  Hundred meter sized objects have been identified by the Cassini spacecraft in
Saturn's A ring through the so-called "propeller" features they create in the
ring. These moonlets should migrate, due to their gravitational interaction
with the ring ; in fact, some orbital variation have been detected. The
standard theory of type I migration of planets in protoplanetary disks can't be
applied to the ring system, as it is pressureless. Thus, we compute the
differential torque felt by a moonlet embedded in a two-dimensional disk of
solid particles, with flat surface density profile, both analytically and
numerically. We find that the corresponding migration rate is too small to
explain the observed variations of the propeller's orbit in Saturn's A-ring.
  However, local density fluctuations (due to gravity wakes in the marginally
gravitationally stable A-ring) may exert a stochastic torque on a moonlet. Our
simulations show that this torque can be large enough to account for the
observations, depending on the parameters of the rings. We find that on time
scales of several years the migration of propellers is likely to be dominated
by stochastic effects (while the former, non-stochastic migration dominates
after ~ 10^{4-5} years). In that case, the migration rates provided by
observations so far suggests that the surface density of the A ring should be
of the order of 700 kg/m^2. The age of the propellers shouldn't exceed 1 to 100
million years, depending on the dominant migration regime.
