The motion of an extended body up to the quadrupolar structure is studied in
the Schwarzschild background following Dixon's model and within certain
restrictions (constant frame components for the spin and the quadrupole tensor,
center of mass moving along a circular orbit, etc.). We find a number of
interesting situations in which deviations from the geodesic motion, due to the
internal structure of the particle, can originate measurable effects. However,
the standard clock-effect for a pair co/counter-rotating bodies spinning
up/down is not modified by the quadrupolar structure of the particle.Comment: 9 pages, latex iopart class document, no figures. Note that the
second term in the rhs of Eq. (1.2) was misprinted in the published version
of the paper [Classical and Quantum Gravity, Vol. 25, 035005 (2008)]. The
results are but correc
