A SIMPLE MATHEMATICAL MODEL FOR ESTIMATING PLANETARY AND SATELLITE CORE DIMENSIONS

A simple mathematical model is developed to facilitate estimates of planetary and satellite core radii. Using estimates of total mass, bulk density, and relevant material (metal, rock, ice) densities derived from spacecraft data and straight forward geologic reasoning, a planet’s core dimensions can be reasonably constrained. The model uses two components (core and mantle) which can easily accommodate more complex stratified situations. After demonstrating the efficacy of the technique for Earth, estimates for all planets of the inner solar system are made which fall within published ranges. Applications to satellites of the outer system, especially Ganymede, yield results which have implications for models of magnetic fields generated by rheologically active metal cores. For instance, we argue that Ganymede’s core radius of approxitely 750 km or 25% of its equatorial radius is too small to accommodate an active metal core. We believe that this model is an excellent tool for making first-order approximations of planetary structure and as a teaching tool.