The conservation of energy, linear momentum and angular momentum areimportant drivers for our physical understanding of the evolution of theUniverse. These quantities are also conserved in Newton's laws of motion undergravity \citep{Newton:1687}. Numerical integration of the associated equationsof motion is extremely challenging, in particular due to the steady growth ofnumerical errors (by round-off and discrete time-stepping,\cite{1981PAZh....7..752B,1993ApJ...415..715G,1993ApJ...402L..85H,1994LNP...430..131M})and the exponential divergence \citep{1964ApJ...140..250M,2009MNRAS.392.1051U}between two nearby solution. As a result, numerical solutions to the generalN-body problem are intrinsically questionable\citep{2003gmbp.book.....H,1994JAM....61..226L}. Using brute force integrationsto arbitrary numerical precision we demonstrate empirically that ensembles ofdifferent realizations of resonant 3-body interactions produce statisticallyindistinguishable results. Although individual solutions using commonintegration methods are notoriously unreliable, we conjecture that an ensembleof approximate 3-body solutions accurately represents an ensemble of truesolutions, so long as the energy during integration is conserved to better than1/10. We therefore provide an independent confirmation that previous work onself-gravitating systems can actually be trusted, irrespective of the intrinsicchaotic nature of the N-body problem.
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