Eccentricity of solid cores suspended in liquid planetary/stellar interiors has never been considered possible, because there seemed to be no theoretical basis for such a consideration. This article presents an analysis of gravity-buoyancy equilibrium of a solid core in spherically symmetric pressure gradient of a spinning planet/star. Elementary mechanics suggests that if a solid core exists - it has to be eccentric. The eccentricity of the Earth core is estimated on the basis of the generally accepted Earth data. Results suggest that what is currently interpreted as a "spinning inner core anisotropy" can actually be caused by the eccentric core, phase locked to the position of the Moon.