  We consider a 5-dimensional model with geometry ${\cal M} = {\cal M}_4 \times
{\cal S}_1$, with compactification radius $R$. The Standard Model particles are
localized onto a brane located at y=0, with identical branes localized at
different points in the extra dimension. Objects located on our brane can orbit
around objects located on a brane at a distance $d=y/R$, with an orbit and a
period significantly different from the standard Newtonian ones. We study the
kinematical properties of the orbits, finding that it is possible to
distinguish one motion from the other in a large region of the initial
conditions parameter space. This is a warm-up to study if a SM-like mass
distribution on one (or more) distant brane(s) may represent a possible dark
matter candidate. After using the same technique to the study of orbits of
objects lying on the same brane ($d=0$), we apply this method to detect generic
deviations from the inverse-square Newton's law. We propose a possible
experimental setup to look for departures from Newtonian motion in the
micro-world, finding that an order of magnitude improvement on present bounds
can be attained at the 95% CL under reasonable assumptions.
