  Experimental discovery of the gravitomagnetic fields generated by
translational and/or rotational currents of matter is one of primary goals of
modern gravitational physics. The rotational (intrinsic) gravitomagnetic field
of the Earth is currently measured by the Gravity Probe B. The present paper
makes use of a parametrized post-Newtonian (PN) expansion of the Einstein
equations to demonstrate how the extrinsic gravitomagnetic field generated by
the translational current of matter can be measured by observing the
relativistic time delay caused by a moving gravitational lens. We prove that
measuring the extrinsic gravitomagnetic field is equivalent to testing
relativistic effect of the aberration of gravity caused by the Lorentz
transformation of the gravitational field. We unfold that the recent Jovian
deflection experiment is a null-type experiment testing the Lorentz invariance
of the gravitational field (aberration of gravity), thus, confirming existence
of the extrinsic gravitomagnetic field associated with orbital motion of
Jupiter with accuracy 20%. We comment on erroneous interpretations of the
Jovian deflection experiment given by a number of researchers who are not
familiar with modern VLBI technique and subtleties of JPL ephemeris. We propose
to measure the aberration of gravity effect more accurately by observing
gravitational deflection of light by the Sun and processing VLBI observations
in the geocentric frame with respect to which the Sun is moving with velocity
30 km/s.
