地球特洛伊天体稳定区域研究

Stability Regions for Earth Trojans

第1颗地球特洛伊天体2010 TK7的发现暗示了可能存在大量未发现的地球特洛伊天体.进行了大量数值模拟并结合频谱分析方法,在初始轨道根数(a,i)平面上,给出了日地系L_4拉格朗日点附近特洛伊天体的稳定分布区域.得到的地球特洛伊天体稳定区域相对前人的结果偏小,完全排除了初始轨道倾角超过37o的稳定区域.细致分析了该稳定区域分布图中的精细结构,发现多种长期共振包括近日点进动ν_2-ν_8长期共振均对地球特洛伊天体的稳定性区域分布具有重要影响,少数轨道还受升交点共振ν_(14)的影响,导致轨道倾角的激发.在(a,i)平面的不同位置处,不同共振的影响程度和影响方式并不一致.

The discovery of the first Earth Trojan, asteroid 2010 TK7, suggests the possible existence of an undetected Earth Trojan swarm. In this paper, through numerical integrations along with spectral analysis technique, the orbital stability map on the initial orbit element （a, i） plane around the L4 point of the Sun-Earth system is presented. Comparing with previous results in literatures, this paper reveals a smaller stable region for the Earth Trojans, and particularly the existence of stable orbits with initial inclination larger than 37° is definitely repelled. The dynamical mechanisms, that may cause the orbital instability of Earth Trojans and consequently form the structures in the stability map, are investigated. The apsidal secular resonances v2 - v8 are all found to play important roles, and the ascending node resonance V14 is responsible for the inclination excitation in a small part of the map. The influences from different secular resonances vary both among different locations on the （a, i） plane and with different periods.