**2.1 Standard of length**

4 Will-be-set-by-IN-TECH

In what follows there will be a sketch, with update bibliography, of relativistic metrology

B) The conventions needed for the description of satellites around the Earth: it is done by means of NASA (USA National Aeronautics and Space Administration) coordinates (Moyer T.D., 2003) firstly in the International Terrestrial Reference System ITRS (with an associated frame ITRF fixed on the Earth surface; see Ref. (IERS, 2004) for the IERS2003 conventions of the International Earth Rotation and Reference System Service IERS) and then in the Geocentric Celestial Reference System GCRS (with an associated non-rotating frame GCRF centered on the Earth center; see Ref. (Soffel M.H. et al, 2003) for the International Astronomic Units

C) The conventions needed for the description of planets and other objects in the Solar System uses the Barycentric Celestial Reference System BCRS (with an associated quasi-inertial Minkowski frame BCRF, if perturbations from the Milky Way are ignored, centered in the barycenter of the Solar System and with the axes specified by means of fixed stars (quasars) in the Hypparcos catalog (Kovalesky J. et al, 1989; Sovers O.J. et al, 1998; Ma C. et al, 1998; Johnstone K.J. et al, 1999; Fey A. et al, 2009)) and ephemerides (see IAU2000 in Ref. (Soffel

While ITRF is essentially realized as a non-relativistic non-inertial frame in Galilei space-time, BCRF is defined as a *quasi-inertial frame*, *non-rotating* with respect to some selected fixed stars, in Minkowski space-time with nearly-Euclidean Newton 3-spaces. The qualification *quasi-inertial* is introduced to take into account general relativity, where inertial frames exist only locally. It can also be considered as a Post-Minkowskian space-time with 3-spaces having a very small extrinsic curvature. GCRF is obtained from BCRF by taking into account Earth's rotation around the Sun with a suitable Lorentz boost with corrections from Post-Newtonian gravity. By taking into account the extension of the geoid and Earth revolution around its axis

New problems emerge by going outside the Solar System. In astronomy the positions of stars and galaxies are determined from the data (luminosity, light spectrum, angles) on the sky, i.e. on a 2-dimensional spherical surface around the Earth with the relations between it and the

Then one needs a description of stars and galaxies as living in a 4-dimensional nearly-Galilei space-time with the International Celestial Reference System ICRS (see Refs. (Kovalesky J. et al, 1989; Sovers O.J. et al, 1998; Ma C. et al, 1998; Johnstone K.J. et al, 1999; Fey A. et al, 2009)), whose materialization ICRF is considered as a "quasi-inertial frame" in a "quasi-Galilei space-time", in accord with the assumed validity of the cosmological and Copernican principles. Namely one assumes a homogeneous and isotropic cosmological Friedmann-Robertson - Walker solution of Einstein equations (the standard ΛCDM cosmological model). In it the constant intrinsic 3-curvature of instantaneous 3-spaces is nearly zero as implied by the CMB data (Bartelmann M., 2010; Bean R., 2009), so that Euclidean 3-spaces (and Newtonian gravity) can be used (all galactic dynamics is Newtonian gravity). See Ref. (Lindegren L. et al, 2003) for the IAU conventions for defining the astrometric radial

Ref. (Kaplan G.H., 2005) contains all the relevant aspects of these conventions.

one goes from the quasi-Minkowskian GCRF to the quasi-Galilean ITRF.

observatory on the Earth done with GPS.

inside the Solar System. It includes

A) Space and time standards.

IAU2000).

M.H. et al, 2003)).

In 1975 in the 15th Meeting CGPM of the General Conference on Weights and Measures (Meeting 15, 1975) the conventional value of the 2-way velocity of light was fixed to be *c* = 299792458 *m s*−1.

In 1983 the 17th Meeting CGPM of the General Conference on Weights and Measures (Meeting 17, 1983) adopted the following standard of length
