  In this paper we use the approach introduced in an earlier paper by Goerss,
Henn, Mahowald and Rezk in order to analyze the homotopy groups of
L_{K(2)}V(0), the mod-3 Moore spectrum V(0) localized with respect to Morava
K-theory K(2). These homotopy groups have already been calculated by Shimomura.
The results are very complicated so that an independent verification via an
alternative approach is of interest. In fact, we end up with a result which is
more precise and also differs in some of its details from that of Shimomura. An
additional bonus of our approach is that it breaks up the result into smaller
and more digestible chunks which are related to the K(2)-localization of the
spectrum TMF of topological modular forms and related spectra. Even more, the
Adams-Novikov differentials for L_{K(2)}V(0) can be read off from those for
TMF.
