Sample of gas streamlines arriving from the upstream direction with respect to the planet (run RADL27k0.01). The core is located at x = r − a_p = 0, y = a_p(φ − φ_p) = 0, z = 0, as indicated by the black circle, and surrounded by a transparent purple sphere with radius r = r_H. Results are shown in the frame co-rotating with the planet. Blue and green streamlines make a perturbed horseshoe orbit. Gas parcels arrive well above the midplane (z >r_H), enter the Hill sphere, and subsequently exit closer to the midplane (z < r_H). The red and orange curves are examples of streamlines that interact strongly with the core. The orange streamline circulates closely around the core (within r < 0.5 r_H), while the red streamline indicates a gas parcel that remains trapped for the duration of the integration.