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We present a formalism for the matter effects in the Earth on low energyneutrino fluxes which is both accurate and has all advantages of a fullanalytic treatment. The oscillation probabilities are calculated up to secondorder term in $\epsilon(x) \equiv 2V(x)E/\Delta m^2$ where $V(x)$ is theneutrino potential at position $x$. We show the absence of large undampedphases which makes the expansion in $\epsilon$ well behaved. An improvedexpansion is presented in terms of the variation of $V(x)$ around a suitablemean value which allows to treat energies up to those relevant for Supernovaneutrinos. We discuss also the case of three-neutrino mixing.Comment: REVTeX 4, 6 pages, 1 figure, several clarifications added, typos  correcte

Precise analytical description of the Earth matter effect on oscillations of low energy neutrinos