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2019A&A...627A..17D -
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Astronomy and Astrophysics, volume 627A, 17-17 (2019/7-1)
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Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber.
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DE ELIA G.C., ZANARDI M., DUGARO A. and NAOZ S.
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Abstract (from CDS):
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Aims. We analyze the behavior of the argument of pericenter ω_{2} of an outer particle in the elliptical restricted three-body problem, focusing on the ω_{2} resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle's ω_{2} precession rate (dω_{2}/dτ). Then, we derived analytical criteria that determine the vanishing of the ω_{2} quadrupole precession rate (dω_{2}/dτ)_{quad} for different values of the inner perturber's eccentricity e_{1}. Finally, we used such analytical considerations and described the behavior of ω_{2} of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i_{2} and the ascending node longitude Ω_{2} associated with the outer particle that vanish (dω_{2}/dτ)_{quad} strongly depend on the eccentricity e_{1} of the inner perturber. In fact, if e_{1}<0.25 (>0.40825), (dω_{2}/dτ)_{quad} is only vanished for particles whose Ω_{2} circulates (librates). For e_{1} between 0.25 and 0.40825, (dω_{2}/dτ)_{quad} can be vanished for any particle for a suitable selection of pairs (Ω_{2}, i_{2}). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e_{1}. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω_{2}, i_{2}) plane. In fact, if ω_{2} librates and Ω_{2} circulates, the extremes of i_{2} at Ω_{2}=90° and 270° do not reach the same value, while if ω_{2} and Ω_{2} librate, the evolutionary trajectory of the particle in the (Ω_{2}, i_{2}) plane shows evidence of an asymmetry with respect to i_{2}=90°. The evolution of ω_{2} associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.

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Abstract Copyright:
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© ESO 2019

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Journal keyword(s):
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planets and satellites: dynamical evolution and stability - minor planets, asteroids: general - methods: numerical
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Simbad objects:
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5

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2020.01.27-01:52:23

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