  In this paper we start a global study of the parameter space (dissipation,
perturbation, frequency) of the dissipative spin-orbit problem in Celestial
Mechanics with the aim of delimiting regions where the dynamics, or at least
some of its important features, is determined. This is done via a study of the
corresponding family of time $2\pi$-maps. In the same spirit as Chenciner in
his 1895 article on bifurcations of elliptic fixed points, we are at first
interested in delimiting regions where the normal hyperbolicity is sufficiently
important to guarantee the persistence of an invariant attractive (resp.
repulsive) circle under perturbation. As a tool, we use an analogue for
diffeomorphisms in this family of R\"ussmann's translated curve theorem in
analytic category.
