  Modified gravity scenarios where a change of regime appears at acceleration
scales $a<a_{0}$ have been proposed. Since for $1 M_{\odot}$ systems the
acceleration drops below $a_{0}$ at scales of around 7000 AU, a statistical
survey of wide binaries with relative velocities and separations reaching
$10^{4}$ AU and beyond should prove useful to the above debate. We apply the
proposed test to the best currently available data. Results show a constant
upper limit to the relative velocities in wide binaries which is independent of
separation for over three orders of magnitude, in analogy with galactic flat
rotation curves in the same $a<a_{0}$ acceleration regime. Our results are
suggestive of a breakdown of Kepler's third law beyond $a \approx a_{0}$
scales, in accordance with generic predictions of modified gravity theories
designed not to require any dark matter at galactic scales and beyond.
