Three-Body Mean Motion Resonances and the Chaotic Structure of the Asteroid Belt
Three-Body Mean Motion Resonances and the Chaotic Structure of the Asteroid Belt
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DOI：
10.1086/300632
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发表时间：
1998-12
期刊：
影响因子：
--
通讯作者：
D. Nesvorný;A. Morbidelli
中科院分区：
文献类型：
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作者：
D. Nesvorný;A. Morbidelli
我们讨论了由大量小行星组成的新型平均运动共振的存在和性质，共振角被定义为小行星、木星和土星平均经度的线性组合（具有整数系数）。我们将这些共振称为三体平均运动共振。在本文中，我们表明，大约 250 颗编号小行星的平均半长轴的异常大振荡与一些最突出的三体平均运动共振有关，并且我们推测共振小行星的实际数量要大得多。在我们的数值积分中检测到的大多数共振体的正李亚普诺夫指数表明了它们轨道的混沌性质。此外，我们通过频率分析表明，三体平均运动共振中的轨道可能会以偏心率缓慢而混乱地扩散。这种扩散的存在可能会对我们目前对小行星带长期演化和物体向近地轨道的输送的理解产生重大影响。
We discuss the existence and the properties of a new type of mean motion resonance populated by a large number of asteroids, the resonant angle being defined as a linear combination (with integer coefficients) of the mean longitudes of asteroid, Jupiter, and Saturn. We call these resonances the three-body mean motion resonances. In the present paper, we show that the anomalous large oscillation of the mean semimajor axis of about 250 numbered asteroids is associated with some of the most prominent three-body mean motion resonances, and we conjecture that the actual number of the resonant asteroids is much larger. The positive Lyapunov exponent detected for the majority of resonant bodies in our numerical integrations suggests the chaotic nature of their orbits. Moreover, we show, using frequency analysis, that orbits in the three-body mean motion resonances may slowly and chaotically diffuse in eccentricity. The existence of such diffusion may have major consequences for our present understanding of the long-term evolution of the asteroidal belt and the delivery of objects to near-Earth orbits.