Non-relativistic limit of Randall-Sundrum model: solutions, applications
  and constraints
  In the Randall-Sundrum model with one brane, we found the approximate and
exact solutions for gravitational potentials and accelerations of test bodies
in these potentials for different geometrical configurations. We applied these
formulas for calculation of the gravitational interaction between two spheres
and found the approximate and exact expressions for the relative force
corrections to the Newton's gravitational force. We demonstrated that the
difference between relative force corrections for the approximate and exact
cases increases with the parameter $l$ (for the fixed distance $r$ between
centers of the spheres). On the other hand, this difference increases with
decreasing of the distance between the centers of the spheres (for the fixed
curvature scale parameter $l$). We got the upper limit for the curvature scale
parameter $l\lesssim 10\, \mu$m. For these values of $l$, the difference
between the approximate and exact solutions is negligible.
