  Astrometry covers a parameter space that cannot be reached by RV or transit
methods to detect terrestrial planets on wide orbits. In addition, high
accuracy astrometric measurements are necessary to measure the inclination of
the planet's orbits. Here we investigate the principles of an artefact of the
astrometric approach. Namely, the displacement of the photo-centre due to
inhomogeneities in a dust disc around the parent star. Indeed, theory and
observations show that circumstellar discs can present strong asymmetries. We
model the pseudo-astrometric signal caused by these inhomogeneities, asking
whether a dust clump in a disc can mimic the astrometric signal of an
Earth-like planet. We show that these inhomogeneities cannot be neglected when
using astrometry to find terrestrial planets. We provide the parameter space
for which these inhomogeneities can affect the astrometric signals but still
not be detected by mid-IR observations. We find that a small cross section of
dust corresponding to a cometary mass object is enough to mimic the astrometric
signal of an Earth-like planet. Astrometric observations of protoplanetary
discs to search for planets can also be affected by the presence of
inhomogeneities. Some further tests are given to confirm whether an observation
is a real planet astrometric signal or an impostor. Eventually, we also study
the case where the cross section of dust is high enough to provide a detectable
IR-excess and to have a measurable photometric displacement by actual
instruments such as Gaia, IRAC or GRAVITY. We suggest a new method, which
consists in using astrometry to quantify asymmetries (clumpiness) in inner
debris discs that cannot be otherwise resolved.
