# A gravitational redshift test using eccentric Galileo satellites

## TL;DR

This study uses data from eccentric Galileo satellites over 1008 days to perform a precise test of gravitational redshift, confirming Einstein's predictions with improved accuracy and marking a significant advancement in experimental gravitation.

## Contribution

It presents the first significant improvement in gravitational redshift testing since 1976, utilizing eccentric satellite data and advanced systematic effect modeling.

## Key findings

- Measured deviation of gravitational redshift: (+0.19 ± 2.48)×10^{-5}
- Improved test accuracy by a factor of 5.6 over previous results
- First enhancement of long-standing gravitational redshift tests since 1976

## Abstract

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 (GNSS), 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 modelling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be $(+0.19 \pm 2.48)\times10^{-5}$ 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.