Space Science Reviews

, 214:5 | Cite as

High Performance Clocks and Gravity Field Determination

  • J. MüllerEmail author
  • D. Dirkx
  • S. M. Kopeikin
  • G. Lion
  • I. Panet
  • G. Petit
  • P. N. A. M. Visser
Part of the following topical collections:
  1. High Performance Clocks with Special Emphasis on Geodesy and Geophysics and Applications to Other Bodies of the Solar System


Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of \(10^{-18}\). This notable achievement along with the direct sensitivity of clocks to the strength of the gravitational field make them practically important for various geodetic applications that are addressed in the present paper.

Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic geodetic concepts and come to the conclusion that the advances in clocks and other metrological technologies will soon require the re-definition of time scales or, at least, clarification to ensure their continuity and consistent use in practice.

The relative frequency shift between two clocks is directly related to the difference in the values of the gravity potential at the points of clock’s localization. According to general relativity the relative accuracy of clocks in \(10^{-18}\) is equivalent to measuring the gravitational red shift effect between two clocks with the height difference amounting to 1 cm. This makes the clocks an indispensable tool in high-precision geodesy in addition to laser ranging and space geodetic techniques.

We show how clock measurements can provide geopotential numbers for the realization of gravity-field-related height systems and can resolve discrepancies in classically-determined height systems as well as between national height systems. Another application of clocks is the direct use of observed potential differences for the improved recovery of regional gravity field solutions. Finally, clock measurements for space-borne gravimetry are analyzed along with closely-related deficiencies of this method like an extra-ordinary knowledge of the spacecraft velocity, etc. For all these applications besides the near-future prospects, we also discuss the challenges that are related to using those novel clock data in geodesy.


General relativity Relativistic geodesy Reference frames Time scales High-precision time measurements Height systems Gravity field recovery 



The International Space Science Institute (ISSI), is acknowledged for having provided the opportunity of presenting the work described in this paper at the Workshop on High Performance Clocks, 30 November - 4 December 2015 in Bern, Switzerland. Jürgen Müller gratefully acknowledges support by the DFG Sonderforschungsbereich (SFB 1128: geo-Q) Relativistic Geodesy and Gravimetry with Quantum Sensors. We are also thankful to two anonymous referees whose peer review and critical comments helped us to significantly improve the presentation of the manuscript.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • J. Müller
    • 1
    Email author
  • D. Dirkx
    • 2
    • 3
  • S. M. Kopeikin
    • 4
    • 5
  • G. Lion
    • 6
  • I. Panet
    • 7
  • G. Petit
    • 8
  • P. N. A. M. Visser
    • 2
  1. 1.Institut für ErdmessungLeibniz Universität HannoverHannoverGermany
  2. 2.Faculty of Aerospace EngineeringDelft University of TechnologyDelftThe Netherlands
  3. 3.Joint Institude for VLBI ERICDwingelooThe Netherlands
  4. 4.Department of Physics and AstronomyUniversity of MissouriColumbiaUSA
  5. 5.Siberian State University of Geosystems and TechnologiesNovosibirskRussia
  6. 6.LNE-SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06LNEParisFrance
  7. 7.LASTIG LAREG, IGN, ENSG, Univ. Paris DiderotSorbonne Paris CitéParisFrance
  8. 8.Bureau International des Poids et MesuresSèvres CedexFrance

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