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3.1.3 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 3.2.1).
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 2003, 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 3.1.6).
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.