Fate of bound systems in phantom and quintessence cosmologies

We study analytically and numerically the evolution of bound systems in universes with accelerating expansion where the acceleration either increases with time towards a Big Rip singularity (phantom cosmologies) or decreases with time (quintessence). We confirm the finding of Caldwell et al. [R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).] that bound structures get dissociated in phantom cosmologies but we demonstrate that this happens earlier than anticipated in Ref. [R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).]. In particular we find that the 'rip time' when a bound system gets unbounded is not the time when the repulsive phantom energy gravitational potential due to the average (ρ+3p) balances the attractive gravitational potential of the mass M of the system. Instead, the 'rip time' is the time when the minimum of the time-dependent effective potential (including the centrifugal term) disappears. For the Milky Way galaxy this happens approximately 180 Myrs before the Big Rip singularity instead of approximately 60 Myrs indicated in [R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).] for a phantom cosmology with w=-1.5. A numerical reconstruction of the dissociating bound orbits is presented