关于章动序列计算中的地球动力学扁率的取值

刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．     

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。     

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。     

用Hamilton方法计算弹性地球的章动序列

本文利用Hamilton方法研究弹性地球自转运动，采用地球模型PREM参数，给出了形状轴的章动序列．结果表明我们的方法是可行的，计算是可靠的．弹性地幔对地球章动的影响仅在毫角秒量级上，它相对液核对地球竟动的影响要小得多．     

考虑地球扁率摄动影响的初轨计算方法

在二体问题意义下的短弧定轨,Laplace型方法是最主要最典型的一种初轨计算方法。若测角资料达到10^-4-10^-5精度(相当于2″—20″之间),那么要使定轨精度达到与其相应的程度,地球非球形引力位中的扁率项摄动应该考虑,在此前提下,同样可以采用相应的Laplace型定轨方法。即给出这种严格包含扁率摄动的初轨计算方法的原理和具体计算过程以及计算实例,除采用多资料定轨方法外,这种方法也是提高初轨计算精度的一种途径,它同样可用于多资料的情况,这种方法对于大扁率主天体(即中心天体)的卫星定轨将更有实用价值。     

太平洋海平面变化及其与地球自转关系的初步分析

本通过分析1996.0至1990.0年期间分布于太平洋海域的88个验潮站所观测到的海平面变化（SLC）资料序列，以及国际地球自转服务的日长变化（△LOD）资料序列，初步研究了海平面变化与地球自转的关系。实测资料的分析结果表明，在年限时间尺度上，日长变化与东太平洋赤道带区域的海平面变化成正相关，而与西太平洋区域的海平面变化成负相关。根据海平面变化具有位相超前的现象，证实海平面的变化可能对地球自转速率产生激发贡献。近30年的资料分析表明，太平洋的平均海平面正以每年1.8毫米的速率上升。通过本研究工作使我们认识到海平面变化的观测数据是深入革球自转研究的一种重要资料源。     

GPS应用于地球动力学研究的进展

介绍了GPS卫星系统的现代化以及IGS(International GPS Service)的最新研究成果；重点介绍了GPS技术在地球动力学研究中，包括国际地球参考架的建立与维护，固体地球形变和海平面变化的监测，科学卫星轨道的确定以及全球和中国地壳运动、地球定向参数的监测，GPS在大气研究和气象预报中的最新进展；评述了GPS技术目前存在的问题，包括与SLR测量之间存在的系统偏差、GPS技术本身可能存在的周年变化和GPS卫星天线相位中心的变化。     

地球的较差转动及其天文动力学效应

文中首先探讨了地球存在较差转动的可能性,证明了即使对于地球这样小的行星,其内部仍然可能存在较差转动。然后对地球较差转动规律及可能引起的三种地球动力学效应进行了分析;这三种地球动力学效应是：地球自转速率的近十年变化,黄赤交角的非摄动长期变化以及液核和固核所引起的近周日自由摆动及其对章动的影响。对这三种地球动力学效应的研究将有助于另一角度了解地球内部的结构及其运动形态。     

An Abridged Model of the Precession–Nutation of the Celestial Pole

Precise astrometric observations show that significant systematic differences of the order of 10 milliarcseconds (mas) exist between the observed position of the celestial pole in the International Celestial Reference Frame (ICRF) and the position determined using the International Astronomical Union (IAU) 1976 Precession (Lieske et al., 1977) and the IAU 1980 Nutation Theory (Seidelmann, 1982). The International Earth Rotation Service routinely publishes these 'celestial pole offsets', and the IERS Conventions (McCarthy, 1996) recommends a procedure to account for these errors. The IAU, at its General Assembly in 2000, adopted a new precession/nutation model (Mathews et al., 2002). This model, designated IAU2000A, which includes nearly 1400 terms, provides the direction of the celestial pole in the ICRF with an accuracy of ±0.1 mas. Users requiring accuracy no better than 1 mas, however, may not require the full model, particularly if computational time or storage are issues. Consequently, the IAU also adopted an abridged procedure designated IAU2000B to model the celestial pole motion with an accuracy that does not result in a difference greater than 1 mas with respect to that of the IAU2000A model. That IAU2000B model, presented here, is shown to have the required accuracy for a period of more than 50 years from 1995 to 2050.     

The Effect Of Zonal Tides On The DynamicalEllipticity Of The EarthAnd Its Influence On The Nutation

In this paper, the expressions of variations of the dynamical ellipticity and the principal moments of inertia due to the deformations produced by the zonal part of the tidal potential are obtained. Starting from these expressions, we have studied from equations related to Hamiltonian theory, their effects on the nutation and finally we have evaluated numerically such influences, with a level of truncation at 0.1 μas. Thus we have shown that some coefficients are quite large with respect to the usual accuracy of up-to-date observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

海洋角动量对地球自转变化的激发

介绍了海洋角动量模型的现状和发展,以及地球自转变化和海洋之间的关系的一些预研究成果．有关的预研究结果表明,海洋可能是地球自转变化的一个激发源,海洋和地球自转变化之间相互影响、相互作用．但两者之间的关系以及作用机制都有待深入研究。     

The Rotation of a Non-Rigid, Non-Symmetrical Earth II: Free Nutations and Dissipative Effects

The study of the rotation of a non-rigid, non-symmetrical Earth with a heterogeneous and stratified liquid core was recently accomplished by González and Getino (1997) through the Hamiltonian formalism. In this work that model is extended by including the effect of the dissipation arising from the mantle–core interaction due to the viscous and electromagnetic coupling. A canonical transformation to a new set of non-singular variables is performed, in order to avoid small divisors in the system of equations. Numerical estimations of the effect of the dissipation are given in form of tables and graphics, and the significance of this effect is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Responses of the Deformable Earth to Different Driving Forces

The spatial and temporal variations of the Earth deformation and the gravitational field are important both in the theoretical research and in the construction of geospatial database. The Earth deforms due to various mechanisms and the deformation further induces changes in the gravitational potential of the Earth, i.e. the deformation-induced additional potential or the Euler gravitational increment. Based on the theory of vector spherical harmonics, we discuss in this paper the Earth deformation and gravitational increment resulting from the tidal force, loading force and the stress of the Earth's surface. We write out the expression for the Euler gravitational potential increment and the relations between different Love numbers. These are all important points in the research on Earth deformation.     

