Angles ϵ (solid lines) between a particle radial velocity V_r ⋆ and its total velocity V, and θ_lim (dashed lines), the maximum angular position of the particle at its ingress or egress. The angles are plotted as a function of time, counted from the escape of a particle from HD 209458b (red line) or HD 189733b (green line). The evolution of the angles is the same for both planets: they decrease with time, and ϵ is always greater than θ_lim. The slope is initially steeper for HD 209458b because of its higher values for β at low velocities, but the trend quickly reverses since β decreases more rapidly with increasing velocity in the wings of the Lyman-α line of HD 209458b (see Figs. 1 and 2).