  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 $2\times10^{-14}$ 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 $1\times10^{-11}$ 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 $4\times10^{-14}$ 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 $1\times10^{-16}$, 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.
