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Two algorithms to construct a consistent first order theory of equilibrium figures of close binary systems. (English) Zbl 1381.70020

Summary: One of the main problems in celestial mechanics is the study of the shape adopted by extended deformable celestial bodies in its equilibrium configuration. In this paper, a new point of view about classical theories on equilibrium figures in close binary systems is offered.
Classical methods are based on the evaluation of the self-gravitational, centrifugal and tidal potentials. The most common technique used by classical methods shows convergence problems. To solve this problem up to first order in amplitudes two algorithms has been developed, the first one based on the Laplace method to develop the inverse of the distance and the second one based on the asymptotic properties of the numerical quadrature formulas.

MSC:

70E50 Stability problems in rigid body dynamics
70F15 Celestial mechanics
70M20 Orbital mechanics
33C55 Spherical harmonics
65D30 Numerical integration
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
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References:

[1] Finlay-Frendulich, E., Celestial Mechanics (1958), Pergamon Press Inc.: Pergamon Press Inc. New York · Zbl 0082.23505
[2] Kopal, Z., Figures of Celestial Bodies (1960), Univ. Wisconsin Press: Univ. Wisconsin Press Madison · Zbl 0093.23804
[3] Jardetzky, W., Theorie of Figures of Celestial Bodies (1958), Interscience Publishers, Inc.: Interscience Publishers, Inc. New York · Zbl 0090.23602
[4] Kopal, Z., Dynamic of Close Binary Systems (1978), Kluwer: Kluwer Dordrecht, Holland
[5] Beech, M., The ellipsoidal variables, Astrophys. Space Sci., 117, 69-81 (1985)
[6] Beech, M., The ellipsoidal variables III. Circularization and synchronization, Astrophys. Space Sci., 125, 69-75 (1986)
[7] López, J. A.; López, A.; López, R., Figures of equilibrium in close binary systems, Celestial Mech. Dynam. Astronom., 17, 661-692 (1992) · Zbl 0850.70125
[8] López Ortí, J. A.; Forner Gumbau, M.; Barreda Rochera, M., A note on the first order theories of equilibrium figures of celestial bodies, Int. J. Comput. Math., 88, 1969-1978 (2011) · Zbl 1305.70026
[9] Arfken, G., Mathematical Methods for Physicists (1985), Academic Press: Academic Press Orlando · Zbl 0135.42304
[10] Hobson, E. W., Theory of Spherical and Elliptical Harmonics (1955), Chelsea: Chelsea New York · Zbl 0004.21001
[11] Forner Gumbau, M., Desarrollos en Serie de los Productos de Algunas Funciones Especiales (2012), Publicacions de la Universitat Jaume I: Publicacions de la Universitat Jaume I Castellón. Spain
[12] Tisserand, F. F., Traité de Mécanique Celeste (1896), Gauthier-Villars: Gauthier-Villars Paris · JFM 27.0807.08
[13] López Ortí, J. A.; Forner Gumbau, M.; Barreda Rochera, M., A method to improve the computation of tidal potential in the equilibrium configuration of a close binary system, Int. J. Comput. Math., 86, 1831-1840 (2009) · Zbl 1347.70022
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