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This paper presents one analytical tidal theory for a viscoelasticmulti-layered body with an arbitrary number of homogeneous layers. Startingwith the static equilibrium figure, modified to include tide and differentialrotation, and using the Newtonian creep approach, we find the dynamicalequilibrium figure of the deformed body, which allows us to calculate the tidalpotential and the forces acting on the tide generating body, as well as therotation and orbital elements variations. In the particular case of thetwo-layer model, we study the tidal synchronization when the gravitationalcoupling and the friction in the interface between the layers is added. Forhigh relaxation factors (low viscosity), the stationary solution of each layeris synchronous with the orbital mean motion (n) when the orbit is circular, butthe spin rates increase if the orbital eccentricity increases. For lowrelaxation factors (high viscosity), as in planetary satellites, if frictionremains low, each layer can be trapped in different spin-orbit resonances withfrequencies n/2,n,3n/2,... . We apply the theory to Titan. The main resultsare: i) the rotational constraint does not allow us confirm or reject theexistence of a subsurface ocean in Titan; and ii) the crust-atmosphere exchangeof angular momentum can be neglected. Using the rotation estimate based onCassini's observation, we limit the possible value of the shell relaxationfactor, when a subsurface ocean is assumed, to 10^-9 Hz, which correspond to ashell's viscosity 10^18 Pa s, depending on the ocean's thickness and viscosityvalues. In the case in which the ocean does not exist, the maximum shellrelaxation factor is one order of magnitude smaller and the correspondingminimum shell's viscosity is one order higher.

Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation