Abstract
Data from single orbital periods of the two Galileo satellites E14 (GSAT 202) and E18 (GSAT 201) in highly eccentric orbits on 4 separate days during portions of 2018–2021 have been used to test a possible violation of Einstein's General Relativity (GR). Precise Galileo E14 and E18 orbit/clock solutions of 5 Analysis Centers (AC), participating in the Multi-GNSS Experiment (MGEX), have been used in the GR validity (scale) tests. Using the AC clock solutions without any orbit corrections, possible single-orbit GR scale variations were detected at the 1 × 10−4 level with the weighted mean of all single-orbit GR scale solutions of (4.1 ± 1.9) × 10−5. In order to correct for possible orbit errors affecting the AC clock solutions, the 5 AC E14 and E18 orbit/clock solutions have been combined for 3 separate days during 2020–21, approximating the Final GPS orbit/clock combination method routinely performed by the International GNSS Service (IGS). All 5 AC E14 and E18 orbit solutions agreed at the 1–2 cm level and most AC clock solutions agreed within 20–60 ps, which is approaching the precision and consistency of the well matured IGS AC GPS orbit/clock solutions. When the combined E14 and E18 AC clock solutions, corrected for the radial orbital errors obtained from the above orbit combinations, were used in the GR tests, the solution of (3.5 ± 3.3) × 10−5 (implying no GR violation) was obtained, based on 5 orbital periods of E14 and E18, during 2020–2021. These GR tests critically rely on well-behaving and stable Passive Hydrogen Maser (PHM) clocks. The E14 PHM clocks behaved well and within the Galileo PHM specifications during the period of 2018–2021, analyzed here. However, up to about mid-2020, the E18 PHM clock behaved poorly, outside the specifications, and could not be used before mid-2020.
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Data availability
The MGEX AC orbit/clock solutions are readily available from the IGS data centers (https://www.igs.org/products-access/#gps-orbits-clocks); ESA orbit/clock solutions are available at http://navigation-office.esa.int/products/gnss-products/.
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Acknowledgements
IGS (Johnston et al. 2017) and ESA solution products have been used and are gratefully acknowledged. François Lahaye, formerly of the Canadian Geodetic Survey, NRCan, has kindly agreed to read this contribution and provided the author with valuable suggestions and comments.
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Appendix
Appendix
See Tables
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See Figs.
E14(GSAT 202) orbital period on June 29, 2020: top—input AC clock solutions, offset and drift-corrected; bottom—AC clock solution residuals after GR adjustments, also indicated here are the noon (↓) and midnight (↑) crossing times
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E14(GSAT 202) high-frequency amplitudes for the orbital period of June 29, 2020: top—the input AC clock solutions, corrected for an offset and drift; bottom—GR adjustment residuals
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E18 (GSAT 201) high-frequency amplitudes for the orbital period of June 29, 2020: top—the input AC clock solutions, corrected for an offset and drift; bottom—GR adjustment residuals
13.
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Kouba, J. Testing of general relativity with two Galileo satellites in eccentric orbits. GPS Solut 25, 139 (2021). https://doi.org/10.1007/s10291-021-01174-3
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DOI: https://doi.org/10.1007/s10291-021-01174-3