A double-star system with each star having the mass of the Sun has an orbital period of 1 year.A second double star system,also with each star having the mass of the Sun,has an orbital period of 8 years.If the separation of the stars in the first system is d and the orbits in both cases are circular,what is the separation of the stars in the second system?
A)0.5d
B)2d
C)4d
D)8d

Question

Quizplus · Accepted Answer

Using Kepler's third law, we know that:

T^2 ∝ r^3

where T is the orbital period and r is the separation between the two stars.

Therefore, we can write:

(T1/T2)^2 = (r1/r2)^3

Plugging in the given values, we get:

(1/8)^2 = (d/r2)^3

Solving for r2, we get:

r2 = d/(1/2) = 2d

However, this gives us the separation of the stars in the second system relative to the separation of the stars in the first system. In order to get the actual separation of the stars in the second system, we need to multiply by the separation of the stars in the first system:

r2 = 2d × d = 4d

Therefore, the answer is C) 4d.

A Double-Star System with Each Star Having the Mass of the Sun