Inertia coefficient considerations and the structure of Jovian planets

Abstract

For Jupiter, an overall density model of the formρ=ρ ₀(1−x ⁿ), withn≈1/3 and$\rho _0 /\bar \rho \approx 10$, is consistent with information presently at hand; for Saturn, however, such a density law would lead to unacceptably high densities in the vicinity of the centre. The limiting cases of the previous law are shown to ben=+∞, corresponding to a homogeneous sphere, andn=−3, corresponding to a particular central particle model, investigated by a number of astronomers over the last hundred years. Forn≤0, the central density becomes +∞. Another possible representation, valid both for Jupiter and Saturn, is the density lawρ=ρ ₀(1−x)^m), with$m \approx \frac{7}{6},\rho _0 /\bar \rho \approx 4.7$ in the case of Jupiter, and$m \approx \frac{5}{3},\rho _0 /\bar \rho \approx 7.5$ in the case of Saturn. Graber's density law based on a maximum entropy principle leads to unacceptably high surface densities, both for Jupiter and Saturn. Finally, the paper investigates the problems involved in fitting two-layered parametrically simple density laws to theoretically derived much more elaborate models of the Jovian planets.