Answer
Newton's first law tells us that in the absence of external forces, a system's CM will travel in a straight line at constant velocity. This is shown on pages 140-141, and similar examples are displayed in Figures 8.21 and 8.23.
If a single star travels through space, it travels in a straight line. The system is the star alone, and its CM is at its exact center.
If wobbly motion is observed, we know that the CM still travels in a straight line, and we know that the star wobbles around the CM. Therefore, the system's CM is not at the star's own center. (Now, system = 2 or more objects.)
There must be another mass nearby, to pull the center of mass away from the star’s center.
