Adiabatic pulsations and convective instability of uniformly rotating gaseous masses

Third-order virial equations are used to investigate the oscillations and the stability of the sequence of uniformly rotating compressible Maclaurin spheroids, referred to in an inertial frame. It is seen that in the case of the oscillations belonging to the third harmonics, the frequency spectrum of the Maclaurin sequence referred to in an inertial frame is distinct from the spectrum of the Maclaurin sequence considered stationary in a rotating frame of reference. Considering the Maclaurin sequence in an inertial frame, the neutral point and the point of onset of dynamical instability (corresponding to the third harmonic deformations) are isolated. They occur for the values of the eccentricitye=0.73113 and 0.96696, respectively. The neutral point is the analogue of the first point of bifurcation along the Dedekind sequence of ellipsoids and is distinct from the neutral point (e=0.89926) along the Maclaurin sequence considered stationary in a rotating frame; this latter point is the analogue of the first point of bifurcation along the Jacobian sequence. Both the Maclaurin sequences in an inertial frame and in a rotating frame become, however, dynamically unstable for the same eccentricitye=0.96696.     

Equations of general relativistic radiation hydrodynamics in Kerr space–time

Equations of fully general relativistic radiation hydrodynamics in Kerr space–time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer–Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF.     

On the adiabatic pulsations of uniformly rotating bodies

The problem of the oscillations and stability of compressible Maclaurin spheroids is reconsidered, on the basis of the third-order virial equations, in an arbitrarily rotating frame of reference. In contrast with the work of Kochhar and Trehan (1974), it is found that the frequencies evaluated in a rotating frame and those evaluated in an inertial frame are related to one another in a very simple way. Numerical calculations made for a wide range of the adiabatic exponent further clarify the effect of compressibility on the natural frequencies.     

Rotational dynamics of celestial bodies

In this paper the ‘class of near homoaxial rotations’ is defined, being suitable for treatment of problems of nonuniform rotation of stars. This class is represented by a proper form of the so-called ‘velocity tensor’, the latter describing efficiently the motion of a deformable finite material continuum in the common frame. The ‘class of particular near homoaxial rotations’ is then defined, characterized by simple transformation equations of the velocity tensor in two noninertial frames; namely, in a ‘frame rotating uniformly’ relative to the common frame, and in a ‘frame rotating nonuniformly’ relative to it. A sufficient condition is also derived so that a near homoaxial rotation be reducible to a particular one. ‘Preferred frames’ are then defined in the sense that they preserve a near homoaxial rotation in its class when referring thismotion; that is, such frames keep invariant the intertial class of the motion. Finally, a method is proposed for constructing a nonuniformly rotating preferred frame, to which a near homoaxial rotation is referred simply as ‘radial distortion’.     

Inertial systems-definitions and realizations

A frame of reference is defined asinertial if the coordinates of bodies, predicted with respect to it on the basis of some mechanical principles, agree with those actually observed. It is pointed out that within the framework of Newtonian mechanics the concept of an inertial frame of reference is global, but within the framework of general relativity only local. The relativistic local inertial frame of the Solar System moves with respect to the Newtonian global frame by the amount of geodetic precession. In all rigor, the concept of a globally privileged inertial system has been rendered meaningless by general relativity, even though the concept of an inertial reference frame remains useful in contemporary celestial mechanics. It is further pointed out that none of the practically determined approximations to an inertial frame of reference (e.g., the dynamical reference frame of celestial mechanics, the FK5) must be regarded as adefinition of an inertial system itself.     

Superluminal Kinematics in the Milne Universe: Causality in the Cosmic Time Order

The causality of superluminal signal transfer in the galaxy background is scrutinized. The cosmic time of the comoving galaxy frame determines a distinguished time order for events connected by superluminal signals. Every observer can relate his rest frame to the galaxy frame, and compare so the time order of events in his proper time to the cosmic time order. In this way all observers arrive at identical conclusions on the causality of events connected by superluminal signals. The energy of tachyons (superluminal particles) is defined in the comoving galaxy frame analogous to the energy of subluminal particles. It is positive in the galaxy frame and bounded from below in the rest frames of geodesically moving observers, so that particle-tachyon interactions can be based on energy-momentum conservation. We study tachyons in a Robertson-Walker cosmology with linear expansion factor and open, negatively curved 3-space (Milne universe). This cosmology admits globally geodesic rest frames for uniformly moving observers, synchronized by Lorentz boosts. In this context we show that no signals can be sent into the past of observers. If an observer emits a tachyonic signal, then the response of a second observer can never reach him prior to the emission, i.e., no predetermination can occur. The proof is based on the positivity of tachyonic energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Partial redistribution effects on line polarization in the presence of velocity fields

Velocity fields in line formation regions strongly affect the line polarization. The conventionally used observer's frame method of solving the polarized transfer equation becomes expensive and inaccurate for partial redistribution problems, when large amplitude velocity fields have to be considered in the observer's frame. An alternative method of solution is the comoving frame method. Partial redistribution problems are solved using comoving frame formalism for line polarization caused by resonance scattering.     

