Orbital Evolution of Scattered Planets

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Abstract
A simple dynamical model is employed to study the possible orbital evolution of scattered planets and phase plane analysis is used to classify the parameter space and solutions. Our results reconfirm that there is always an increase in eccentricity when the planet was scattered to migrate outward when the initial eccentricity is zero. Applying our study on the Solar System and considering the existence of the Kuiper Belt, this conclusion implies that Neptune was dynamically coupled with the Kuiper Belt in the early phase of the Solar System, which is consistent with the simulational model in Thommes, Duncan & Levison (1999).

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