  In the current paper, we further improved the model for the migration of
planets introduced in Del Popolo et al. (2001) and extended to time-dependent
planetesimal accretion disks in Del Popolo and Eksi (2002). In the current
study, the assumption of Del Popolo and Eksi (2002), that the surface density
in planetesimals is proportional to that of gas, is released. In order to
obtain the evolution of planetesimal density, we use a method developed in
Stepinski and Valageas (1997) which is able to simultaneously follow the
evolution of gas and solid particles for up to 10^7 yrs. Then, the disk model
is coupled to migration model introduced in Del Popolo et al. (2001) in order
to obtain the migration rate of the planet in the planetesimal. We find that
the properties of solids known to exist in protoplanetary systems, together
with reasonable density profiles for the disk, lead to a characteristic radius
in the range 0.03-0.2 AU for the final semi-major axis of the giant planet.
