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Mercury is expected to deviate from the classical Cassini state since thisstate is defined for a uniformly precessing rigid planet. We develop anextended Cassini state model that includes the variations (or nutations) inobliquity and deviation induced by the slow precession of the pericenter. Themodel also describes the constant shift over time in mean obliquity anddeviation associated with the short-periodic tidal deformations of Mercury,characterized by the tidal love number k2 and by the ratio k2/Q of the tidalLove number over the tidal quality factor, respectively. This model is thenused to interpret Mercury's orientation, including the deviation from theclassical 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 tidaldeformations on the spin precession behavior. We also show explicitly thatPeale's equation is sometimes wrongly cited in the literature, resulting inwrong estimates of the polar moment of inertia, and review the importance ofmany effects that change the determination of the polar moment of inertia fromobliquity measurements.  From the observed orientation of Stark et al. (2015b), we estimate thatC/MR^2=0.3434+/-0.0102, which is ~0.9% smaller than the estimate by Stark etal. (2015b) themselves. That difference is due to our refinements of theCassini 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 momentof inertia but may be of the order of precision that can be reached withBepiColombo mission (<=0.3%).

Obliquity of Mercury: influence of the precession of the pericenter and of tides