  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 Einstein's 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.
