相对论天体力学和后牛顿运动方程

叙述了与Astrod工程有关的相对论天体力学基础内容。包括相对论天体力学，广义相对论基本原理，PPN方法体系，PPN多体问题，PPN二体问题。高阶PN二体问题等。     

自转二体问题中的PPN摄动力三分量S.T.W

本文导出了自转二体问题的PPN运动方程.并由此方程出发,得到了几种类型的自转产生的可积的PPN摄动力的三分量S.T.W.其适用性一般包括了自转效应较显著的天体系统,从而为完全解决自转二体问题的PPN效应奠定了基础.     

天文动力学和天体力学

叙述了与Astrod工程有关的天体力学和天文动力学的基本结果和学科概况 ,内容包括二体问题、摄动理论、人造地球卫星运动、限制性三体问题等     

天文动力学和天体力学

叙述了与Astrod工程有关的天体力学和天文动力学的基本结果和学科概况，内容包括二体问题，摄动理论，人造地球卫星运动，限制性三体问题等。     

中国天文学会学术会议(序号90):天体测量、天体力学和大地测量中的相对论问题(1989年8月1—6日,嵊泗)

中国天文学会天文地球动力学专业委员会,上海市天文学会和江苏省天文学会于1989年8月1—6日在浙江嵊泗联合举办了“天体测量,天体力学和大地测量中的相对论问题”(Relativity in Astrometry,Celestial Mechanics and Geodesy)研讨会。来自天体测量,天体力学,大地测量和天体物理领域的专家35人参加了会议。会议就相对论时空观,相对论参考系和相对论天体力学三个专题作了系统综述和讨论,并结合科研工作进展就VLBI,激光测距在测地工作中应用所需考虑的相     

相对论天体力学

本文综合评述正在建立的一门新学科－相对论天体力学，其中包括基础理论课题（分为相对论质点组动力学和相对论伸体动力学）和具体天体运动理论课题（又分为相对论太阳系动力学和相对论恒星系统动力学）。最后对最新建立的系统理论ＤＳＸ方法作简短介绍。     

序言

天文学和物理学的发展是息息相关的。从历史的角度来看 ,牛顿动力学体系和万有引力定律建立在天文观测和地面实验的基础上。牛顿动力学体系和万有引力定律在天体力学上的应用 ,到 1 9世纪上半叶海王星的预测 ( 1 845年 )和发现 ( 1 846年 )达到高潮。由于观测和天体力学轨道理论的发展 ,Ｌｅｖｅｒｒｉｅｒ于 1 859年发现了水星近日点的异常进动 ,这是第一个观测到的相对论性引力效应。一系列的实验和理论的进展 ,促成了爱因斯坦于 1 91 5年提出了 (广义 )相对论。对于白矮星 ,脉冲星 ,类星体 ,星系核、微波背景辐射及元素丰度等的观测证实…     

天体力学的展望

现代天体力学范畴除包含经典天体力学外,还包括天文动力学和星系动力学(其中不用统计力学)。现代天体力学的研究课题可归纳为三类:①具体天体的运动理论,其中的天体包括经典天体力学的研究对象月球,天然卫星,大行星,小行星和彗星,还有人体天体,双星,聚星和星系;②天体力学在地学和空间科学中的应用以及天体力学与其他学科或天文学分支的边缘领域中的课题;③天体力学的基础理论课题。 最后提出,太阳系的结构和演化、天体力学与其他学科或天文学分支的边缘领域,以及三体问题的定性和分析理论,有可能在近期内获得较快进展。     

IAU第114次学术讨论会概况

国际天文学联合会(IAU)第114次学术讨论会“天体力学和天休测量中的相对论问题”,于1985年5月28日至31日在苏联名城列宁格勒举行。与会代表138人分别来自欧、亚、北美、南美等大洲的20个国家;其中东道主苏联代表80人,约占总人数的58％;美国代表15人,中国代表2人(万籁、赵君亮),其他国家代表1—5人不等。 学术讨论会在聂瓦河畔列宁格勒作家俱乐部的     

