**5. Concluding remarks**

As we have seen relativistic metrology is a field in rapid evolution and subject to continuous refinements.

The existing standard of length will survive till when the technology will allow us to detect the deviations from Euclidean instantaneous 3-spaces implied by Post-Newtonian general relativity. For instance in Ref. (Turyschev S.G. et al, 2006) there is a proposal of a space mission LATOR (Laser Astrometric Test Of Relativity), in which two spacecrafts behind the Sum will form a triangle with the International Space Station ISS. This would allow us to measure the three angles of the triangle to see whether their sum is 2*π* as required by an instantaneous Euclidean 3-space.

The development of optical atomic clocks will allow us to develop a new generation of gravimeters for the local study of the gravitational field of the Earth (now also investigated with the satellites GOCE (Gravity field and steady-state Ocean Circulation Explorer, ESA), CHAMP (CHAllenging Mini-Satellite Payload, GeoForschungsZentrum GFZ), GRACE (Gravity Recovery and Climate Experiment, Center for Space Research, Austin Texas)). One open problem to get a reliable theory of heights over the reference geoid is the comparison of the measurements of gravimeters on the two sides of an ocean. But a byproduct of the ACES mission will be the possibility of such a comparison, by synchronizing the optical atomic clocks of the gravimeters with the ACES clocks on the International Space Station ISS (Svelha D. et al, 2008). As a consequence standard non-relativistic geodesy will be replaced by relativistic geodesy.

Also the transformation from the non-relativistic ITRS on the Earth surface to the relativistic GCRS around the Earth will be accomplished. This will put full control on possible semi-relativistic precessional effects near the Earth surface.

Space navigation inside the Solar System will require refinements of BCRS. In particular to test deviations from Einstein theory of general relativity (the one used in BCRS). See for instance the recent interest in the Pioneer anomaly (Turyshev S.G. et al, 2010) and the endless number of proposals for its explanation.

Regarding ICRS we need a general relativistic relativistic version of it taking into account the non-Euclidean nature of the 3-space as 3-sub-manifolds of space-time. The unsolved problems of dark energy and dark matter, required by the standard ΛCDM cosmological model starting from the hypothesis of homogeneity and isotropy of space-time, are pushing towards inhomogeneous cosmological space-times in which the 3-spaces have small internal 3-curvature but a non zero external 3-curvature. The first step will be to face these problems inside the Milky Way finding a *relativistic* galactic celestial reference frame extending the existing BCRF. To this end the GAIA (Global Astrometric Interferometer for Astrophysics) mission of ESA (Jordi C., 2011; Jordan S., 2008; Klioner S.A. et al, 2005), to be launched in 2012, for the 3-dimensional cartography of our galaxy (position, proper velocity, radial velocity and spectroscopic data for about one billion stars) will be a first relevant step.
