Low scale unification, Newtonʹs law and extra dimensions

Motivated by recent work on low energy unification, in this short note we derive corrections on Newtonʹs inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the corrections are of Yukawa type. Inside the compactified space of n-extra dimensions the sub-leading term is proportional to the (n+1)-power of the distance over the compactification radius ratio. Some physical implications of these modifications are briefly discussed.