For a static single-zone planet assuming that 1) the pressure and density are connected by the equationP =K Q 1+1/n–s, 2) a complete spherical symmetry is preserved and the system is in hydrostatic equilibrium; in section II, the expressions for the field equations have been obtained in suitable dimensionless forms. In section III the solution of the field equations forn=0 (which represents a homogeneous liquid) has been given in explicit form; for other prescribed value ofn=2/5 it has been pointed out that solutions must be performed by numerical integrations. Expressions for the mass-radius relation, the ratio of central to average density, the total energy, the proper energy and gravitational potential energy, which give some informations about the internal structure of the planet, have also been given in this section. Section IV discusses the velocity of sound at the centre of the planet. A few concluding remarks regarding the structure of the planet have been given in section V.