  The Earth's density distribution can be approximately considered piecewise
continuous at the scale of two-flavor oscillations of typical solar neutrinos,
such as the beryllium-7 and boron-8 neutrinos. This quite general assumption
appears to be enough to analytically calculate the day-night asymmetry factor
for such neutrinos. Using the explicit time averaging procedure, we show that,
within the leading-order approximation, this factor is determined by the
electron density within about one oscillation length under the detector,
namely, in the Earth's crust (and upper mantle for high-energy neutrinos). We
also evaluate the effect of the inner Earth's structure on the observed
asymmetry and show that it is suppressed and mainly comes from the neutrinos
observed near the winter and summer solstices. As a result, we arrive at the
strict interval constraint on the asymmetry, which is valid within quite a wide
class of Earth models.
