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Secular free inclinations in the main Kuiper Belt

Presentation #202.03 in the session Dynamics Beyond Neptune.

Published onApr 25, 2022
Secular free inclinations in the main Kuiper Belt

There is a complex inclination structure present in the transneptunian object (TNO) orbital distribution in the main classical belt regions between orbital semimajor axes of 39 and 48 au. The long-term (secular) gravitational effects of the giant planets make the TNO orbits precess, but non-resonant objects maintain a nearly constant ‘free’ inclination I free with respect to a local precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object’s local forced pole. We show that the simplest method, based on the Laplace-Lagrange secular theory, is unable to give correct forcing poles for objects near the secular resonance, resulting in poorly conserved I free values. We thus implement an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding a significantly more accurate free inclination for non-resonant objects. In addition, using 4-Gyr numerical integrations we show that the vast majority (96%) of the classicals have their I free conserved to <1 degree, demonstrating the advantage of using this quantity in studies of the TNO population and primordial inclination profile; our computed distributions only reinforce the idea of a very co-planar surviving ’cold’ primordial population, overlain by a large I-width implanted ’hot’ population.

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