  In this paper we characterize planar central configurations in terms of a
sectional curvature value of the Jacobi-Maupertuis metric. This
characterization works for the $N$-body problem with general masses and any
$1/r^{\alpha}$ potential with $\alpha> 0$. We also observe dynamical
consequences of these curvature values for relative equilibrium solutions.
These curvature methods work well for strong forces ($\alpha \ge 2$).
