Abstract
This paper ascertains the distortion of the density distribution within a self-gravitating body in hydrostatic equilibrium under the influence of rotation.
For this purpose, the Poisson equation has been solved by using the undistorted density profile ϱo(a) within the Laplacian to obtain the distorted density ϱ(a, θ). 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 in a previous paper (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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References
Hobson, E. W.: 1955,The Theory of Spherical and Ellipsoidal Harmonics, Chelsea, New York.
Kopal, Z.: 1960,Figures of Equilibrium of Celestial Bodies, University of Wisconsin Press, Madison.
Lanzano, P.: 1962,Icarus 1, 121.
Lanzano, P.: 1974,Astrophys. Space Sci. 29, 161.
Lass, H.: 1950,Vector and Tensor Analysis, McGraw-Hill, New York.
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Lanzano, P. Density distortion within a rotating body. Astrophys Space Sci 37, 173–181 (1975). https://doi.org/10.1007/BF00646071
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DOI: https://doi.org/10.1007/BF00646071