eudo-true’ solution of planetary orbital evolution. Next， we compare the test integration with the main integration， N−1. For the period of 3 × 105 yr， we see a difference in mean anomalies of the Earth between the two integrations of ∼0.52°(in the case of the N−1 integration). This difference can be extrapolated to the value ∼8700°， about 25 rotations of Earth after 5 Gyr， since the error of longitudes increases linearly with time in the symplectic map. Similarly， the longitude error of Pluto can be estimated as ∼12°. This value for Pluto is much better than the result in Kinoshita & Nakai (1996) where the difference is estimated as ∼60°.
3 Numerical results – I. Glance at the raw data
In this section we briefly review the long-term stability of planetary orbital motion through some snapshots of raw numerical data. The orbital motion of planets indicates long-term stability in all of our numerical integrations: no orbital crossings nor close encounters between an
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