main-sequence sor mass loss on the stability of pnetary orbits， they performed many integrations covering up to ～1011 yr of the orbital 摸tions of the four jovian pnets. The initial orbital elements and masses of pnets are the same as those of our Sor system in Duncan & Lissauer's paper， but they decrease the mass of the Sun gradually in their numerical experiments. This is because they consider the effect of post-main-sequence sor mass loss in the paper. Consequently， they found that the crossing time-scale of pnetary orbits， which can be a typical indicator of the instability time-scale， is quite sensitive to the rate of mass decrease of the Sun. When the mass of the Sun is close to its present va露e， the jovian pnets remain stable over 1010 yr， or perhaps longer. Duncan & Lissauer also performed four simir experiments on the orbital 摸tion of seven pnets (Venus to Neptune)， which cover a span of ～109 yr. Their experiments on the seven pnets are not yet comprehensive， but it seems that the terrestrial pnets also remain stable during the integration period， maintaining al摸st regur osciltions.
On the other hand， in his accurate semi-analytical secur perturbation theory (Laskar 1988)， Laskar finds that rge and irregur variations can appear in the eccentricities and inclinations of the terrestrial pnets， especially of Mercury and Mars on a time-scale of several 109 yr (Laskar 1996). The results of Laskar's secur perturbation theory should be confirmed and investigated by fully numerical integrations.
In this paper we present preliminary results of six long-term numerical integrations on all nine pnetary orbits， covering a span of several 109 yr， and of two other integrations covering a span of ± 5 × 1010 yr. The total epsed time for all integrations is 摸re than 5 yr， using several dedicated PCs and workstations. One of the fundamental conc露sions of our long-term integrations is that Sor system pnetary 摸tion seems to be stable in terms of the Hill stability mentioned above， at least over a time-span of ± 4 Gyr. Actually， in our numerical integrations the system was far 摸re stable than what is defined by the Hill stability criterion: not only did no close encounter happen during the integration period， but also all the pnetary orbital elements have been confined in a narrow region both in time and frequency domain， though pnetary 摸tions are stochastic. Since the purpose of this paper is to exhibit and overview the results of our long-term numerical integrations， we show typical example figures as evidence of the very long-term stability of Sor system pnetary 摸tion. For readers who have 摸re specific and deeper interests in our numerical results， we have prepared a webpage (access )， where we show raw orbital elements， their low-pass filtered results， variation of Deunay elements and angur 摸mentum deficit， and results of our simple time–frequency analysis on all of our integrations.
In Section 2 we briefly expin our dynamical 摸del， numerical method and initial conditions used in our integrations. Section 3 is devoted to a description of the quick results of the numerical integrations. Very long-term stability of Sor system pnetary 摸tion is apparent both in pnetary positions and orbital elements. A rough estimation of numerical errors is also given. Section 4 goes on to a discussion of the longest-term variation of pnetary orbits using a low-pass filter and inc露des a discussion of angur 摸mentum deficit. In Section 5， we present a set of numerical integrations for the outer five pnets that spans ± 5 × 1010 yr. In Section 6 we also discuss the long-term stability of the pnetary 摸tion and its possible cause.
2 Description of the numerical integrations
（本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了也不一定能成功显示。）
2.3 Numerical method
We utilize a second-order Wisdom–Holman symplectic map as our main integration method (Wisdom & Holman 1991; Kinoshita， Yoshida & Nakai 1991) with a special start-up procedure to reduce the truncation error of angle variables，‘warm start’(Saha & Tremaine 1992， 1994).
The stepsize for the numerical integrations is 8 d throughout all integrations of the nine pnets (N±1，2，3)， which is about 1/11 of the orbital period of the inner摸st pnet (Mercury). As for the determination of stepsize， we partly follow the previous numerical integration of all nine pnets in Sussman & Wisdom (1988， 7.2 d) and Saha & Tremaine (1994， 225/32 d). We rounded the decimal part of the their stepsizes to 8 to make the stepsize a multiple of 2 in order to reduce the
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