  Experimental verification of the existence of gravimagnetic fields generated
by currents of matter is important for a complete understanding and formulation
of gravitational physics. Although the rotational `intrinsic' gravimagnetic
field has been extensively studied and is now being measured by the Gravity
Probe B, the `extrinsic' gravimagnetic field generated by the translational
current of matter is less well studied. The present paper uses the
post-Newtonian parametrized Einstein and light geodesics equations to show that
the `extrinsic' gravimagnetic field generated by the translational current of
matter can be measured by observing the relativistic time delay and/or light
deflection caused by the moving mass. We prove that the `extrinsic'
gravimagnetic field is generated by the relativistic effect of the aberration
of the gravity force caused by the Lorentz transformation of the metric tensor
and the Levi-Civita connection. We show that the Lorentz transformation of the
gravity field variables is equivalent to the technique of the retarded
Lienard-Wiechert gravitational potentials predicting that a light particle is
deflected by gravitational field of a moving body from its retarded position so
that both general-relativistic phenomena -- the aberration and the retardation
of gravity -- are tightly connected and observing the aberration of gravity
proves that gravity has a causal nature. We explain in this framework the 2002
deflection experiment of a quasar by Jupiter where the aberration of gravity
from its orbital motion was measured with accuracy 20%. We describe a theory of
VLBI experiment to measure the gravitational deflection of radio waves from a
quasar by the Sun, as viewed by a moving observer from the geocentric frame, to
improve the measurement accuracy of the aberration of gravity to a few percent.
