国内天文地球动力学中的潮汐研究

简要说明了天文地球动力学范畴内所研究的潮汐现象，包括由日月引潮力引起的固体潮、海洋潮、大气潮和由于地球自转轴的极移引起的极潮，以及这些潮汐对地球自转和地球自转的测量产生的效应。重点阐述中国天文学界在这一领域里的研究成果。这些研究涉及潮汐影响地球自转的机制，也就是各种潮汐效应与极移、自转速率变化和章动的关系，包括构建这类关系的理论模型，分析潮汐对它们的影响，利用中国古代丰富的天象记录计算地球自转的长期减慢，计算弹性或滞弹地球的洛夫数，依据某一地球模型计算潮汐效应或章动序列等等。研究也涉及在测量地球自转参数的不同技术中各种潮汐效应对测量结果产生的影响及其改正，并涉及与潮汐有关的观测方法的优化和数据处理过程的改进。最后介绍了中国学者所发现的脉冲星的周期和周期变率测量中的潮汐效应，尽管它们的量级甚微，但不容忽视。     

Tidal-friction theory of the Earth-Moon system

The standard discussion of tidal friction in the Earth-Moon system has been that given by Jeffreys in successive editions ofThe Earth over the past several decades. It is herein shown to contain several erros vitiating its results. The dynamical equation utilised for finding the rate of change of angular velocity of the Earth fails to take account of the fact that the moment of inertia of the Earth may be changing with time, and all subsequent equations which depend on this are incorrect as a result. Simple equations have been left unsolved that ought to have been solved, and the alleged numerical conclusions in no way follow from the values set down initially for the observed apparent secular accelerations of the Moon and Sun.The revised dynamical equations are shown to enable the lunar and solar tidal couples to conform to theory, and may imply that the moment of inertia of the Earth is decreasing at a non-negligible rate. Recognition of this is the key to the whole problem. The only available hypothesis providing adequate contraction is that following from the phase-change theory of the nature of the terrestrial core, and the value of the rate of decrease of moment of inertia calculated from this is in close agreement with that implied by modern improved values of the secular accelerations.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Comparison of irregular variations in the Earth’s rotation rate and parameters of geophysical and atmospheric processes with events on the sun

A study of the Earth’s rotation in space reveals a complex pattern of variations in its orientation, the excitation mechanisms of these variations, and their manifestations in various natural processes. The Earth’s rotation rate is not constant but exhibits complex fluctuations that account for some fraction of 10⁸ (corresponding to variations of several milliseconds (ms) in the length of the day). These variations span a wide spectrum of time scales, from hours to centuries or longer, reflecting the fact that they are produced by a wide variety of geophysical and astronomical processes. We discuss the results of our statistical comparison of long series of observations to reveal the most coherent variations. The spectral composition of the experimental time series has been determined using modified periodogram and single-channel autoregression methods. A comparative analysis has been performed by a two-channel autoregression spectral estimation method. The results of our comparison of the time series suggest that the fluctuations with periods of about 73 years are highly coherent.     

On the apparent secular accelerations of the Moon and the Sun

The discussion of tidal friction in the Earth-Moon system given in successive editions ofThe Earth by Jeffreys is shown to contain a serious dynamical error. When the treatment is corrected, it shows that the moment of inertia of the Earth must be changing. The apparent secular accelerations of the Moon and Sun require a diminishing moment of inertia, and the rate is in agreement with the phase-change hypothesis for the nature of the core.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Determination of secular polar motion from astronomical observations: Priority of Aleksandr Orlov

The aim of this article is to draw attention to the priority of the well-known astronomer and geophysicist, member of the Academy of Sciences of Ukraine A.Ya. Orlov (1880–1954) in the determination of the following parameters describing the secular motion of the earth’s poles: speed (4 mas/year) and direction (69° west). These results (1954) are based on the astronomical observations from 1900 to 1950 with zenith telescopes at international latitude stations. Orlov is well known in the world astronomical community as the founder of the Poltava Gravimetric Observatory, the Main Astronomical Observatory, and the national research school of global geodynamics. However, his pioneering work on secular polar motion is little known worldwide. At present, Orlov’s estimates for secular polar motion have been verified by century-long observations (1900–2012) obtained with different telescopes at many observatories worldwide and by different, both astronomical and space-based, methods (LLS, VLBI, GNSS, etc.).     

