We investigated spherically symmetric solution for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars. It was shown that the assumption of a polytropic equation, , at the center of the star only suffices to integrate the equations explicitly. Our exact solution yields many fruitful results such as stellar stability, spherical oscillation and collapses of stars. Pressure, temperature, and density profiles inside stars were obtained. Central densities, pressures and temperatures of the Newtonian stars such as Sun, Jupiter and Saturn were also calculated. Collapse and expansion mechanism was explained by the heat transfer mechanism inside star. The upper bound value of white dwarf mass obtained by the Newtonian cosmological fluid equations turns out to be comparable to the static limit of Chandrasekhar one. Motion of the Universe was also discussed within the framework of Newtonian mechanics. Our calculation results without considering nuclear reactions inside stars may be applicable to the formation of protostars.