A test of Newton's law of gravity in the low acceleration regime using globular clusters is presented and new results for the core collapsed globular cluster NGC 7099 given. The run of the gravitational potential as a function of distance is probed by studying the velocity dispersion profile of the cluster, as derived from a set of 125 radial velocities with accuracy better than 1km/s. The velocity dispersion profile is traced up to ~18pc from the cluster center. The dispersion is found to be maximal at the center, then decrease until 10+/-2pc from the center, well inside the cluster tidal radius of 42pc. After that the dispersion remains basically constant with an average value of 2.2+/-0.3km/s. Assuming a total V magnitude of M(V)=-7.43mag for NGC 7099, the acceleration at 10+/-2pc from the center is 1.1+0.4-0.3{tau}x10-8cm/s2^, where {tau} is the mass-to-light ratio. Thus, for {tau}>~2 typical of globular clusters, the flattening of the velocity dispersion profile occurs for a value of the internal acceleration of gravity that is fully consistent with a0=1.2x10-8cm/s2 observed in galaxies. This new result for NGC 7099 brings to 4 the clusters with velocity dispersion profile probing acceleration below a0. All four have been found to have a flat dispersion profile at large radii where the acceleration is below a0, thereby mimicking elliptical galaxies qualitatively and quantitatively. Whether this indicates a failure of Newtonian dynamics in the low acceleration limit or some more conventional dynamical effect (e.g., tidal heating) is still unclear. However, the similarities emerging between very different globular clusters, as well as between globular clusters and elliptical galaxies, seem to favor the first of these two possibilities. (1 data file).