Beth A, Garnier P, Toublanc D,
, 2015, , Icarus, ISSN: 0019-1035
© 2015 The Authors.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 generalisation of the study by Bishop and Chamberlain (Bishop, J., Chamberlian, J.W. . Icarus 81, 145-163). In this first paper, we present the complete solutions of particles trajectories, which are not conics, under the influence of the solar radiation pressure with some assumptions. This problem is similar to the classical Stark problem (Stark, J. . Ann. Phys. 348, 965-982). This problem was largely tackled in the literature and more specifically, recently by Lantoine and Russell (Lantoine, G., Russell, R.P. . Celest. Mech. Dynam. Astron. 109, 333-366) and by Biscani and Izzo (Biscani, F., Izzo, D. . Mon. Not. R. Astron. Soc. 439, 810-822) as we will discuss in this paper. We give here the full set of solutions for the motion of a particle (in our case for an atom or a molecule), i.e. the space coordinates and the time solution for bounded and unbounded trajectories in terms of Jacobi elliptic functions. We thus provide here the complete set of solutions for this so-call Stark effect (Stark, J. . Ann. Phys. 348, 965-982) in terms of Jacobi elliptic functions (Jacobi, C.G.J. . Fundamenta nova theoriae functionum ellipticarum. Sumtibus fratrum), which may be used to model the trajectories of particles in planetary exospheres.