s also given. Section 4 goes on to a discussion of the longest-term variation of planetary orbits using a low-pass filter and includes a discussion of angular momentum deficit. In Section 5， we present a set of numerical integrations for the outer five planets that spans ± 5 × 1010 yr. In Section 6 we also discuss the long-term stability of the planetary motion 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，贴上来了起点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 planets (N±1，2，3)， which is about 1/11 of the orbital period of the innermost planet
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