  We present N-body simulations of planetary accretion beginning with 1 km
radius planetesimals in orbit about a 1 solar mass star at 0.4 AU. The initial
disk of planetesimals contains too many bodies for any current N-body code to
integrate; therefore, we model a sample patch of the disk. Although this
greatly reduces the number of bodies, we still track in excess of 10^5
particles. We consider three initial velocity distributions and monitor the
growth of the planetesimals. The masses of some particles increase by more than
a factor of 100. Additionally, the escape speed of the largest particle grows
considerably faster than the velocity dispersion of the particles, suggesting
impending runaway growth, although no particle grows large enough to detach
itself from the power law size-frequency distribution. These results are in
general agreement with previous statistical and analytical results. We compute
rotation rates by assuming conservation of angular momentum around the center
of mass at impact and that merged planetesimals relax to spherical shapes. At
the end of our simulations, the majority of bodies that have undergone at least
one merger are rotating faster than the breakup frequency. This implies that
the assumption of completely inelastic collisions (perfect accretion), which is
made in most simulations of planetary growth at sizes 1 km and above, is
inappropriate. Our simulations reveal that, subsequent to the number of
particles in the patch having been decreased by mergers to half its initial
value, the presence of larger bodies in neighboring regions of the disk may
limit the validity of simulations employing the patch approximation.
