Hill radius (the gravitational zone of Pluto's influence) of 6 million km, or out to 69% for retrograde moons. However, only the inner 3% of the region where prograde orbits would be stable is occupied by satellites, and the region from Styx to Hydra is packed so tightly that there is little room for further moons with stable orbits within this region. An intense search conducted by New Horizons confirmed that no moons larger than 4.5 km in diameter exist out to a distances up to 180,000 km from Pluto (6% of the stable region for prograde moons), assuming Charon-like albedoes of 0.38 (for smaller distances, this threshold is still smaller). The orbits of the moons are confirmed to be circular and coplanar, with inclinations differing less than 0.4° and eccentricities less than 0.005. The discovery of Nix and Hydra suggested that Pluto could have a ring system. Small-body impacts can create debris that can form into a ring system. However, data from a deep-optical survey by the Advanced Camera for Surveys on the Hubble Space Telescope, by occultation studies, and later by New Horizons, suggest that no ring system is present. Resonances Styx, Nix, and Hydra are thought to be in a 3-body orbital resonance with orbital periods in a ratio of 18:22:33; the respective ratio of orbits is 11:9:6. The ratios should be exact when orbital precession is taken into account. Hydra and Nix are in a simple 2:3 resonance. Styx and Nix are in an 11:9 resonance, while the resonance between Styx and Hydra has a ratio of 11:6. This means that in a recurring cycle there are 11 orbits of Styx for every 9 of Nix and 6 of Hydra. The ratios of synodic periods are then such that there are 5 Styx–Hydra conjunctions and 3 Nix–Hydra conjunctions for every 2 conjunctions of Styx and Nix. If denotes the mean longitude and the libration angle, then the resonance can be formulated as . As with the Laplace resonance of the Galilean satellites of Jupiter, triple conjunctions never occur. librates about 180° with an amplitude of at least 10°. All of the outer circumbinary moons are also close to mean motion resonance with the Charon–Pluto orbital period. Styx, Nix, Kerberos, and Hydra are in a 1:3:4:5:6 sequence of near resonances, with Styx approximately 5.4% from its resonance, Nix approximately 2.7%, Kerberos approximately 0.6%, and Hydra approximately 0.3%.