  (Abridged) We present global disc and local shearing box simulations of
planets interacting with a MHD turbulent disc. We examine the torque exerted by
the disc on the embedded planets as a function of planet mass, and thus make a
first study of orbital migration of planets due to interaction with turbulent
discs. Global simulations were performed for a disc with H/R=0.07 and planet
masses M_p=3,10,30 Earth masses, and 3 Jupiter masses. Shearing box runs were
performed for values of (M_p/M_*)/(H/R)^3=0.1,0.3,1.0 and 2.0, M_* being the
central mass. These allow embedded and gap forming planets to be examined. In
all cases the instantaneous torque exerted on a planet showed strong
fluctuations. In the embedded cases it oscillated between negative and positive
values, and migration occurs as a random walk, unlike the usual type I
migration. Running time averages for embedded planets over 20-25 orbital
periods show that large fluctuations occur on longer time scales, preventing
convergence of the average torque to well defined values, or even to a well
defined sign. Fluctuations become relatively smaller for larger masses, giving
better convergence, due to the planet's perturbation of the disc becoming
larger than the turbulence in its vicinity. Eventually gap formation occurs,
with a transition to type II migration. The existence of significant
fluctuations occurring in turbulent discs on long time scales is important for
lower mass embedded protoplanets. If significant fluctuations occur on the
longest disc evolutionary time scales, convergence of torque running averages
for practical purposes will not occur, and the migration behaviour of low mass
protoplanets considered as an ensemble would be very different from predictions
of type I theory for laminar discs.
