We derive analytic expressions, and approximate them in closed form, for the effective detection aperture for Cerenkov radio emission from ultra-high-energy neutrinos striking the Moon. The resulting apertures are in good agreement with recent Monte Carlo simulations and support the conclusion of James & Protheroe (2009)that neutrino flux upper limits derived from the GLUE search (Gorham et al.2004) were too low by an order of magnitude. We also use our analytic expressions to derive scaling laws for the aperture as a function of observational and lunar parameters. We find that at low frequencies downward-directed neutrinos always dominate, but at higher frequencies, the contribution from upward-directed neutrinos becomes increasingly important, especially at low neutrino energies. Detecting neutrinos from Earth near the GZK regime will likely require radio telescope arrays with extremely large collecting area and hundreds of hour of exposure time. Higher energy neutrinos are most easily detected using lower frequencies. Lunar surface roughness is a decisive factor for obtaining detections at higher frequencies and higher energies.
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