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• W3102861019 abstract "Based on the value of the orbital eccentricity of an object and also its proximity to the exact resonant orbit in a three-body system, the pendulum approximation [S. F. Dermott and C. D. Murray, Nature (London) 319, 201 (1983)] or the second fundamental model of resonance [M. H. Andoyer, Bull. Astron. 20, 321 (1903); J. Henrard and A. Lemaı̂tre, Celest. Mech. 30, 197 (1983)] are commonly used to study the motion of that object near its resonant state. In this paper, we present the method of partial averaging as an analytical approach to study the dynamical evolution of a body near a resonance. To focus attention on the capabilities of this technique, a restricted, circular and planar three-body system is considered and the dynamics of its outer planet while captured in a resonance with the inner body is studied. It is shown that the first-order partially averaged system resembles a mathematical pendulum whose librational motion can be viewed as a geometrical interpretation of the resonance capture phenomenon. The driving force of this pendulum corresponds to the gravitational attraction of the inner body and its contribution, at different resonant states, is shown to be proportional to es, where s is the order of the resonance and e is the orbital eccentricity of the outer planet. As examples of such systems, the cases of (1:1), (1:2), and (1:3) resonances are discussed and the results are compared with known planetary systems such as the Sun–Jupiter–Trojan asteroids." @default.
• W3102861019 created "2020-11-23" @default.
• W3102861019 creator A5015342505 @default.
• W3102861019 date "2002-07-01" @default.
• W3102861019 modified "2023-10-09" @default.
• W3102861019 title "Resonance dynamics and partial averaging in a restricted three-body system" @default.
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• W3102861019 doi "https://doi.org/10.1063/1.1482148" @default.
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