We discuss the IAU resolutions B1.3, B1.4, B1.5, and B1.9 that were adopted during the 24th General Assembly in Manchester, 2000, and provides details on and explanations for these resolutions. It is explained why they present significant progress over the corresponding IAU 1991 resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics, and metrology. In fact, most of these resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and the Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the resolutions are explicated and justified. Some models (e.g., for higher spin moments) that serve the purpose of estimating orders of magnitude have actually never been published before.

er, the great increase in precision of current, and foreseeable, observational techniques in the solar system makes it now necessary to reconsider this traditional (post-Newtonian) way of tackling the gravitational dynamics of N-body systems.Indeed, modern technology is giving us access to highprecision data on both the global celestial mechanics of the solar system, and the local relativistic gravitational environment of the Earth, and on the way they fit together. We have in mind high-precision techniques such as 43 3273 1991 The American Physical Society 3274 THIBAULT DAMOUR, MICHAEL SOFFEL, AND CHONGMING XU 43 the following. Concerning the global mechanics of the solar system: radar ranging to the planets (with, e.g. , a few meters accuracy for the Viking landers on Mars), laser ranging to the Moon (few centimeters level), and the timing of millisecond pulsars (sub-microsecond level).Concerning the local environment of the Earth: the comparison, at the 100 nanosecond level, of stable atomic clocks (via, for instance, the Global Positioning System) and laser ranging to artificial satellites (such as LAGEOS, at the 1-cm level). Concerning the fitting of the local Earth environment to the global structure of the solar system, and/or of the external universe at large, we have in mind, in particular, the very long baseline interferometry technique, which determines baselines on the surface of the Earth, and the position of the rotation pole, with centimeter accuracy, the length of the day at the few millisecond level, and relative angles between distant objects, as seen on the Earth, with a precision better than a milliarcsecond. For an introduction to these techniques, and a review of their impact on general relativity see Soffel.In order to match the high precision of this wealth of (present and forseeable) data, one needs a correspondingly accurate relativistic theory of celestial mechanics able to describe both the global gravitational dynamics of a system of N extended bodies, the local gravitational structure of each, arbitrarily composed and shaped, rotating deformable body, and the way each of these X local structures meshes into the global one. The traditional post-Newtonian approach to relativistic celestial mechanics fails, for both conceptual and technical reasons, to bring a satisfactory answer to this problem. This traditional post-Newtonian approach uses only one global coordinate system x"=(ct, x,y, z), to describe an N bodysystem, and models itself on the Newtonian approach to celestial mechanics consisting of decomposing the problem into two subproblems [Tisserand' (Vol. I, pp. 51 -52);Pock j: (i) the external problem, to determine the motion of the centers of mass of the N bodies; (ii) the internal problem, to determine the motion of each body around its center of mass. However, the treatments of both subproblems in the traditional post-Newtonian approach are unsatisfactory. The external problem is attacked by introducing some collective variable, say z'(t), i=1,2,3, generalizing the Newtonian c...

The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first postNewtonian approximation of general relativity. The derivation uses our recently introduced multireference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass kame of each body, relativistic inertial effects combine with post-Newtonian self-and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d Alembert s principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of the post-Newtonian multipole moments of the other bodies. PACS number(s): 95

The rotational laws of motion for arbitrarily shaped, weakly self-gravitating bodies, members of gravitationally interacting N-body systems, are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our previously introduced framework, characterized by the combined use of N local (body-attached) reference systems with one global reference system, and by the introduction of new sets of relativistic multipole moments, and relativistic tidal moments. We show how to associate with each body (considered in its corresponding local frame) a first-post-Newtonian-accurate spin vector, whose local-time evolution is entirely determined by the coupling between the multipole moments of that body and the tidal moments it experiences. The leading relativistic effects in the spin motion are discussed: gravitational Larmor theorem (de SitterFokker -Eddington precession) and post-Newtonian contributions to the torque associated with the quadrupole moment and the quadrupole tidal tensor.PACS number(s): 95.10.Ce, 04.20.Me

In recent years, microblog systems such as Twitter and Sina Weibo have averaged multimillion active users. On the other hand, the microblog system has become a new means of rumor-spreading platform. In this paper, we investigate the machine-learning-based rumor identification approaches. We observed that feature design and selection has a stronger impact on the rumor identification accuracy than the selection of machine-learning algorithms. Meanwhile, the rumor publishers' behavior may diverge from normal users', and a rumor post may have different responses from a normal post. However, mass behavior on rumor posts has not been explored adequately. Hence, we investigate rumor identification schemes by applying five new features based on users' behaviors, and combine the new features with the existing well-proved effective user behaviorbased features, such as followers' comments and reposting, to predict whether a microblog post is a rumor. Experiment results on real-world data from Sina Weibo demonstrate the efficacy and efficiency of our proposed method and features. From the experiments, we conclude that the rumor detection based on mass behaviors is more effective than the detection based on microblogs' inherent features.