天球参考系实现中的问题评述

本文评述了在建立历表参考架和恒星参考架过程中所面临的问题和困难，回顾了建立河外射电天球参考架的发展历史，并介绍了其目前状况，讨论了河外射电天球参考架在与其他天球参考架连接过程中所遇到的问题及其可能的解决途径。     

The Copernican principle in compact space–times

Copernicus realized that we are not at the centre of the Universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the Universe, some galaxy could be. A finite universe also picks out a preferred frame: the frame in which the universe is smallest. Although we are not likely to be at the centre of the Universe, we must live in the preferred frame (if we are at rest with respect to the cosmological expansion). We show that the preferred topological frame must also be the comoving frame in a homogeneous and isotropic cosmological space–time. Some implications of topologically identifying time are also discussed.     

A method for spherical harmonic analysis of Compton – Getting corrected 3-d energetic particle distributions

A method is described whereby a particle distribution measured by a number of telescopes (four in this application), observing the whole sky, mounted upon a spinning spacecraft, can be resolved into a set of spherical harmonics. The coefficients of the expansion are used to estimate the anisotropy of the particles and components of the anisotropy in different frames of reference (e.g., solar wind frame, RTN frame, spacecraft frame, etc.) for specific energy channels. For the transformation of the distribution function between frames of reference moving each other, the respective Compton–Getting correction is performed by a new geometrical approach. The respective energy change is also evaluated.     

相对论喷束模型中表现速度计算的修正

在相对论喷束模型中，假设源的核在观测者静止坐标系中不动的前提下，推出了现在已得到广泛承认和采用的计算相对论等离子团横向视速度的公式．随着观测精度的提高，对核固定不动的假设提出了怀疑，认为有必要重新估价表现横向速度公式的正确性，并在更普遍的框架下，找出该公式的修正形式．本文试图对几种根据目前对射电源一般结构认识提出的模型，初步探讨这种修正的可行性．     

研制低纬子午环初衷的沿革

介绍了在低纬子午环研制过程中，如何跟踪国内外测量方法和科学技术的发展，调整该仪器的主要课题目标：开始时仅计划在低纬度地区进行天体位置的绝对测定，改善基本星表系统；在１ｍ望远镜试验ＣＣＤ底片重迭法成功后，打算把该仪器绝对测定的恒星位置与河外天体联系起来，间接地建立准惯性天球参考架；当国外传统子午环配备ＣＣＤ测微器作相对测量后，提出了在该仪器上配备ＣＣＤ测微器作绝对测定的方法，用其观测数据直接建立实用的准惯性天球参考架，并为太阳系和银河系研究提供有用数据的总体目标。     

The significance of the Hansen Ideal space frame

Known and unknown properties of Hansen Ideal coordinates are summarized. It is shown that the ideal space frame is a general and necessary component of basic celestial mechanics and astrodynamics, as well as of any theory of motion. A typical consequence is the intimate correlation of the Hansen frame with the Lagrange constraint within the method of the variation of the parameters. The use of observations in the ideal frame may allow conclusions on the intergalactic fundamental coordinate system (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

近地卫星运动的坐标系附加摄动在拟平均根数法中的处理

在常用的历元地心天球坐标系中研究和处理近地卫星的轨道问题,就必须考虑由于地球赤道面摆动所引起的坐标系附加摄动,正因为如此,给实际工作带来一些麻烦.关于这一问题,曾提出了一种针对瞬根数和平根数之间的转换(仅与坐标系附加摄动的短周期项有关)的解决途径,但并未涉及采用分析法进行轨道外推的有关问题(这与坐标系附加摄动的长期和长周期项有关),这对处理近地卫星的轨道问题而言显然是不完整的.这里结合拟平均根数法进一步改进原提出的方法,较完善地解决这一坐标系附加摄动的计算问题.在此前提下,对于卫星定轨和预报及其相关工作,无论是采用数值法还是分析法,均可采用同一坐标系,即历元(目前是J2000.0)地心天球坐标系.     

