  The Earth's density distribution can be approximately considered piecewise
continuous at the scale of two-flavor oscillations of neutrinos with energies
about 1 MeV. This quite general assumption appears to be enough to analytically
calculate the day-night asymmetry factor. Using the explicit time averaging
procedure, we show that, within the leading-order approximation, this factor is
determined by the electron density immediately before the detector, i.e. in the
Earth's crust. Within the approximation chosen, the resulting asymmetry factor
does not depend either on the properties of the inner Earth's layers or on the
substance and the dimensions of the detector. For beryllium neutrinos, we
arrive at the asymmetry factor estimation of about $-4 \times 10^{-4}$, which
is at least one order of magnitude beyond the present experimental resolution,
including that of the Borexino experiment.
