  We use Gaia DR2 systemic proper motions of 45 satellite galaxies to constrain
the mass of the Milky Way using the scale free mass estimator of Watkins et al.
(2010). We first determine the anisotropy parameter $\beta$, and the tracer
satellites' radial density index $\gamma$ to be $\beta$=$-0.67^{+0.45}_{-0.62}$
and $\gamma=2.11\pm0.23$. When we exclude possible former satellites of the
Large Magellanic Cloud, the anisotropy changes to
$\beta$=$-0.21^{+0.37}_{-0.51}$. We find that the index of the Milky Way's
gravitational potential $\alpha$, which is dependent on the mass itself, is the
parameter with the largest impact on the mass determination. Via comparison
with cosmological simulations of Milky Way-like galaxies, we carried out a
detailed analysis of the estimation of the observational uncertainties and
their impact on the mass estimator. We found that the mass estimator is biased
when applied naively to the satellites of simulated Milky Way halos. Correcting
for this bias, we obtain for our Galaxy a mass of
$0.58^{+0.15}_{-0.14}\times10^{12}$M$_\odot$ within 64 kpc, as computed from
the inner half of our observational sample, and
$1.43^{+0.35}_{-0.32}\times10^{12}$M$_\odot$ within 273 kpc, from the full
sample; this latter value extrapolates to a virial mass of
$M_\mathrm{vir\,\Delta=97}$=$1.51^{+0.45}_{-0.40} \times 10^{12}M_{\odot}$
corresponding to a virial radius of R$_\mathrm{vir}$=$308\pm29$ kpc. This value
of the Milky Way mass lies in-between other mass estimates reported in the
literature, from various different methods.
