On the role and the properties ofn body central configurations

The role central configurations play in the analysis ofn body systems is outlined. Emphasis is placed on collision orbits, expanding gravitational systems, andn body zero radial velocity surfaces. In the second half of the paper, properties of cenral configurations are discussed. Here, emphasis is placed on describing a different approach to analyze these configurations, one which is related to the classical problem of the weightedsth mean values of a vector. This approach is illustrated by discussing the non-degeneracy of central configurations and by describing central configurations in various dimensions. This is a written version of a talk given at Oberwolfach, August, 1978.proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August 1978.This research was supported in part by an NSF Grant.