We consider the 3-dimensional gravitational $n$-body problem, $n\ge 2$, in
spaces of constant Gaussian curvature $\kappa\ne 0$, i.e.\ on spheres ${\mathbb
S}_\kappa^3$, for $\kappa>0$, and on hyperbolic manifolds ${\mathbb
H}_\kappa^3$, for $\kappa<…