Instability of the Gravitational N ‐Body Problem in the Large‐ N Limit

Abstract

We use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1.3 ? 105, 2 orders of magnitude greater than in previous experiments. For the first time, a clear N-dependence of the perturbation growth rate is seen, ?e ? ln N. The e-folding time for N = 105 is roughly 1/20 of a crossing time.