小偏心距下一阶共振宽度的发散
On the Divergence of First Order Resonance Widths at Low Eccentricities
摘要：
轨道共振在行星系动力学中起着重要的作用。经典的理论分析发现，教科书报告的天平动宽度的一阶平均运动共振发散近圆形轨道。在这里，我们研究的性质，这种分歧与非微扰分析的几个一阶共振内部的一个小行星质量的行星。我们发现，一阶共振有两个分支，近心共振区和近心共振区。当偏心率接近零时，这些区域的中心偏离标称谐振位置，但它们的宽度收缩。我们还报告了一个新的发现的“桥梁”之间的相邻的一阶共振：在低偏心率，一阶共振的离心天平动区顺利地连接到附近的一阶共振的离心天平动区。这些桥可以促进共振迁移跨越大的径向距离在行星系，完全在低偏心率制度。
英文摘要：
Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first order mean motion resonances diverge for nearly circular orbits. Here we examine the nature of this divergence with a non-perturbative analysis of a few first order resonances interior to a Jupiter-mass planet. We show that a first order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centers of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of "bridges" between adjacent first order resonances: at low eccentricities, the apocentric libration zone of a first order resonance smoothly connects with the pericentric libration zone of the neighboring first order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low eccentricity regime.
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