论文标题
适当的谐振行星横断小行星的元素
Proper elements for resonant planet-crossing asteroids
论文作者
论文摘要
适当的要素是准运动的准整合物，这意味着它们可以在某个时间段上被认为是恒定的，并且可以用一些参数来描述长期演变。近地物（NEOS）通常具有较大的偏心率，因此它们可以越过行星的轨道。此外，其中一些人目前与行星的平均动感共鸣。因此，以前用于计算主皮无体适当元素的方法不适用于此类对象。在本文中，我们介绍了一种技术，以计算与行星平均动作共鸣的行星横断小行星的适当要素。首先，我们从数字上平均在快速角度上平均哈密顿量，同时保持所有共鸣术语，并描述如何继续轨道越过奇点以外的解决方案。然后从平均轨道跨溶液的频率分析中提取适当的元素。我们提供了一些已知共鸣的NEO的适当元素，并提供了与非谐振模型的比较。这些示例表明，有必要考虑到准确的正确元素的共振的效果。
Proper elements are quasi-integrals of motion, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution 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 from 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.
