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• W2950681750 abstract "In a planetary or satellite system, idealized as n small bodies in an initially coplanar with concentric orbits around a large central body obeying the Newtonian point-particle mechanics, resonant perturbations will cause a dynamical evolution of the orbital radii except for cases with highly specific mutual relationships. In particular, the most stable situation can be achieved only when each planetary orbit is roughly twice as far from the Sun as the preceding one. This has been empirically observed by Titius (1766) and Bode (1778). By reformulating the problem as a hierarchical sequence of (unrestricted) 3-body problems and considering only the gravitational interactions among the central body and the body of interest and the adjacent outer body in the orbits, it is proved that the resonant perturbations from the outer body will destabilize the inner body (and vice versa) unless its mean orbital radius is a unique and specific multiple of β, the distal multiplier, of the inner body. In this way a sequence of concentric orbits can each stabilize the adjacent inner orbit, and since the outermost orbit is already tied to the collection of the inner orbits by conservation of total angular momentum, the entire configuration is stabilized." @default.
• W2950681750 created "2019-06-27" @default.
• W2950681750 creator A5077413563 @default.
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• W2950681750 date "2005-01-01" @default.
• W2950681750 modified "2023-09-26" @default.
• W2950681750 title "DYNAMICAL DERIVATION OF BODE'S LAW" @default.
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• W2950681750 doi "https://doi.org/10.1142/s0218271805006195" @default.
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