The zero-velocity surface is a concept that relates to the N-body problem of gravity. The zero-velocity surface is particularly significant when working with weak gravitational interactions among orbiting bodies.
Given a group of galaxies which are gravitationally interacting, the zero-velocity surface is used to determine which objects are gravitationally bound (i.e. not overcome by the Hubble expansion) and thus part of a galaxy cluster, such as the Local Group.
The zero-velocity surface is also an important parameter in finding Lagrange points.