  This paper deals with the rotation and figure evolution of a planet near the
3/2 spin-orbit resonance and the exploration of a new formulation of the creep
tide theory (Folonier et al. 2018). This new formulation is composed by a
system of differential equations for the figure and the rotation of the body
simultaneously (which is the same system of equations used in Folonier et al.
2018), different from the original one (Ferraz-Mello, 2013, 2015a) in which
rotation and figure were considered separately. The time evolution of the
figure of the body is studied for both the 3/2 and 2/1 spin-orbit resonances.
Moreover, we provide a method to determine the relaxation factor gamma of
non-rigid homogeneous bodies whose endpoint of rotational evolution from tidal
interactions is the 3/2 spin-orbit resonance, provided that (i) an initially
faster rotation is assumed and (ii) no permanent components of the flattenings
of the body existed at the time of the capture in the 3/2 spin-orbit resonance.
The method is applied to Mercury, since it is currently trapped in a 3/2
spin-orbit resonance with its orbital motion and we obtain 4.8 times 10 -8 s -1
lower than gamma lower than 4.8 times 10 -9 s -1 . The equatorial prolateness
and polar oblateness coefficients obtained for Mercury's figure with such range
of values of gamma are the same as the ones given by the Darwin-Kaula model
(Matsuyama and Nimmo 2009). However, comparing the values of the flattenings
obtained for such range of gamma with those obtained from MESSENGER's
measurements (Perry et al. 2015), we see that the current values for Mercury's
equatorial prolateness and polar oblateness are 2-3 orders of magnitude larger
than the values given by the tidal theories.
