Testing horndeski gravity with S2 star orbit

We have explored a completely new and alternative way to restrict the parameter space of Horndeski theory of gravity. Using its Newtonian limit, it is possible to test the theory at a regime where, given its complexity and the small magnitude of the expected effects, it is poorly probed. At Newtonian level, it gives rise to a generalized Yukawa-like Newtonian potential which we have tested using S2 star orbit data. Our model adds five parameters to the General Relativity model, and the analysis constrains two of them with unprecedented precision to these energy scales, while only gives an exclusion region for the remaining parameters. We have shown the potential of weak-field tests to constrain Horndeski gravity opening, as a matter of fact, a new avenue that deserves to be further, and deeply, explored near in the future.