In this talk, I will discuss the long time dynamics of a compact compressible viscous gases into vacuum under the self-gravitation. Such a problem is governed by the compressible Navier-Stokes –Poisson system with either uniform or degenerate viscosities. In particular, I will present some of the recent results on the nonlinear asymptotic stability of the Lane-Emden solution and the idea and techniques of the analysis. These works are joinly with Tao LUO and Huihui ZENG