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This paper deals with the rotation and figure evolution of a planet near the3/2 spin-orbit resonance and the exploration of a new formulation of the creeptide theory (Folonier et al. 2018). This new formulation is composed by asystem of differential equations for the figure and the rotation of the bodysimultaneously (which is the same system of equations used in Folonier et al.2018), different from the original one (Ferraz-Mello, 2013, 2015a) in whichrotation and figure were considered separately. The time evolution of thefigure 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 ofnon-rigid homogeneous bodies whose endpoint of rotational evolution from tidalinteractions is the 3/2 spin-orbit resonance, provided that (i) an initiallyfaster rotation is assumed and (ii) no permanent components of the flatteningsof 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 3/2spin-orbit resonance with its orbital motion and we obtain 4.8 times 10 -8 s -1lower than gamma lower than 4.8 times 10 -9 s -1 . The equatorial prolatenessand polar oblateness coefficients obtained for Mercury's figure with such rangeof 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 flatteningsobtained for such range of gamma with those obtained from MESSENGER'smeasurements (Perry et al. 2015), we see that the current values for Mercury'sequatorial prolateness and polar oblateness are 2-3 orders of magnitude largerthan the values given by the tidal theories.

Rotation and figure evolution in the creep tide theory. A new approach and application to Mercury