# 4.1.3 Reference systems and time scales

Author(s): Sergei Klioner

Gaia data processing is based on the rigorous relativistic definitions of reference systems including time scales as their integral parts. All reference systems are defined in the framework of General Relativity theory by their respective metric tensors that can be found in the literature. A set of rigorous 4-dimensional relativistic transformations ensures correct use of various coordinates and time scale as needed.

The primary reference system used in the data modelling is the Barycentric Celestial Reference System (BCRS; Soffel et al. 2003). The BCRS has its origin at the solar-system barycentre and its axes are aligned with the ICRS. The time-like coordinate of the BCRS is TCB. The motions of Gaia and other solar-system objects are thus described in terms of the space-like coordinates of the BCRS, $x^{i}(t)$, using TCB as the independent time variable $t$. In particular, Gaia makes use of the TCB-based solar system ephemeris INPOP10e (see Section 4.2.1). Gaia also uses TCB-compatible values of all relevant astronomical constants (Klioner et al. 2010). The motions of all objects beyond the solar-system are also parametrized in terms of BCRS coordinates, but here the independent time variable $t$ should be understood as the time at which the event would be observed at the solar-system barycentre, i.e. the time of observation corrected for the Rømer delay (Klioner 2003a, Sect.8). This convention is necessitated by the, in general, poor knowledge of distances beyond the solar-system. The resulting astrometric catalogue is also parametrized by TCB.

The Centre-of-Mass Reference System (CoMRS; Klioner 2004) is a physically adequate local (proper) reference system for the Gaia spacecraft. The origin coincides with the centre of mass of the Gaia satellite. The CoMRS is chosen to be kinematically non-rotating, that is, it is related to the BCRS by the generalized Lorentz transformation without spatial rotation. The coordinate basis of the CoMRS at its origin coincides with a particular form of tetrad co-moving with the observer. This means that the CoMRS description of observables coincides with the classical tetrad representation in cases where a tetrad is sufficient for modelling. However, the CoMRS is a complete rigorously-defined 4-dimensional reference system suitable to describe local physical processes localized in the body of Gaia satellite. Its coordinate time at the origin coincides with the proper time of Gaia – the reading of an ideal clock co-moving with the satellite. The CoMRS gives a relativistic definition of the Gaia attitude that is defined as a Euclidean spatial rotation in the CoMRS coordinates. The CoMRS is also used in the relativistic model of observations as well as in the model for the calibration of Gaia’s on-board clock.

The Geocentric Celestial Reference System (GCRS; Soffel et al. 2003) is only used in Gaia for processing of auxiliary time transfer data (time couples, see Section 4.1.6). In particular, the GCRS is used to compute the BCRS position of the ESA ground stations at particular moments of time. The time scales related to GCRS (TCG, TT, etc.) are also only used in the intermediate calculations related to the calibration of Gaia’s clock.