  We propose a high precision satellite experiment to further test Einstein's
General Relativity and constrain extended theories of gravity. We consider the
frequency shift of a photon radially exchanged between two observers located on
Earth and on a satellite in circular orbit in the equatorial plane. In General
Relativity there exists a peculiar satellite-distance at which the static
contribution to the frequency shift vanishes since the effects induced by pure
gravity and special relativity compensate, while it can be non-zero in modified
gravities, like in models with screening mechanisms. As an experimental device
placed on the satellite we choose a system of hydrogen atoms which can exhibit
the $1$s spin-flip transition from the singlet (unaligned proton-electron
spins) to the triplet (aligned proton-electron spins) state induced by the
absorption of photons at $21.1$cm. The observation of an excited state would
indicate that the frequency of the emitted and absorbed photon remains
unchanged according to General Relativity. On the contrary, a non-zero
frequency shift, as predicted in extended theories of gravity, would prevent
the spin-flip transition and the hydrogen atoms from jumping into the excited
state. Such a detection would signify a smoking-gun signature of new physics
beyond special and general relativity.
