相对论天体力学和后牛顿运动方程

叙述了与Astrod工程有关的相对论天体力学基础内容。包括相对论天体力学、广义相对论基本原理、PPN方法体系、PPN多体问题、PPN二体问题。高阶PN二体问题等     

视超光速运动的相对论超光速模型

从相对论出发，在视超光速源质心相对于观测者静止的条件下，推导出两个向相反方向运动的视超光速子源之间的视速度方程，这一方程包含了相对论射束模型的表现横向速度公式，且对高、低速不同条件均为适用。     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

On Spinor Equations of Motion and their “Possible Integrals”

The motion of one point mass of the classical mechanics is treated by means of the relativistic spinor regularization (KUSTAANHEIMO 1975). Most general spinor equations of motion (2.9)‒(2.10)and the differential equations(3.16)‒(3.25)for the “possible integrals” (3.2)‒(3.11)of these quations of motion are deduced. If the force is a superposition of a conservative central force and of another force perpendicular to radius vector and velocity (Chapter 4, Case D), then the theory yields scalar and spinor integrals (4.7), (4.10)‒(4.12), (4.14)‒(4.15), (4.17), (4.28) that enable a parametric representation of the orbit by quadratures, as soon as one solution of a RICCATI differential equation (4.33) has been found.     

Relativistic fireworks

We have studied a model of relativistic fireworks. In this model it is assumed that a series of explosions occur. In each explosion the fragments fly apart in arbitrary directions with a given velocity which is a parameter in the model.We have succeeded in obtaining an exact expression for the distribution of fragments in velocity space aftern explosions.We present an exact solution also in the limiting case of small velocity steps where the process turns into a diffusion in velocity space.The development in configuration space has been obtained through Monte-Carlo numerical simulations.The model has been applied to metagalactic cosmology. Although single explosions cannot reach the highest redshifts observed in the Hubble expansion the fireworks model offers a possibility to reach thesez-values in a few explosions.The model gives a density inhomogeneity of 20% over a tenth of the Hubble distance as seen from a typical position. Observations show a considerably greater irregular variation.The model gives a local velocity dispersion which is too great to comply with observations. A development of the model is suggested.     

Relativistic theory of the Moon's motion

Relativistic corrections for the elements and coordinates of the Moon have been obtained in the framework of the PPN-formalism. The influence of the coordinate conditions on the observational effects was studied.     

相对论多方球的稳定性

本文从理论的角度，讨论了静态相对论多方球的稳定性问题，给出稳定性对球体物质的绝热指数的依赖关系．     

Spinor: Visible and Infrared Spectro-Polarimetry at the National Solar Observatory

The Spectro-Polarimeter for Infrared and Optical Regions (SPINOR) is a new spectro-polarimeter that will serve as a facility instrument for the Dunn Solar Telescope at the National Solar Observatory. This instrument is capable of achromatic polarimetry over a very broad range of wavelengths, from 430 to 1600 nm, allowing for the simultaneous observation of several visible and infrared spectral regions with full Stokes polarimetry. Another key feature of the design is its flexibility to observe virtually any combination of spectral lines, limited only by practical considerations (e.g., the number of detectors available, space on the optical bench, etc.). Visiting Astronomers, National Solar Observatory, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the National Science Foundation.     

Linearization of dynamical systems using integrals of the motion

A method is presented which transforms certain non-linear differential equations of dynamics into linear equations by introducing a new independent variable and by utilizing the integrals of motion. As examples of special interest the linearizations of unperturbed and perturbed Keplerian motions are discussed.     

Relativistic hierarchical cosmology

While Euclidean models with uniform matter density have a number of radio sources of flux density greater thanF at frequencyv that varies asN(>F, v)¹ F ^–3/2, hierarchical models with = ₀ r ^–2 haveN(>F,)F ^–1/2 (Section 1). Since the observed dependency isN(>F,)F ^–1.8, severe density and/or luminosity evolution must be present in a workable hierarchical cosmology (Section 2). The same argument applies (Section 3) to the number of sources of apparent luminosity greater thanl,N(>l) and (Section 4) to the number of sources within redshift distancez from the local origin. To give agreement with empirical data demandsq _o=+1 and large first and second derivatives with respect to time of the number source density (Section 5). The adoption ofq _o=+1 allows one to show (Section 6) that a Lemaitre-type hierarchical Universe with a long coasting or waiting time can give agreement with observations of the numbers of QSO's etc. if the age of the Universe is more than 10¹³ yr. The dependence of the effective Hubble parameter onk(t), (t) andR (Section 7) leads one to suggest that ak=0, =0 hierarchy with 0 might be the simplest acceptable form of model Universe. Section 8 (Conclusion) points out that further data on source count anisotropies should allow the component levels of the hierarchy to be delineated.     

