摄动函数高阶展开与长期共振  

Higher-order Expansion of Perturbed Function and Secular Resonance

作　　者：王文磊 许雪晴[1,2] 周永宏[1,2,3] 廖新浩 WANG Wen-lei;XU Xue-qing;ZHOU Yong-hong;LIAO Xin-hao(Shanghai Astronomical Observatory,Chinese Academy of Sciences,Shanghai 200030,China;Key Laboratory of Planetary Sciences,Shanghai Astronomical Observatory,Chinese Academy of Sciences,Shanghai 200030,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院上海天文台,上海200030 [2]中国科学院行星科学重点实验室,上海200030 [3]中国科学院大学天文与空间科学学院,北京100049

出　　处：《天文学进展》2018年第3期325-340,共16页Progress In Astronomy

基　　金：国家自然科学基金(11673053;11773057;11673049)

摘　　要：研究三体系统的长期共振效应,有助于了解系统的稳定性。在雅可比坐标系下建立了第三体摄动一般运动模型,将摄动函数按照半长径之比展开到十六极矩。通过对摄动函数进行轨道双重平均,消除了内外轨道的短周期项。基于限制性三体模型,分别在内摄和外摄两类情形下进行讨论。外摄情形下十六极矩项对系统结构的演化只有微弱的影响,而内摄情形下系统会出现新的共振和混沌现象。在圆型内摄情形下,系统出现了类似于Lidov-Kozai效应的近点共振。区别于Lidov-Kozai效应只在近心点幅角ω2=±90?时可能存在平衡点,十六极矩近似下,在ω2为0?和180?时也可能存在平衡点。角动量Z轴分量的取值会影响共振平衡点的数量、位置和稳定性。在椭圆型内摄情形下,系统在十六极矩近似下激发出新的轨道翻转,且翻转没有周期性,呈现混沌现象。十六极矩近似下的轨道翻转明显区别于八极矩近似下的轨道翻转,特别是,当半长径之比相当大时,十六极矩近似下偏心率的振幅明显大于八极矩近似下偏心率的振幅。Research about the secular resonance effect of the three-body systems helps to understand the stability of these systems.This study establishes a general motion model for three-body systems in Jacobi coordinates,and the perturbed functions are expanded up to the hexadecapole order,with the semi-major axis ratio.Meanwhile,the short-period terms of the internal and external orbits are eliminated by double averaged method.Basing on the restricted three-body model,the investigation is discussed in two cases.(1)The perturbing body is outer,the hexadecapole term has only weak effects on the long-term evolution of the system.(2)The perturbing body is inner,the system will have new resonance and chaos phenomena.The inner part also need to be considered with two cases.(a)The orbit of the perturbing body is circular,the system exists the precession of the argument of periapse,which is similar to Lidov-Kozai effect with an equilibrium point ofω2=±90°,whichω2 is argument of pericenter,while this system under the hexadecapole-level approximation also has possible equilibrium points ofω2=0°andω2=180°.In addition,the quantity,position and stability of equilibrium point will be affected by the angular momentum of Z axis component.(b)The interior orbit is elliptical,new orbital flips will be excited with the hexadecapole approximation,which are chaotic and not periodic.Moreover,these orbital flips are obviously different from those with octupole approximation.Specifically,while the semi-major axis ratio is quite large,the amplitude of eccentricity under the hexadecapole approximation is significantly greater than that under the octupole approximation.

关 键 词：天体力学 长期摄动 轨道演化 十六极矩 

分 类 号：P133[天文地球—天体力学]