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

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