Hydrostatic equilibrium of three concentric masses in rotation

A system of three concentric homogeneous masses in rotation with angular velocity, omega, may represent a simple model of the earth-ocean-atmosphere system. Their hydrostatic pressures and gravitational potentials are determined. The hydrostatic pressure, P sub 1, and the gravitational potential, U sub 1, depend on R sup 2. The gravitational potential, U sub 4, depends on R sup -1 (R is the radius). The remaining parameters depend on R sup 2 and R sup -1. These pressures and potentials are important in the gravity waves research in the interface earth-ocean-atmosphere.