Some dissipative problems in celestial mechanics

In this thesis we study the long term dynamics of some models of celestial mechanics including dissipative effects. Our objective is to characterize solutions with physical relevance from a theoretical point of view. We deal with three models derived from the Two-Body problem. First, we consider the Kepler problem with a biparametric family of dissipative forces, with a singularity at the origin. This family represents several physical phenomena. Here we give a fairly complete description of the qualitative asymptotic behavior of the solutions for a wide range of the parameters. Additionally, we discuss the existence of an asymptotic first integral in some cases. Second, we investigate the spin-orbit problem with a family of dissipative tidal torques. We do so using its full non-autonomous form and allowing large orbital eccentricities. Specifically, we are interested in the existence and asymptotic stability of a particular periodic solution that represents the capture into the synchronous spin-orbit resonance. Our quantitative results are in correspondence with real data of systems such as the Earth-Moon system. Third, we develop a planar version of the Full Two-Body Problem model that generalizes the dissipative spin-orbit model for two extended bodies with mutual spin interaction: the spin-spin model. Following the analogy, we characterize with analytical tools an asymptotically stable periodic solution that represents the double synchronous resonance. Likewise, our results are applied to real bodies such as the Pluto-Charon system and the binary asteroid 617 Patroclus. Our results are based upon analytical methods from dynamical systems, nonlinear analysis, theory of real analytic functions, etc., combined with numerical simulations to validate the results.