  Exchange symmetry in acceleration partitions the configuration space of an N
particle, one-dimensional, gravitational system into N! equivalent cells. We
take advantage of the resulting small angular extent of each cell to construct
a related integrable version of the system that takes the form of a central
force problem in N-1 dimensions. The properties of the latter, including the
construction of trajectories, as well as several continuum limits, are
developed. Dynamical simulation is employed to compare the two models. For a
class of initial conditions, excellent agreement is observed.
