ON THE RELIABILITY OF GRAVITATIONAL N-BODY INTEGRATIONS

In a self-gravitating system of point particles such as a spherical star cluster, small disturbances to an orbit grow exponentially on a time-scale comparable with the crossing time. The results of N-body integrations are therefore extremely sensitive to numerical errors: in practice it is almost impossible to follow orbits of individual particles accurately for more than a few crossing times. We demonstrate that numerical orbits in the gravitational N-body problem are often shadowed by true orbits for many crossing times. This result enhances our confidence in the use of N-body integrations to study the evolution of stellar systems.