a) Scattering of a planetesimal in the stellar frame. The planetesimal comes in along the x-axis and the planet moves in the positive y-direction. The z-axis is perpendicular to the orbital plane. b) Unit vectors x and x′ (and y and y′) lie in the orbital plane, but are rotated with respect to each other by an angle α. c) The scattering in the frame of the planet. The planetesimal comes in along the x′-axis, with impact parameter b. It is scattered in the (y′ − z)-plane over an angle θ.