Energy and momentum are conserved in Newton's laws of gravitation.
Numerical integration of the equations of motion should comply to
these requirements in order to guarantee the correctness of a
solution, but this turns out to be insufficient. The steady growth of
numerical errors and the exponential divergence, renders numerical
solutions over more than a dynamical time-scale meaningless. Even
time reversibility is not a guarantee for finding the definitive
solution to the numerical few-body problem. As a consequence,
numerical N-body simulations produce questionable results. Using
brute force integrations to arbitrary numerical precision I will
demonstrate empirically that the statistics of an ensemble of resonant
3-body interactions is independent of the precision of the numerical
integration, and conclude that, although individual solutions using
common integration methods are unreliable, an ensemble of approximate
3-body solutions accurately represent the ensemble of true solutions.