  Mercury is expected to deviate from the classical Cassini state since this
state is defined for a uniformly precessing rigid planet. We develop an
extended Cassini state model that includes the variations (or nutations) in
obliquity and deviation induced by the slow precession of the pericenter. The
model also describes the constant shift over time in mean obliquity and
deviation associated with the short-periodic tidal deformations of Mercury,
characterized by the tidal love number k2 and by the ratio k2/Q of the tidal
Love number over the tidal quality factor, respectively. This model is then
used to interpret Mercury's orientation, including the deviation from the
classical Cassini state, in terms of parameters of Mercury's interior.
  We determine and solve analytically the angular momentum equation,
highlighting the respective roles of the pericenter precession and tidal
deformations on the spin precession behavior. We also show explicitly that
Peale's equation is sometimes wrongly cited in the literature, resulting in
wrong estimates of the polar moment of inertia, and review the importance of
many effects that change the determination of the polar moment of inertia from
obliquity measurements.
  From the observed orientation of Stark et al. (2015b), we estimate that
C/MR^2=0.3434+/-0.0102, which is ~0.9% smaller than the estimate by Stark et
al. (2015b) themselves. That difference is due to our refinements of the
Cassini state model (0.1%) and to their wrong use of Peale's equation (0.8%).
The difference is smaller than the actual precision (3-4%) on the polar moment
of inertia but may be of the order of precision that can be reached with
BepiColombo mission (<=0.3%).
