Gaia is a cornerstone mission in the science programme of the European Space Agency (ESA). The spacecraft construction was approved in 2006, following a study in which the original interferometric concept was changed to a direct-imaging approach. Both the spacecraft and the payload were built by European industry. The involvement of the scientific community focusses on data processing for which the international Gaia Data Processing and Analysis Consortium (DPAC) was selected in 2007. Gaia was launched on 19 December 2013 and arrived at its operating point, the second Lagrange point of the Sun-Earth-Moon system, a few weeks later. The commissioning of the spacecraft and payload was completed on 19 July 2014. The nominal five-year mission started with four weeks of special, ecliptic-pole scanning and subsequently transferred into full-sky scanning mode. We recall the scientific goals of Gaia and give a description of the as-built spacecraft that is currently (mid-2016) being operated to achieve these goals. We pay special attention to the payload module, the performance of which is closely related to the scientific performance of the mission. We provide a summary of the commissioning activities and findings, followed by a description of the routine operational mode. We summarise scientific performance estimates on the basis of in-orbit operations. Several intermediate Gaia data releases are planned and the data can be retrieved from the Gaia Archive, which is available through the Gaia home page.

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...

Context. Gaia Data Release 1 (DR1) contains astrometric results for more than 1 billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14 months of its operational phase. Aims. We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results. Results. For about two million of the brighter stars (down to magnitude ∼11.5) we obtain positions, parallaxes, and proper motions to Hipparcostype precision or better. For these stars, systematic errors depending for example on position and colour are at a level of ±0.3 milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to ∼10 mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1 mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03 mas yr −1 . The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas yr −1 . Conclusions. Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The present results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame.

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

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Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the Hipparcos and Tycho-2 catalogues -a realisation of the Tycho-Gaia Astrometric Solution (TGAS) -and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr −1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 Hipparcos stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr −1 . For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data.

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