The first part of this thesis describes a modeling of the auroral emission of Jupiter in the ultraviolet. The aim of this work is to quantify how these emissions allow to constrain the energy of the electrons that precipitate in the upper atmosphere of the planet at polar latitudes. Two kinds of emissions are studied : the one of the Lyman alpha line of atomic hydrogen and those of H2. The auroral electron precipitation is modeled with a kinetic transport code. The H Lyman alpha line profile and intensity are obtained with a radiative transfer code. Synthetic spectra of H2 emissions are calculated. By studying the variability of the lines as a function of the energy of the precipitating electrons, we show that only high resolution observations will allow to put strong constraints on the electron precipitation. The second part of this thesis presents the first calculation of the H Lyman alpha emission of a hot Jupiter ever realized. If it were detected, this line would allow to constrain the environment of the extrasolar planets. The stars' emission is much more intense than that of the planet, which transforms the detection of the planetary line in a very difficult challenge. Up to now, the only estimations of contrast that have been realized are based on extrapolations of Jupiter's emission. Here we present tools that are adequate to calculate the emission of hot Jupiters. They take into account the particularities of their atmosphere, like their high ionization degree and their temperatures that exceed 10,000 K. We calculate the Lyman alpha emission of two hot Jupiters, by taking into account the auroral, thermal and dayglow contributions. In the case of the hot Jupiter HD 209458b, we show that current facilities do not allow to detect the planetary emission. On the other hand, the detection of the Lyman alpha line of the planet HD 189733b seems to be within reach of the Hubble Space Telescope.
