numerical errors is 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 x 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，贴上来了也不一定能成