Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984azh....61..854v&link_type=abstract
(Astronomicheskii Zhurnal, vol. 61, Sept.-Oct. 1984, p. 854-859) Soviet Astronomy (ISSN 0038-5301), vol. 28, Sept.-Oct. 1984, p.
Astronomy and Astrophysics
Astronomy
3
Boundary Value Problems, Celestial Mechanics, Free Vibration, Gravitational Fields, Perturbation Theory, Boundary Conditions, Eigenvalues, Gauss-Markov Theorem, Integrals, Jupiter (Planet)
Scientific paper
The free vibration of a self-gravitating gas-liquid sphere is investigated analytically. A perturbation technique is developed to calculate the eigenfrequency corrections caused by changing from standard boundary conditions to the generalized boundary conditions derived by Vorontsov (1984) to account for a phase transition at the boundary. Numerical results are presented for a model of Jupiter with a density discontinuity at the phase transition to metallic hydrogen (Zharkov and Trubitsyn, 1980) and shown to be in good agreement with the direct computations of Vorontsov (1984). The extension of the perturbation approach to the free oscillation of an elastic sphere such as the earth is discussed.
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