Dixon's extended bodies and weak gravitational waves

General relativity considers Dixon’s theory as the standard theory to deal
with the motion of extended bodies in a given gravitational background. We discuss
here the features of the “reaction” of an extended body to the passage of a weak
gravitational wave. We find that the body acquires a dipolar moment induced by its
quadrupole structure. Furthermore, we derive the “world function” for the weak field
limit of a gravitational wave background and use it to estimate the deviation between
geodesics and the world lines of structured bodies. Measuring such deviations, due to
the existence of cumulative effects, should be favorite with respect to measuring the
amplitude of the gravitational wave itself.