Abstract
In Chapter II of this book we investigated in some detail the equilibrium forms of the components of close binary systems, of arbitrary internal structure, distorted by rotational and tidal forces, defined as surfaces over which the potential of all forces acting within the system remained constant. Such an approach to a study of the components ran, however, into difficulties increasing rapidly with increasing requirements of precision — so much so that within the scope of Chapter II we were unable to progress in our description of the surfaces beyond quantities second order in surficial distortion produced by equilibrium tides, and of third order in polar flattening caused by centrifugal force of axial rotation.
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Bibliographical Notes
For a more general discussion of the relevant parts of the restricted problem of three bodies cf., e.g., A. Wintner, The Analytical Foundations of Celestial Mechanics, Princeton Univ. Press, 1941, Chapter VI (and the references quoted therein)
V. G. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies, Academic Press, New York, 1967; Chapters 4 and 10. The non-existence of the Jacobian energy integral of the eccentric restricted problem (with the two finite masses describing elliptic orbit) was proved by Z. Kopal and R. A. Lyttleton (1963).
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© 1978 D. Reidel Publishing Company, Dordrecht, Holland
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Kopal, Z. (1978). The Roche Model. In: Dynamics of Close Binary Systems. Astrophysics and Space Science Library, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9780-6_6
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DOI: https://doi.org/10.1007/978-94-009-9780-6_6
Publisher Name: Springer, Dordrecht
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