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In summary, the falling of comets onto the Moon leads to formation of ice with definite chemical and isotopic composition in cold traps: The ratio D/H is higher than for other sources of water. Another distinguishing property of "cometary ice" is that it could contain the compounds SO2 and CO2 also. To explain the amount of ice observed by Lunar Prospector, a single low-speed impact of a comet with Dcom ~ 5 km with the Moon is sufficient. The comet hypothesis of the origin of lunar ice can be checked during the next lunar missions, and, if confirmed, then definite progress will have been made in understanding the composition and, accordingly, the nature of comets.