The Warped Plane of the Classical Kuiper Belt

By numerically integrating the orbits of the giant planets and of test particles for four billion years, we follow the evolution of the location of the midplane of the Kuiper belt. The Classical Kuiper belt conforms to a warped sheet that precesses with a 1.9 Myr period. The present-day location of the Kuiper belt plane can be computed using linear secular perturbation theory: the local normal to the plane is given by the theory’s forced inclination vector, which is specific to every semi-major axis. The Kuiper belt plane does not coincide with the invariable plane, but deviates from it by up to a few degrees in stable zones. A Kuiper belt object keeps its free inclination relative to the Kuiper belt plane nearly constant, even while the plane departs from the trajectory predicted by linear theory. The constancy of free inclination simply reflects the undamped amplitude of free oscillation. Current observations of Classical Kuiper belt objects are consistent with the plane being warped by the giant planets alone, but the sample size will need to increase by a few times before confirmation exceeds 3σ in confidence. In principle, differences between the theoretically expected plane and the observed plane could be used to infer as yet unseen masses orbiting the Sun, but carrying out such a program would be challenging. Subject headings: comets: general — Kuiper belt — solar system: general — celestial mechanics 1.