  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 stellar 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 third paper, we investigate the effect of the
stellar radiation pressure on the Circular Restricted Three Body Problem
(CR3BP), called also the photogravitational CR3BP, and its implication on the
escape and the stability of planetary exospheres, especially for Hot Jupiters.
In particular, we describe the transformation of the equipotentials and the
location of the Lagrange points, and we provide a modified equation for the
Hill sphere radius that includes the influence of the radiation pressure.
Finally, an application to the hot Jupiter HD 209458b reveals the existence of
a blow-off escape regime induced by the stellar radiation pressure.