Very small bodies in the solar system: The Earth's atmosphere as detector

Particles of mass less than about 1 gm are a minor fraction of the total matter impinging on the Earth averaged over millennia time scales. However, these particles dominate during a single particular year and produce the most obvious evidence of incoming extra-terrestrial matter in the form of ablation trails in the atmosphere which are visible at night as meteors.Observations of meteors give astronomical information on the composition, structure, and cometary associations of the particles. The composition is deduced from optical spectra of meteors, whilst telescopic studies of the trails during formation give information on the physical structure of the particles. Any cometary associations are deduced from measurement of meteor orbits determined photographically, using television, or by radar.Meteors occur in the atmosphere at heights from about 70 to 120 km. Optical observations are restricted to night-time and usually under conditions of low moonlight. A typical television based detector can record +8^M meteors with a sporadic rate of 15–20 per hour and velocities accurate to about 3%. The luminosity of the trail is strongly dependent on the velocity of the meteoroid (to about the third power).Radar observations of meteors are unrestricted by weather or time of day, and can readily detect meteors at least two orders of magnitude smaller in mass than those detectable optically. Again the observations are heavily biased toward the higher velocities as the electron line density varies approximately asV ^3.5. However, the higher the velocity of the meteoroid the greater the height of the meteor trail, and the reduced probability of radar detection due to rapid diffusion of the trail. Thus radar observations tend to select meteors in the intermediate velocity range 30–40 km s^–1.     

On the evolution of the lunar orbit

It is generally accepted that the Earth-Moon separation is at present increasing due to tidal dissipation. Values for the corresponding lunar deceleration and the related slowing of the Earth's rotation are obtained from astronomical observations and by studies of ancient eclipses. Extrapolation of these values leads to a close approach of the Earth and Moon 1–3 b.y. BP. However, justification for such an extrapolation is required. It has been hypothesized that periodicities in the Precambrian stromatolites can be used to determine the number of solar days in a lunar month prior to 500 m.y. BP. These data combined with dynamic constraints on the number of solar days in a lunar month indicate a close approach of the Earth and Moon at 2.85 ± 0.25 b.y. BP. It is suggested that the mare volcanism on the Moon and high-temperature Archean volcanism on the Earth prior to this date were caused by tidal heating. It is also suggested that the strong tidal heating during a close approach could have contributed to the formation of the first living organisms.     

Hypothesis of variable g and the secular accelerations of the Sun and the Moon

It is known that the observed secular accelerations of the Sun and Moon are not consistent with the tidal interactions of the Earth with the Sun and Moon. Following Dicke, the hypothesis of variable constant of gravity is adopted and expressions for the accelerations are derived. It is shown that if the theoretical ratio of the acceleration is equated the observed one, a unique value for —/G can be calculated. Adopting the accelerations obtained by Fotheringham, Newton, Muller and Stephenson, and Stephenson, it is found that — /G ranges from 1.4 × 10^–11 to 3.3 × 10^–11 yr^–1. This estimate is consistent with the one based upon the comparison of the lunar accelerations measured with respect to atomic and ephemis times.     

On the planetary acceleration and the rotation of the Earth

We have developed a cosmological model for the Earth rotation and planetary acceleration that gives a good account (data) of the Earth astronomical parameters. These data can be compared with the ones obtained using space-base telescopes. The expansion of the universe has shown to have an impact on the rotation of planets, and in particular, the Earth. The expansion of the universe causes an acceleration that is exhibited by all planets.     

