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. Which statement describes the distances at which they orbit the centre of mass?

a) The low mass star is closer to the centre of mass.
b) The high mass star is closer to the centre of mass.
c) Both stars orbit at the same distance from the centre of mass.
d) The distance of each star depends on their individual masses.

Answer 1

In a circular binary system, the heavier star which is 3 times more massive than the lighter one will orbit closer to the center of mass, and the lighter star will orbit farther from it.

Step-by-step explanation:

In a circular binary system with two stars of different masses, the distances at which they orbit the center of mass are proportional to their masses. According to the dynamics of binary systems, the heavier star, being 3 times more massive than its companion, will be closer to the center of mass of the system. Conversely, the star with the lower mass will orbit at a greater distance from the center of mass, analogous to how a seesaw balances with different weights at different distances from the fulcrum. In a visual binary system, this would result in the more massive star having a smaller orbital size, and because both stars have the same orbital period, the more massive and thus inner star will also have a slower orbital velocity compared to the less massive, outer star.