Resonance Structure of Kuiper Belt Objects and Their Dynomical Evolution

自从1992年首次发现以来，已经发现了大约130个柯伊伯带天体，它们位于海王星轨道之外。它们被认为是行星体的残留物，它们的动力学行为可能为太阳系早期行星的形成提供了一些信息。在这项研究中，我们研究了平均运动共振、长期共振、二次共振和Kozai共振等共振的动力学结构，并将这些结构与主带小行星的动力学结构进行了比较。下面我们总结了本文的主要结果：1)对于平均运动共振，我们主要研究了(p：p+1)与海王星的共振。除1：2平均运动共振外，平均运动共振的临界变元在180ﾟ附近摆动，主小行星带的临界变元在0ﾟ附近摆动，在平均运动共振区，我们寻求与Kozai共振、长期共振和S…的双重共振2)在不同初始条件下，我们在平均运动共振区附近分布了约35000个天体，在外巨行星的摄动下积分了它们的轨道，并研究了它们的稳定性。它们之间的稳定轨道的行为与半解析方法的行为很好地吻合。从我们的数值模拟中，我们发现了混沌但有趣的轨道，这是半解析方法没有预测到的。它们有的从外部进入共振区，有的走出共振区。这种过渡性变化的时间尺度相当长。这一现象主要是由天王星的摄动引起的，三体近似的数值实验证实了这一点，其中扰动体只是海王星，不会发生过渡性变化。较少

About 130 Kuiper belt objects, which are located outside of Neptune orbit, have been found since the first discovery in 1992. They are believed to be the remnants of planetesimals and their dynamical behaviors may have some information on the planetary formation at the early stage of the solar system. In this study we investigate the dynamical structures of resonances such as mean motion resonances, secular resonances, secondary resonances, and Kozai resonance and compare these structures with those of asteroids in the main belt.In the following we summarize the main results of this investigation.1)As for the mean motion resonances we mainly study (p : p+1) resonances with Neptune. Other than 1 : 2 mean motion resonance, the critical arguments of the mean motion resonances librate around 180ﾟ, On the other hand the critical arguments in the main asteroid belt librate around 0ﾟ, In the mean motion resonance area we seek the double resonance with Kozai resonance, secular resonance, and s … More econdary resonance with use of semi-analytical methods and then we confirm the existence of the double resonance and study their stability.2)We distribute about 35000 bodies near the mean motion resonance regions with different initial conditions and integrate their orbits over five million years under the perturbations from outer giant planets and study their stability. The behaviors of the stable orbits among them are in good agreement with those from the semi-analytical methods. From our numerical simulations, we found the chaotic but interesting orbits which are not predicted from the semi-analytical method. Some of them enter the resonance region from the outside and some of them get out of the resonance region. The time scale of this transitional variation is quite long. This phenomena is caused from the perturbation from mainly Uranus, which is confirmed from the numerical experiment of the three-body approximation, where the disturbing body is only Neptune and the transitional variation does not occur. Less