Constraining the range of Yukawa gravity interaction from S2 star orbits II: Bounds on graviton mass

Recently LIGO collaboration discovered gravitational waves \cite{Abbott_16} predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO \& VIRGO team presented an upper limit on graviton mass such as $m_g < 1.2 \times 10^{-22} eV$ (Abbott et al. (LIGO collaboration) PRL 116 (2016) 061102). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity to evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center.