Astronomy and Astrophysics – Astrophysics
Scientific paper
Oct 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..37..173l&link_type=abstract
Astrophysics and Space Science, vol. 37, Oct. 1975, p. 173-181.
Astronomy and Astrophysics
Astrophysics
Density Distribution, Poisson Equation, Rotating Bodies, Distortion, Gravitational Fields, Laplace Equation, Spherical Harmonics
Scientific paper
The distortion of the density distribution within a self-gravitating body in hydrostatic equilibrium under the influence of rotation is ascertained. For this purpose, the Poisson equation has been solved using the undistorted density profile within the Laplacian to obtain the distorted density. The Laplacian has been expressed in terms of a system of curvilinear coordinates for which the equipotential surfaces constitute a family of fundamental surfaces. In performing the requisite algebraic manipulations, the Clairaut and Radau equations developed earlier by Lanzano (1974) were utilized to eliminate the derivatives of the elements pertaining to the equipotential surfaces. The density distortion has been obtained up to third-order terms in a small rotational parameter.
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