[en] 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 and Protheroe that neutrino flux upper limits derived from the GLUE search 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 lower neutrino energies. Detecting neutrinos from Earth near the Greisen-Zatsepin-Kuz'min regime will likely require radio telescope arrays with extremely large collecting area (A_e ∼ 10⁶ m²) and hundreds of hours 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 (ν∼> 300 MHz) and higher energies (E ∼> 10²¹ eV).