# Does the Centre of Mass of a binary star system accelerate?

At the COM of a binary star system (where both stars has a different mass), the net force at the centre of mass is non-zero.

Does this mean that the COM will be accelerating? And if so, wouldn't the velocity of the binary star system keep on increasing?

However, it doesn't make sense if the velocity keeps increasing. So what is the error here?

• "At the COM of a binary star system (where both stars has a different mass), the net force at the centre of mass is non-zero." What makes you think this? Commented Oct 9, 2022 at 2:03
• We can have an external potential that accelerates the center of mass of a binary star system. Indeed, every binary star system in a galaxy has an accelerating center of mass because the system orbits around the center of the galaxy. If that potential is zero, however, then the center of mass will not accelerate. Commented Oct 9, 2022 at 2:48

## 1 Answer

It is not entirely clear what you mean by "the net force at the centre of mass," since forces act on objects, and there need not be an object at the centre of mass. Presumably, you mean to say that the gravitational field is non-zero at the centre of mass; i.e. if there were on object at the centre of mass, the net force on it would be non-zero. This does not mean that the centre of mass will accelerate, but rather that an object at the centre of mass will accelerate.