双星系中两子星的自转对双星轨道变化的后牛顿效应

在以前研究的基础上继续研究了双星两子星的自转对轨道变化的后牛顿效应，给出自转对轨道产生的长期摄动效应和周期摄动效应。理论结果表明，两子星的自转对轨道半长轴、轨道偏心率、近星点角和平近点经度均产生周期摄动效应，但对前两个轨道根数不产生长期摄动效,人对后两个轨道根数产生长期摄动效应，并利用理论结果对6颗双星系：EK Cep、GT Cep、NY Cep、V448 Cyg和V451 Oph中两子星的自转对轨道产生周期和长期摄动效应做了数值计算，数值结果显示：对于两个质量较大快速自转的双星系，由此产生的后牛顿铲应是不能忽视的。     

关于天体自转产生的PPN效应的讨论

根据后牛顿方法,得到了自转因素产生的轨道根数的参数化后牛顿效应。这种效应对轨道根数a、e、i、M没有长期摄动,只对ωΩ产生长期摄动,并且对所有轨道根数不产生长周期摄动,只产生短周期摄动。     

双星多方模型的形状及其对同步子星轨道要素的摄动影响

研究了双星多方模型的形状对同步子星轨道要素的摄动影响，假定两子星在同一轨道面上运动，推出了主星对伴星的轨道要素的摄动量，理论结果表明，双星多方模型对轨道半长轴和偏心率只有周期项摄动，无长期摄动，但对近星点和历元平近点角除有周期摄动外还有长期摄动效应。文中将理论结果应用于同步双星βＰｅｒ（大陵五双星）的计算上，除计算了两个子星的形状（椭率）外对同步子星的轨道要素变化的周期项振幅和长期项的效应做了数值     

中心体自转对天体轨道要素变化的后牛顿效应

本文给出了在三种引力理论为中心自转对天体轨道要素变化产生的后牛顿摄动效应的研究结果。研究结果表明：六个轨道要素除长钾不受摄动影响外其它五个要素均有周期摄动，特别升交点经度和近星点经度还有长期摄动效应。最后将文中的理论结论同前人的工作做了比较还应用于行星自转对卫星轨道要素变化的摄动效应计算上。作者在文[1]中研究了天体轨道要素变化的后牛顿效应，但在该文中并没有考虑中心体自转的影响。本文研究了三种引力理论（Einstein,Brans-Dick和Nordtvedt)中的这方面效应，并给出理论和数值的研究结果。     

双星多方模型的形状及其对同步子星轨道要素的摄动影响

研究了双星多方模型的形状对同步子星轨道要素的摄动影响。假定两子星在同一轨道面上运动，推出了主星对伴星的轨道要素的摄动量。理论结果表明：双星多方模型对轨道半长轴和偏心率只有周期项摄动，无长期摄动，但对近星点和历元平近点角除有周期摄动外还有长期摄动效应。文中将理论结果应用于同步双星βＰｅｒ（大陵五双星）的计算上。除计算了两个子星的形状（椭率）外对同步子星的轨道要素变化的周期项振幅和长期项的效应做了数值计算     

太阳多方模型对行星轨道要素变化的长期摄动影响

本文利用天体力学中的摄动理论和天体物理学中的气体星多方模型理论研究了太阳多方模型对行星轨道要素变化的长期摄动影响。文中给出了太阳日多方指数ｎ＝３的模型由于自转、扁度和内部密度分布等因素对行星轨道要素变化的长期摄动效应的理论结果。研究结果表明：行星轨道要素除长轴、偏心率和轨道倾角不受长期摄动外升交点经度、近日点经度以及平近点角均受长期摄动的影响。最后利用理论结果对行星轨道要素的长期投动效应做了数值计算，数值结果在表１中给出。     

天体自转因素导致的相对论性效应

本文在PPN框架中得到了太用系内自转因素产生的瞬时轨道根数改正的一阶封闭分析解.轨道半长径和偏心率不受长期效应的影响,只受周期效应的影响;轨道倾角、升交点经度、近星点角距,平近点角既受长期效应又受周期效应的影响.我们用两种引力理论分别计算了太阳自转对地内大行星及—些小行星轨道,行星自转对自然卫星轨道,地球自转对人造卫星轨道所产生的各相对论性效应.     

