The Moon provides a huge effective detector volume for ultrahigh energy cosmic neutrinos, which generate coherent radio pulses in the lunar surface layer due to the Askaryan effect. In light of presently considered lunar missions, we propose radio measurements from a Moon-orbiting satellite. First systematic Monte Carlo simulations demonstrate the detectability of Askaryan pulses from neutrinos with energies above 10(20) eV at the very low fluxes predicted in different scenarios.