Relativistic corrections to the Kompaneets equation

We study the Sunyaev–Zeldovich effect for clusters of galaxies. We explore the relativistic corrections to the Kompaneets equation in terms of two different expansion approximation schemes, namely, the Fokker–Planck expansion approximation and delta function expansion approximation. We show that two expansion approximation formalisms are equivalent under the Thomson approximation, which is extremely good approximation for the CMB photon energies. This will clarify the situation for existing theoretical methods to analyse observation data.     

Linearization: Laplace vs. Stiefel

The method for processing perturbed Keplerian systems known today as the linearization was already known in the XVIII^th century; Laplace seems to be the first to have codified it. We reorganize the classical material around the Theorem of the Moving Frame. Concerning Stiefel's own contribution to the question, on the one hand, we abandon the formalism of Matrix Theory to proceed exclusively in the context of quaternion algebra; on the other hand, we explain how, in the hierarchy of hypercomplex systems, both the KS-transformation and the classical projective decomposition emanate by doubling from the Levi-Civita transformation. We propose three ways of stretching out the projective factoring into four-dimensional coordinate transformations, and offer for each of them a canonical extension into the moment space. One of them is due to Ferrándiz; we prove it to be none other than the extension of Burdet's focal transformation by Liouville's technique. In the course of constructing the other two, we examine the complementarity between two classical methods for transforming Hamiltonian systems, on the one hand, Stiefel's method for raising the dimensions of a system by means of weakly canonical extensions, on the other, Liouville's technique of lowering dimensions through a Reduction induced by ignoration of variables.     

Relativistic dynamics of expanding sources

Given a relativistically expanding source, the transformation of the emission spectrum from the comoving frame of the source to the observer's frame is calculated. In particular, we deal with two special cases, that of a uniformly expanding sphere and that of a cylinder. In each case we consider a power-law spectrum with two distinct regions — the optically thick and thin parts — and transform those regions separately. The results are discussed, and a generalized procedure for transforming a spectrum of unspecified form is outlined. This procedure takes into account any bulk motion by the source as well as expansion. Finally, applications of this procedure to astrophysical sources are briefly discussed.     

Relativistic time scales in the solar system

This paper deals with a self-consistent relativistic theory of time scales in the Solar system based on the construction of the hierarchy of dynamically non-rotating harmonic reference systems for a four-dimensional space-time of general relativity. In our approach barycentric (TB) and terrestrial (TT) times are regarded as the coordinate times of barycentric (BRS) and geocentric (GRS) reference systems, respectively, with an appropriate choice of the units of measurement. This enables us to avoid some of the inconsistencies and ambiguities of the definitions of these scales as these are currently applied. International atomic time (TAI) is shown to be the physical realization of TT on the surface of the Earth. This realization is achieved by a specific procedure to average the readings of atomic clocks distributed over the terrestrial surface, all of them synchronized with respect to TT. Extending TAI beyond the Earth's surface may be performed along a three-dimensional hypersurface TT = const. The unit of measurement of TAI coincides with TB and TT units and is equal to the SI second on the surface of the geoid in rotation. Due to the specific choice of the units of measurement the TB scale differs from the TT (TAI) scale only by relativistic nonlinear and periodic terms resulting from the planetary and lunar theories of motion. The proper time ₀ of any terrestrial observer coincides with the coordinate time of the corresponding topocentric reference system (TRS) evaluated at its origin. ₀ is reacted to TT (TAI) by the relativistic transformation involving the GRS velocity of the observer, its height above the geoid and the quadrupole tidal gravitational potential of the external masses. The impact of introducing TB and TT on the units of measurement of length and the basic astronomical constants is discussed.     

MHD Simulations of Relativistic Jets

In a series of time dependent numerical simulations we have performed a parameter study of magnetised relativistic jets. We have found that the impact of the magnetic field on the morphology of a jet depends strongly on the configuration of the field.     

木星掩星的相对论效应

本文计算了木星掩星的相对论效应的数量级,同时讨论了利用木星掩星观测法检验广义相对论光线偏折效应的可能性。