How do astronomers verify if two stars constitute a binary system using proper motion?

Answer

By observing if the stars drift through the galaxy together in the same direction and at the same speed.

Proper motion refers to the change in an object's position across the sky over time. When two stars share a common proper motion, it serves as a strong indicator that they are moving through the galaxy in unison. This synchronized movement suggests that the stars are gravitationally tethered to one another rather than just happening to be in the same line of sight. This collective movement is a hallmark of binary systems, as they orbit a common center of mass and travel through space as a bound, single entity.

How do astronomers verify if two stars constitute a binary system using proper motion?
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