  Non-baryonic Dark Matter (DM) appears in galaxies and other cosmic structures
when and only when the acceleration of gravity, as computed considering only
baryons, goes below a well defined value a0=1.2e-8 cm/s/s. This might indicate
a breakdown of Newton's law of gravity (or inertia) below a0, an acceleration
smaller than the smallest probed in the solar system. It is therefore important
to verify whether Newton's law of gravity holds in this regime of
accelerations. In order to do this, one has to study the dynamics of objects
that do not contain significant amounts of DM and therefore should follow
Newton's prediction for whatever small accelerations. Globular clusters are
believed, even by strong supporters of DM, to contain negligible amounts of DM
and therefore are ideal for testing Newtonian dynamics in the low acceleration
limit. Here, we discuss the status of an ongoing program aimed to do this test.
Compared to other studies of globular clsuters, the novelty is that we trace
the velocity dispersion profile of globular clusters far enough from the center
to probe gravitational accelerations well below a0. In all three clusters
studied so far the velocity dispersion is found to remain constant at large
radii rather than follow the Keplerian falloff. On average, the flattening
occurs at the radius where the cluster internal acceleration of gravity is
1.8+-0.4 x 10^{-8} cm/s/s, fully consistent with MOND predictions.
