  We study the frequency shift of photons generated by rotating gravitational
sources in the framework of curvature based Extended Theories of Gravity. The
discussion is developed considering the weak-field approximation. Following a
perturbative approach, we analyze the process of exchanging photons between
Earth and a given satellite, and we find a general relation to constrain the
free parameters of gravitational theories. Finally, we suggest the Moon as a
possible laboratory to test theories of gravity by future experiments which can
be, in principle, based also on other Solar System bodies.
