ON THE ORIGINAL DISTRIBUTION OF THE ASTEROIDS .3. ORBITS BETWEEN JUPITER AND SATURN

We study the stability of orbits between Jupiter and Saturn in the planar case, with Jupiter and Saturn represented by fixed ellipses. In the band of long-lived orbits centered on 1.35 and 1.45 Jovian distances, we find some orbits that survive for longer than 800,000 Jupiter periods, although most do not. A careful examination of the consequences of inaccuracies in the numerical integration on the stability of orbits shows that stable orbits remain stable even when we degrade the accuracy by a factor of a quarter of a million. Thus we believe that the long-delayed onset of instability is a consequence of the celestial mechanics and not an artifact of the numerical integration. We routinely calculated Lyapunov exponents and found a correlation between the Lyapunov time and the time to cross the orbit of one of the planets, but the Lyapunov times were typically much shorter (by a factor of 100 or more). © 1990.