  The spin and quadrupole moment of the supermassive black hole at the Galactic
center can in principle be measured via astrometric monitoring of stars
orbiting at milliparsec (mpc) distances, allowing tests of general relativistic
"no-hair" theorems (Will 2008). One complicating factor is the presence of
perturbations from other stars, which may induce orbital precession of the same
order of magnitude as that due to general relativistic effects. The expected
number of stars in this region is small enough that full N-body simulations can
be carried out. We present the results of a comprehensive set of such
simulations, which include a post-Newtonian treatment of spin-orbit effects. A
number of possible models for the distribution of stars and stellar remnants
are considered. We find that stellar perturbations are likely to obscure the
signal due to frame-dragging for stars beyond ~0.5 mpc from the black hole,
while measurement of the quadrupole moment is likely to require observation of
stars inside ~0.2 mpc. A high fraction of stellar remnants, e.g. 10-Solar-mass
black holes, in this region would make tests of GR problematic at all radii. We
discuss the possibility of separating the effects of stellar perturbations from
those due to GR.
