We report on our efforts to test the Einstein Equivalence Principle by measuring the gravitational redshift with the VLBI spacecraft RadioAstron , in an eccentric orbit around Earth with geocentric distances as small as \sim 7,000 km and up to 350,000 km .
The spacecraft and its ground stations are each equipped with stable hydrogen maser frequency standards , and measurements of the redshifted downlink carrier frequencies were obtained at both 8.4 and 15 GHz between 2012 and 2017 .
Over the course of the \sim 9 d orbit , the gravitational redshift between the spacecraft and the ground stations varies between 6.8 \times 10 ^ { -10 } and 0.6 \times 10 ^ { -10 } .
Since the clock offset between the masers is difficult to estimate independently of the gravitational redshift , only the variation of the gravitational redshift is considered for this analysis .
We obtain a preliminary estimate of the fractional deviation of the gravitational redshift from prediction of \epsilon = -0.016 \pm 0.003 _ { stat } \pm 0.030 _ { syst } with the systematic uncertainty likely being dominated by unmodelled effects including the error in accounting for the non-relativistic Doppler shift .
This result is consistent with zero within the uncertainties .
For the first time , the gravitational redshift has been probed over such large distances in the vicinity of Earth .
About three orders of magnitude more accurate estimates may be possible with RadioAstron using existing data from dedicated interleaved observations combining uplink and downlink modes of operation .