Initial equations are obtained, similarity criteria are estimated and a project of simulation experiment is proposed for the gravitational differentiation of liquid cores of planets and natural satellites. It is assumed that, first, the liquid core in an adiabatic state without thermal convection and, second, the inner solid core grows during the crystallization of a heavy component from the liquid core in such a way that the buoyancy force acting on a lighter component is directed strictly along the radius. It is also assumed that the radial distribution of density in the liquid core does not change during the time interval considered. These three natural assumptions enable an analytical description of basic hydrostatic effects controlling slow growth of the solid core, gravitational stratification of the liquid core, and sources of related compositional convection. The similarity criteria of such convection are mostly the same as for thermal convection. Additional criteria are the concentration contrast ~1/10 in the Earth, the compressibility of the liquid core ~10%, and the thickness of a concentration boundary layer ~10-7 that, controlling the freezing-out of the liquid at the inner sphere, can give rise to asymmetry of the solid core. The excitation threshold of the compositional convection is much higher than a similar threshold for thermal convection, and the compositional convection itself can arise only at an intermediate stage of the gravitational differentiation of the core. Observed magnetic fields are largely due to compositional convection in the Earth's core and, probably, in deep interiors of Mercury. At the contemporary evolutionary stage of Venus' interiors, the intensity of compositional convection is most likely insufficient for the magnetic field excitation and it is undoubtedly too weak in the Mars' interiors.