  We compare the rigorous equations describing the motion of spinning test
particles in gravitational and electromagnetic fields, and show that if the
Mathisson-Pirani spin condition holds then exact gravito-electromagnetic
analogies emerge. These analogies provide a familiar formalism to treat
gravitational problems, as well as a means for comparing the two interactions.
Fundamental differences are manifest in the symmetries and time projections of
the electromagnetic and gravitational tidal tensors. The physical consequences
of the symmetries of the tidal tensors are explored comparing the following
analogous setups: magnetic dipoles in the field of non-spinning/spinning
charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter
spacetimes. The implications of the time projections of the tidal tensors are
illustrated by the work done on the particle in various frames; in particular,
a reciprocity is found to exist: in a frame comoving with the particle, the
electromagnetic (but not the gravitational) field does work on it, causing a
variation of its proper mass; conversely, for "static observers," a stationary
gravitomagnetic (but not a magnetic) field does work on the particle, and the
associated potential energy is seen to embody the Hawking-Wald spin-spin
interaction energy. The issue of hidden momentum, and its counterintuitive
dynamical implications, is also analyzed. Finally, a number of issues regarding
the electromagnetic interaction and the physical meaning of Dixon's equations
are clarified.
