The debate on gravity theories to extend or modify General Relativity is very active today because of the issues related to ultra-violet and infra-red behavior of Einsteins theory. In the first case, we have to address the Quantum Gravity problem. In the latter, dark matter and dark energy, governing the large scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar-tensor or Horava-Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense-Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe-B satellites.
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