  Many exoplanets were detected thanks to the radial velocity method, according
to which the motion of a binary system around its center of mass can produce a
periodical variation of the Doppler effect of the light emitted by the host
star. These variations are influenced by both Newtonian and non-Newtonian
perturbations to the dominant inverse-square acceleration; accordingly,
exoplanetary systems lend themselves to test theories of gravity alternative to
General Relativity. In this paper, we consider the impact of Standard Model
Extension (a model that can be used to test all possible Lorentz violations) on
the perturbation of radial velocity, and suggest that suitable exoplanets
configurations and improvements in detection techniques may contribute to
obtain new constraints on the model parameters.
