ANALYTIC MODELS OF PLANETARY-ATMOSPHERES - POWER-OF-RADIUS AND OTHER FUNCTIONS FOR STRUCTURE AND CONTENT

For spherical atmospheres of ideal gases in hydrostatic equilibrium, the barometric equation has two kinds of functional solutions when gravity and temperature are assumed to be proportional to arbitrary powers of radius. Normalized pressure is given either by a restricted solution, which is a power of normalized radius, or more broadly by the exponential of a function of radius. Atmospheric models have been based on several special cases of the exponential type. In some applications, however, the power-of-radius model may be more versatile and useful since all of the functions that describe atmospheric structure (temperature, pressure, density, pressure scale height, and density scale height) and content (density integrated along semi-infinite vertical and infinite tangential straight paths) are simple powers of radius. Starting from the exponential solution for pressure, the general result for vertical content involves more esoteric functions or is infinite while the tangential content, when finite, is not expressible as a standard function. For particular cases where the tangential content or its derivatives are finite and tractable, a mix of modified Bessel and modified Struve functions can come into play. There is a special interest here in the simpler power-law models as building blocks for a superposition-of-models technique that is under development. Preliminary results involving the superposition of two model densities have demonstrated that it is feasible to illustrate, study, and elucidate connections between distinctive atmospheric structure and the resulting features of remote sensing measurements as obtained in stellar and spacecraft occultation experiments. This paper is the first of several planned on this subject. It is limited to a consideration of the properties of the power-of-radius and exponential types of models for representing atmospheric structure and content. © 1993 by Academic Press, Inc.