Gravitating bodies of Ramsay type.

The paper examines the stability of equilibrium and natural oscillations of a Ramsay-type planet, which consists of spherical layers of an incompressible fluid of constant (within each layer) density. The radial stability of the planet with an arbitrary number of layers is studied in the case when all the phase transitions are stable, and the relationship between Ramsay's stability criterion and the potential-energy minimum principle is investigated. The degree to which knowledge of the radial stability makes it possible to assess stability with regard to arbitrary disturbances is examined, and the possibility of analyzing the small-oscillation spectrum of the planet is considered.