ype of resonance， later confirmed by Milani， Nobili & Carpino (1989).
An argument θ4=PN+ 3 (ΩPΩN) librates around 180° with a long period， 5.7 × 108 yr.
In our numerical integrations， the resonances (i)–(iii) are well maintained， and variation of the critical arguments θ1，θ2，θ3 remain similar during the whole integration period (Figs 14–16 ). However， the fourth resonance (iv) appears to be different: the critical argument θ4 alternates libration and circulation over a 1010-yr time-scale (Fig. 17). This is an interesting fact that Kinoshita & Nakai's (1995， 1996) shorter integrations were not able to disclose.
6 Discussion
What kind of dynamical mechanism maintains this long-term stability of the planetary system? We can immediately think of two major features that may be responsible for the long-term stability. First， there seem to be no significant lower-order resonances (mean motion and secular) between any pair among the nine planets. Jupiter and Saturn are close to a 5:2 mean motion resonance (the famous ‘great inequality’)， but not just in the resonance zone. Higher-order resonances may cause the chaotic nature of the planetary dynamical motion， but they are not so strong as to destroy the stable planetary motion within the lifetime of the real Solar system. The second feature， which we think is more important for the long-term stability of our planetary system， is the difference in dynamical distance between terrestrial and jovian planetary subsystems (Ito & Tanikawa 1999， 2001). When we measure planetary separations by the mutual Hill radii (R_)， separations among terrestrial planets are greater than 26RH， whereas those among jovian planets are less than 14RH. This difference is directly related to the difference between dynamical features of terrestrial and jovian planets. Terrestrial planets have smaller masses， shorter orbital periods and wider dynamical separation. They are strongly perturbed by jovian