Neptune has five narrow ring arcs, spanning about 40 degrees in longitude, which are apparently confined against the rapid azimuthal and radial spreading that normally results from inter-particle collisions. A gravitational resonance based on the vertical motion of the nearby neptunian moon Galatea was proposed to explain the trapping of the ring particles into a sequence of arcs. But recent observations have indicated that the arcs are away from the resonance, leaving their stability again unexplained. Here we report that a resonance based on Galatea's eccentricity is responsible for the angular confinement of the arcs. The mass of the arcs affects the precession of Galatea's eccentric orbit, which will enable a mass estimate from future observations of Galatea's eccentricity.