ICRF与Gaia-CRF参考架特性分析

天体测量学是天文学中最古老的分支之一, 它是天文学的基础, 对天体物理学和大地测量学的许多方面至关重要.天体测量学的核心任务之一就是建立一个高精度天文参考系, 以便利用这样的惯性参照系来描述天体的位置和运动、研究银河系的运动学特征及对同一天体在不同波段的对应体进行位置认证和比较.当前的天文参考系是参照银河系外天体(主要是活动星系核)的位置来定义的, 称为国际天球参考系(ICRS).在实测上, 与之相对应的基本星表为国际天球参考架(ICRF), 它由甚长基线干涉测量(VLBI)技术在S/X、K和X/Ka波段的观测资料解算而得, 位置精度达到数十微角秒($\mathrm{\mu as}$)水平.另一方面, Gaia卫星的观测也将在光学波段建立类似精度的光学参考架(Gaia-CRF).ICRF与Gaia-CRF的连接成为天体测量领域需要解决的重大问题之一, 这要求对ICRF与Gaia-CRF参考架特性进行细致深入的分析. 首先, 分析了ICRF的整体特性.VLBI星表的内部符合精度估计值在$\mathrm{10\mu as}$和$\mathrm{40\mu as}$之间, 依赖于射电源的观测次数.这一结果一方面验证了ICRF3星表给出的位置噪声水平, 也说明了VLBI技术在天体测量方面的潜力.利用Gaia的河外源位置为参考, 分析了历代ICRF星表的外部符合精度, 指出ICRF3 X/Ka波段参考架存在约$\mathrm{200\mu as}$的系统误差.最后, 发明了一种评估射电源全天分布均匀性的量化指标并改进了ICRF定义源筛选策略, 结果表明相较于ICRF2而言, 这一方法能将ICRF轴指向稳定性提高2至3倍.这些工作很好地解释并补充了国际上ICRF3工作组的相关结果. 其次, 研究Gaia-CRF的参考架性质.使用了相对于依巴谷参考架的全局旋转和结合银河系动力学分析两种方法来评估Gaia-CRF1的惯性水平, 指出Gaia-CRF1可能存在约$\mathrm{0.3mas\cdot yr^{-1}}$的剩余旋转.对于Gaia-CRF2, 研究了其系统精度与河外源样本极限星等的依赖关系, 发现Gaia-CRF2的整体精度几乎不受星等差的影响.这一结果可作为未来ICRF与Gaia-CRF连接源选择的参考. 活动星系核的光学-射电位置差是影响参考架连接精度的重要因素之一.本文首次将光学-射电位置差研究延伸到K和Ka波段, 并研究其与河外源性质参数的相关性, 发现: 光学-射电位置差与星等的相关性是由于星等差而非真实的物理原因造成的, 因此在前人工作中被忽略的暗源也有可能作为ICRF与Gaia-CRF连接源.此外, 本文提出了一种新的参考架连接方法, 即在Gaia-CRF2框架下重新处理VLBI的历史观测资料.先期结果发现使用Gaia-CRF2来替代ICRF3尚不足以显著提高VLBI产品的精度, 但未来在Gaia-CRF参考架精度进一步提高后, 此方法仍值得进一步检验. 本文的研究, 一方面指出了ICRF与Gaia-CRF参考架中可能存在的种种问题, 另一方面也为将来光学与射电参考架连接提供了第一手的参考资料.     

The asteroid ephemerides program at the U.S. Naval Observatory

The U.S. Naval Observatory has begun a program of ephemeris improvement and reference frame determination from the main belt asteroids. The program is, currently, starting out with a limited set of observations of the larger asteroids to determine the equator and equinox corrections for the USNO W1J00 transit circle observations catalog, and, if possible, improve the orbits of these asteroids based on this limited set of observations. For this project, transit circle observations of the Sun and the planets Mercury through Jupiter, are also being used to determine the equator, equinox, and ephemeris corrections, the next goal is to improve the orbits of the larger asteroids in the optical reference frame using observation series that cover a much longer period of time. This will allow the exploration of the differences between the dynamical reference frame based on radar observations of main belt asteroids and its relation with the optical reference frame. Other goals include the exploration of the mass distribution in the main asteroid belt from high precision observations, and the effect of this mass on the ephemerides of the major planets.     

The relativistic equations of motion for a satellite in orbit about a finite-size,rotating Earth

The relativistic equations of motion are derived for N self-gravitating, rotating finite bodies. These equations are then applied to the near-Earth satellite orbit determination problem. The apparent change of the shape of the Earth from the Earth centered frame to the Solar System barycentric frame changes the value of the Newtonian potential term in the metric. This in turn leads to a simplification of the equations of motion in the barycentric frame.     

空间VLBI与天文地球动力学

介绍了空间VLBI的精密定轨及其在天文地球动力学应用研究中的最新进展．指出因为空间VLBI的时延和时延率观测量同时涉及到射电参考系、动力学参考系和地固参考系,所以特别适合于参考系的直接连接工作．对为评价参考系连接的精度而发展的协方差分析理论也作了介绍,还分析了将时延和时延率资料用于精密定轨时遇到的困难及其解决办法．     

The Existence and Stability of Families of Displacement Two-Body Orbits

The two-body problem is considered with an additional thrust induced acceleration. Stationary solutions are obtained to this problem in a rotating frame of reference which generates families of displaced circular orbits when viewed from an internal frame of reference. The existence and stability of these orbits is considered along with applications such as in-situ observations of Saturn's ring system and spacecraft proximity operations. This revised version was published online in July 2006 with corrections to the Cover Date.