Jumping mechanisms of Trojan asteroids in the planar restricted three- and four-body problems
Jumping mechanisms of Trojan asteroids in the planar restricted three- and four-body problems
复制标题
平面受限三体和四体问题中特洛伊小行星的跳跃机制
DOI：
10.1007/s10569-015-9609-4
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发表时间：
2015
影响因子：
1.6
通讯作者：
Kenta Oshima and Tomohiro Yanao
中科院分区：
文献类型：
--
作者：
汪正元;中村正明;桂 法称;Kenta Oshima and Tomohiro Yanao
我们在平面限制性三体和四体问题的框架内，探索特洛伊小行星在稳定的拉格朗日点附近的运输的最小动力学机制。这种传输被称为特洛伊小行星的“跳跃”，已经在复杂的太阳系模型中进行了数值观测。然而，其动力学机制还没有得到充分的研究。本文的研究表明，在太阳-木星平面限制性三体问题中，从围绕不稳定拉格朗日点的不稳定周期轨道发出的不变流形调解了特洛伊小行星的跳跃。当这些不变流形通过离散映射投影到配置空间上时，它们形成同宿纠缠和波瓣。因此，由此产生的波瓣动力学解释了木星特洛伊小行星跳跃的机制。另一方面，在日地平面受限三体问题中，不稳定周期轨道的不变流形没有明显的同宿纠缠或波瓣，这表明跳跃是很难发生的。结果表明，在太阳-地球-金星平面限制性四体问题的框架内，金星的摄动效应对于地球特洛伊小行星跳跃的开始是重要的。本文给出的结果可以为传输机制以及与、和相关的弹道设计提供新的见解。
We explore minimal dynamical mechanisms for the transport of Trojan asteroids between the vicinities of the stable Lagrange pointsandwithin the framework of the planar restricted three- and four-body problems. This transport, called “jumping” of Trojan asteroids, has been observed numerically in the sophisticated Solar System models. However its dynamical mechanisms have not been fully explored yet. The present study shows that invariant manifolds emanating from an unstable periodic orbit around the unstable Lagrange pointmediate the jumping of Trojan asteroids in the Sun–Jupiter planar restricted three-body problem. These invariant manifolds form homoclinic tangles and lobes when projected onto the configuration space through a discrete mapping. Thus the resulted lobe dynamics explains the mechanism for the jumping of Jupiter’s Trojan asteroids. In the Sun–Earth planar restricted three-body problem, on the other hand, invariant manifolds of an unstable periodic orbit arounddo not exhibit clear homoclinic tangles nor lobes, indicating that the jumping is very difficult to occur. It is then shown that the effect of perturbation of Venus is important for the onset of the jumping of Earth’s Trojan asteroids within the framework of the Sun–Earth–Venus planar restricted four-body problem. The results presented here could shed new insights into the transport mechanism as well as trajectory design associated with,, and.