Abstract
Attention is paid to the Eulerian perturbation of the gravitational potential. A solution for it is derived by integration of Poisson’s perturbed second-order differential equation, successively, in terms of the distribution of the Eulerian perturbation of the mass density and the distribution of the components of the Lagrangian displacement throughout the star. Next, it is shown that the solution of Laplace’s equation that is involved in the general integral solution of Poisson’s equation is identically zero for a linearly perturbed star because of the boundary condition relative to the gravitational potential imposed on the star’s surface. Finally, the Cowling approximation is presented.
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Smeyers, P. (2010). The Eulerian Perturbation of the Gravitational Potential. In: Linear Isentropic Oscillations of Stars. Astrophysics and Space Science Library, vol 371. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13030-4_8
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DOI: https://doi.org/10.1007/978-3-642-13030-4_8
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