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How can scattering Kuiper belt objects become Centaur objects?

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Kuiper belt objects (KBOs) transition into Centaur objects through gravitational interaction with Neptune.12

While many KBOs occupy metastable orbits that remain stable for hundreds of millions to billions of years, some objects chaotically diffuse out of these stable regions. Those that experience significant gravitational influence from Neptune are classified as "scattering KBOs". These objects occupy unstable orbits on million-year timescales, effectively serving as a transitional population.2

As these scattering objects are perturbed inward by Neptune’s gravity, they move out of the Kuiper belt and into the region of the giant planets, where they are identified as Centaurs. Because these new orbits are unstable and prone to planetary collisions or ejection from the solar system, Centaurs have short lifetimes and must be continually replenished by this scattering process from the Kuiper belt. Ultimately, these objects may continue their evolution toward becoming short-period comets.123