The simplest examples of the gravitational slingshot are a binary which scatters a single star and the breakup of an initially bound three-body system. Resulting recoil may eject both the single body and the binary from the system. If galactic nuclei contain supermassive objects which form binaries, these processes may have especially dramatic astronomical consequences (Saslaw, Valtonen & Aarseth, 1974). They are also important in ordinary star clusters with N ≲ 102, and in the very center of richer clusters.

Performing large numbers of three-body experiments shows how scattering behaves. There is an amusing contrast with high energy physics. Our (inexpensive) gravitational accelerator is a computer. We experiment not to find the microscopic law describing the interaction – we've known that since Newton – but to understand realistic applications of this law. Even our relatively low energy particles, typical stars moving at ~ 102 km s-1, have kinetic energies exceeding ~ 1050GeV!

Although there are a great many exact mathematical results on the analytical dynamics of three-body systems, they usually apply only under very restricted circumstances. Normally they are asymptotic or perturbation calculations (see Arnold, 1978; Pars, 1965). These are not sufficient to understand the rich range of important phenomena occurring in realistic physical scattering, so we must resort to numerical simulations and approximate non-linear analyses (see Heggie, 1975(a, b), reference in Section 48).