The origin of the most energetic particles in nature, the ultra-high-energy (UHE) cosmic rays, is still a mystery. Only the most energetic of these have sufficiently small angular deflections to be used for directional studies, and their flux is so low that even the 3,000 km2 Pierre Auger detector registers only about 30 cosmic rays per year of these energies. A method to provide an even larger aperture is to use the lunar Askaryan technique, in which ground-based radio telescopes search for the nanosecond radio flashes produced when a cosmic ray interacts with the Moon's surface. The technique is also sensitive to UHE neutrinos, which may be produced in the decays of topological defects from the early universe. Observations with existing r...