  In this paper, we further develop the model for the migration of planets
introduced in Del Popolo, Gambera and Ercan, and extended to time-dependent
planetesimal accretion disks in Del Popolo and Eksi. More precisely, the
assumption of Del Popolo and Eksi that the surface density in planetesimals is
proportional to that of gas is released. Indeed, the evolution of the radial
distribution of solids is governed by many processes: gas-solid coupling,
coagulation, sedimentation, evaporation/condensation, so that the distribution
of planetesimals emerging from a turbulent disk does not necessarily reflect
that of gas. In order to describe this evolution we use a method developed in
Stepinski and Valageas which, using a series of simplifying assumptions, is
able to simultaneously follow the evolution of gas and solid particles for up
to $10^7 {\rm yr}$. Then, the distribution of planetesimals obtained after
$10^7 {\rm yr}$ is used to study the migration rate of a giant planet through
the migration model introduced in \cite{DP1}. This allows us to investigate the
dependence of the migration rate on the disk mass, on its time evolution and on
the value of the dimensionless viscosity parameter alpha. We find that in the
case of disks having a total mass of $10^{-3}-10^{-1} M_{\odot}$, and
$10^{-4}<\alpha<10^{-1}$, planets can migrate inward over a large distance
while if $M_{\rm d}<10^{-3} M_{\odot}$ the planets remain almost at their
initial position for $\alpha>10^{-3}$ and only in the case $\alpha<10^{-3}$ the
planets move to a minimum value of orbital radius of $\simeq 2 {\rm AU}$.
Moreover, the observed distribution of planets in the period range 0-20 days
can be easily obtained from our model.
