Recently, the LIGO-Virgo collaboration discovered gravitational waves and in their first publication on the subject the authors also presented a graviton mass constraint as mg < 1.2 × 10-22 eV  (see also more details in a complimentary paper ). In our previous papers we considered constraints on Yukawa gravity parameters  and on graviton mass from analysis of the trajectory of S2 star near the Galactic Center . In the paper we analyze a potential to reduce upper bounds for graviton mass with future observational data on trajectories of bright stars near the Galactic Center. Since gravitational potentials are different for these two cases, expressions for relativistic advance for general relativity and Yukawa potential are different functions on eccentricity and semimajor axis, it gives an opportunity to improve current estimates of graviton mass with future observational facilities. In our considerations of an improvement potential for a graviton mass estimate we adopt a conservative strategy and assume that trajectories of bright stars and their apocenter advance will be described with general relativity expressions and it gives opportunities to improve graviton mass constraints. In contrast with our previous studies, where we present current constraints on parameters of Yukawa gravity  and graviton mass  from observations of S2 star, in the paper we express expectations to improve current constraints for graviton mass, assuming the GR predictions about apocenter shifts will be confirmed with future observations. We concluded that if future observations of bright star orbits during around fifty years will confirm GR predictions about apocenter shifts of bright star orbits it give an opportunity to constrain a graviton mass at a level around 5 × 10-23 eV or slightly better than current estimates obtained with LIGO observations.
Zakharov, A. F., Jovanović, P., Borka, D., & Jovanović, V. B. (2018). Constraining the range of Yukawa gravity interaction from S2 star orbits III: Improvement expectations for graviton mass bounds. Journal of Cosmology and Astroparticle Physics, 2018(4). https://doi.org/10.1088/1475-7516/2018/04/050