Context. We present the second Gaia data release, Gaia DR2, consisting of astrometry, photometry, radial velocities, and information on astrophysical parameters and variability, for sources brighter than magnitude 21. In addition epoch astrometry and photometry are provided for a modest sample of minor planets in the solar system. Aims. A summary of the contents of Gaia DR2 is presented, accompanied by a discussion on the differences with respect to Gaia DR1 and an overview of the main limitations which are still present in the survey. Recommendations are made on the responsible use of Gaia DR2 results. Methods. The raw data collected with the Gaia instruments during the first 22 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into this second data release, which represents a major advance with respect to Gaia DR1 in terms of completeness, performance, and richness of the data products. Results. Gaia DR2 contains celestial positions and the apparent brightness in G for approximately 1.7 billion sources. For 1.3 billion of those sources, parallaxes and proper motions are in addition available. The sample of sources for which variability information is provided is expanded to 0.5 million stars. This data release contains four new elements: broad-band colour information in the form of the apparent brightness in the GBP (330–680 nm) and GRP (630–1050 nm) bands is available for 1.4 billion sources; median radial velocities for some 7 million sources are presented; for between 77 and 161 million sources estimates are provided of the stellar effective temperature, extinction, reddening, and radius and luminosity; and for a pre-selected list of 14 000 minor planets in the solar system epoch astrometry and photometry are presented. Finally, Gaia DR2 also represents a new materialisation of the celestial reference frame in the optical, the Gaia-CRF2, which is the first optical reference frame based solely on extragalactic sources. There are notable changes in the photometric system and the catalogue source list with respect to Gaia DR1, and we stress the need to consider the two data releases as independent. Conclusions. Gaia DR2 represents a major achievement for the Gaia mission, delivering on the long standing promise to provide parallaxes and proper motions for over 1 billion stars, and representing a first step in the availability of complementary radial velocity and source astrophysical information for a sample of stars in the Gaia survey which covers a very substantial fraction of the volume of our galaxy.

Context. Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these results performed within the astrometry task. Methods. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G < 14 mag) sources, 0.1 mas at G = 17 mag, and 0.7 mas at G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr −1 , respectively. The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas yr −1 . From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas yr −1 in proper motion are seen on small (< 1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.

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.

Abstract. The GAIA astrometric mission has recently been approved as one of the next two "cornerstones" of ESA's science programme, with a launch date target of not later than mid-2012. GAIA will provide positional and radial velocity measurements with the accuracies needed to produce a stereoscopic and kinematic census of about one billion stars throughout our Galaxy (and into the Local Group), amounting to about 1 percent of the Galactic stellar population. GAIA's main scientific goal is to clarify the origin and history of our Galaxy, from a quantitative census of the stellar populations. It will advance questions such as when the stars in our Galaxy formed, when and how it was assembled, and its distribution of dark matter. The survey aims for completeness to V = 20 mag, with accuracies of about 10 µas at 15 mag. Combined with astrophysical information for each star, provided by on-board multi-colour photometry and (limited) spectroscopy, these data will have the precision necessary to quantify the early formation, and subsequent dynamical, chemical and star formation evolution of our Galaxy. Additional products include detection and orbital classification of tens of thousands of extra-Solar planetary systems, and a comprehensive survey of some 10 5 −10 6 minor bodies in our Solar System, through galaxies in the nearby Universe, to some 500 000 distant quasars. It will provide a number of stringent new tests of general relativity and cosmology. The complete satellite system was evaluated as part of a detailed technology study, including a detailed payload design, corresponding accuracy assesments, and results from a prototype data reduction development.

