How is the existence of an astrometric binary determined?

The determination of an astrometric binary hinges upon the oscillatory motion of the visible member of a binary system. In an astrometric binary, one star is typically visible while the other, which is often fainter or not visible at all, exerts a gravitational influence on the visible star.

As the visible star moves in response to this gravitational pull, it exhibits a measurable wobble or oscillation in its motion against the background of more distant stars. This movement is a key indicator of the presence of an unseen companion. By analyzing this motion, astronomers can infer the mass and orbit of the hidden star even without directly observing it.

In contrast, the other options do not effectively reveal the presence of an astrometric binary. Observing both stars simultaneously is not usually feasible due to the nature of the binary. Calculating the orbital period requires having information about the orbits, which might not be available if only one star is visible. Visual observation of brightness would only indicate the presence of stars but wouldn't provide insights into the gravitational effects that suggest the existence of an unseen companion star.