  Observations of the precessing orbits of stars very near the massive black
hole in the galactic center could provide measurements of the spin and
quadrupole moment of the hole and thereby test the no-hair theorem of general
relativity. Since the galactic center is likely to be populated by a
distribution of stars and small black holes, their gravitational interactions
will perturb the orbit of any given star. We estimate the effects of such
perturbations using analytic orbital perturbation theory, and show that for a
range of possible stellar distributions, and for an observed star sufficiently
close to the black hole, the relativistic spin and quadrupole effects will be
larger than the effects of stellar cluster perturbations. Our results are
consistent those from recent numerical N-body simulations by Merritt et al.
