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1.
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.  相似文献   

2.
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.  相似文献   

3.
Based on the most complete list of the results of an individual comparison of the proper motions for stars of various programs common to the Hipparcos catalog, each of which is an independent realization of the inertial reference frame with regard to stellar proper motions, we redetermined the vector ω of residual rotation of the ICRS system relative to the extragalactic reference frame. The equatorial components of this vector were found to be the following: ωx=+0.04±0.15 mas yr?1, ωy=+0.18±0.12 mas yr?1, and ωz=?0.35±0.09 mas yr?1.  相似文献   

4.
In most courses on continuum mechanics the law of angular momentum is studied about a fixed point (usually about the origin of the frame). In this article we clarify this law about any point in three-dimensional Euclidean space and discuss the law, about any point, for an observer in a rotating frame.  相似文献   

5.
We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits and subsequently bifurcating families. The Lyapunov families arise from the polygonal equilibrium of n bodies in a rotating frame of reference. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, then the orbit is also periodic in the inertial frame. We prove that a dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, correspond to choreographies. We present a sample of the many choreographies that we have determined numerically along the Lyapunov families and along bifurcating families, namely for the cases \(n=3\), 4, and 6–9. We also present numerical results for the case where there is a central body that affects the choreography, but that does not participate in it. Animations of the families and the choreographies can be seen at the link below.  相似文献   

6.
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.  相似文献   

7.
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.  相似文献   

8.
For a conservative dynamical system withn deg. of freedom we show that the equations of variation along an orbit may be written with respect to an orthonormal moving frame (a generalized Frenet frame) in which the tangential variation is given by a quadrature and the normal andn-2 binormal variations are solutions ofn-1 coupled second order equations of the form of Hill's equation.  相似文献   

9.
We consider the problem of the relative motion both of the substructures of the Local Group of galaxies (revealed via the S-tree method), and of the velocity of the Local Group itself. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via a 3D reconstruction procedure, which uses information on the radial velocities of the galaxies but does not take account of their distances. Once the bulk motion of the substructures is estimated we also consider, in combination with the observed cosmic microwave background (CMB) dipole, the mean velocity of the Local Group itself. Assigning to the Local Group the mean motion of its main substructures, we evaluate its peculiar velocity in Milky Way frame V LG→MW = (−7 ± 303, −15 ± 155, +177 ± 144) or 178 km s−1 toward galactic coordinates l  = 245 and b  = +85. Combined with the CMB dipole V MW→CMB, we obtain a Local Group velocity in CMB frame: V LG→CMB = (−41 ± 303, −497 ± 155, 445 ± 144) or 668 km s−1 towards l  = 265 and b  = 42. This estimation is in good agreement, within the 1 σ level, with the estimation of Yahil et al.  相似文献   

10.
The sensitivity and versatility of SKA will provide microarcsec astrometric precision and high quality milliarcsec-resolution images by simultaneously detecting calibrator sources near the target source. To reach these goals, we suggest that the long-baseline component of SKA contains at least 25% of the total collecting area in a region between 1000 and 5000 km from the core SKA. We also suggest a minimum of 60 elements in the long-baseline component of SKA to provide the necessary (u–v) coverage. For simultaneous all-sky observations, which provide absolute astrometric and geodetic parameters, we suggest using 10 independent subarrays each composed of at least six long-baseline elements correlated with the core SKA. We discuss many anticipated SKA long-baseline astrometric experiments: determination of distance, proper motion and orbital motion of thousands of stellar objects; planetary motion detections; mass determination of degenerate stars using their kinetics; calibration of the universal distance scale from 10 to 107 pc; the core and inner-jet interactions of AGN. With an increase by a factor of 10 in absolute astrometric accuracy using simultaneous all sky observations, the fundamental quasar reference frame can be defined to <10 μas and tied to the solar-system dynamic frame to this accuracy. Parameters associated with the earth rotation and orientation, nutation, and geophysical parameters, can be accurately monitored. Tests of fundamental physics include: solar and Jovian deflection experiments, the sky frame accuracy needed to interpret the gravity wave/pulsar-timing experiment, accurate monitoring of spacecraft orbits that impact solar system dynamics.  相似文献   

