【作者】 杨远玲；

【导师】 聂清香；

【作者基本信息】 山东师范大学 ， 理论物理， 2006， 硕士

【摘要】 Kuiper带天体简称KBOs,是近十几年来在海王星外面新发现的一群类冰状天体。现今所观测到的KBOs大部分都分布在30～50AU(1AU为地球到太阳的距离),但根据猜测其最远可到达Oort云。由于KBOs被认为是太阳系最初形成时留下的残骸,所以它可能保留有太阳系形成时最原始的信息,对它的研究将有力地推动太阳系的形成和演化的研究,同时它也是理解KBOs中某些特殊星体(比如双星)和短周期彗星起源的关键。尤其是近几年来,大量数据表明太阳系以外也有行星系统,而KBOs动力学中的行星迁移过程也可以应用到这些行星系统中。因此,对KBOs动力学的研究也有益于人们对太阳系外行星系统的研究。自1992年第一颗KBO发现后,KBOs的数目每年都在以惊人的速度增加着,截至到2006年已达到近千颗。根据已观测到的KBOs的动力学特性,常把它们划分为三种类型:经典型(CKBOs),共振型(RKBOs)和散射型(SKBOs),其中研究较多的是CKBOs和RKBOs,统称为KBOs主带天体。一般来说,SKBOs的形成是由于海王星的散射作用,这一点已经得到数值实验的验证;对于KBOs主带天体的形成常见的几种理论为行星迁移机制,大星子散射机制,长期共振迁移机制和恒星交会机制等,但这几种机制都未能单独完全地解释KBOs主带天体的分布和轨道特性。本文的研究工作包括3大部分:(1)利用目前所观测到的KBOs的最新数据,对其轨道特性进行了分析,展示出了KBOs的轨道半长径、偏心率和轨道倾角的分布规律。(2)对当今应用在天体力学中解决N体问题的几种数值模拟方法做了比较,针对大量KBOs轨道长期演化的特点,选择了长期误差积累小和耗机时少的方法——Hermite算法。(3)应用Hermite算法到太阳、海王星、冥王星和KBOs的N体问题模型中,对目前所观测到的具有确定轨道的481个KBOs做了长达9. 9×108年的轨道演化数值模拟。该模拟不同于更多还原

【Abstract】 Kuiper belt objects (KBOs) is a group of ice-shaped celestial bodies that isfound in the last ten years. Most of them are between 30AU and 50AU(1AU is thedistance between the earth and the sun). But according to speculation, they canreach Oort cloud the furthest. Commonly, KBOs are considered to be the debris ofprimordial solar system, so they may have retained the information of the mostprimitive solar system. It’s an effectively push for the research of the solar system.In addition, it is also considered the key for understanding some special KBOs(such as double stars) and the origin of short period comets. Especially in recentyears, large quantities of data show existence of planetary systems beyond thesolar system and the study of KBOs can also be applied to these planetary systems.Therefore, the study dynamics of KBOs can also be beneficial to these planetarysystems.Since the first KBOs found in 1992, the number of KBOs increases in anoticeable speed annually. Up to 2006,it reaches to 1,000 nearly. Base on thedynamics character of the observed KBOs, they are often divided into three types:the classical KBOs (CKBOs), the resonance KBOs (RKBOs) and the scatterKBOs (SKBOs). Among them, more research is done on CKBOs and RKBOs,which is called KBOs main belt bodies. Commonly it’s considered that SKBOsare formed by Neptune’s scatter. This has received the proving of the numericalexperiment. There are several theories to explain the form of KBOs main beltbodied, such as planets migration mechanism, big planetesimal scatter mechanism,secular resonance mechanism and stellar encounter mechanism. But all thesemechanism can’t explain the distribution and orbital character separately andcompletely. Though the planets migration mechanism affects widely, it’s not fitthe fact. We analyzed the cause and it’s that the initial condition is not suit to thefact. In this particle, we attempts to find the initial distribution of KBOs bysimulating the KBOs orbits going with the time back up. By this, we discuss themechanism of present KBOs’ distribution.Our research includes 3 parts: (1) using the present observed data of KBOs,we analyze the character of orbits and show the rule of the semimajor axis,eccentricity and inclination. (2) Comparing the several algorithms for resolvingN-bodies problem in Celestial mechanics, and considering the character of KBOs,we chose the Hermite algorithms, which has less energy error and less computingtime. (3) Using the Hermite algorithms to the N-body model of Neptune, Plutoand KBOs, we did a numeral simulation of 9. 9× 108 years long, which include481 KBOs of having certain orbits. This simulation is different from anyone’swork before, whose characteristic is using the ‘anti-time’ integral method. It isbased on the present observed data of KBOs as initial condition and along withthe time back up which the step is negative. Our aim is to search the initialdistribution of KBOs before 9. 9× 108 years.The main results are as follows:(1) By the distribution of KBOs, we found that there is not fundamentaldistinction comparing with the result of a few years ago though the number ofcertain KBOs increases constantly. And there is still a collection in 3:2 resonancezones, in which the eccentricities and inclinations are bigger relatively, and thedistribution of CKBOs beyond 3:2 resonance zones is nearly normal.(2) Comparing the three common algorithms in celestialmechanics—Runge-Kutta-Fehlberg algorithm (RKF), Symplectic algorithm (Sym)and Hermite algorithm (Hermite), the result shows that the RKF’s precision isrelatively good, but the time for computing is long. The cumulative error becomesrelatively fast with the increasing of mass. Sym’s precision is less than RKF, butthe computing time has been markedly improved. And because it can maintain theconfiguration of Hamilton system, the error is stable, especially in the N-bodyproblem. However, it can be impacted by the mass largely and the error is close toHermite method when the mass is small. The error of Hermite is the largest, but ittends to slow down in experiments of many bodies. The computing time is theleast and the construction is also the simplest. Taking into account the largernumber of KBOs with the smaller quality (relative to the big planet, they arenegligible), we choose the Hermite algorithm.(3) Using the Hermite algorithm and the N-body model, we studied the testparticles, which have been assumed the initial conditions. Result shows, if theeccentricity and inclination of KBOs bigger, it’s easier to be inspired by the majorplanets.(4) In all the past research, it’s simulated by assuming the initial orbitalcondition at the time when KBOs origin, and the time as the starting time. Andfinally they always compare the result with the fact today. The results of thismethod have great relations with the initial conditions. But it is difficult to set theinitial conditions consistent with the actual. So the results are doubtful. In thisarticle, we use the ‘anti-time’ integral method, and the present observational datafor the initial conditions KBOs. We ascend the original distribution and the resultshould be reliable. The result shows that the distribution of KBOs may be normalbefore a long time. After a long evolvement course, the asteroids were inspired inthe original location or captured by the gravitational action of the major planetsfrom distance and finally the shape with several resonance zones is formed. Fromthe separated analysis of KBOs, we know that if the eccentricity and inclination ofKBOs is bigger, it’s easier to be inspired by the major planets, and it’s easiergoing to the resonance zones.In addition, our research is also different with the past research. In the allpast research, a lot of little particles are distributed evenly in a broader scope. Thiswill be not only inconsistent with the actual initial conditions, but a very largevolume calculation. However, our simulate method is relatively simple, it offers avaluable way for the research of KBOs.更多还原