中国天文学会学术会议(序号165):天体力学学术讨论会

中国天文学会天体力学专业委员会和卫星动力学专业委员会联合举办的“天体力学学术讨论会”于1994年11月1－5日在浙江省温州瑞安市召开，参加会议的有中国科学院、高等院校和测绘系统的全国各地15个单位的37名代表。该会议得到瑞安市府和科委的大力支持和赞助。瑞安市副市长周正野、科委主任吴承宽同志出席了会议开幕式。这次天体力学学术讨论会包括22届IAU大会介绍、学术报告和中国天体力学的发展方向专题讨论三方面内容。参加22届IAU大会的代表黄天衣向大家介绍了22届大会的概况，特别是与天体力学专业有关的学术活动、研究热点和组织…     

Specialized celestial mechanics systems for symbolic manipulation

Construction and application of the current high accuracy analytical theories of motion of celestial bodies necessitates the development of specialized software for the implementation of analytical algorithms of celestial mechanics. This paper describes a typical software package of this kind. This package includes a universal Poisson processor for the rational functions of many variables, a tensorial processor for purposes of relativistic celestial mechanics, a Keplerian processor valid for the solutions of the two body problem in the form of a Poisson series, Taylor expansions in powers of time and closed expressions, and an analytical generator of celestial mechanics functions, facilitating the immediate implementation of the present analytical methods of celestial mechanics. The package is completed with a numerical-analytical interface designed, in particular, for the fast evaluation of the long Poisson series.     

Orbit Propagation with Lie Transfer Maps in the Perturbed Kepler Problem

The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another.     

The Inverse Problem of Dynamics for Systems with Non-Stationary Lagrangian

We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric family of evolving orbits. An equation for non-stationary space symmetrical ‘potential’ function of such Lagrangian is given and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic invariants of non-stationary two-body problem containing a tangential force are found. This revised version was published online in July 2006 with corrections to the Cover Date.     

The two-body problem in the (truncated) PPN — Theory

The solution of the two-body problem in the (truncated) PPN theory is presented. It is given in two different analytical forms (the Wagoner-Will and Brumberg representation) and by the method of osculting elements.Work supported in part by the Deutsche Forschungsgemeinschaft (DFG), SFB78.     

General relativity and satellite orbits: The motion of a test particle in the Schwarzschild metric

The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ^?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km.     

Studies in the application of recurrence relations to special perturbation methods

The integration by recurrent power series of certain differential equations occurring in celestial mechanics is shown to be very much more efficient and accurate than that produced by classical one step methods. It is shown that for any such system of differential equations the machine time taken to carry out an integration is a minimum for a certain choice of the number of terms taken in the recurrent power series. In the two-body orbits considered this number is about 15. For the same accuracy criterion the power series is faster than the Runge-Kutta method of the fourth order by a factor which varies between 6 and 15 depending on the eccentricity of the orbit.

     

天文常数中的相对论问题

现代天文观测技术的日新月异、广义相对论的１ＰＮ近似方法在天体力学和天体测量中的广泛应用,使得有必要在１ＰＮ框架中严格而细致地重新审查天文常数系统。在相对论框架里,太阳系天体的质量应当定义为ＢＤ质量,它们的相对变化不超过１０＾－１９,可视为守恒量;引力势满足的方程不再是Ｐｏｉｓｓｏｎ方程而与坐标规范的选择有关,引力势也不再能用传统的球谐函数展开。应当选定一种规范,并且以ＢＤ多极矩作为天文常数。黄赤交     

Limits of predictability of gravitational systems

The concept of finite predictability of gravitational many-body systems is related to the non-deterministic nature of celestial mechanics and of dynamics, in general. The basic, fundamental reasons for the uncertainty of predictions are as follows: (1) the initial conditions are known only approximately since they are obtained either from observations or from approximate computations; (2) the equations of motion given by a selected model describe the actual system only approximately; (3) the physical constants of the dynamical system have error limits; (4) the differential equations of motion are non-integrable and numerical integration methods must be used for solution, generating errors in the final result at every integration step.In addition to these reasons, mostly depending on our techniques, there are some more fundamental reasons depending on the nature of the dynamical system investigated. These are the appearance of regions of instability, non-integrability and chaotic motion.Details, effects and controls of these regions for finite predictability are discussed for various dynamical systems of importance in celestial mechanics with special emphasis on planetary systems.     

Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20 thcentury.However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings,asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.