地球动力学扁率及其与岁差章动的关系

由岁差常数求得的日月岁差是天文学的重要参数之一,它和地球动力学扁率相联系。地球动力学扁率在章动理论的计算中也是一个重要的物理量。介绍了由不同的观测方法和模型给出的地球动力扁率值,并讨论了它也岁差的关系和对章动计算的影响。在刚体地球章动振幅的计算中,地球动力学扁率值起着尺度因子的作用,要改善刚体地球章动振幅的计算,需要修改目前的黄经总岁差值。非刚体地球章动的转换函数中所采用的简正模和常数都直接或间接地依赖地球动力学扁率值。在IAU1980章动理论中,计算刚体地球章动振幅所使用的地球动力学扁率值计算转换函数中简正模频率和常数所使用的地球动力学扁率值并不一致。随着观测和计算精度的提高,地球动力学扁率值的不一致将影响章动振幅的计算。在建立刚体地球章地动理论中,如何解释地球动力学扁率值的差异,如何选取地球动力学扁率值,还有待进一步的研究。     

地球表层物质非均匀分布对地球动力学扁率的贡献

全球动力学扁率(H)是研究地球自转与岁差的-个重要物理量.由对岁差的观测有Hobs=0.0032737≈1/305.5.该文依据内部场理论重新计算了流体静平衡态下的地球内部几何扁率剖面,结果与Denis(1989)的结果相吻合.该文还推导了三阶扁率精度下日的计算式,并计算出PREM地球模型的H理论值为HPREM=1/308.5,这与其他人的结果一样,与观测值之间存在1%的差别.为了研究这个差别的来源,该文将PREM模型中均一的上地壳层与海洋层替换为ECCO、GTOPO30和ETOPO5等真实的地球表层数据,结果表明替换后得到的H更加偏离观测值.此结果说明来自于地幔及更深处质量异常引起的正面影响可能要比先前预期的高,并为地壳均衡理论提供了间接的证据.     

非刚体地球的受迫章动奥波策项和倾斜模

讨论了非刚体地球受迫章动奥波策项与简正模表达式中倾斜模的关系。结果表明天球历书极章动中倾斜振项对应于角动量极的章动,在球历书极章动与角动量极的章动奥波策项之和。同时还给出了岁差速率与自转极的章动奥波策项间的数学关系。     

火星的岁差和章动

火星是类地行星，火星动力学的研究不仅具有科学意义，而且还具有实际应用价值。火星的空间探测获得了许多有关火星极运动的重要资料，它与理论值的比较是检验火星内部结构的重要手段，也是为改进火星岁差章动理论提供依据的有效途径。介绍了当前国际上有关火星的岁差和章动研究的进展，分别对刚体火星的章动序列、火星内部结构参数化模型的建立和火星自转的简正模作了描述，并进行了简单的讨论。     

章动常数改正的测定

本文提出在由以河外星系为定标的恒星自行与恒星星表自行相比较求解岁差常数改正的方法中,同时考虑章动常数误差的影响,进而在求解岁差常数采用值的改正值的同时确定章动常数采用值的改正值。     

弹性地球各种几何轴和物理轴的定义

基于经典的弹性地球自转动力学理论,建立了极移和章动的联合动力学方程。由此给出了弹性地球各种几何轴和物理轴(Tisserand轴、自转轴、瞬时形状轴、角动量轴、CEP和CIP轴)的极移、岁差章动的动力学方程,明确了各种轴的定义及其之间的理论关系。理论研究表明,联合动力学方程要比经典动力学方程综合性强易于理解,可同时求解极移和章动,特别是在文[1]理论中出现的倾斜模(TOM),在此只是作为了一个特解而存在。     

关于天球参考报

章动序列计算和地球定向参数测定需要一个中间的天球参考极作参照，1984年，采用IAU1980章动理论，选取天球历书极作为参考极，利用改善岁差章动模型和由天文测地新技术确定地球定向参数实现的天球历书极，其精度可达0．1mas，随着理论和观测精度的提高，在微角秒量级下，章动和极移模型中周日和半周日成分分应被考虑，地球定向参数的高频成分已被测定，因此天球历书极的原先定义不再适用，需要更改，叙述了不同天球参考极的概念，天球历书极的定义，评述了天球历书极目前实现及其缺陷，介绍了新的天球参考极－天球中间极的定义及其实现。     

有关非刚体地球章动研究的进展

对目前国际上有关非刚体地球章动研究的时展作了简要回顾，重点介绍了包含海洋和大气的非刚体地球章动模型和有关研究工作，并对将来的发展方向作了讨论。     

对EOP(GSFC)96R01中极偏移序列的分析(英文)

分析了１９７９年８月至１９９６年１月之间由ＭａｒｋⅢＶＬＢＩ时延资料得到的ＩＡＵ１９８０章动模型在经度（δψ）和交角（δε）方向的偏移序列,得到了对ＩＡＵ１９８０章动模型中主项系数的改正,并检测了自由地核章动。计算步骤依照常规资料处理方法设计,并采用了一些分析技巧以便充分利用资料的整个时段和减小端部效应对参数解的影响。对拟合残差序列的进一步分析表明,自由地核章动是统计显著的,但其参数尤其是其振幅可能具有时变性质,表现为在经度和交角方向自１９８６至１９９５年的持续减弱。     

