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 Ekşi ( 2002 ) .
In the current study , the assumption of Del Popolo and Ekşi ( 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 } \mathrm { 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 .