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The Hill sphere radius of Pluto is about $r$ = 6 million km. Most of the Kuiper belt is in prograde motion around the Sun (like Pluto). Pluto's average speed is under a lazy 5 km/s for an orbital period of about 248 years. If the difference in orbital speed between Pluto and an average KBO is just 1 km/s, then Pluto will "sweep out" $\pi r^2 *86,...


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