对EOP（GSFC）96R 01中极偏移序列的分析

分析了１９７９年８月至１９９６年１月之间由ＭａｒｋⅢ ＶＬＢＩ时延资料得到的ＩＡＵ１９８０间动模型在经度（δψ）和交角（δψ）方向的偏移序列,得到了对ＩＡＵ１９８０章动模型中主项系数的改正,并检测了自由地核章动。计算步骤依照常规资料处理方法设计,并采用了一些分析技巧以便充分利用资料的整个时段和减小端部效应对参数解的影响。对拟合残差序列的进一步分析表明,自由地核章动是统计显著的,但其参数尤其是其振幅     

On the precession constant: Values and constraints on the dynamical ellipticity; link with Oppolzer terms and tilt-over-mode

The luni-solar precession, derived by theoretical considerations from the precession of the equator, is one of the most important parameters for computing not only precession but also nutations, due to its relation to the dynamical flattening. In this paper, we review the numerical values of this parameter, from the geodynamical point of view as well as the astronomical point of view, from the observational point of view as well as from the theoretical point of view. In particular, we point out a difference of about 1 percent between the global Earth dynamical flattening derived from the astronomical observations and the values derived from the different geophysical computations. The nutation amplitudes depend on the Earth dynamical flattening and this dependence is amplified by a resonance at an important normal mode, the Tilt-Over-Mode (TOM). Since the astronomical point of view as well as the geophysical one are confronted, we also take the opportunity to make the link between the TOM and the expressions of the nutations of the different axes which, in turn, are related with one another by the Oppolzer terms. Both, the Oppolzer terms and the TOM originate from a reference frame tilt effect. In writing the link between the nutational motions of the different axes, and so, in writing the Oppolzer terms, we also make the link with the precessional motion.     

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain). This revised version was published online in July 2006 with corrections to the Cover Date.     

Remarks on dynamical ellipticity at the Earth's

In this paper, two factors — the redistribution of the density and the variation in the angular velocity of the Earth rotation, that affect the adopted value of the flattening for equidensity surface within the Earth, are discussed. The computational results show that the contribution of the redistribution of the density in the Earth interior (especially in the core) on the change of the flattening at the core-mantle boundary (CMB) is marginal, and that the calculated value of the flattening at the CMB can be in good agreement with the VLBI observed value so long as the fact that the angular velocity of the Earth rotation has undergone the tidal evolution is taken into account. As a result, this paper presents a set of recommended values of the dynamical parameters of the Earth (see Table III) for computing Earth's forced nutation series.     

Considerations concerning the non-rigid Earth nutation theory

This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earth's density and theological properties) for the calculation of the Earth's transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earth's transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earth's nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5.Each level is discussed at the state of the art of the developments.     

A core-mantle interaction in the rotation of the Earth

Effects of an interaction between the mantle and the core of the Earth on its rotational motion are investigated. Assuming that the Earth consists of a rigid mantle and a rigid core with a frictional coupling and a kind of inertial coupling between them, the equations of motion are derived, and they are solved in a close approximation. The solution gives the expressions for the precession, the nutation, the secular changes in the obliquity and the rotational speed, the polar motion and so on as functions of the magnitudes of these forces. A numerical estimation shows that the effect of the friction on the amplitude and phase of the nutation is small for a reasonable intensity of the friction while inertial coupling force has a decisive influence on the amplitude, and an appropriately chosen value of the latter force gives a nutation which closely agrees with observations. It is also indicated that this torque remarkably lessens the rates of the secular changes in the obliquity and the rotational speed. The possibility of a periodical change in the amplitude of the polar motion is suggested as a result of the interaction between the two consituents.     

Forced nutations of a two-layer Earth model

In this paper we present a theory of the Earth rotation for a model composed of an inelastic mantle and a liquid core, including the dissipation in the core–mantle boundary (CMB). The main features of the theory are: (i) to be Hamiltonian, therefore the computation of some complex inner torques can be avoided; (ii) to be self-consistent and non-dependent on a previous rigid Earth theory, so there is no need to use transfer functions; (iii) to be analytical, the solution being derived by perturbation methods. Numerical nutation series deduced from the theory are compared with the IERS 96 empirical series, an accuracy better than 0.8 mas in providing celestial ephemeris pole (CEP) offsets .     

Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic

The IAU Working Group on Precession and the Equinox looked at several solutions for replacing the precession part of the IAU 2000A precession–nutation model, which is not consistent with dynamical theory. These comparisons show that the (Capitaine et al., Astron. Astrophys., 412, 2003a) precession theory, P03, is both consistent with dynamical theory and the solution most compatible with the IAU 2000A nutation model. Thus, the working group recommends the adoption of the P03 precession theory for use with the IAU 2000A nutation. The two greatest sources of uncertainty in the precession theory are the rate of change of the Earth’s dynamical flattening, ΔJ₂, and the precession rates (i.e. the constants of integration used in deriving the precession). The combined uncertainties limit the accuracy in the precession theory to approximately 2 mas cent⁻². Given that there are difficulties with the traditional angles used to parameterize the precession, z_A, ζ_A, and θ_A, the working group has decided that the choice of parameters should be left to the user. We provide a consistent set of parameters that may be used with either the traditional rotation matrix, or those rotation matrices described in (Capitaine et al., Astron. Astrophys., 412, 2003a) and (Fukushima Astron. J., 126, 2003). We recommend that the ecliptic pole be explicitly defined by the mean orbital angular momentum vector of the Earth–Moon barycenter in the Barycentric Celestial Reference System (BCRS), and explicitly state that this definition is being used to avoid confusion with previous definitions of the ecliptic. Finally, we recommend that the terms precession of the equator and precession of the ecliptic replace the terms lunisolar precession and planetary precession, respectively.