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.

中文翻译：

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蠕变潮理论中的旋转和图形演化：一种新的水星方法和应用

本文涉及 3/2 自旋轨道共振附近行星的自转和图形演化，以及对蠕变潮理论新公式的探索（Folonier 等人，2018 年）。这个新公式由一个同时用于图形和身体旋转的微分方程组组成（与 Folonier et al. 2018 中使用的方程组相同），与原始方程不同（Ferraz-Mello，2013， 2015a)，其中旋转和图形被分开考虑。研究了 3/2 和 2/1 自旋轨道共振的身体形状的时间演变。此外，我们提供了一种确定非刚性均质体的弛豫因子 gamma 的方法，其潮汐相互作用的旋转演化终点是 3/2 自旋轨道共振，假设 (i) 假设初始旋转速度更快，并且 (ii) 在 3/2 自旋轨道共振中捕获时不存在物体扁平的永久分量。该方法适用于水星，因为它目前被困在 3/2 自旋轨道共振及其轨道运动中，我们得到 4.8 倍 10 -8 s -1 比伽马低 4.8 倍 10 -9 s -1 。对于具有这种伽马值范围的水星图形，获得的赤道平面度和极扁度系数与达尔文-考拉模型（Matsuyama 和 Nimmo 2009）给出的相同。但是，将针对此类伽马范围获得的平坦化值与从 MESSENGER 的测量中获得的值（Perry 等人，2015 年）进行比较，我们看到 Mercury 的当前值