Context. Gaia Early Data Release 3 (Gaia EDR3) gives trigonometric parallaxes for nearly 1.5 billion sources. Inspection of the EDR3 data for sources identified as quasars reveals that their parallaxes are biased, that is, they are systematically offset from the expected distribution around zero, by a few tens of microarcseconds. Aims. We attempt to map the main dependences of the parallax bias in EDR3. In principle, this could provide a recipe for correcting the EDR3 parallaxes. Methods. Quasars provide the most direct way for estimating the parallax bias for faint sources. In order to extend this to brighter sources and a broader range of colours, we used differential methods based on physical pairs (binaries) and sources in the Large Magellanic Cloud. The functional forms of the dependences were explored by mapping the systematic differences between EDR3 and DR2 parallaxes. Results. The parallax bias is found to depend in a non-trivial way on (at least) the magnitude, colour, and ecliptic latitude of the source. Different dependences apply to the five- and six-parameter solutions in EDR3. While it is not possible to derive a definitive recipe for the parallax correction, we give tentative expressions to be used at the researcher’s discretion and point out some possible paths towards future improvements.

Context. The Gaia satellite will observe about one billion stars and other point-like sources. The astrometric core solution will determine the astrometric parameters (position, parallax, and proper motion) for a subset of these sources, using a global solution approach which must also include a large number of parameters for the satellite attitude and optical instrument. The accurate and efficient implementation of this solution is an extremely demanding task, but crucial for the outcome of the mission. Aims. We aim to provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework. Methods. The astrometric core solution is a simultaneous least-squares estimation of about half a billion parameters, including the astrometric parameters for some 100 million well-behaved so-called primary sources. The global nature of the solution requires an iterative approach, which can be broken down into a small number of distinct processing blocks (source, attitude, calibration and global updating) and auxiliary processes (including the frame rotator and selection of primary sources). We describe each of these processes in some detail, formulate the underlying models, from which the observation equations are derived, and outline the adopted numerical solution methods with due consideration of robustness and the structure of the resulting system of equations. Appendices provide brief introductions to some important mathematical tools (quaternions and B-splines for the attitude representation, and a modified Cholesky algorithm for positive semidefinite problems) and discuss some complications expected in the real mission data. Results. A complete software system called AGIS (Astrometric Global Iterative Solution) is being built according to the methods described in the paper. Based on simulated data for 2 million primary sources we present some initial results, demonstrating the basic mathematical and numerical validity of the approach and, by a reasonable extrapolation, its practical feasibility in terms of data management and computations for the real mission.

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.

Context. We present the early installment of the third Gaia data release, Gaia EDR3, consisting of astrometry and photometry for 1.8 billion sources brighter than magnitude 21, complemented with the list of radial velocities from Gaia DR2. Aims. A summary of the contents of Gaia EDR3 is presented, accompanied by a discussion on the differences with respect to Gaia DR2 and an overview of the main limitations which are present in the survey. Recommendations are made on the responsible use of Gaia EDR3 results. Methods. The raw data collected with the Gaia instruments during the first 34 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium and turned into this early third data release, which represents a major advance with respect to Gaia DR2 in terms of astrometric and photometric precision, accuracy, and homogeneity. Results. Gaia EDR3 contains celestial positions and the apparent brightness in G for approximately 1.8 billion sources. For 1.5 billion of those sources, parallaxes, proper motions, and the (GBP − GRP) colour are also available. The passbands for G, GBP, and GRP are provided as part of the release. For ease of use, the 7 million radial velocities from Gaia DR2 are included in this release, after the removal of a small number of spurious values. New radial velocities will appear as part of Gaia DR3. Finally, Gaia EDR3 represents an updated materialisation of the celestial reference frame (CRF) in the optical, the Gaia-CRF3, which is based solely on extragalactic sources. The creation of the source list for Gaia EDR3 includes enhancements that make it more robust with respect to high proper motion stars, and the disturbing effects of spurious and partially resolved sources. The source list is largely the same as that for Gaia DR2, but it does feature new sources and there are some notable changes. The source list will not change for Gaia DR3. Conclusions. Gaia EDR3 represents a significant advance over Gaia DR2, with parallax precisions increased by 30 per cent, proper motion precisions increased by a factor of 2, and the systematic errors in the astrometry suppressed by 30–40% for the parallaxes and by a factor ~2.5 for the proper motions. The photometry also features increased precision, but above all much better homogeneity across colour, magnitude, and celestial position. A single passband for G, GBP, and GRP is valid over the entire magnitude and colour range, with no systematics above the 1% level