Gravitational Redshift Test Using Eccentric Galileo Satellites

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 $(0.19\pm 2.48)\times {10}^{-5}$ 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.

Figure 1

Data analysis flowchart: as input we use ESOC orbit and clock solution files, SLR residuals, as well as clock on-ground characterization. The evaluation of systematics is completely independent from the clock measurements.

Figure 2

Raw clock bias ${\tau }_{\mathrm{ESOC}}$, as read in the ESOC clock solution file.

Figure 3

Clock bias pre-fit residuals are obtained by removing from the raw clock bias ${\tau }_{\mathrm{ESOC}}$ a daily linear fit. Here only the times taken into account in the analysis are shown.

Figure 4

GR prediction, clock data (after removal of a daily linear fit) and residuals are shown for 2 days from March 31, 2016. The peak-to-peak effect is around $0.4\mu \mathrm{s}$, therefore the model and systematic effects at orbital period should be controlled down to 4 ps in order to have a $1\times {10}^{-5}$ uncertainty on the LPI violation parameter $\alpha$.