The Newtonian potentials and dynamics of a stratified ellipsoid

Astronomy and Astrophysics – Astronomy

Scientific paper

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Astronomical Models, Celestial Mechanics, Ellipsoids, Elliptical Galaxies, Potential Theory, Astrodynamics, Dynamic Models, Rotation, Tensors

Scientific paper

Exact equations for the potentials of a stratified ellipsoid at both an exterior and an interior point are obtained, as well as for the potential of an ellipsoid shell. It is proven that the potential found for the ellipsoid has first derivatives which are everywhere continuous, and that it satisfied the Laplace equation outside the ellipsoid and the Poisson equation inside. Certain dynamical properties of the ellipsoid are established; in particular, relying on the obtained expression for the potential of an ellipsoidal shell, the virial tensor for a sub-ellipso d is determined. It is shown that if the flattening of the layers is variable, the virial tensor of the sub-ellipsoid cannot be identified with the gravitational energy tensor. An expression for the rotational energy of the ellipsoid is obtained.

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