Approximate General Solution Of The Two-Dimensional Duffing Dynamical System

This paper presents the approximate general solution of the triple well, double oscillator non-linear dynamical system. This system is non-integrable and the approximate general solution is calculated by application of the Last Geometric Theorem of Poincaré (Birkhoff, 1913, 1925). The original problem, known as the Duffing one, is a 1 degree of freedom system that, besides the conservative force component, includes dumping and external forcing terms (see details in the web site: http://www.uncwil.edu/people/hermanr/chaos/ted/chaos.html). The problem considered here is a 2 degree of freedom, autonomous and conservative one, without dumping, and of axisymmetric potential. The space of permissible motions is scanned for identification of all solutions re-entering after from one to nine oscillations and the precise families of periodic solutions are computed, including their stability parameter, covering all cases with periods T corresponding to 4osc/T. Seven sub-domains of the space of solutions were investigated in detail by zooming, an operation that proved the possibility to advance the accuracy of the approximate general solution to the level permitted by the integration routine. The approximation of the general solution, although impressive, provides clear evidence of the complexity of the problem and the need to proceed to larger period families. Nevertheless, it allows prediction of the areas where chaos and order regions in the Poincaré surfaces of section are to be expected. Examples of such surfaces of sections, as well as of types of closed solutions, are given. Two peculiar points of the space of solutions were identified as crossing, or source points from which infinite families of periodic solutions emanate. The morphology and stability of solutions of the problem are studied and discussed.     

形变地球对不同驱动力的响应

地球形变位移场和重力场的时空变化无论在基础理论研究,还是在地理空间信息建设中都具有重要的意义.地球在各种力学机制的作用下产生了形变,形变又导致地球引力位的变化,即形变附加位或Euler引力位增量.基于矢量球函数的基本理论,讨论了引潮力、负载力和地表应力对地球形变和引力位增量的影响,给出了均匀不可压缩地球模型的Euler引力位增量的具体表达式和Love数的理论关系.可为地球形变的理论研究提供参考和依据.     

The rate of granule ripple movement on Earth and Mars

The rate of movement for 3- and 10-cm-high granule ripples was documented in September of 2006 at Great Sand Dunes National Park and Preserve during a particularly strong wind event. Impact creep induced by saltating sand caused ∼24 granules min⁻¹ to cross each cm of crest length during wind that averaged ∼9 m s⁻¹ (at a height well above 1 m), which is substantially larger than the threshold for saltation of sand. Extension of this documented granule movement rate to Mars suggests that a 25-cm-high granule ripple should require from hundreds to thousands of Earth-years to move 1 cm under present atmospheric conditions.     

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time and six constants. If, under disturbance, we endow the “constants” with time dependence, the perturbed orbital or angular velocity will consist of a partial time derivative and a convective term that includes time derivatives of the “constants”. The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional dependence of the velocity on the time and “constants” stays unaltered under disturbance. “Constants” satisfying this constraint are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer elements are time-dependent even in the unperturbed setting, the role of “constants” is actually played by their initial values.) The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations render the elements nonosculating. In the theory of orbits, the planetary equations yield nonosculating elements when perturbations depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function [Efroimsky, M., Goldreich, P.: J. Math. Phys. 44, 5958–5977 (2003); Astron. Astrophys. 415, 1187–1199 (2004); Efroimsky, M.: Celest. Mech. Dyn. Astron. 91, 75–108 (2005); Ann. New York Acad. Sci. 1065, 346–374 (2006)]. It complicates both the Lagrange- and Delaunay-type planetary equations and makes the Delaunay equations noncanonical. In attitude dynamics, whenever a perturbation depends upon the angular velocity (like a switch to a noninertial frame), a mere amendment of the Hamiltonian makes the equations yield nonosculating Andoyer elements. To make them osculating, extra terms should be added to the equations (but then the equations will no longer be canonical). Calculations in nonosculating variables are mathematically valid, but their physical interpretation is not easy. Nonosculating orbital elements parameterise instantaneous conics not tangent to the orbit. (A nonosculating i may differ much from the real inclination of the orbit, given by the osculating i.) Nonosculating Andoyer elements correctly describe perturbed attitude, but their interconnection with the angular velocity is a nontrivial issue. The Kinoshita–Souchay theory tacitly employs nonosculating Andoyer elements. For this reason, even though the elements are introduced in a precessing frame, they nevertheless return the inertial velocity, not the velocity relative to the precessing frame. To amend the Kinoshita–Souchay theory, we derive the precessing-frame-related directional angles of the angular velocity relative to the precessing frame. The loss of osculation should not necessarily be considered a flaw of the Kinoshita–Souchay theory, because in some situations it is the inertial, not the relative, angular velocity that is measurable [Schreiber, K. U. et al.: J. Geophys. Res. 109, B06405 (2004); Petrov, L.: Astron. Astrophys. 467, 359–369 (2007)]. Under these circumstances, the Kinoshita–Souchay formulae for the angular velocity should be employed (as long as they are rightly identified as the formulae for the inertial angular velocity).