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

Wide binaries as a critical test of Classical Gravity