ases of eccenicity or inclination in any orbital elements of the planets， which may be revealed by still longer-term numerical integrations. we have also performed a couple of ial integrations including motions of the outer five planets over the duration of ± 5 x 1010 yr. the result indicates that the three major resonances in the neptune–pluto system have been maintained over the 1011-yr time-span.
1 inoduction
1.1definition of the problem
the question of the stability of o