Analytic Models of Planetary Atmospheres: Occultation Transform Pairs

Abstract

The occultation technique for the study of planetary atmospheres has been proven to be effective. Two integrals that are related to an Abel transform pair describe the fundamental connection between the vertical structure of atomspheric refractivity and its occultation signature. There has not been even one example of an exact analytic pair of solutions of these integrals for use as an aid to technique development and basic understanding of the occultation problem. Several exact pairs are developed here, where a different one of each pair is a simple power law and the other is a series of power-law terms. A method is outlined for representing characteristic atmospheric vertical structures and occultation signatures by superposition, and aspects of the results on exact pairs and on superposition are verified by comparison with known solutions for a gravitational lens.