  The second-generation beam combiner at the Very Large Telescope (VLT),
GRAVITY, observes the stars orbiting the compact object located at the center
of our galaxy, with an unprecedented astrometric accuracy of 10 $\mu$as. The
nature of this compact source is still unknown since black holes are not the
only candidates explaining the four million solar masses at the Galactic
center. Boson stars are such an alternative model to black holes. This paper
focuses on the study of trajectories of stars orbiting a boson star and a Kerr
black hole. We put in light strong differences between orbits obtained in both
metrics when considering stars with sufficiently close pericenters to the
compact object, typically $\lesssim 30~M$. Discovery of closer stars to the
Galactic center than the S2 star by the GRAVITY instrument would thus be a
powerful tool to possibly constrain the nature of the central source.
