  In a previous paper we have shown that the function \Gamma(M,
EOS)=\alpha\beta_{GR}/\Lambda^{0.9}(R) is constant (~ 0.4) for pre
main-sequence stars (PMS), white dwarfs (WD) and for some neutron star (NS)
models, where \alpha_{GR} and \beta_{GR} are the form-factors of the
gravitational potential energy and of the moment of inertia. To investigate the
structural evolution of another type of celestial bodies, we use the MESA code
to extend these calculations to gaseous planets. We show that this function is
conserved for all models during the whole planetary evolution and is
independent of the planet mass. We also analyse the cases for which this
function is not conserved during some stellar evolutionary phases. For the PMS
to the WD cooling sequences, we have found a connection between the strong
variations of \Gamma(M, EOS) during the intermediary evolutionary phases and
the specific nuclear power. A threshold for the specific nuclear power was
determined. Below this limit this function is invariant (~ 0.4) for these
models, i.e., at the initial and final stages (PMS and WD). Concerning NS, we
study the influence of the equation of state (EOS) on this function and refine
the exponent of the auxiliary function \Lambda(R) to be ~ 0.8. It is shown that
the function \Gamma(M, EOS) is also invariant (~ 0.4) and is independent of the
EOS and of the stellar mass. Therefore, we confirm that regardless of the final
products of the stellar evolution, NS or WD, they recover the initial value of
\Gamma(M, EOS) ~ 0.4 acquired at the PMS. Finally, we have introduced a
macroscopic stability "criterion" for neutron star models based on the
properties of the relativistic product \alpha\beta_{GR}.
