Geodetic methods to determine the relativistic redshift at the level of 10-18 in the context of international timescales: a review and practical results

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Denker, H.; Timmen, L.; Voigt, C.; Weyers, S.; Peik, E. et al.: Geodetic methods to determine the relativistic redshift at the level of 10-18 in the context of international timescales: a review and practical results. In: Journal of Geodesy 92 (2017), S. 487–516. DOI:

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Sum total of downloads: 216

The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in (Formula presented.) level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about (Formula presented.), equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about (Formula presented.).
License of this version: CC BY 4.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2017
Appears in Collections:Fakultät für Bauingenieurwesen und Geodäsie

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pos. country downloads
total perc.
1 image of flag of Germany Germany 161 74.54%
2 image of flag of United States United States 18 8.33%
3 image of flag of Italy Italy 10 4.63%
4 image of flag of China China 9 4.17%
5 image of flag of Netherlands Netherlands 5 2.31%
6 image of flag of No geo information available No geo information available 2 0.93%
7 image of flag of Greece Greece 2 0.93%
8 image of flag of France France 2 0.93%
9 image of flag of Singapore Singapore 1 0.46%
10 image of flag of Czech Republic Czech Republic 1 0.46%
    other countries 5 2.31%

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