New measurements of the velocity dispersion of the globular cluster \omega Centauri allow to trace its gravitational potential down to an acceleration of 8 \times 10 ^ { -9 } cm s ^ { -2 } .
It is found that the dispersion profile remains flat well inside the tidal radius as soon as the acceleration of gravity approaches a _ { 0 } , a result that finds its simplest explanation within the contest of MOND .
A similar behavior is observed in the globular cluster M15 showing this is not a peculiar features of \omega Centauri .
This result is surprising and suggestive of a failure of Newton ’ s law at low accelerations .