  We investigate the random flight process that arises as the Boltzmann-Grad
limit of a random scatterer Lorentz gas with variable scatterer density in a
gravitational field. For power function densities we show how the parameters of
the model determine recurrence or transience of the vertical component of the
trajectory. Finally, our methods show that, with appropriate scaling of space,
time and the density of obstacles, the trajectory of the particle converges to
a diffusion with explicitly given parameters.
