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.
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