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The evolution of a small satellite inside a more massive truncated isothermalspherical halo is studied using both the Theory of Linear Response fordynamical friction and N-Body simulations. The analytical approach includes theeffects of the gravitational wake, of the tidal deformation and the shift ofthe barycenter of the primary, so unifying the local versus globalinterpretation of dynamical friction. Sizes, masses, orbital energies andeccentricities are chosen as expected in hierarchical clustering models. Wefind that in general the drag force in self-gravitating backgrounds is weakerthan in uniform media and that the orbital decay is not accompanied by asignificant circularization. We also show that the dynamical friction timescale is weakly dependent on the initial circularity. We provide a fittingformula for the decay time that includes the effect of mass and angularmomentum loss. Live satellites with dense cores can survive disruption up to anHubble time within the primary, notwithstanding the initial choice of orbitalparameters. Dwarf spheroidal satellites of the Milky Way, like Sagittarius Aand Fornax, have already suffered mass stripping and, with their presentmasses, the sinking times exceed 10 Gyr even if they are on very eccentricorbits.Comment: 27 pages including 9 figures. Accepted for publication in the  Astrophysical Journal. Part 2, issue November 10 1999, Volume 52

Dynamical Friction and the Evolution of Satellites in Virialized Halos: The Theory of Linear Response