LHB model (Gomes et al., 2005). That model argues that the ratio of Saturn’s and Jupiter’s orbital periods was smaller than 2, but requires that it was not too much smaller than this value. Otherwise, the mass of the planetesimal disk remaining after the disappearance of the gas would not have been sufficient to drive Saturn across the 1:2 resonance with Jupiter, which is required to trigger the planetary instability responsible for the origin of the LHB. Thus, it is important to investigate if other resonances between Jupiter and Saturn are possible in the context of the mechanism of MS01, or if there are possibilities to leave the resonance towards the end of the gas disk lifetime.

With these goals in mind, this paper is structured as follows. In Sect. \[MS\] we briefly review MS01 result using a very similar simulation (and the same numerical code), and then we discuss the dependence of the results on the initial location of Saturn. In Sect. \[dependences\] we use the algorithm of Crida et al. (2007) to investigate how the dynamics of the Jupiter-Saturn couple depends on the disk’s aspect ratio and viscosity, and also on numerical parameters such as disk’s resolution and 