On a stability of liquid gravitating bodies containing small solid cores

Well-known Ramsey-Lighthill results concerning the instability of gravitating two-phase liquid bodies with small cores are generalized for the case of a solid elastic core. It is shown that the planet with a small more dense core from isotropic elastic material is unstable if the ratio rhosub(0s) > 3/2rhosub(0l), where rhosub(0s) and rhosub(0l) are solid and liquid phase densities, is realized. This condition is fully analogous to the Ramsey-Lighthill condition which has been established earlier for the case of compressible and barotropic liquid cores