11.
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)  相似文献   

12.
We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the second order, but only when there are no direct interactions between the orientation of the bodies. Here we expand the potential up to the fourth order and we show that the secular problem obtained after averaging over fast angles, as for the precession model of Boué and Laskar [Boué, G., Laskar, J., 2006. Icarus 185, 312-330], is integrable, but not trivially. We describe the general features of the motions and we provide explicit analytical approximations for the solutions. We demonstrate that the general solution of the secular system can be decomposed as a uniform precession around the total angular momentum and a periodic symmetric orbit in the precessing frame. More generally, we show that for a general n-body system of rigid bodies in gravitational interaction, the regular quasiperiodic solutions can be decomposed into a uniform precession around the total angular momentum, and a quasiperiodic motion with one frequency less in the precessing frame.  相似文献   

13.
The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced.  相似文献   

14.
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.  相似文献   

15.
刘牛 《天文学报》2021,62(6):70
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.  相似文献   

16.
In the frame of the Starburst Model, we show that the evolution of a massive stellar cluster in a high metallicity environment can reproduce the observed emission-line spectrum and the UV-optical Spectral Energy Distribution of the Seyfert 2 galaxies and LINERs. We apply the results of our models to three objects: NGC 5506, NGC 5643 and Mk 348.  相似文献   

17.
Constraints of the laboratory physics on the model of the universe are considered. The constraints are derived from the measurement procedure for the flux of electromagnetic radiation and valid for any model of the universe. In classical physics, an observer in the frame of the detector can measure the transformation (1+z)?1 for the energy flux of the electromagnetic wave emitted in the frame of the source but cannot any transformation for space and time between the frames of the source and detector. In quantum mechanics, the energy of the electromagnetic radiation as a function of the distance may be measured as a redshifted frequency of photon (1+z) or as a decrease of the intensity of radiation (1+z).  相似文献   

18.
In this paper we demonstrate the importance of cosmic rays for the dynamics of the interstellar medium. We present the first 3D-MHD numerical simulations of the Parker instability triggered by cosmic rays accelerated in randomly distributed supernova remnants. We show that in the presence of galactic rotation a net radial magnetic field is produced as a result of the cosmic ray injection and Coriolis force. This process provides a possibility of very efficient magnetic field amplification within the general frame of so called fast galactic dynamo proposed by Parker (1992).  相似文献   

19.
In the present paper we give an axiomatic system of causal space and its topological structure, that is convenient for many kinds of spacetime frame reference. We give also a topology of the pure states, according to axiomatic foundation of quantum mechanics by J. Jauch. Finally, we attempt to unify, from, a causality point of view, the microcosmos and mega(macro)cosmos supported by the transition probability.  相似文献   

20.
We present the first results of an ongoing spectroscopic survey of galaxies selected in the rest frame ultraviolet (UV). The source catalogue has been constructed from a flux-limited sample of stars, galaxies and QSOs imaged at 2000 Å in Selected Area 57 with the FOCA balloon-borne imaging camera. Accurate positions for the UV sources have been obtained by matching with optical counterparts using APM scans of the Palomar Sky Survey limited at B   20.5. Here we present results derived from optical spectroscopy conducted with the WIYN telescope and the WHT for 142 faint sources. The redshift distribution for this UV-selected sample extends over 0 <  z  < 0.5, and a high fraction of the sources show intense nebular emission lines and UV–optical colours bluer than normal Hubble sequence galaxies. Such UV-selected surveys are thus a very efficient way to locate and study intermediate-redshift galaxies undergoing intense star formation. Although our sample is currently small, we derive a rest frame UV luminosity function with a steep faint-end slope consistent with that found for late-type galaxies in optical samples. However, the integrated luminosity density derived implies a volume-averaged star formation rate higher than other recent estimates, assuming a normal initial mass function. If representative of other UV fields, as suggested by UV number count studies, our data imply that the local abundance of star-forming galaxies may have been underestimated, and consequently claims for strong evolution in the global star formation rate in the range 0 <  z  < 1 overstated. An intensive study of a large UV-selected sample is likely to reveal important information on the declining population of star-forming galaxies of all types.  相似文献   

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