地球场的广义相对论效应对人造卫星轨道的影响

从计及J2项的地球重力场度规出发，我们导出在这样的度规场中人造卫星的摄动加速度及在径向、横向和轨道面法向等方面的摄动函数，进而计算了轨道一阶导数的平均值，讨论了在这种重力场中卫星的轨道特性。其主要结论是：1、球形地球的广义相对论摄动仅对近地点角距ω和平近点角τ产生长期项，而地球J2项的广义相对论效应不仅对这两个根数有长期摄动，而且对升效点角距Ω出有长期摄动。值得注意的是这两种广义相对论效应对半长轴a，偏心率e及倾角i都没有长期摄动；2、球形地球的广义相对论效应对倾角i和升交点角距Ω仅有短周期摄动，但地球J2项的广义相对论效应除了对它们有短周期摄动外，还有长周期摄动，对Ω甚至还有长期摄动。     

在电离中电感应阻力对带电卫星轨道根数的摄动影响

研究了在高空电离层中运动的带电荷的卫星受电感应阻力后对轨道根数产生的摄动影响。研究结果表明 ,电感应阻力对带电卫星的轨道半长轴、轨道偏心率、近地点赤经、历元平赤经均有周期摄动影响 ,但除对半长轴有长期摄动效应外对其它轨道根数均无长期摄动。轨道倾角和升交点赤经不受摄动影响。文中以飞行在高度 1 50 0km的电离层中的导体卫星作为算例。计算结果显示 :带电导体卫星在高空电离层中带有一定电量时电感应阻力对轨道半长轴的缩短产生显著效应     

在电离中电感应阻力对带电卫星轨道根数的摄动影响

研究了在高空电离层中运动的带电荷的卫星受电感应阻力后对轨道根数产生的摄动影响。研究结果表明，电感应阻力对带电卫星的轨道半长轴、轨道偏心率、近地点赤经、历元平赤经均有周期摄动影响，但除对半生长轴有长期摄动效应外对其它轨道根数均无长期摄动。轨道倾角和升交点赤经不受摄动影响。文中以飞行在高度1500km的电离层中的导体卫星作为算例。计算结果显示：带电导体卫星在高空电离层中带有一定电量时电感应阻力对轨道半长轴的缩短产生显著效应。     

Parameterized post-Newtonian orbital effects in extrasolar planets

Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets.     

On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.     

Numerical simulation of the Moon's rotation in a rigorous relativistic framework

This paper describes a numerical simulation of the rigid rotation of the Moon in a relativistic framework.Following a resolution passed by the International Astronomical Union(IAU) in 2000,we construct a kinematically non-rotating reference system named the Selenocentric Celestial Reference System(SCRS) and give the time transformation between the Selenocentric Coordinate Time(TCS) and Barycentric Coordinate Time(TCB).The post-Newtonian equations of the Moon's rotation are written in the SCRS,and they are integrated numerically.We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques as well as geodetic precession.We find two dominant periods associated with this correction:18.6 yr and 80.1 yr.In addition,the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed,and we have found that the main periods of this precession are 27.3 d,2.9 yr,18.6 yr and 80.1 yr.     

On derivation of EIH (Einstein–Infeld–Hoffman) equations of motion from the linearized metric of general relativity theory

The half-century old idea of Infeld to use the variational principle of the general relativity field equations is reminded to show that the commonly employed EIH (Einstein–Infeld–Hoffman) equations of motion may be derived from the linearized (weak-field) metric alone. Based on it, the linearized metric might be sufficient for post-Newtonian celestial mechanics and astrometry enabling one to derive the post-Newtonian equations of motion and rotation of celestial bodies as well as the post-Newtonian equations of light propagation within the general relativity framework.     

