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Proper elements for resonant planet-crossing asteroids

Abstract : Proper elements are quasi-integrals of motion of a dynamical system, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution of the system with a few parameters. Near-Earth objects (NEOs) generally have a large eccentricity, and therefore they can cross the orbits of the planets. Moreover, some of them are known to be currently in a mean-motion resonance with a planet. Thus, the methods previously used for the computation of main-belt asteroid proper elements are not appropriate for such objects. In this paper, we introduce a technique for the computation of proper elements of planet-crossing asteroids that are in a mean-motion resonance with a planet. First, we numerically average the Hamiltonian over the fast angles while keeping all the resonant terms, and we describe how to continue a solution beyond orbit-crossing singularities. Proper elements are then extracted by a frequency analysis of the averaged orbit-crossing solutions. We give proper elements of some known resonant NEOs and provide comparisons with non-resonant models. These examples show that it is necessary to take into account the effect of the resonance for the computation of accurate proper elements.
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Submitted on : Sunday, July 10, 2022 - 11:23:11 AM
Last modification on : Tuesday, August 2, 2022 - 4:30:59 AM

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M. Fenucci, G. F. Gronchi, M. Saillenfest. Proper elements for resonant planet-crossing asteroids. Celestial Mechanics and Dynamical Astronomy, 2022, 134, ⟨10.1007/s10569-022-10078-4⟩. ⟨insu-03718977⟩

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