Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6 [Cross-Listing]

In this paper we propose to use satellites Galileo~5 and~6 to perform a test of the gravitational redshift. The best test to date was performed with the Gravity Probe A experiment (1976) with an accuracy of $1.4\times 10^{-4}$. Here we show that considering realistic noise and systematic effects, and thanks to a highly eccentric orbit, it is possible to improve the GP-A limit to an accuracy around $(3-4)\times 10^{-5}$ after one year of integration of Galileo~5 and~6 data.