Asteroid Proper Elements and the Dynamical Structure of the Asteroid Main Belt
Asteroid Proper Elements and the Dynamical Structure of the Asteroid Main Belt
复制标题
小行星固有元素与小行星主带的动力结构
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Z. Knežević
中科院分区：
文献类型：
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作者：
A. Milani;Z. Knežević
摘要我们计算了12,573颗小行星的适当元素，包括所有轨道精确到足以用于家族识别的小行星。这是用我们的迭代分析算法的升级版本完成的，结果是在主带的低到中等倾角和偏心率区域（在500万年以上的适当e和sin I的典型不稳定性≤0.0015）的大多数小行星的精确度显着提高。这种稳定性已被验证的数值积分（在一个现实的模型）的35个测试用例。在一小部分情况下，适当的元素计算的准确性降低了一些共振的影响，无论是在平均运动或长期。我们已经能够列出几乎所有情况下导致这种退化的共振，以这种方式，这些共振都被正确地标记为“共振代码”。“这个共振列表，包括我们工作之前不知道的九个高度长期共振，提供了小行星主带动力学结构的详细地图。我们调查的长期动力学的一些这些长期的共振，并发现两个非常大的振幅振荡的偏心率和不规则行为的小行星受一个或多个共振。我们展示了这些共振在适当的元素空间的几何形状和它们与小行星分布和最突出的家庭的关系。本文的第二部分详细描述了这个版本的真元理论相对于以前发表的真元理论（A. Milani和Z. Kneževic，1990，Celest. 49，347-411; 1992，Icarus 98，211-232）。我们讨论了成功的一些这些改进的情况下，以前降低的准确性，我们也评论失败的一些尝试的改进。我们猜想，我们的理论非常接近任何分析理论的准确性的基本限制，这是由于存在无限的共振网络和混沌运动的发生。因此，我们认为，对这一理论的进一步改进只会是局部性质的，只会影响小行星群的一小部分。
Abstract We have computed proper elements for 12,573 asteroids, including all the ones with orbits accurate enough to be useful for family identification. This was done with an upgraded version of our iterative analytical algorithm, resulting in significantly improved accuracy for most asteroids in the low to moderate inclination and eccentricity region of the main belt (typical instability in the proper e and sin I being ≤0.0015 over 5 Myr). This stability has been verified by numerical integrations (within a realistic model) of 35 test cases. In a small percentage of cases, the accuracy of the proper elements computation was degraded by the effects of some resonance, either in mean motion or secular. We have been able to list the resonances responsible for this degradation in almost all the cases, in such a way that these are properly flagged with a "resonance code." This list of resonances, including nine high-degree secular resonances not known before our work, provides a detailed map of the dynamical structure of the asteroid main belt. We investigate the long-term dynamics of some of these secular resonances and find both very large amplitude oscillations of the eccentricity and irregular behavior for asteroids affected by one or more resonances. We show the geometry of these resonances in the proper elements space and their relationship with the asteroid distribution and with the most prominent families. In the second part of the paper, we give a detailed description of the improvements of this version of the proper elements theory with respect to the previously published ones (A. Milani and Z. Kneževic, 1990, Celest. Mech. 49, 347-411; 1992, Icarus 98, 211-232). We discuss the success of some of these improvements in cases which were previously of degraded accuracy, and we also comment on the failure of some attempted improvements. We conjecture that our theory is very close to the fundamental limitations to the accuracy of any analytical theory, which result from the fact that there is an infinite web of resonances and from the occurrence of chaotic motions. Thus we think that further improvements of this theory will only be of local nature and will affect only a fraction of the asteroid population.