  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 $N\gg 1$ bodies.
