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Fig. C.1


Orbital evolution of a single planetesimal initially located at the semi-major axis ap,0 = 14.3 AU. Panel a: the evolutionary path of the planetesimal in the plane whose vertical and horizontal axes are the eccentricity, e, and the difference in semi-major axis between the planetesimal, a and planet, ap, respectively;both are normalised by the reduced Hill radius, h (see Eq. (20)). The time sequence is colour-coded. Dashed line indicates the boundary of the feeding zone. Dotted lines are eye-guide ones that show the resonance centre of the 2:1, 5:3 and 3:2 mean motion resonances (MMRs) with the planet, from left to right. Panels b and c: the temporal changes in the resonance angle (see Eq. (C.5)) and in the semi-major axis of the planetesimal normalised by that of the resonance centre, ac (see Eq. (C.2)), respectively, for the 3:2 MMR. The dotted lines indicate the resonant width of the 3:2 MMR. Panel d: the orbits of the planetesimal on the co-rotating flame with themigrating planet. Blue, green and red dots show the path of the planetesimal for e = 0, 0.2 and 0.4, respectively.The gray dots show the orbit of the planetesimal after escaping from the resonance. The black circle shows the Hill sphere of the planet.

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