Radiation pressure dynamics in planetary exospheres: A “natural” framework

Abstract

Constituent atoms of a planetary exosphere are subject to an effective radiation pressure resulting from resonant scattering of solar photons. When this is taken into account, particle trajectories can depart significantly from Keplerian conterparts, with consequent effects on exospheric structure. This paper introduces and explores a reformulation of exospheric mechanics with radiation pressure based on parabolic-cylindrial coordinates. With the aid of a previously unutilized constant of motion, considerable insight into trajectory behavior is gained without explicit integration of the equations of motion; this new constant is identified as a remmant of the Laplace-Runge-Lenz vector invariant of the Keplerian problem. The existence of this constant permits the derivation of analytic expressions for exospheric quantities along the subsolar and antisolar axes when the exobase is uniform and collisions are neglected. To illustrate the usefulness of this formalism, “tail” ratios (i.e., ratios of bound component densities along the midnight axis to those along the noon axis) are presented for the H exospheres of Venus, Earth, and Mars, and for the Na exosphere of Mercury.