 :::::I have been looking for information on where Vitagliano got the information that numerically integrated orbits are good for 80,000 years. JPL seldom claims accuracy beyond ±3000 years, and their longest ephemeris was for ±10,000 years, but it was unrealesed - probably special-purpose for some researcher's needs. At the bottom of this  Vitagliano compares positions of various bodies with and without asteroids to perturb them, giving us a worst case. Unfortunately, he does not give his results to better than 0°.01, which is larger than the expected error. At that level, their is little diffierence in the results, but errors that large could cause the outer planets, with their small disks, to miss each other! Vitagliano's Solex is derived from JPL's ephemerides, thus we can't expect it to be better in accuracy.   