Radar observations of Mercury have provided the startling discovery of
the probable existence of substantial deposits of ices in permanently
shaded polar regions [Butler et al., 1993; Harmon et al., 1994]. This
has renewed the old argument about the existence of such deposits in
the polar regions of the Moon. It is most likely necessary for volatil
es to be able to migrate to the polar regions of these bodies in order
to build up such deposits. This paper presents the results of the ext
ension of a Monte Carlo simulation of the migration of molecules on th
e surface of Mercury by Butler et al. [1993]. The results of the simul
ations show that for typical conditions on Mercury, similar to 5-15% o
f all H2O which is placed randomly on the surface migrates to stable (
permanently shaded) polar regions. For the Moon the numbers are simila
r to 20-50%. The numbers for the migration of CO2 are similar to 2% fo
r Mercury and similar to 13% for the Moon. These percentages are simil
ar to those previously calculated and support the idea of ice deposits
in the polar regions of both Mercury and the Moon.