  For the non-rotating gaseous stars modeled by the compressible Euler-Poisson
system with general pressure law, Lin and Zeng [18] proved a turning point
principle, which gives the sharp linear stability/instability criteria for the
non-rotating gaseous stars. In this paper, we prove that the sharp linear
stability criterion for the non-rotating stars also implies nonlinear orbital
stability against general perturbations provided the global weak solutions
exist. If the perturbations are further restricted to be spherically symmetric,
then nonlinear stability holds true unconditionally in the sense that the
existence of global weak solutions near the non-rotating star can be proved.
