  We show how by studying the Earth matter effect on oscillations of solar and
supernova neutrinos inside the Earth one can in principle reconstruct the
electron number density profile of the Earth. A direct inversion of the
oscillation problem is possible due to the existence of a very simple analytic
formula for the Earth matter effect on oscillations of solar and supernova
neutrinos. From the point of view of the Earth tomography, these oscillations
have a number of advantages over the oscillations of the accelerator or
atmospheric neutrinos, which stem from the fact that solar and supernova
neutrinos are coming to the Earth as mass eigenstates rather than flavour
eigenstates. In particular, this allows reconstruction of density profiles even
over relatively short neutrino path lengths in the Earth, and also of
asymmetric profiles. We study the requirements that future experiments must
meet to achieve a given accuracy of the tomography of the Earth.
