zed by their strong dependence on initial conditions.
From that point of view， many of the previous long-term numerical integrations included only the outer five planets (Sussman & Wisdom 1988; Kinoshita & Nakai 1996). This is because the orbital periods of the outer planets are so much longer than those of the inner four planets that it is much easier to follow the system for a given integration period. At present， the longest numerical integrations published in journals are those of Duncan & Lissauer (1998). Although their main target was the effect of post-main-sequence solar mass loss on the stability of planetary orbits， they performed many integrations covering up to ∼1011 yr of the orbital motions of the four jovian planets. The initial orbital elements and masses of planets are the same as those of our Solar system in Duncan & Lissauer's paper， but they decrease the mass of the Sun gradually in their numerical experiments. This is because
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