  Astrometric detection of an unseen companion is based on analysis of apparent
motion of its host star around the system's barycentre. Systems with orbital
period close to one year may escape detection if orbital motion of their host
stars are observationally indistinguishable from parallax effect. Additionally,
the astrometric solution may produce a biased parallax estimation for such
systems. We examine effects of orbital motion of the Earth on astrometric
detectability in terms of correlation between the Earth's orbital position and
position of the star relative to its system barycentre. The $\chi^2$ statistic
for parallax estimation is calculated analytically, leading to expressions that
relate the decrease in detectability and accompanying parallax bias to the
position correlation function. The impact of the Earth's motion critically
depends on the exoplanet's orbital period, diminishing rapidly as the period
deviates from one year. Selection effects against one-year period systems is
therefore expected. Statistical estimation shows that the corresponding loss of
sensitivity results in a typical 10 per cent increase in detection threshold.
Consideration of eccentric orbits shows that the Earth's motion has no effect
on detectability for $e\ge0.5$. Dependence of detectability on other
parameters, such as orbital phases and inclination of the orbit plane to the
ecliptic, are smooth and monotonic because they are described by simple
trigonometric functions.
