A calculation of Saturn's gravitational contraction history

A gravitational-contraction history is calculated for a homogeneous quasi-equilibrium Saturn model of solar composition without a rock-ice core and without allowance for the possible separation of hydrogen and helium. The calculations begin at the time when Saturn's radius was ten times its current value, and the subsequent gravitational contraction is followed for 4.5 billion years. The results obtained are given in terms of the path of the evolving model on the H-R diagram, the variation of central temperature with central density, the time variation of radius and internal luminosity, and the energy changes that take place during the evolution. These results are compared with those of similar calculations for Jupiter, and the internal structure of the evolutionary models is examined in detail. The Saturn calculations yield a radius at the current epoch that is 9% larger than the observed value and an excess luminosity comparable to that observed. It is noted that an inhomogeneous model containing a solar-mix envelope and a central rocky core has a radius equal to the observed value.