Secular Variation of Earth's Rotation: Inferred from the Chinese Ancient Shoushi Calendar (Ad 1281)

The Shoushi calendar (epoch of AD 1281, Yuan dynasty) is famous and very accurate in ancient China. It has evolved perfect and complete theoretical models of solar system objects, such as solar and lunar motions during that period. Almost every part of this work corresponds to the modern astronomical yearbooks. Compiled by native Chinese astronomers, it sums up through their studies many real observing results. The mathematical methods were adopted in this calendar before the foundation of Newton’s mechanical system. It is presented in this paper that the indirect system is also very useful to recover the real observing historical material. By selecting these calculating results, we may sum up the integral data of the secular variation of the Earth’s rotation from 1000 BC to AD 1500. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the accelerations of the Moon and Sun,the constant of gravitation,and the origin of mountains

In a previous paper Lyttleton (1976) has shown that the apparent secular accelerations of the Sun and Moon, as given by de Sitter, can be largely explained if the Earth is contracting at the rate required by the phase-change hypothesis for the nature of the core. More reliable values for these accelerations have since become available which warrant a redetermination of the various effects concerned on the basis of constantG, and this is first carried out in the present paper. The lunar tidal couple, which is the same whetherG is changing or not, is found to be (4.74±0.38)×10²³ cgs, about three-quarters that yielded by the de Sitter values, while within the theory the Moon would take correspondingly longer to reach close proximity to the Earth at about 1.5×10⁹ years ago.The more accurate values of the accelerations enable examination to be made of the effects that a decreasingG would have, and it is shown that a valueG/G=–3×10^–11 yr^–1 can be weakly satisfied compared with the close agreement found on the basis of constantG, while a value as large numerically asG/G=–6×10^–11 yr^–1 seems to be definitely ruled out. On the iron-core model, an intrinsic positive component of acceleration of the angular velocity cannot be reconciled at all with the secular accelerations even for constantG, and far less so ifG is decreasing at a rate suggested by any recent cosmological theory.ItG=0, the amount of contraction available for mountain-building would correspond to a reduction of surface area of about 49×10⁶ km² and a volume to be redistributed of 160×10⁹ km³ if the time of collapse were 2.5×10⁹ years ago. For earlier times, the values are only slightly reduced. IfG/G=–3×10^–11 yr^–1, the corresponding values are 44×10⁶ km² and 138×10⁹ km³ for collapse at –2.5×10⁹ yr, and not importantly smaller at 38×10⁶ km² and 122×10⁹ km³ for collapse at –4.5×10⁹ yr. Any of these values would suffice to account in order of magnitude for all the eras of mountain-building. An intense brief period of mountain-building on an immense scale would result from the Ramsey-collapse at whatever time past it may have occurred.     

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。     

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。     

Relation of a contracting earth to the apparent accelerations of the sun and moon

The tidal theory of the evolution of the lunar orbit has remained inconsistent with the observational values of the apparent secular accelerations of the Sun and Moon since it was first developed by Jeffreys in 1920. Allowance for a changing moment of inertia of the Earth enables the discrepancy to be completely removed if a decrease is occurring at a rate of just about the amount already required by the phase-change theory of the nature of the terrestrial core. The agreement of the resulting theory with the latest determinations of the lunar acceleration increases confidence in the phase-change hypothesis. On the other hand the theory renders it most unlikely that a changing constant of gravitation will prove necessary to account for the observations. On the present theory of itself the Moon would have been extremely close to the Earth only about 10⁹ yr ago which suggests that some additional process may at times have influenced the lunar orbit.     

An Interpretation of the Non-Tidal Secular Variation in the Earth Rotation: the Interaction Between the Solar Wind and the Earth's Magnetosphere

The long period variation of the earth rotation is generally explained by the tidal friction. The tidal friction, however, is not the only source to influence the earth rotation in long term. In this paper, by means of the interaction between the solar wind and the magnetosphere of the earth, the additional magnetic pressure will exist in the magnetic tail due to the crowding and sparseness of the magnetic lines in the consideration of the earth rotation, which could be considered as a source of effecting the long term variation of the earth rotation. It is shown in this paper that this mechanism can produce angular deceleration of the Earth rotation in the magnitude of ω = −1.7 × 10-22 s-2. This result might be a prompt to search for other sources in the secular variation of the rate of the Earth rotation variation further in order to regulate the observed result with the theoretical one. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the negative correlation between solar activity and solar rotation rate

An increase in solar activity is shown to be accompanied by a decrease in solar rotation rate. This effect has been established from various indices; it manifests itself as cyclic and secular variations in the global magnetic field, in the observations of the magnetic field of the Sun as a star, and in the observations of the solar corona. Some possible explanations of this effect are discussed.     

YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam's Approximation

The rotation states of small asteroids and meteoroids are determined primarily by their collisions, gravitational torques due to the Sun and planets (in the case of close encounters), and internal dissipative effects (that relax the free-precession energy toward the fundamental state of principal-axis rotation). Rubincam has recently pointed out that thermal reemission on irregular-shaped bodies also results in a torque that may secularly change both the rotation rate and the orientation of the spin axis (the so-called YORP effect). Here we pursue investigation of this effect. Keeping the zero thermal-relaxation approximation of Rubincam and the assumption of the principal-axis rotation, we study the YORP effect both for precisely determined shapes of near-Earth asteroids and also for a large statistical sample of automatically generated shapes by the Gaussian-sphere technique of Muinonen. We find that the asymptotic state of the YORP evolution is characterized by an arbitrary value of the obliquity, with higher but nearly equal likelihood of 0°/180° and 90° states. At the adopted approximation, the most typical feature of this end state of the YORP evolution is secular deceleration of the rotation rate, which means that at some instant collisions will randomize the rotation state. In a minority of cases, the final state of the obliquity evolution leads to a permanent acceleration of the body's rotation, eventually resulting in rotational fission. The YORP-induced slow evolution may also play an important role in driving the rotation state of small asteroids toward the resonances between the forced precession due to the solar torque and perturbations of the orbital node and inclination. We find that for small Themis asteroids these resonances are isolated in the relevant range of frequencies, and the YORP evolving rotation may be either temporarily captured or rapidly jump across these resonances. In contrast, the possible values of the forced precession for small Flora asteroids may be resonant with clustered, nonisolated lines of the orbital perturbation. The individual rotation histories of small Flora asteroids may be thus very complicated and basically unpredictable. We comment on possible astronomical consequences of these results.     

引力常数变化对地球自转长期变化的影响

探讨和估计了各种引力常数变化理论对地球角速度和日长变化的影响。各种引力常数变化理论包括了引力常数G随时间、空间以及速度变化等几个方面的影响。另外也估计了对地球自转角速度和日长变化产生的效应。其中有些研究对探讨地球自转变化也有启发意义。     

Exospheric zonal winds between 540 and 620 km from the orbit of Explorer 24

Data on the variation of the orbital inclination of the balloon satellite Explorer 24 (1964-76A) from 1964 to 1968 have been used to determine zonal winds between 540 and 620 km. In this height region the effect of zonal winds on the orbital inclination may become very small compared to other perturbations like accelerations due to the geopotential, lunisolar gravitation and the solar radiation pressure. It is demonstrated especially that the solar radiation pressure may become the most significant force changing the orbital inclination. The diurnal mean zonal winds derived from Explorer 24 point to an exospheric rotation rate which is about 6–10% less than the rotation rate of the Earth in the analyzed height region. Since the possible errors of the data analysis are of a similar order of magnitude, it can not be excluded that the exosphere corotates with the Earth. Furthermore, a local time dependence of the zonal winds could be detected. The diurnal varitation of the zonal wind is shown to be in good agreement with the theoretical model of Blum and Harris. Our results are discussed and compared with all previous investigations of orbital inclination changes of satellites above 350 km.     

Comparison Between Halo cme Expansion Speeds Observed on the Sun,the Related Shock Transit Speeds to Earth and Corresponding Ejecta Speeds at 1 au

We have compared characteristics of 38 halo coronal mass ejections observed on the Sun by the Large Angle and Spectrometric Coronagraph onboard SOHO with their corresponding counterparts observed near Earth by the magnetic field and plasma instruments onboard the ACE, WIND and SOHO satellites, in the period from January 1997 to April 2001. We only have selected events that have some associated interplanetary ejecta structure at 1 AU and we have compared the lateral expansion speeds of these halo CMEs and the corresponding ejecta speeds near Earth. We found that there is a high correlation between these two speeds. The results are very similar to the study done by Lindsay et al. (1999) using observations made by Solwind and SMM coronagraphs, and Helios-1 and PVO plasma and interplanetary field data from the period of 1979 to 1988. Also, we reviewed the relation between the CME-related shock transit speed to Earth and the ejecta speeds near Earth. This kind of relation is very important to estimate ejecta speeds of events for which no interplanetary observations are available.