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 modeled to include the effects of Galactic tides and stellar mass perturbers, over the lifetime of the solar neighborhood. 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 neighborhood wide binaries from the Hipparcos catalog, 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 a0 = 1.2 × 10-10m.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.