  The study of the dynamics of a two-body system in modified gravity
constitutes a more complex problem than in Newtonian gravity. Numerical methods
are typically needed to solve the equations of geodesics. Despite the
complexity of the problem, the study of a two-body system in $f(R)$ gravity
leads to a new exciting perspective hinting the right strategy to adopt in
order to probe modified gravity. Our results point out some differences between
the {\em semiclassical} (Newtonian) approach, and the {\em relativistic}
(geodesic) one thus suggesting that the latter represents the best strategy for
future tests of modified theories of gravity. { Finally, we have also
highlighted the capability of forthcoming observations to serve as smoking gun
of modified gravity revealing a departure from GR or further reducing the
parameter space of $f(R)$ gravity}. \keywords{$f(R)$ gravity \and binary system
\and geodesics \and precession
