Dynamics of a high-eccentricity planet in a large planetesimal disc
Abstract: Clustering of orbital characteristics for distant Solar System objects has been proposed to indicate the presence of a ninth planet. Simulations show that the planets orbit would have to have a mass of 5–10 Solar masses, a semi-major axis of 400–800 AU, an eccentricity of 0.2–0.5 and an inclination of 15–25°. Simulations of a planet scattering off a giant planet into a highly eccentric orbit, show that the scattered planet can circularise its orbit by dynamical friction with a planetesimal disc, providing a hypothesis of the origins of Planet Nine. The simulations show an increase in the planets inclination not explained by dynamical friction. In this thesis a further examination of the increasing inclination is presented. Some of the theory of the Kozai–Lidov resonance, phase space, dynamical friction and the Miyamoto–Nagai potential is presented. The results show that a highly eccentric planet travelling through a planetesimal disc is reliably circularised and achieves high inclination at some point of its evolution. The phase space for the Kozai–Lidov resonance for this setup is explored. Additional fixed points at 0 and 180 degrees, which are not present in the regular Kozai cycle, are found to play a major role in the dynamics as the planet is circularised. An attempt was made to model the planetesimal disc with the Miyamoto–Nagai potential. Simulations were performed for different values of the disc parameters. The resulting phase portraits lacked the additional fixed points produced by the planetesimal disc.
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