Title: Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation,
Abstract: This paper presents one analytical tidal theory for a viscoelastic
multi-layered body with an arbitrary number of homogeneous layers. Starting
with the static equilibrium figure, modified to include tide and differential
rotation, and using the Newtonian creep approach, we find the dynamical
equilibrium figure of the deformed body, which allows us to calculate the tidal
potential and the forces acting on the tide generating body, as well as the
rotation and orbital elements variations. In the particular case of the
two-layer model, we study the tidal synchronization when the gravitational
coupling and the friction in the interface between the layers is added. For
high relaxation factors (low viscosity), the stationary solution of each layer
is synchronous with the orbital mean motion (n) when the orbit is circular, but
the spin rates increase if the orbital eccentricity increases. For low
relaxation factors (high viscosity), as in planetary satellites, if friction
remains low, each layer can be trapped in different spin-orbit resonances with
frequencies n/2,n,3n/2,... . We apply the theory to Titan. The main results
are: i) the rotational constraint does not allow us confirm or reject the
existence of a subsurface ocean in Titan; and ii) the crust-atmosphere exchange
of angular momentum can be neglected. Using the rotation estimate based on
Cassini's observation, we limit the possible value of the shell relaxation
factor, when a subsurface ocean is assumed, to 10^-9 Hz, which correspond to a
shell's viscosity 10^18 Pa s, depending on the ocean's thickness and viscosity
values. In the case in which the ocean does not exist, the maximum shell
relaxation factor is one order of magnitude smaller and the corresponding
minimum shell's viscosity is one order higher.