  In this paper we present a new approach to tidal theory. Assuming a Maxwell
viscoelastic rheology, we compute the instantaneous deformation of celestial
bodies using a differential equation for the gravity field coefficients. This
method allows large eccentricities and it is not limited to quasi-periodic
perturbations. It can take into account an extended class of perturbations,
including chaotic motions and transient events. We apply our model to some
already detected eccentric hot Jupiters and super-Earths in planar
configurations. We show that when the relaxation time of the deformation is
larger than the orbital period, spin-orbit equilibria arise naturally at
half-integers of the mean motion, even for gaseous planets. In the case of
super-Earths, these equilibria can be maintained for very low values of
eccentricity. Our method can also be used to study planets with complex
internal structures and other rheologies.
