This paper deals with the problem of water permanence on the surface of the Moon Possible zones where water ice can survive are called cold traps (K. Watson, B. C. Murray, and H. Brown 1961, J. Geophys. Res. 66, 3033-3045). These are zones of the Moon permanently obscured where the temperatures are low enough to preserve ice far billions of years. In this work we developed a model for the topographic temperatures of complex craters whose shape was approximated by a capsized frustum of a circular right cone. Double-shaded areas were simulated by embedding a small hemispherical crater in the shadowed part of the previous one. Their temperatures were calculated using the R. R. Hedges, Jr. (1980, Proc. Lunar Planet. Sci. Conf. 11th, 2463-2477) model. First we verified that our results were in agreement with those of previous models. Our results confirm those obtained by J. R. Salvail and F. P. Fanale (1994, Icarus 111, 441-445), and in agreement with Hedges (1980), we found that the lowest temperatures are reached by Tycho-like craters that are the larger and shallower among the examined cases. When small craters are embedded in the shaded area of larger ones, their temperatures are low enough to preserve other volatiles like CO2 (Hodges 1980). In particular, if we consider double-shaded areas in Blot-like craters, the temperatures are lower than 103 K in a shell of almost 20 degrees around the poles, thus allowing the preservation of ices. For geometrical reasons a hemispherical crater embedded in the bottom of a Biot-like crater cold remain in the shadowed area for latitude values lower than those reached by an analogous crater embedded in Sosigene or Tycho-like craters. Therefore the latitudinal radius of polar frost caps could be greater than that predicted by previous models that did not consider double-shaded areas. However double shielding occurs in only a fraction of the secondary craters; therefore, in this case eventual deposits of ice would be of smaller dimensions compared with the case of primary shielding. Analysis of the Clementine radar data (S. Nozette, C. L. Lichtenberg, P. Spudis, R. Bonner, W. Ort, E. Malaret, M. Robinson, and E. hi. Shoemaker 1996, Science 274, 5292-5300) and the Lunar Prospector neutron spectrometer data seems to be consistent with the presence of water ice in very low concentrations across a significant number of craters, thus confirming the old hypothesis of Watson et ai. (1961). (C) 1999 Academic Press.
