Theory for planetary exospheres: I. Radiation pressure effect on dynamical trajectories

TL;DR

This paper derives complete analytical solutions for particle trajectories in planetary exospheres considering radiation pressure, extending previous work and providing new formulations applicable to classical Stark problems.

Contribution

It presents the full set of exact solutions for particle trajectories under solar radiation pressure, including new solutions and simplified forms for known cases.

Findings

Exact solutions for particle trajectories affected by radiation pressure

Comparison with previous studies and new formulations

Application to classical Stark problem with Jacobi elliptic functions

Abstract

The planetary exospheres are poorly known in their outer parts, since the neutral densities are low compared with the instruments detection capabilities. The exospheric models are thus often the main source of information at such high altitudes. We present a new way to take into account analytically the additional effect of the radiation pressure on planetary exospheres. In a series of papers, we present with an Hamiltonian approach the effect of the radiation pressure on dynamical trajectories, density profiles and escaping thermal flux. Our work is a generalization of the study by Bishop and Chamberlain (1989). In this first paper, we present the complete exact solutions of particles trajectories, which are not conics, under the influence of the solar radiation pressure. This problem was recently partly solved by Lantoine and Russell (2011) and completely by Biscani and Izzo (2014). We give here the full set of solutions, including solutions not previously derived, as well as simpler formulations for previously known cases and comparisons with recent works. The solutions given may also be applied to the classical Stark problem (Stark,1914): we thus provide here for the first time the complete set of solutions for this well-known effect in term of Jacobi elliptic functions.