  In a previous work (arXiv:1609.05654v2), an experimental setup aiming at the
measurement of deviations from the Newtonian $1/r^2$ distance dependence of
gravitational interactions was proposed. The theoretical idea behind this setup
was to study the trajectories of a "Satellite" with a mass $m_{\rm S} \sim
{\cal O}(10^{-9})$ $\mathrm{g}$ around a "Planet" with mass $m_{\rm P} \in
[10^{-7},10^{-5} ]$ $\mathrm{g}$, looking for precession of the orbit. The
observation of such feature induced by gravitational interactions would be an
unambiguous indication of a gravitational potential with terms different from
$1/r$ and, thus, a powerful tool to detect deviations from Newton's $1/r^2$
law. In this paper we optimize the proposed setup in order to achieve maximal
sensitivity to look for {\em Beyond-Newtonian} corrections. We study in detail
possible background sources that could induce precession and quantify their
impact on the achievable sensitivity. We conclude that a dynamical measurement
of deviations from newtonianity can test Yukawa-like corrections to the $1/r$
potential with strength as low as $\alpha \sim 10^{-2}$ for distances as small
as $\lambda \sim 10 \, \mu\mathrm{m}$.
