  The evolution of a bound system in the expanding background has been
investigated in this paper. The background is described by a FRW universe with
the modified holographic dark energy model, whose equation of state parameter
changes with time and can cross the phantom boundary. To study the evolution of
the bound system, an interpolating metric is considered, and on this basis the
geodesics of a test particle are given. The equation of motion and the
effective potential are also derived from the geodesics. By studying the the
effective potential and the evolution of the radius of a test particle in the
bound system of the Milky Way galaxy, we have found that the galaxy would go
through three stages: expands from a singular point; stays in a discoid for a
period of time; big rip in the future. With the help of analysing the critical
angular momentum, we find that the test particle needs less angular momentum to
escape from the center mass as time passes.
