question

The distance between two stars of masses 3M
S
and 6M
S
is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and M
S
is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period nT, where T is the period of Earth's revolution around the Sun. The value of n is __________.

Accepted Answer

For earth-sun system,
$$T_0^2 = {{4{\pi ^2}} \over {G{M_S}}} 	imes {R^3}$$ ..... (i)
For binary system
$${T^2} = {{4{\pi ^2}} \over {G[3{M_S} + 6{M_S}]}} 	imes {(9R)^3}$$ .... (ii)
Using Eqs. (i) and (ii), we get
T = 9T
0
So, n = 9

Gravitation

Integer / Numeric Answer Type