Trajectories of two tracer particles integrated forward in time inside the Hill sphere. Both particles start in the midplane with the same distance to the protoplanetary core and only slightly different azimuthal angles. The starting location was chosen specifically to show the sensitivity of the path to the initial conditions. The dashed magenta lines are the atmospheric radius R_atm as defined in Sect. 2.2. The planetary core has a radius of R_core = 0.044 R_Hill and is displayed as a gray circle. The white ring in the top left panel is also recycled, but is not part of the trajectory of the two example tracer particles. Top left: midplane view. Top right: view of the xz-plane. Bottom left: Distance to the z-axis . Bottom right: distance to the midplane (z-coordinate). Both tracer particles start to spiral outward in the midplane. The tracer particle represented by the orange line escapes the Hill sphere much faster than the particle represented by the blue line, indicating a strong dependence on the initial conditions of the tracer particle.