  Under Newtonian dynamics, the relative motion of the components of a binary
star should follow a Keplerian scaling with separation. Once orientation
effects and a distribution of ellipticities are accounted for, dynamical
evolution can be modelled to include the effects of Galactic tides and stellar
mass perturbers, over the lifetime of the solar neighbourhood. This furnishes a
prediction for the relative velocity between the components of a binary and
their projected separation. Taking a carefully selected small sample of 81
solar neighbourhood wide binaries from the {\it Hipparcos} catalogue, we
identify these same stars in the recent Gaia DR2, to test the prediction
mentioned using the latest and most accurate astrometry available. The results
are consistent with the Newtonian prediction for projected separations below
7000 AU, but inconsistent with it at larger separations, where accelerations
are expected to be lower than the critical $a_{0}=1.2 \times 10^{-10} $ { m
s$^{-2}$} value of MONDian gravity. This result challenges Newtonian gravity at
low accelerations and shows clearly the appearance of gravitational anomalies
of the type usually attributed to dark matter at galactic scales, now at much
smaller stellar scales.
