Characteristic lengths along the line of initial position Y_i for different distances D. Each curve is labelled above the panels: the parameter ρ_C (Eq. (33)) is drawn in yellow; the initial starting distance is drawn in magenta; the extreme reachable radii ρ₁, ρ₂, and ρ₃ (Eq. (22)) are drawn in red, green, and blue. As a function of Y_i, the parameter ρ_C is monotonous if D ⩾ D_lim (panels a, b), it crosses 1 in one additional point if D = D_crit (panel c), and in two additional points if D < D_crit (panel d–f). The type of trajectory of the particle with initial position Y_i is determined by the location of its initial distance ρ_i with respect to the characteristic lengths ρ₁, ρ₂, and ρ₃: the trajectory is of type T₂ when ρ₁ < ρ_i < ρ₂; T₃ when ρ_i > ρ₃; and T₁ when ρ_i > ρ₁ (with no ρ₂, ρ₃). We note that trajectories of type T₂ are only possible for D < D_crit (panel d–f).