**6. References**


18 Will-be-set-by-IN-TECH

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

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

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

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

[1] ACES 2010 - ESA: Atomic Clock Ensemble in Space (ACES), *http* :

[2] Alba D. and Lusanna L., 2010, *Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames*, Int.J.Geom.Methods in Physics 7, 33 (2010) (arXiv 0908.0213) and *II. Applications: Rotating Frames, Sagnac Effect, Faraday Rotation, Wrap-up Effect*,

[3] Alba D. and Lusanna L., 2007, *Generalized Radar 4-Coordinates and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers*, Int.J.Mod.Phys. D16, 1149 (2007) (arXiv

[5] Ashby N., 2003, *Relativity in the Global Positioning System*, Living Rev. Relat. 6, 1 (2003);

[6] Bartelmann M., 2010, *The Dark Universe*, Rev.Mod.Phys. 82, 331 (2010) (arXiv 0906.5036). [7] Basri S.A., 1965, *Operational Foundation of Einstein's General Theory of Relativity*,

[9] Bize S., Laurent P., Abgrall M., Marion H., Maksimovic I., Cacciapuoti L., Grünert J., Vian C., Pereira dos Santos F., Rosenbusch P., Lemonde P., Santarelli G., Wolf P., Clairon

//*www*.*esa*.*int*/*SPECIALS*/*HSF*−*Research*/*SEMJSK*0*YDUF*−0.*htlm*.

[4] Arias E.F., 2005, *The Metrology of Time*, Phil.Trans.R.Soc. A363, 2289 (2005).

spectroscopic data for about one billion stars) will be a first relevant step.

Int.J.Geom.Methods in Physics, 7, 185 (2010) (arXiv 0908.0215).

[8] Bean R., *TASI 2009. Lectures on Cosmic Acceleration* (arXiv 1003.4468).

see also *http* : //*www*.*usno*.*navy*.*mil*/*USNO*/*time*/*gps*.

semi-relativistic precessional effects near the Earth surface.

by relativistic geodesy.

of proposals for its explanation.

**6. References**

gr-qc/0501090).

Rev.Mod.Phys. 37, 288 (1965).

A., Luiten A., Tobar M. and Salomon C., 2005, *Cold Atom Clocks and Applications* , J.Phys. B38, S449 (2005), special issue *Atoms, Quanta and Relativity: a Century after Einstein's Miracolous Year*.




20 Will-be-set-by-IN-TECH

[33] *IERS Conventions (2003)*, eds. McCarthy D.D. and Petit G., IERS TN 32 (2004), Verlag des

[34] ITUR International Telecommunications Union Recommendation ITU-R TF.460-6, 2007,

[35] Johnstone K.J. and de Vegt Chr., 1999, *Reference Frames in Astronomy*, Annu. Rev. Astron.

[36] Jordan S., 2008, *The GAIA Project: Technique, Performance and Status*, Astron.Nachr. 329,

[37] Jordi C., 2011, *The European Space Agency Gaia Mission: Exploring the Galaxy*, (arXiv

[38] Kaplan G.H., 2005, *The IAU Resolutions on Astronomical Reference Systems, Time Scales and Earth Rotation Models*, U.S.Naval Observatory circular No. 179 (2005) (arXiv

[39] Klioner S.A. and Soffel M.H., 2004, *Refining the Relativistic Model for GAIA: Cosmological Effects in the BCRS*, Proc. of the Symposium *The Three-Dimensional Universe with GAIA*,

[40] Kovalevski J., Mueller I.I. and Kolaczek B., 1989, *Reference Frames in Astronomy and*

[41] Lemonde P., Laurent P., Santarelli G., Abgrall M., Sortais Y., Bize S., Nicolas C., Zhang S., Clairon A., Dimarcq N., Petit P., Mann A., Luiten A., Chang S. and Salomon C., 2001 *Cold Atom Clocks on Earth and Space*, in *Frequency Measurement and Control, Advanced Techniques*

[42] Lindegren L. and Dravins D., 2003, *The Fundamental Definition of 'Radial Velocity'*,

[43] Ludlow A.D., Zelevinsky T., Campbell G.K., Blatt S., Boyd M.M., de Miranda M.H.G., Martin M.J., Thomsen J.W., Foreman S.M., Jun Ye, Fortier T.M., Stalnaker J.E., Diddams S.A., Le Coq Y., Barber Z.W., Poli N., Lemke N.D., Beck K.M., and Oates C.W., 2008, *Sr Lattice Clock at 1 Œ 10–16 Fractional Uncertainty by Remote Optical Evaluation with a Ca*

[44] Lusanna L., 2011, *Canonical Gravity and Relativistic Metrology: from Clock Synchronization*

[45] Ma C., Arias E.F., Eubanks T.M., Fey A.L., Gontier A.M., Jacobs C.S., Sovers O.J., Archinal B.A. and Charlot P., 1998, *The International Celestial Reference Frame as Realized*

[46] McCarthy D.D. and Seidelmann P.K., 2009, *Time: from Earth Rotation to Atomic Physics*

[47] *15th Meeting of the General Conference on Weights and Measures*, Resolution 2, 1975 (*http* :

[48] *17th Meeting of the General Conference on Weights and Measures*, Resolution 1, 1983 (*http* :

[49] Moyer T.D., 2003, *Formulation for Observed and Computed Values of Deep Space Network*

[50] Parker T.E., 2010, *Long-Term Comparison of Caesium Fountain Primary Frequency Standards*,

[51] Perlick V., 1987, *Characterization of Standard Clocks by means of Light Rays and Freely Falling*

Paris, pp. 305-309 (ESA SP-576, January 2005) (arXiv astro-ph/0411363).

*and Future Trends*, ed.A.N.Luiten (Springer, Berlin, 2001).

*to Dark Matter as a Relativistic Effect*, (arXiv 1108.3224).

*by Very Long Baseline Interferometry*, AJ 116, 516 (1998).

*Data Types for Navigation* (John Wiley, New York, 2003).

//*www*.*bipm*.*org*/*en*/*CGPM*/*db*/15/2/).

//*www*.*bipm*.*org*/*en*/*CGPM*/*db*/17/1/).

*Particles*, Gen.Rel.Grav. 19, 1059 (1987).

Astron.Astrophys. 401, 1185 (2003) (arXiv astro-ph/0302522).

*Standard-Frequency and Time-Signal Emissions*.

875 (2008) (DOI 10.1002/asna.200811065).

*Geophysics* (Kluwer, Dordrecht, 1989).

*Clock*, Science 319, 1805 (2008).

(Wiley, NewYork, 2009).

Metrologia 47, 1 (2010).

Astrophys. 37, 97 (1999).

BKG.

1105.6166).

astro-ph/0602086).

