Question

two stars in deep space are very far from any other objects. the two stars orbit the center of mass of the two - star system in circular orbits at constant speed. which of the following claims is correct about the motion of the center of mass of the two - star system?
a the center of mass also moves in circular motion.
b the center of mass does not accelerate.
c the acceleration of the center of mass depends on the relative masses of the stars.
d the acceleration of the center of mass depends on the relative speeds of the stars.

Explanation:

Step1: Analyze the system

The two - star system is isolated (very far from other objects). According to the law of conservation of momentum and the property of the center of mass, for an isolated system, the center of mass moves with a constant velocity.

Step2: Analyze acceleration

Since the velocity of the center of mass is constant, by the formula \(a=\frac{\Delta v}{\Delta t}\), if \(\Delta v = 0\) (constant velocity), then \(a = 0\).

Answer:

B. The center of mass does not accelerate.