关于天球历书极的定义

本文讨论了1980 IAU章动理论中关于天球历书极的定义。由于液核地球具有近周日自由极移,所以不能认为天球历书极对于地固坐标系没有近周日运动。建议把天球历书极的定义改为: “参考极的选择使得这个极相对于空固坐标系没有自由章动,对于地固坐标系没有日月极移;即它是消除日月极移的地球角动量极。”     

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。     

VLBI基线定向的奥波策项变换矩阵

本文推算了甚长基线干涉仪基线定向的奥波策项变换矩阵,指出:(1)由于奥波策项变换矩阵可以预告,使用天球历书极将使基线定向的坐标变换模型比使用伍拉德极更简单;(2)如果用甚长基线干涉仪来求周日极移,则必须使用伍拉德极。     

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。     

天球和地球历书原点

国际天球参考系的使用、观测精度的提高和方法的改善要求采用与地球轨道运动无关的运动赤道上的起算点，Guinot提出的非旋转原点可作为这样一种选择。非旋转原点依赖于天球参考极。IAU决定从2003年起采用天球中间极作为天球参考极。非旋转原点在天球参考系的使用，可给出在天球中间极赤道上的天球历书原点，非旋转原点在地球参考系的使用，可给出在天球中间极赤道上的地球历书原点。回顾了非旋转原点的概念、以历书原点为参考的天球参考系和地球参考系的坐标变换，经出了在微角秒精度下天球参考极的坐标和历书原点的位置，讨论了采用历书原点对测定UT1的影响，指出当岁差章动模型、天极补偿、分点改正得到改善时，基于历书原点的UT1定义不需要更改，从而保证了UT1的连续。     

最新规范的参考系及有关问题

在简要阐明参考系、参考架及其历史重大进程的基础上,对几种重要的、最新规范的参考系/参考架(质心天球参考系和地心天球参考系、国际天球参考系、国际地球参考系、太阳系动力学参考系等)的定义、实现和特点作了评述和分析,并对最新规范中与参考系、参考架有关的某些新概念的定义和新模式的应用(自2003年开始贯彻),如:天球中介极(CIP)、天球历书原点(CEO)、地球历书原点(TEO)、地球自转角的新定义、岁差-章动新模式的应用,作了阐述和讨论。     

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。     

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。     

周年Z项的分析

本文用天津、北京、上海和武汉四个台站的观测资料计算了纬度变化中的周年Z项,分析了十几年中周年Z项的变化规律和稳定情况,并利用这些资料计算了主章动项、半年章动项和周年章动项的振幅,以期在提高地极坐标精度方面以及理论方面得出一些有益的结论。     

章动常数检测的一些问题

利用重新归算的ILS 1900—1978年的资料,对各种纲要组合计算了章动常数改正值。发现章动常数有一明显的变化趋势。分析了章动常数误差与用连锁法计算的赤纬、自行改正之间的关系,并考虑了改正这种影响的方法。推导了观测资料的精度、长度,Ω的位相与计算的章动常数的精度的关系。     

Kinematical modeling of the Earth rotation,focusing on the Oppolzer terms in a rigid Earth and the Oppolzer-like terms in an elastic Earth

Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation (in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the motion of the outer bodies is taken into account.     

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.     

On the effect of the mantle elasticity on the earth's rotation

Starting from the Hamiltonian model for a solid Earth with an elastic mantle previously developped by the authors, analytical expressions are derived which give the nutation series corresponding to the plane perpendicular to the angular momentum vector, to the plane perpendicular to the rotational axis and to the equator of figure, as well as the series that give the polar motion. The effects of the different perturbations — solid Earth, centrifugal and tidal potentials — are calculated separately. The corrections due to the elasticity of the mantle, which mostly correspond to the Oppolzer terms, are calculated with an accuracy of 10^–6 arc sec., given that the intrinsic observational accuracy has reached 0.01 mas.     

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.     

A precise modeling of Eros 433 rotation

Thanks to the recent data obtained from the NEAR space probe, we calculate in this paper, with a precision never reached so far for an asteroid, the precession and the nutation of Eros 433. In a preliminary step, we show that Eros obliquity has a remarkable value of 89.0° which tends to align its figure axis along the orbital plane. This very specific obliquity has some consequences on the motion of the axis of figure: one is the very small amplitude of the precession in longitude, for which we get the value . Moreover, we calculate Eros nutation for the figure axis due to the Sun, after developing the perturbing potential at the 4th order of the eccentricity. We show that the figure axis undergoes very large oscillations in the direction perpendicular to Eros orbital plane, due to the nutation in obliquity. Peak to peak, these oscillations reach 55″, which is far larger than the amplitudes of the nutations of the Earth due to the Sun (of the order of 2″). Moreover, we give the analytical developments of Δψ and Δε, both for the axis of angular momentum, and the axis of figure.     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

Numerical derivation of forced nutation terms for a rigid earth

We compare the results of a numerical integration of the Euler equations for a rigid Earth model covering a time span of 250 years with Kinoshita's theory for the forced nutations and with a new nutation series by Kinoshita and Souchay. We also present numerical corrections to some of the analytically derived nutation terms.     

Lander radioscience for obtaining the rotation and orientation of Mars

The paper presents the concept, the objectives, the approach used, and the expected performances and accuracies of a radioscience experiment based on a radio link between the Earth and the surface of Mars. This experiment involves radioscience equipment installed on a lander at the surface of Mars. The experiment with the generic name lander radioscience (LaRa) consists of an X-band transponder that has been designed to obtain, over at least one Martian year, two-way Doppler measurements from the radio link between the ExoMars lander and the Earth (ExoMars is an ESA mission to Mars due to launch in 2013). These Doppler measurements will be used to obtain Mars’ orientation in space and rotation (precession and nutations, and length-of-day variations). More specifically, the relative position of the lander on the surface of Mars with respect to the Earth ground stations allows reconstructing Mars’ time varying orientation and rotation in space.Precession will be determined with an accuracy better by a factor of 4 (better than the 0.1% level) with respect to the present-day accuracy after only a few months at the Martian surface. This precession determination will, in turn, improve the determination of the moment of inertia of the whole planet (mantle plus core) and the radius of the core: for a specific interior composition or even for a range of possible compositions, the core radius is expected to be determined with a precision decreasing to a few tens of kilometers.A fairly precise measurement of variations in the orientation of Mars’ spin axis will enable, in addition to the determination of the moment of inertia of the core, an even better determination of the size of the core via the core resonance in the nutation amplitudes. When the core is liquid, the free core nutation (FCN) resonance induces a change in the nutation amplitudes, with respect to their values for a solid planet, at the percent level in the large semi-annual prograde nutation amplitude and even more (a few percent, a few tens of percent or more, depending on the FCN period) for the retrograde ter-annual nutation amplitude. The resonance amplification depends on the size, moment of inertia, and flattening of the core. For a large core, the amplification can be very large, ensuring the detection of the FCN, and determination of the core moment of inertia.The measurement of variations in Mars’ rotation also determines variations of the angular momentum due to seasonal mass transfer between the atmosphere and ice caps. Observations even for a short period of 180 days at the surface of Mars will decrease the uncertainty by a factor of two with respect to the present knowledge of these quantities (at the 10% level).The ultimate objectives of the proposed experiment are to obtain information on Mars’ interior and on the sublimation/condensation of CO₂ in Mars’ atmosphere. Improved knowledge of the interior will help us to better understand the formation and evolution of Mars. Improved knowledge of the CO₂ sublimation/condensation cycle will enable better understanding of the circulation and dynamics of Mars’ atmosphere.