  Earth-based radar observations of the rotational dynamics of Mercury (Margot
et al. 2012) combined with the determination of its gravity field by MESSENGER
(Smith et al. 2012) give clues on the internal structure of Mercury, in
particular its polar moment of inertia C, deduced from the obliquity (2.04 +/-
0.08) arcmin.
  The dynamics of the obliquity of Mercury is a very-long term motion (a few
hundreds of kyrs), based on the regressional motion of Mercury's orbital
ascending node. This paper, following the study of Noyelles & D'Hoedt (2012),
aims at first giving initial conditions at any time and for any values of the
internal structure parameters for numerical simulations, and at using them to
estimate the influence of usually neglected parameters on the obliquity, like
J3, the Love number k2 and the secular variations of the orbital elements. We
use for that averaged representations of the orbital and rotational motions of
Mercury, suitable for long-term studies.
  We find that J3 should alter the obliquity by 250 milli-arcsec, the tides by
100 milli-arcsec, and the secular variations of the orbital elements by 10
milli-arcsec over 20 years. The resulting value of C could be at the most
changed from 0.346mR^2 to 0.345mR^2.
