  Accurate astrometry is a key deliverable for the next generation of
multi-conjugate adaptive optics (MCAO) systems. The MCAO Visible Imager and
Spectrograph (MAVIS) is being designed for the Very Large Telescope Adaptive
Optics Facility and must achieve 150 $\mu$as astrometric precision (50 $\mu$as
goal). To test this before going on-sky, we have created MAVISIM, a tool to
simulate MAVIS images. MAVISIM accounts for three major sources of astrometric
error, high- and low-order point spread function (PSF) spatial variability,
tip-tilt residual error and static field distortion. When exploring the impact
of these three error terms alone, we recover an astrometric accuracy of 50
$\mu$as for all stars brighter than $m=19$ in a 30s integration using
PSF-fitting photometry. We also assess the feasibility of MAVIS detecting an
intermediate mass black hole (IMBH) in a Milky Way globular cluster. We use an
N-body simulation of an NGC 3201-like cluster with a central 1500 M$_{\odot}$
IMBH as input to MAVISIM and recover the velocity dispersion profile from
proper motion measurements. Under favourable astrometric conditions, the
dynamical signature of the IMBH is detected with a precision of ~0.20 km/s in
the inner ~4" of the cluster where HST is confusion-limited. This precision is
comparable to measurements made by Gaia, HST and MUSE in the outer ~60" of the
cluster. This study is the first step towards building a science-driven
astrometric error budget for an MCAO system and a prediction of what MAVIS
could do once on sky.
