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