On the tidal-energy tensor for two homogeneous coaxial ellipsoids

Details On the tidal-energy tensor for two homogeneous coaxial ellipsoids On the tidal-energy tensor for two homogeneous coaxial ellipsoids

Oct 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001an....322..217c&link_type=abstract

Astronomische Nachrichten, vol. 322, no. 4, p. 217-221

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The tidal-energy tensor for two homogeneous and coaxial ellipsoids, one lying completely within the other, is investigated in connection with the tidal action exerted by the outer ellipsoid on the inner one. Making reference to the explicit expression found in a previous paper of ours, it is shown that the generic component of the tidal-energy tensor, (i) may be expressed as the product of the corresponding component of the self-energy tensor related to the inner ellipsoid, by the density ratio, and the shape factor ratio, and (ii) equals the one due to any homogeneous, outer ellipsoid, for which the product of the density and a specified shape factor remains unchanged; in particular, the outer ellipsoid may be similar and similarly placed with respect to the inner one. In addition, an explicit expression for the Clausius-virial tensor is derived. Analogous results for the corresponding scalar quantities are also given. Further attention is paid to the particular case of spheroids.

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