The orbits of about 3000 fictitious asteroids, representing a process. The previous studies included simulations with sample sizes of possible distribution of bodies in the early Solar System, were a few hundred. In this study, the behavior of about 3000 objects was investigated by numerical integration spanning 38,000 years to considered in order to achieve better coverage of the orbital element reproduce the observed distribution of outer belt asteroids. This space. This did not allow for very long integration times. Consequently, in addition to identifying orbits that escape from the outer belt, the integration interval allowed for a much larger sample size than estimate of the largest Lyapunov characteristic exponent was calculated previous studies. For additional information on non-escape orsimultaneously with the orbit integration. The slope of the logarithm of bits, the behavior of the estimate of the largest Lyapunov charthe last 5000 and 20,000 values of this estimate was computed with the acteristic number was utilized to identify strongly chaotic orbits. method of least squares to determine whether the estimate appeared to The equations of the regularized planar elliptic restricted three have converged, or was still decreasing. These intervals correspond to body problem were derived to handle close encounters with the last 3800 and 15,300 years of the integration. Any orbit which did Jupiter. The semimajor axis distribution for non-escape orbits not have approximately constant, large negative slope were classified as showed an excess of bodies compared with the observed districhaotic. (Constant negative slope for all times implies a largest Lyapunov characteristic number (LCN) value of zero.)
bution. This excess is associated with mean motion resonances.
A new feature of this simulation is the use of regularization to remove When the strongly chaotic orbits are eliminated, the resulting the singularity at the secondary body of the elliptic restricted problem, distribution of orbits shows qualitative agreement with the presthus achieving better numerical handling of close approaches to Jupiter.