Gravitational collapse of Newtonian stars

We investigate spherically symmetric solutions for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars of ideal gas. Using simple ansatze it is shown that the assumption of a polytrope, P-0 = kappa rho(0)(gamma), at the center of the star only suffices to obtain analytic solutions. We find collapse behavior for gamma less than or equal to 4/3 and oscillatory behavior for gamma > 4/3 along with the discussion on their mechanisms. For the oscillatory behavior we obtained the frequency of small oscillation omega which is root 2 times that obtained by Zel'dovich and Novikov.