Europa-induced Overlapping of Secondary Resonances in the 4:3 Jupiter-Ganymede Unstable Resonant Orbit Family

The overlapping of mean-motion resonances is useful for low-energy space mission design, but while most related prior work uses a planar CRTBP model, tours of multi-moon systems require using resonances affected by two moons. In this work, we investigate Jupiter-Ganymede unstable 4:3 resonant orbits in a concentric circular restricted 4-body model for the Jupiter-Europa-Ganymede system. We show that despite their high order, secondary resonances between these orbits and Europa have a large effect, especially 11/34, 12/37, 23/71, 25/77, 34/105, and 35/108; we also find strong evidence that the associated resonant islands overlap. We then compute many of the new objects which appear inside the secondary resonances, which gives final confirmation of the secondary resonance overlap.

平运动共振（mean-motion resonance）的重叠特性可用于低能耗航天任务设计，但现有多数相关前期研究均采用平面圆限制性三体问题（Circular Restricted Three-Body Problem, CRTBP）模型；而多卫星系统的轨道巡游设计，需考虑受两颗卫星共同影响的共振效应。本研究针对木卫二-木卫三-木星系统的同心圆限制性四体模型（concentric circular restricted 4-body model），探究了木星-木卫三的不稳定4:3共振轨道。研究表明，尽管此类轨道阶数较高，其与木卫二间的次级共振（secondary resonance）仍会产生显著影响，尤以11/34、12/37、23/71、25/77、34/105及35/108共振为甚；同时我们发现了相关共振岛（resonant islands）发生重叠的有力证据。随后我们计算了大量出现在次级共振区域内的新轨道体，最终证实了次级共振重叠现象的存在。