Hi again.

I forgot that the hydrogen on Jupiter and Saturn is diatomic. Being diatomic also means they can rotate. The rotational speed vr of the atoms in a molecule should be considered as well. I have already calculated that for orbiting planets and binary stars and the contribution to the radially outward acceleration is a = vr^2/2/r averaged over one revolution. This will be the value regardless of the orientation of the rotating molecule. Since vr is approximately = v_rms in thermodynamic balance the contribution to the gravitational constant g becomes
g = g_gravitational - v_surface^2/r -2*v_rms^2/3r - 2*v_rms^2/2 =
= g_gravitaional - v_surface^2/r -5*v_rms^2/3r

I am not entirely sure if the molecules rotational contribution is 2*v_rms^2/2 but it seems so since there are either two degrees of freedom or two atoms. So I think with either view that the contribution is 2*v_rms^2/2.

With the molecular contribution 2.5 times greater than before figures become different.

Earth: g = 9.717, 0.95% lower
Venus: g = 8.756, 1.3 % lower

Equilibrium temperatures
At a certain temperature the centrifugal acceleration from thermal motion will compensate for gravity's pull.
g = 5*v_rms^2/3r = v_rms=sqrt(3*g*r/5) = T = v_rms^2*Mm/3/R = g*r*Mm/5/r

Jupiter equilibrium temperatu T = 86 000 K
Saturn equilibrium temperatu T = 28 800 K
These temperatures are not reached within the interior of those planets as far as Internet sites say. But the effect, if properly determined, would change the calculation about the interior of those and other planets. Even the liquid cores would have an adiabatic heat gradient dependent on thermal motion.

Maybe the equilibrium temperatures could be reached in stars.

David