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We have carried out a study of the velocity dispersion of the stars in theoutskirts of the globular cluster Omega Centauri, finding that the velocitydispersion remains constant at large radii rather than decrease monotonically.The dispersion starts to be constant for an acceleration of gravity of a =2.1e-8 cm/s/s. A similar result is obtained reanalyzing existing data for theglobular cluster M15 where the profile flattens out for a = 1.7e-8 cm/s/s. Inboth cases the acceleration is comparable to that at which the effect of darkmatter becomes relevant in galaxies. Explanations for this result withinNewtonian dynamics exist (e.g. cluster evaporation, tidal effects, presence ofdark matter) but require ad hoc tuning of the relevant parameters in order tomake in both clusters the dispersion profile flat starting exactly at the sameacceleration. We suggest that this result, together with a similar one forPalomar 13 and the anomalous behavior of spacecrafts outside the solar system,may indicate a breakdown of Newton's law in the weak acceleration regime.Although not conclusive, these data prompt for the accurate determination ofthe internal dynamics of as many GCs as possible.Comment: Accepted for publication on A&A Letters. Four pages + 2 figure

Using globular clusters to test gravity in the weak acceleration regime