Appendix 1 - Limits and conditions on planetary models

Summary

Introduction

The only observed mechanical data we have for any planet are the mass and moment of inertia, and infinite sets of models can be constructed consistent with such pairs of data. The sets of models are not, however, unbounded, and, further, certain models are in some sense more probable than others. It is the purpose of this appendix to set out the bounds on two particular models and to give some most probable models. The models considered are: that of two zones, each of constant density, and that in which the density is determined by hydrostatic compression alone. The terrestrial planets may be modelled by the former, and the major planets by the latter. Neither model can represent the complexities of actual planets but, given only two data, no more elaborate model is justified. Guided by the constitution of the Earth, and by such seismic data as are available for the Moon, it is natural to choose the two-zone model as an approximation to the structures of the terrestrial planets. In this model, the maximum pressure is such that changes of density under self-compression are less than differences of density arising from differences of chemical composition or crystal structure in different parts of the planet. Thus, a model comprising two zones of different density is chosen as a basis for study of the terrestrial planets.