Final answer:
In a binary star system where Star A has a mass of 2 M⊙ and Star B has a mass of 4 M⊙, the center of mass will be located closer to Star B due to its greater mass.
Step-by-step explanation:
If Star A has a mass of 2 M⊙ and Star B has a mass of 4 M⊙, we are looking to find where the center of mass (COM) would be located between the two. In a binary star system, two stars orbit around their shared COM. The star with the greater mass will be closer to the COM. By knowing the mass ratio, we can determine that the COM will be closer to Star B because it has a greater mass.
Since mass is a key factor in determining the position of the center of mass, and since Star B has twice the mass of Star A, the COM will be closer to Star B. Imagine a seesaw with two objects; the heavier object must be closer to the pivot point (COM) for balance. Similarly, for our binary stars, Star B will dictate the COM's position, causing it to be located closer to Star B due to its increased mass.
Therefore, if we were to label the two stars A and B, with A being the less massive and B being the more massive, the COM would be found not at letter position 'A' but closer to letter position 'B' due to the mass difference.