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tokens: We thank the Centre National d’Etudes Spatiales (CNES, France) and the French CNRS/INSU for continuous support for the preparation of the Gaia mission. This work benefited from travel support from the European Science Foundation through the GREAT Research Network Program. Some of the computations were done on the Mesocentre SIGAMM machine, hosted by the Observatoire de la Côte d’Azur. The first two authors would like to thank Naia for her numerous (and efficient) attempts to postpone the revision of this paper. We warmly thank C.A.L. Bailer-Jones for his constructive remarks, which helped to improve this article. We are also sincerely grateful to D. Katz for his help with regard to the in-flight RVS characteristics.