On the equilibrium of a distorted heterogeneous ellipsoidal mass. III: The heterogeneous spheroidal mass

In our Paper I, Bernoulli's theorem was employed in an approximate form to study the equilibrium of a self-gravitating homogeneous distorted spheroid, with internal differential vorticity currents, where, for ease, the Bernoulli constant k was taken as being the same everywhere, eventually leading this to inconsistencies, which are no longer present when each streamline has its own k. In the current paper we investigate, through a simple and general rotation law, the equilibrium of a heterogeneous body composed of two concentric distorted spheroids core and envelope whose axes are not correlated. The model yields, for each value of the body's relative density, five-parametric series of figures, constrained by certain geometrical and physical limits. The pertinent distribution for the angular velocity is by cylinders coaxial with the rotation axis. Contrary to what was stated in our Papaer II, the distribution by disks is impossible.

VIVO