Minimum energy configurations in the N-body problem and the celestial mechanics of granular systems

Minimum energy configurations in Celestial Mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual Celestial Mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for N = 1, 2, 3 and develops hypotheses on the relative equilibria and minimum energy configurations for N ≫ 1 bodies.