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Titlebook: Stability of the Solar System and Its Minor Natural and Artificial Bodies; Victor G. Szebehely (Richard B. Curran Chair of En Book 1985 D.

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Existence and Stability of Circular Orbits in Axially-Symmetric Gravitational Fields orbits in the neighborhood of bodies with such symmetry are established. Application is made to: (i) circular orbits about an oblate planet, (ii) circular orbits in the plane of a thin ring or disk, (iii) circular orbits about a planet plus ring or disk, and (iv) circular orbits in the classical tw
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Methods of Stability Analysis in the Solar Systemwhose stability is analysed either in the general or in the restricted circular model (Sections 1 and 4). The relationship and different use of the two models is discussed in Section 4. Section 2 summarizes the way in which the problem of proving hierarchical stability for a very long time can be ta
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Stability in Celestial Mechanicsunifies several fields of sciences, nevertheless, the selection of the appropriate definitions, conditions and disturbances to a variety of problems requires careful evaluation. In this paper several general ideas of stability research are discussed after establishing a few basic concepts. The lectu
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Resonance Sweeping in the Solar Systeme tool to understand some basic mechanism in the long term evolution of the Solar System. After summarizing the principal results of this theory in Section 1, we describe briefly two applications. The first one concerns the Kirkwood’s Gaps in the Asteroid belt (section 2). We show how a small displa
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The Three-Body Problem with Two Small Masses: A Singular-Perturbation Approach to the Problem of Sat satisfying Hill’s lunar equation. The discussion of Hill’s problem with appropriate boundary conditions at infinity correctly predicts that Saturn’s coorbiting satellites Janus and Epimetheus exchange orbits at the close encounter, whereas the F ring shepherds (1980S26 and 1980S27) do not.
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On the Evolution of the Lunar Orbitproperties of the solution are derived. In the actual lunar case, the situation is much more complex, because the long periodic variations of the excentricity of the Earth’s orbit induces large perturbations in the simplified equations. Some numerical results of the latter case are presented.
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