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Titlebook: Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems; Archie E. Roy Book 1988 Kluwer Academic Publishers 1988 Celestial

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Dynamical Evolution of Planetary Systems and the Significance of Bode’s Lawome a very regular system such as the actual solar system. The evolution of a number of sample planetary systems with varying original distributions has been examined to determine the degree of “arbitrariness”allowed to the initial conditions which will yet yield the regularities presently observed
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Where are the Saturnian Trojans?tune. Such orbits show no sign of instability, for at least a million years. For Saturn the existence of such orbits is surprising because of the periodic proximity of Jupiter. We discuss the results of our numerical study, and consider the possibilities of observational confirmation of our conclusi
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Orbital Evolutioninvolves the variations of the energy and angular momentum integrals of a subgroup of an isolated N body system..When there are only gravitational interactions between the bodies, the conditions for evolution are outlined and some examples are given. This is in particular applied to the case when th
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Planetary Perturbation Theory from Lie Series, including Resonance and Critical Argumentsn properties of the first- and second-order periodic terms in planetary perturbation theory, indicating how periodic terms of further orders may be derived. Then the formal solution of the complete problem, including long-term changes, is derived, by use of further transformations, including a furth
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General Formulas for Three-Body Resonances. − (p+q)λ. + pλ., where p and q are integers and λ., λ., and λ. are the mean longitudes of any three gravitationally interacting bodies revolving in coplanar orbits about the same primary. The formulas extend and generalize earlier results published by several authors on Laplacian resonances in the
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