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Here we study possible improvements of the existing constraints on the upperbound of graviton mass by the analysis of the stellar orbits around thesupermassive SMBH at the GC in the framework of Yukawa gravity. A motivationfor this study is a recent detection of Schwarzschild precession in the orbitof S2 star around the SMBH at the GC by the GRAVITY Collaboration in 2020. Theauthors indicated that the orbital precession of the S2 star is close to theGeneral Relativity (GR) prediction, but with possible small deviation from it,and parametrized this effect by introducing an ad hoc factor in theparameterized PPN equations of motion. Here we use the value of this factorpresented by GRAVITY in order to perform two-body simulations of the stellarorbits in massive gravity using equations of motion in the modified PPNformalism, as well as to constrain the range of massive interaction $\Lambda$.From the obtained values of $\Lambda$, and assuming that it corresponds to theCompton wavelength of graviton, we then calculated new estimates for the upperbound of graviton mass which are found to be independent, but consistent withthe LIGO's estimate of graviton mass from the first GW signal GW150914 (laterthis graviton mass estimation was significantly improved with consequentobservations of GW events). We also performed calculations including MCMCsimulations in order to constrain the bounds on graviton mass in the case of asmall deviation of the stellar orbits from the corresponding GR predictions andshowed that our method could further improve previous estimates for upperbounds on the graviton mass. It is also demonstrated that such analysis of theobserved orbits of S-stars around the GC in the frame of the Yukawa gravityrepresents a tool for constraining the upper bound for the graviton mass, aswell as for probing the predictions of GR or other gravity theories.

Improvement of graviton mass constraints using GRAVITY's detection of Schwarzschild precession in the orbit of S2 star around the Galactic Center