  One major objective of MESSENGER and BepiColombo spatial missions is to
accurately measure Mercury's rotation and its obliquity in order to obtain
constraints on internal structure of the planet. Which is the obliquity's
dynamical behavior deriving from a complete spin-orbit motion of Mercury
simultaneously integrated with planetary interactions? We have used our SONYR
model integrating the spin-orbit N-body problem applied to the solar System
(Sun and planets). For lack of current accurate observations or ephemerides of
Mercury's rotation, and therefore for lack of valid initial conditions for a
numerical integration, we have built an original method for finding the
libration center of the spin-orbit system and, as a consequence, for avoiding
arbitrary amplitudes in librations of the spin-orbit motion as well as in
Mercury's obliquity. The method has been carried out in two cases: (1) the
spin-orbit motion of Mercury in the 2-body problem case (Sun-Mercury) where an
uniform precession of the Keplerian orbital plane is kinematically added at a
fixed inclination (S2K case), (2) the spin-orbit motion of Mercury in the
N-body problem case (Sun and planets) (Sn case). We find that the remaining
amplitude of the oscillations in the Sn case is one order of magnitude larger
than in the S2K case, namely 4 versus 0.4 arcseconds (peak-to-peak). The mean
obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference
of 10.8 arcseconds. These theoretical results are in a good agreement with
recent radar observations but it is not excluded that it should be possible to
push farther the convergence process by drawing nearer still more precisely to
the libration center.
