  Most binaries are undetected. Astrometric reductions of a system using the
assumption that the object moves like a single point mass can be biased by
unresolved binary stars. The discrepancy between the centre of mass of the
system (which moves like a point mass) and the centre of light (which is what
we observe) introduces additional motion. We explore the extent to which binary
systems affect single object models fit to astrometric data. This tells us how
observations are diluted by binaries and which systems cause the largest
discrepancies - but also allows us to make inferences about the binarity of
populations based on observed astrometric error. By examining a sample of mock
observations, we show that binaries with periods close to one year can mimic
parallax and thus bias distance measurements, whilst long period binaries can
introduce significant apparent proper motion. Whilst these changes can soak up
some of the error introduced by the binary, the total deviation from the best
fitting model can be translated into a lower limit on the on-sky separation of
the pair. Throughout we link these predictions to data from the Gaia satellite,
whilst leaving the conclusions generalizable to other surveys.
