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In this paper, we present a formalism designed to model tidal interactionwith a viscoelastic body made of Maxwell material. Our approach remains regularfor any spin rate and orientation, and for any orbital configuration includinghigh eccentricities and close encounters. The method is to integratesimultaneously the rotation and the position of the planet as well as itsdeformation. We provide the equations of motion both in the body frame and inthe inertial frame. With this study, we generalize preexisting models to thespatial case and to arbitrary multipole orders using a formalism taken fromquantum theory. We also provide the vectorial expression of the secular tidaltorque expanded in Fourier series. Applying this model to close-in exoplanets,we observe that if the relaxation time is longer than the revolution period,the phase space of the system is characterized by the presence of severalspin-orbit resonances, even in the circular case. As the system evolves, theplanet spin can visit different spin-orbit configurations. The obliquity isdecreasing along most of these resonances, but we observe a case where theplanet tilt is instead growing. These conclusions derived from the seculartorque are successfully tested with numerical integrations of the instantaneousequations of motion on HD 80606b. Our formalism is also well adapted toclose-in super-Earths in multiplanet systems which are known to have non-zeromutual inclinations.

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology