  A novel experimental setup to measure deviations from the $1/r^2$ distance
dependence of Newtonian gravity was proposed in arXiv:1609.05654. The
underlying theoretical idea was to study the orbits of a microscopically-sized
planetary system composed of a ``Satellite'', with mass $m_{\rm S} \sim {\cal
O}(10^{-9})$ g, and a ``Planet'', with mass $M_{\rm P} \sim {\cal O} (10^{-5})
$ g at an initial distance of hundreds of microns. The detection of precession
of the orbit in this system would be an unambiguous indication of a central
potential with terms that scale with the distance differently from $1/r$. This
is a huge advantage with respect to the measurement of the absolute strength of
the attraction between two bodies, as most electrically-induced background
potentials do indeed scale as $1/r$. Detection of orbit precession is
unaffected by these effects, allowing for better sensitivities. In
arXiv:2106.08611, the impact of other subleading backgrounds that may induce
orbit precession, such as, {\em e.g.}, the electrical Casimir force or general
relativity, was studied in detail. It was found that the proposed setup could
test Yukawa-like corrections, $\alpha \times \exp(-r/\lambda)$, to the $1/r$
potential with couplings as low as $\alpha \sim 10^{-2}$ for distances as small
as $\lambda \sim 10$ $\mu$m, improving by roughly an order of magnitude present
bounds. In this paper, we start to move from a theoretical study of the
proposal to a more realistic implementation of the experimental setup. As a
first step, we study the impact of air viscosity on the proposed setup and see
how the setup should be modified in order to preserve the theoretical
sensitivity achieved in our previous works.
