We present an improved model for the antenna phase center motion effect for high-gain mechanically steerable ground-based and spacecraft-mounted antennas that takes into account non-perfect antenna pointing. Using tracking data of the RadioAstron spacecraft we show that our model can result in a correction of the computed value of the effect of up to 2×10^-14 in terms of the fractional frequency shift, which is significant for high-accuracy spacecraft tracking experiments. The total fractional frequency shift due to the phase center motion effect can exceed 1×10^-11 both for the ground and space antennas depending on the spacecraft orbit and antenna parameters. We also analyze the error in the computed value of the effect and find that it can be as large as 4×10^-14 due to uncertainties in the spacecraft antenna axis position, ground antenna axis offset and misalignment, and others. Finally, we present a way to reduce both the ground and space antenna phase center motion effects by several orders of magnitude, e.g. for RadioAstron to below 1×10^-16, by tracking the spacecraft simultaneously in the one-way downlink and two-way phase-locked loop modes, i.e. using the Gravity Probe A configuration of the communications links.

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 ∼7000 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 ∼9 d orbit, the gravitational redshift between the spacecraft and the ground stations varies between 6.8×10-10 and 0.6×10-10. 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 [Formula preseted] 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.

We present an approach to testing the gravitational redshift effect using the RadioAstron satellite. The experiment is based on a modification of the Gravity Probe A scheme of nonrelativistic Doppler compensation and benefits from the highly eccentric orbit and ultra-stable atomic hydrogen maser frequency standard of the RadioAstron satellite. Using the presented techniques we expect to reach an accuracy of the gravitational redshift test of order 10-5, a magnitude better than that of Gravity Probe A. Data processing is ongoing, our preliminary results agree with the validity of the Einstein Equivalence Principle.