  Observations of stars and pulsars orbiting the black hole in the center of
the Milky Way offer the potential of measuring not only the mass of the black
hole but also its spin and quadrupole moment, thereby providing observational
verification of the no-hair theorem. The relativistic effects that will allow
us to measure these higher moments of the gravitational field, however, are
very small and may be masked by drag forces that stars and pulsars experience
orbiting within the hot, tenuous plasma that surrounds the black hole. The
properties of this plasma at large distances from the central object have been
measured using observations of the extended X-ray emission that surrounds the
point source. At distances comparable to the black-hole event horizon, the
properties of the accretion flow have been constrained using observations of
its long-wavelength emission and polarization, as well as of the size of the
emitting region at 1.3 mm. I use models of the plasma density and temperature
at various distances from the black hole to investigate the effect of
hydrodynamic drag forces on future measurements of the higher moments of its
gravitational field. I find that hydrodynamic drag does not preclude
measurements of the black hole spin and quadrupole moment using high-resolution
observations of stars and pulsars that orbit within a few thousand
gravitational radii from its horizon.
