Astrometric detection of binary companions and planets: Acceleration of proper motion

Apparent acceleration of proper motion is one of the observable manifestations of orbital motion in binary stars. Owing to the increasing accuracy of astrometric measurements, it may also be a method to detect binarity of stars. This paper presents some analytical expressions for the effects of binary motion on proper motions when the orbital period is at least several times the span of observations. We estimate orbit dimensions and distances at which low‐mass companions and planets may be detected around main‐sequence stars, using preliminary estimates of precision for the AMEX, GAIA and SIM space missions.