  The Istituto Nazionale di Geofisica e Vulcanologia has been involved since
its foundation in the forecast of the conditions in which a radio link that
makes use of propagation by means of ionospheric wave takes place. In the last
times it gained interest also the precise forecast of the trajectory covered by
a radio wave propagating into the atmosphere, specifically into the ionosphere,
which can be considered, at first approximation, as an inhomogeneous medium,
defined by a refraction index slowly varying in time. This work describes the
theoretical bases to study a trajectory; they substantially make use of the
methods of the geometrical optics. Such theoretical bases find applications in
numerical methods to calculate the trajectories, as quoted in references
[Bianchi, 2009].
