Question

Two stars with different masses are in a circular binary system. The heavier star is 3 times more massive than the low mass star. The high mass star is 3 Astronomical Units (AU) away from the centre of mass. What is the distance between the 2 stars?

a) 1 AU
b) 2 AU
c) 3 AU
d) 6 AU

Answer 1

The total distance between the two stars in the circular binary system, where one star is three times more massive than the other, is 12 AU. This is calculated by summing the distances of each star from the center of mass, where the heavier star is 3 AU away, and the lighter star is 9 AU away. Therefore, the correct answer to the question is 12 AU.

Step-by-step explanation:

In a binary star system, two stars orbit around their center of mass. According to the scenario provided, we have two stars with different masses in a circular binary system, where the heavier star is three times more massive than the lighter one and is located 3 AU from the center of mass. The total mass ratio of the system is therefore 1:3, which implies that the lighter star must be located at a distance from the center of mass that is three times further away than the heavier star, to maintain the center of mass at a stable point.

Since the heavier star is 3 AU from the center of mass, the lighter star must be 9 AU away on the opposite side, since it has to be three times as far to balance the system (3 times 3 AU = 9 AU).

The total distance between the two stars is the sum of the distances from each star to the center of mass, which is 3 AU + 9 AU = 12 AU. Therefore, the correct answer to the question is:

• d) 12 AU