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Gravitational Redshift Test Using Eccentric Galileo Satellites
Open accessAbstract
We report on a new test of the gravitational redshift and thus of local position invariance, an integral part of the Einstein equivalence principle, which is the foundation of general relativity and all metric theories of gravitation. We use data spanning 1008 days from two satellites of Galileo, Europe's global satellite navigation system, which were launched in 2014, but accidentally delivered on elliptic rather than circular orbits. The resulting modulation of the gravitational redshift of the onboard atomic clocks allows the redshift determination with high accuracy. Additionally, specific laser ranging campaigns to the two satellites have enabled a good estimation of systematic effects related to orbit uncertainties. Together with a careful conservative modeling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be (0.19±2.48)×10^{-5} at 1 sigma, improving the best previous test by a factor 5.6. To our knowledge, this represents the first reported improvement on one of the longest standing results in experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment back in 1976.
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“The parameter is constrained at the 10 À5 level (Delva et al. 2018;Herrmann et al. 2018).”
From Fundamental constants: from measurement to the universe, a window on gravitation and cosmology (2025) · cites this paper as Delva et al. 2018
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Scargle, J. D. (1982) · The Astrophysical Journal · doi:10.1086/160554 · Cited by 7,454
Numerical Recipes: The Art of Scientific Computing
Ziegel, E. R., Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1987) · Technometrics · doi:10.2307/1269484 · Cited by 6,704
Least-squares frequency analysis of unequally spaced data
Lomb, N. (1976) · Astrophysics and Space Science · doi:10.1007/bf00648343 · Cited by 5,724
Modified gravity and cosmology
Clifton, T., Ferreira, P. G., Padilla, A., & Skordis, C. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.01.001 · Cited by 4,630
The Confrontation between General Relativity and Experiment
Will, C. M. (2014) · Living Reviews in Relativity · doi:10.12942/lrr-2014-4 · Cited by 3,996
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007) · Cambridge University Press eBooks · Cited by 3,328
EGU General Assembly Conference Abstracts
Bell, A., Main, I. G., Atkinson, M., Vicente, R. F., Meredith, P. G., & Boon, S. A. (2013) · Cited by 2,408
Search for new physics with atoms and molecules
Safronova, M. S., Budker, D., DeMille, D. P., Kimball, D. F. J., Derevianko, A., & Clark, C. W. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.025008 · Cited by 1,642
International Geomagnetic Reference Field: the 12th generation
Thébault, E., Finlay, C. C., Beggan, C., Alken, P., Aubert, J., Barrois, O., Bertrand, F., Bondar, T., Boness, A., Brocco, L., et al. (2015) · Earth Planets and Space · doi:10.1186/s40623-015-0228-9 · Cited by 1,513
Altamimi, Z., Rebischung, P., Métivier, L., & Collilieux, X. (2016) · Journal of Geophysical Research: Solid Earth · doi:10.1002/2016jb013098 · Cited by 1,427
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- P. Delva, 2015, Proceedings of the ILRS Technical Workshop, Matera, Italy, 2015
- 2010, IERS Conventions (2010)
- F. Gini, 2014, CISAS-University of Padova
- P. Wolf, 1995, Astron. Astrophys., 304, 653
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Pernot-Borràs, M. (2020) · theses.fr (ABES) · doi:10.70675/c7f9aa83z0947z4242zb871z38dab976b964
Литвинов, Д. А., & Алакоз, А. В. (2025) · Astronomy Letters · doi:10.1134/s1063773726700040
Cordierite-based optical resonators with extremely low thermal expansion
Wagner, N., Legero, T., & Kroker, S. (2026) · Optical Materials Express · doi:10.1364/ome.599638
Ruby, A., Shen, W., Shaker, A., Zhang, P., Wu, K., Ashry, M., & Shen, Z. (2026) · The European Physical Journal C · doi:10.1140/epjc/s10052-026-15897-5
Xu, R. L., Shen, W., Fok, H. S., Zhang, P., Li, L., Wang, L., Wu, K., Ning, A., Xie, Y., Shen, Z., et al. (2026) · The European Physical Journal C · doi:10.1140/epjc/s10052-026-15885-9 · Cited by 1
Anonymous, Qin, C.-G., Gong, Q.-L., Ma, Z., Tan, Y.-J., & Shao, C.-G. (2026) · Physical review. D/Physical review. D. · doi:10.1103/qk9j-42hx
Mengyuan, 韩. H., Xiaolei, 关. G., Xun, 高. G., Jia, 张. Z., Tiantian, 史. S., & Chen, J. (2026) · Acta Optica Sinica (Online) · doi:10.3788/aosol260548
Comment on ‘Matter waves and clocks do not observe uniform gravitational fields’
Nobili, A. M., & Laureijs, R. (2026) · Physica Scripta · doi:10.1088/1402-4896/aeb1fd
Metadata
- Authors
- Delva, P., Puchades, N., Schönemann, E., Dilssner, F., Courde, C., Bertone, S., Gonzalez, F., Hees, A., Le Poncin-Lafitte, C., Meynadier, F., Prieto-Cerdeira, R., Sohet, B., Ventura-Traveset, J., & Wolf, P.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- European Space Operations Centre (DE)
- Observatoire de la Côte d’Azur (FR)
- University of Bern (CH)
- European Space Research and Technology Centre (NL)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2018-12-04
- Volume
- 121
- Issue
- 23
- Pages
- 231101-231101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2903259321
- Cited by
- 210
- References
- 37
- Citations by year
- 2026: 16 · 2025: 21 · 2024: 39 · 2023: 32 · 2022: 32 · 2021: 19 · 2020: 28 · 2019: 22 · 2018: 1
- FWCI
- 9.42
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- European Space Agency
- Generalitat Valenciana (APOSTD2017)
- Observatoire de Paris
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
- Physical Sciences › Engineering › Aerospace Engineering › GNSS positioning and interference
- Keywords
- gravitational redshift, local position invariance, Einstein equivalence principle, Galileo satellites, eccentric orbits, onboard atomic clocks, laser ranging, orbit uncertainty, tests of general relativity
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