Since Jupiter and Saturn are considered to be composed primarily of hydrogen, its pressure-density equation of state is needed for computational models of their interiors. Until recently, experimental data were limited to 20 kbar statically and 40 kbar dynamically. Since the majority of a major planet is at a pressure in excess of this, there were only theoretical calculations available for modeling.
Wigner-Seitz type calculations have been shown to be accurate at determining the equations of state of the alkali metals. Hence, it has been assumed that the equation of state of metallic hydrogen can be calculated in the same way with fair confidence. However, the molecular hydrogen equation of state has been much more ellusive. The many attempts at modeling the interatomic forces have led to rather scattered pressure density relationships.
The planetary model situation is further complicated by the expectation that the transition from the molecular to the metallic phase will be in conjunction with a relatively large density change.
Recently, data from new experiments have become available; in one case up to 8 Mbar. The data are not in disagreement with many calculations on hydrogen, but the resolution is not yet adequate to determine accurately and confidently, the pressure and the densities of the molecular to metallic phase transition. The accuracy of these parameters in turn affect the models of the planetary interiors, such as the radii of the metallic sphere and high density core.
This paper will discuss the details of these relations and the possible affects of the speculative properties of metallic hydrogen.