The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids
The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids
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2010 TK7 的轨道：其他地球特洛伊小行星可能的稳定区域
DOI：
10.1051/0004-6361/201118374
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发表时间：
2012-05-01
影响因子：
6.5
通讯作者：
Zhou, L.
中科院分区：
文献类型：
--
作者：
Dvorak, R.;Lhotka, C.;Zhou, L.
第一个地球特洛伊被观察到并发现在拉格朗日点L4附近的一个有趣的轨道上。因此，在目前的研究中，我们对其轨道的稳定性进行了详细的调查，并进一步扩展了研究，以了解发现其他地球特洛伊行星的可能性。我们的结果是通过三种不同的方法得出的。首先，导出空间椭圆型受限三体问题的解析映射，求出动力学问题的相空间结构。然后，我们在相空间几何的背景下探索小行星的稳定性，包括我们太阳系其他行星的间接影响。在第二种方法中，我们使用精确的数值方法对不同动力学模型中的轨道进行时间上的前后积分。在400个克隆轨道的基础上，推导了地球特洛伊小行星2010 TK7被捕获和逃逸的概率。为此，在第三种方法中，我们对地球拉格朗日点的稳定区域进行了广泛的数值研究。我们提出了一个详细的参数研究可能稳定的蝌蚪和马蹄形轨道额外的地球特洛伊，即相对于半长轴和数以千计的虚拟特洛伊的倾角。所有这三种方法都得出这样的结论：地球特洛伊小行星2010 TK7发现自己处于稳定区域边缘的不稳定区域；在这种稳定状态下可能会发现更多的地球特洛伊小行星。
The first Earth Trojan has been observed and found to be on an interesting orbit close to the Lagrange point L4. In the present study, we therefore perform a detailed investigation of the stability of its orbit and moreover extend the study to give an idea of the probability of finding additional Earth Trojans. Our results are derived using three different approaches. In the first, we derive an analytical mapping in the spatial elliptic restricted three-body problem to find the phase space structure of the dynamical problem. We then explore the stability of the asteroid in the context of the phase space geometry, including the indirect influence of the additional planets of our Solar system. In the second approach, we use precise numerical methods to integrate the orbit forward and backward in time in different dynamical models. On the basis of a set of 400 clone orbits, we derive the probability of capture and escape of the Earth Trojan asteroid 2010 TK7. To this end, in the third approach we perform an extensive numerical investigation of the stability region of the Earth’s Lagrangian points. We present a detailed parameter study of possible stable tadpole and horseshoe orbits of additional Earth Trojans, i.e. with respect to the semi-major axes and inclinations of thousands of fictitious Trojans. All three approaches lead to the conclusion that the Earth Trojan asteroid 2010 TK7 finds itself in an unstable region on the edge of a stable zone; additional Earth Trojan asteroids may be found in this regime of stability.