We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of a global viscosity solutions for the Hamilton-Jacobi equation H(x,du(x))=h. Our hyperbolic motion is in fact a calibrating curve of the viscosity solution. The presented results can also be viewed as a new application of Marchal’s theorem, whose main use in recent literature has been to prove the existence of periodic orbits. Joint work with Ezequiel Maderna.