Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter, we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these, we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.

Figure 1

Top: Correction as applied to the ESOC clock data for the first day in GPS week 1938 (a linear drift has been removed). The correction is the difference of Eq. (3) and the numerically integrated redshift model along the perturbed real orbit of GSAT-0202. This includes the redshift contribution from the mass quadrupole ($J_2$) which is shown separately in addition. Bottom: An FFT of the differentiated clock estimates of GSAT-0202 for GPS week 1938 before and after the correction was applied.

Figure 2

Distribution of daily test parameter results for clocks 1, 3, and 5. Error bars are the $1\sigma$ fit errors from the respective least squares fit. Gaps in the data of clocks 1 and 3 are when there was no clock transmission. Note, also, that we exclude 13 days in the data of clock 5 coinciding with an interruption of clock operation of PHM A following day 670.

Figure 3

Shown are the marginalized posteriors including the systematic corrections for the single clocks as well as for the combination of all three clocks. The vertical lines in the plots mark the posterior mean as well as the equal tailed 68% (dashed lines) and 95% (dotted lines) intervals. Numbers stated in the graphs are all times ${10}^{-5}$.