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arXiv 1612.01451astro-ph.EP
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土星F环位置的简单模型

A simple model for the location of Saturn's F ring

Luis Benet, Àngel Jorba

摘要:

在本文中,我们介绍了一个简化的模型来了解土星F环的位置。该模型是一个由土星引力场定义的平面限制性五体问题,包括它的第二带谐波$J_2$,牧羊人卫星普罗米修斯和潘多拉,以及泰坦。我们计算精确的长时间数值积分(约250万)非相互作用的测试粒子最初位于普罗米修斯和潘多拉的轨道之间的区域,并解决他们是否逃脱或保持被困在这个区域。我们得到了一个广泛的区域的初始条件的测试粒子仍然受到限制。我们考虑一个动态稳定性指标的测试粒子的运动定义通过计算的标准偏差的相关动力学量的平均值的比率,特别是,平均运动和半长轴。这个指标清楚地分离出一个子集的捕获的初始条件,出现非常本地化的条纹在初始半长轴和偏心空间的最稳定的轨道。仅保留这些测试颗粒,我们得到一个狭窄的偏心环,显示尖锐的边缘和集体对齐。稳定环粒子的累积条纹的半长轴可以与共振相关联,主要涉及普罗米修斯的外林德布拉德共振和共旋转共振,但不限于此。潘多拉内部的林德布拉德和共旋转共振以及低阶三体共振通常与间隙一致,即,不稳定地区。比较我们的结果与标称数据的F环显示出一定的对应关系。

英文摘要:

In this paper, we introduce a simplified model to understand the location of Saturn's F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic $J_2$, the shepherd moons Prometheus and Pandora, and Titan. We compute accurate long-time numerical integrations of (about 2.5 million) non-interacting test-particles initially located in the region between the orbits of Prometheus and Pandora, and address whether they escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We consider a dynamical stability indicator for the test particles' motion defined by computing the ratio of the standard deviation over the average value of relevant dynamical quantities, in particular, for the mean-motion and the semi-major axis. This indicator separates clearly a subset of trapped initial conditions that appear as very localized stripes in the initial semi-major axis and eccentricity space for the most stable orbits. Retaining only these test particles, we obtain a narrow eccentric ring which displays sharp edges and collective alignment. The semi-major axis of the accumulation stripes of the stable ring-particles can be associated with resonances, mostly involving Prometheus' outer Lindblad and co-rotation resonances, but not exclusively. Pandora's inner Lindblad and co-rotation resonances as well as low-order three-body resonances typically coincide with gaps, i.e., regions of instabilities. Comparison of our results with the nominal data for the F ring shows some correspondence.

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