Post-Newtonian satellite orbits

The first post-Newtonian approximation of general relativity is used to account for the motion of solar system bodies and near-Earth objects which are slow moving and produce weak gravitational fields. The \(n\)-body relativistic equations of motion are given by the Einstein-Infeld-Hoffmann equations. For \(n=2\), we investigate the associated dynamics of two-body systems in the first post-Newtonian approximation. By direct integration of the associated planar equations of motion, we deduce a new expression that characterises the orbit of test particles in the first post-Newtonian regime generalising the well-known Binet equation for Newtonian mechanics. The expression so obtained does not appear to have been given in the literature and is consistent with classical orbiting theory in the Newtonian limit. Further, the accuracy of the post-Newtonian Binet equation is numerically verified by comparing secular variations of known expression with the full general relativistic orbit equation.     

Averaged rotational dynamics of an asteroid in tumbling rotation under the YORP torque

The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The general rotational equations of motion are derived and approximated with an illumination function expanded up to second order. The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state.     

On the energy integral for first post-Newtonian approximation

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials \(W^j (j=1,2,3)\), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.     

On the equilibrium figures of an ideal rotating liquid in the post-Newtonian approximation of general relativity

Maclaurin's P-ellipsoid, which is an equilibrium figure in the post-Newtonian approximation of general relativity, is constructed in the neighbourhood of Maclaurin's classical ellipsoid. Its shape and rotation velocity are investigated. It is shown that in the case of a P-ellipsoid with the mass and the angular momentum of a basic ellipsoid the effects of general relativity reduce the rotation velocity and decrease its volume.     

The dynamical evolution of uniformly rotating asteroids subject to YORP

A detailed derivation is given of the effect of solar radiation on the rotational dynamics of asteroids, commonly called the YORP effect. The current derivation goes beyond previous discussions published in the literature and provides a comprehensive secular dynamical analysis of the effect of solar radiation torques acting on a uniformly rotating body, and the evolution of its rotation state over time. Our predicted model has the global radiation properties of the asteroid as explicit parameters, and hence can be specified independent of these parameters. The resulting secular equations for the rotation rate and rotation pole are characterized by three parameters of the body's shape and explicitly includes the effect of thermal inertia on the evolution of these rotation state parameters. With this detailed model, in conjunction with estimated asteroid shapes and poles, we compute the expected YORP torques and dynamic response of several asteroids and the change in rotation rate for specific shapes as a function of obliquity. Finally, we define a convenient dimensionless parameter that is only a function of the body geometry and that can be used to characterize the effects of YORP.     

Relativistic Celestial Mechanics on the verge of its 100 year anniversary

As we are now approaching 2015, both the General Relativity Theory (GRT) and the relativistic Celestial Mechanics based on it will soon arrive at their 100 year anniversaries. There is no border between Newtonian and relativistic Celestial Mechanics. The five-decade period of intensive development of Celestial Mechanics in the second half of the 20th century left many interesting techniques and problems uncompleted. This lecture reviews some problems of Newtonian and relativistic Celestial Mechanics worthy of further investigation. Concerning Newtonian mechanics, these problems include general solution of the three-body problem by means of the series of polynomials, construction of the short-term and long-term theories of motion using the fast converging elliptic function expansions, and representation of the rotation of the planets in the form compatible with the General Planetary Theory reducing the problem to the combined secular system for translatory motion and rotation. Relativistic problems considered here include the determination of the main relativistic effects in the motion of a satellite, e.g. the Moon, and in the rotation of the primary planet using the Newtonian theories of motion and rotation combined with the relativistic transformation of the reference systems, the use of the linearized weak-field GRT metric as a basis of relativistic Celestial Mechanics in the post-Newtonian approximation, and the motion of the Solar System bodies at the cosmological background in the framework of the basic cosmological models. The exposition of the chosen relativistic problems is preceded by reminding the basic features of relativistic Celestial Mechanics with discussing some present tendencies concerning the Parametrized Post-Newtonian formalism, International Astronomical Union resolutions, and standardization of the GRT routines.