Partly with Jacques Fejoz, Richard Montgomery, Stefan Fleischer and Manuel Quaschner. The past and future of scattering particle systems is partly determined by their asymptotic velocity, that is, the Cesàro limit of the velocity. That this exists for bounded interactions and all initial conditions, is part of a statement sometimes called ‘asymptotic completeness’. The same statement does not apply to individual initial conditions in celestial mechanics. However, at least for up to four particles, nonexistence of asymptotic velocity is a measure zero phenomenon. We explain some new ideas connected with the proof (Poincaré section techniques for wandering sets, non-deterministic particle systems, and walks on a poset of set partitions).