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Monitoring the orbits of stars around Sgr A* offers the possibility ofdetecting the precession of their orbital planes due to frame dragging, ofmeasuring the spin and quadrupole moment of the black hole, and of testing theno-hair theorem. Here we investigate whether the deviations of stellar orbitsfrom test-particle trajectories due to wind mass loss and tidal dissipation ofthe orbital energy compromise such measurements. We find that the effects ofstellar winds are, in general, negligible. On the other hand, for the mosteccentric orbits (e>0.96) for which an optical interferometer, such as GRAVITY,will detect orbital plane precession due to frame dragging, the tidaldissipation of orbital energy occurs at timescales comparable to the timescaleof precession due to the quadrupole moment of the black hole. As a result, thisnon-conservative effect is a potential source of systematic uncertainty intesting the no-hair theorem with stellar orbits.

Deviation of Stellar Orbits from Test Particle Trajectories Around Sgr A* Due to Tides and Winds