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On the equilibrium figure of close-in planets and satellites

Many exoplanets have been observed close to their parent stars with orbital periods of a few days. As for the major satellites of the Jovian planets, the figure of these planets is expected to be strongly shaped by tidal forces. However, contrarily to Solar System satellites, exoplanets may present high values for the obliquity and eccentricity due to planetary perturbations, and may also be captured in spin-orbit resonances different from the synchronous one. Here we give a general formulation of the equilibrium figure of those bodies, that makes no particular assumption on the spin and/or orbital configurations. The gravity field coefficients computed here are well suited for describing the figure evolution of a body whose spin and orbit undergo substantial variations in time.