  We have carried out a study of the velocity dispersion of the stars in the
outskirts of the globular cluster Omega Centauri, finding that the velocity
dispersion 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 the
globular cluster M15 where the profile flattens out for a = 1.7e-8 cm/s/s. In
both cases the acceleration is comparable to that at which the effect of dark
matter becomes relevant in galaxies. Explanations for this result within
Newtonian dynamics exist (e.g. cluster evaporation, tidal effects, presence of
dark matter) but require ad hoc tuning of the relevant parameters in order to
make in both clusters the dispersion profile flat starting exactly at the same
acceleration. We suggest that this result, together with a similar one for
Palomar 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 of
the internal dynamics of as many GCs as possible.
