Celestial mechanics solutions that escape

We establish the existence of an open set of initial conditions through which pass solutions without singularities to Newton's gravitational equations in R3 on a semi-infinite interval in forward time, for which every pair of particles separates like At,A>0, as t→∞. The solutions are constructable as series with rapid uniform convergence and their asymptotic behavior to any order is prescribed. We show that this family of solutions depends on 6N parameters subject to certain constraints.