We study in this paper the capture of a massless particle into an isolated, first order Corotation Eccentric Resonance (CER), in the framework of the Planar, Eccentric and Restricted Three-Body problem near a m+1:m mean motion commensurability (m integer). While capture into Lindblad Eccentric Resonances (where the perturber's orbit is circular) has been investigated years ago, capture into CER (where the perturber's orbit is elliptic) has not yet been investigated in detail. Here, we derive the generic equations of motion near a CER in the general case where both the perturber and the test particle migrate. We derive the probability of capture in that context, and we examine more closely two particular cases: (i) if only the perturber is migrating, capture is possible only if the migration is outward from the primary. Notably, the probability of capture is independent of the way the perturber migrates outward; (ii) if only the test particle is migrating, then capture is possible only if the algebraic value of its migration rate is a decreasing function of orbital radius. In this case, the probability of capture is proportional to the radial gradient of migration. These results differ from the capture into Lindblad Eccentric Resonance (LER), where it is necessary that the orbits of the perturber and the test particle converge for capture to be possible. Possible applications for planetary satellites are discussed.
The interactions among objects in a mean motion resonance are important for the orbital evolution of satellites and rings, especially Saturn's ring arcs and associated moons. In this work, we examine interactions among massive bodies in the same corotation eccentricity resonance site that affect the orbital evolution of those bodies using numerical simulations. During these simulations, the bodies exchange angular momentum and energy during close encounters, altering their orbits. This energy exchange, however, does not mean that one body necessarily moves closer to exact corotation when the o…
Origin of the chaotic motion of the Saturnian satellite Atlas
我们重新审视阿特拉斯的动态。使用卡西尼国际空间站2004年2月至2013年8月的天体测量观测，库珀等人（2015年）发现了阿特拉斯目前受到54：53共转偏心率共振（CER）和54：53林德布拉德偏心率共振（LER）的干扰。他们证明了阿特拉斯的轨道是混沌的，李雅普诺夫时间为10年，这是与普罗米修斯的耦合共振相互作用（CER/LER）的直接结果。在这里，我们使用CoraLin分析模型（El Moutamid et al. 2014）研究了两种共振之间的相互作用，表明混沌区几乎填满了卫星轨道所占据的所有共转位置。四个70：67的半圆型平均运动与潘多拉的共振也是重叠的，但这些共振的影响要弱得多。频率分析使我们能够突出54：53共振之间的耦合，并确认一个简化的系统，包括由于普罗米修斯和土星的扁率的扰动只捕捉到动力学的基本特征。
Planetary formation theories and, more specifically, migration models predict that planets can be captured in mean-motion resonances (MMRs) during the disc phase. The distribution of period ratios between adjacent planets shows an accumulation in the vicinity of the resonance, which is not centred on the nominal resonance but instead presents an offset slightly exterior to it. Here we extend on previous works by thoroughly exploring the effect of different disc and planet parameters on the resonance offset during the disc migration phase. The dynamical study is carried out for several first-or…
We present an analytical model to study the dynamics of the outer edge of Saturn's A ring. The latter is influenced by 7:6 mean motion resonances with Janus and Epimetheus. Because of the horseshoe motion of the two co-orbital moons, the ring edge particles are alternately trapped in a corotation eccentricity resonance (CER) or a Lindblad eccentricity resonance (LER). However, the resonance oscillation periods are longer than the 4-year interval between the switches in the orbits of Janus and Epimetheus. Averaged equations of motion are used, and our model is numerically integrated to describe…
The Cassini spacecraft discovered many close-in small satellites in Saturnian system, and several of them exhibit exotic orbital states due to interactions with Mimas and the oblateness of the planet. This work is devoted to Methone, which is currently involved in a 15:14 Mean-Motion Resonance with Mimas. We give an in deep study the current orbit of Methone by analyzing and identifying the short, resonant and long-term gravitational perturbations on its orbit. In addition, we perform numerical integrations of full equations of motion of ensembles of close-in small bodies orbiting the non-cent…
The statistical results of transiting planets show that there are two peaks around 1.5 and 2.0 in the distribution of orbital period ratios. A large number of planet pairs are found near the exact location of mean motion resonances (MMRs). In this work, we find out that the depletion and structures of gas disk play crucial roles in driving planet pairs out of exact location of MMRs. Under such scenario, planet pairs are trapped into exact MMRs during orbital migration firstly and keep migrating in a same pace. The eccentricities can be excited. Due to the existence of gas disk, eccentricities …
对任意倾角的三体问题中的共振捕获进行了数值研究。无质量的粒子被设置为从1：5共振之外与一颗质量为1000的行星漂移，从而遇到行星的不同平均运动共振的网络。随机构造的样本探索0至180度倾角的参数空间，增量为5度，总计近6x10^5个数值模拟。30个共振内部和外部的行星的位置进行监测。我们发现，逆行共振是出乎意料的更有效的捕获比逆行共振，共振顺序不一定是一个很好的指标，在任意倾角的捕获效率。捕获概率显着下降，在中等样本偏心度的初始倾角范围内[10度，110度]。轨道反演是可能的初始圆形轨道与倾角范围[60度，130度]。在1：1共轨共振中的捕获在大的逆行倾角时很可能发生。如果行星的轨道偏心率大于0.1，则通过偏心Kozai-Lidov机制的作用降低捕获概率。捕获的不对称性出现在内部和外部共振之间，因为被捕获的轨道优先被捕获在内部共振中。逆行共振的相对俘获效率表明，逆行轨道上的达摩克洛和半人马座小行星的动力学寿命必须明显大于逆行轨道上的动力学寿命，这意味着最近发现的逆行共振小行星2006 BZ 8，2008 SO 218，2009 QY 6和1999 LE 31（Morais和Nynui，2013，MNRAS 436，L30）可能是在外部巨行星之间徘徊的最古老的小天体之一。
The motion of a satellite can experience secular resonances between the precession frequencies of its orbit and the mean motion of the host planet around the star. Some of these resonances can significantly modify the eccentricity (evection resonance) and the inclination (eviction resonance) of the satellite. In this paper, we study in detail the secular resonances that can disturb the orbit of a satellite, in particular the eviction-like ones. Although the inclination is always disturbed while crossing one eviction-like resonance, capture can only occur when the semi-major axis is decreasing.…
Comparative orbital evolution of transient Uranian co-orbitals: exploring the role of ephemeral multibody mean motion resonances
天王星有三个已知的共轨道：83982 Crantor（2002 GO 9），2010 EU 65和2011 QF 99。在这里，我们对这些瞬态共轨道的轨道演化进行了比较分析，以更好地了解它们是如何首先被捕获的，以及是什么使它们动态不稳定。我们还在已知的天体中寻找额外的临时天王星共轨候选者。我们的N体模拟表明，2011 QF 99的长期稳定性是由木星和海王星控制的;在成为特洛伊之前，它短暂地进入了与木星的1：7平均运动共振和与海王星的2：1平均运动共振。在这些短暂的两体平均运动共振事件，拱心共转共振也被观察到。对于已知的共轨道，土星是目前主要的不稳定力的来源，但这还不足以将一个次要的天体从与天王星的1：1的轨道中弹射出来。这些物体必须与木星和海王星进入平均运动共振，以便被捕获或成为路过的半人马座。小行星2010 EU 65，可能是来自奥尔特云的访客，由于其相对较低的离心率，可能已经稳定了好几百万年。此外，我们表明，已知对象的轨道特性和发现情况可以用来概述一个实用的策略，通过该策略可以找到更多的天王星的共轨道。
