On the equilibrium of a distorted heterogeneous ellipsoidal mass. I. The homogeneous mass

Departing from a mono-parametric fourth-order surface equation for an ellipsoid (rather than of the second order, as in the classical homogeneous figures), we investigate the hydrostatic equilibrium of a heterogeneous mass, whose homogeneous version - which will be the only one considered in the current paper - resembles a Jacobi ellipsoid, with the proviso that ours is static, its equilibrium being established by a differential vorticity motion. The Jacobi series, which is complete, turns out to be a particular case of ours, which are truncated by the value of the surface equation parameter, that further determines if the angular velocity steadily increases from the equator to the pole, or vice versa; or if it has a maximum value between them. The spheroidal model - our version of a Maclaurin spheroid - is treated as a particular case of the ellipsoidal one. © Copyright 2015: Instituto de Astronomía, Universidad Nacional Autónoma de México.

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