  Tidal interactions between neighboring objects span across the whole
admissible range of lengths in nature: from, say, atoms to clusters of galaxies
i.e. from micro to macrocosms. According to current cosmological theories,
galaxies are embedded within massive non-baryonic dark matter (DM) halos, which
affects their formation and evolution. It is therefore highly rewarding to
understand the role of tidal interaction between the dark and luminous matter
in galaxies. The current investigation is devoted to Early-Type Galaxies
(ETGs), looking in particular at the possibility of establishing whether the
tidal interaction of the DM halo with the luminous baryonic component may be at
the origin of the so-called "tilt" of the Fundamental Plane (FP). The extension
of the tensor virial theorem to two-component matter distributions implies the
calculation of the self potential energy due to a selected subsystem, and the
tidal potential energy induced by the other one. The additional assumption of
homeoidally striated density profiles allows analytical expressions of the
results for some cases of astrophysical interest. The current investigation
raises from the fact that the profile of the (self + tidal) potential energy of
the inner component shows maxima and minima, suggesting the possible existence
of preferential scales for the virialized structure, i.e. a viable explanation
of the so called "tilt" of the FP. It is found that configurations related to
the maxima do not suffice, by themselves, to interpret the FP tilt, and some
other relation has to be looked for.
