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Chronometric Geodesy: Methods and Applications

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Relativistic Geodesy

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 196))

Abstract

The theory of general relativity was born more than one hundred years ago, and since the beginning has striking prediction success. The gravitational redshift effect discovered by Einstein must be taken into account when comparing the frequencies of distant clocks. However, instead of using our knowledge of the Earth’s gravitational field to predict frequency shifts between distant clocks, one can revert the problem and ask if the measurement of frequency shifts between distant clocks can improve our knowledge of the gravitational field. This is known as chronometric geodesy. Since the beginning of the atomic time era in 1955, the accuracy and stability of atomic clocks were constantly ameliorated, with around one order of magnitude gained every ten years. Now that the atomic clock accuracy reaches the low \(10^{-18}\) in fractional frequency, and can be compared to this level over continental distances with optical fibres, the accuracy of chronometric geodesy reaches the cm level and begins to be competitive with classical geodetic techniques such as geometric levelling and GNSS/geoid levelling. Moreover, the building of global timescales requires now to take into account these effects to the best possible accuracy. In this chapter we explain how atomic clock comparisons and the building of timescales can benefit from the latest developments in physical geodesy for the modelization and realization of the geoid, as well as how classical geodesy could benefit from this new type of observable, which are clock comparisons that are directly linked to gravity potential differences.

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Notes

  1. 1.

    Resolution 1 of the 13th General Conference on Weights and Measures (CGPM) [7].

  2. 2.

    This is based on the numbers given in table 1 of [10] and table 1 of [11]: the relative accuracy of the gravitational part of the relativistic shift effect is taken as \((\sqrt{18^2+10^2+7^2}\ \mathrm{ns}) / (179 \ \mathrm{ns})\).

  3. 3.

    In the Newtonian sense, the geoid is the equipotential of the Earth’s gravity (Newtonian) potential, which best coincides with the (mean) surface of the oceans.

  4. 4.

    All IAU Resolutions can be found at http://www.iau.org/administration/resolutions/general_assemblies/.

  5. 5.

    projects.npl.co.uk/itoc.

  6. 6.

    See http://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies.html.

  7. 7.

    One can notice that the separation between a gravitational red-shift and a Doppler effect is specific to the chosen coordinate system. One can read the book by Synge [121] for a different interpretation in terms of relative velocity and Doppler effect only.

  8. 8.

    Here we use notation \(W_\mathrm{geoid}\) instead of the commonly used \(W_0\), in order to emphasize that there is no generally accepted conventional and unified value of the geoid gravity potential value.

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Acknowledgements

The authors would like to thank Jérôme Lodewyck (SYRTE/Paris Observatory) for providing Fig. 1, and Martina Sacher (Bundesamt für Kartographie und Geodäsie, BKG, Leipzig, Germany) for providing information on the EVRF2007 heights and uncertainties, the associated height transformations, and a new UELN adjustment in progress. This research was supported by the European Metrology Research Programme (EMRP) within the Joint Research Project “International Timescales with Optical Clocks” (SIB55 ITOC), as well as the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centre 1128 “Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q)”, project C04. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. We gratefully acknowledge financial support from Labex FIRST-TF and ERC AdOC (Grant No. 617553).

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  1. SYRTE Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, LNE 61 avenue de l’Observatoire, 75014, Paris, France

    Pacome Delva

  2. Institut für Erdmessung, Leibniz Universität Hannover (LUH), Schneiderberg 50, 30167, Hannover, Germany

    Heiner Denker

  3. LASTIG LAREG IGN, ENSG, Univ Paris Diderot, Sorbonne Paris Cité, 35 rue Hélène Brion, 75013, Paris, France

    Guillaume Lion

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    Dirk Puetzfeld

  2. ZARM, University of Bremen, Bremen, Germany

    Claus Lämmerzahl

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Delva, P., Denker, H., Lion, G. (2019). Chronometric Geodesy: Methods and Applications. In: Puetzfeld, D., Lämmerzahl, C. (eds) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_2

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