  The dynamics of planetesimals and planetary cores may be strongly influenced
by density perturbations driven by magneto-rotational turbulence in their natal
protoplanetary gas disks. Using the local shearing box approximation, we
perform numerical simulations of planetesimals moving as massless particles in
a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows
turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of
$\alpha \sim 10^{-2}$, with root-mean-square density perturbations of
$\sim$10%. We measure the statistical evolution of particle orbital properties
in our simulations including mean radius, eccentricity, and velocity
dispersion. We confirm random walk growth in time of all three properties, the
first time that this has been done with direct orbital integration in a local
model. We find that the growth rate increases with the box size used at least
up to boxes of eight scale heights in horizontal size. However, even our
largest boxes show velocity dispersions sufficiently low that collisional
destruction of planetesimals should be unimportant in the inner disk throughout
its lifetime. Our direct integrations agree with earlier torque measurements
showing that type I migration dominates over diffusive migration by stochastic
torques for most objects in the planetary core and terrestrial planet mass
range. Diffusive migration remains important for objects in the mass range of
kilometer-sized planetesimals. Discrepancies in the derived magnitude of
turbulence between local and global simulations of magneto-rotationally
unstable disks remains an open issue, with important consequences for planet
formation scenarios.
