# How many solar system objects that can really qualify as a KBO are likely to enter Pluto's Hill sphere each day?

A comment below Which celestial body is able to come closest to Pluto? says that

Technically, many, many small Kuiper belt objects enter Pluto's Hill Sphere (or sphere of influence SOI) every day.

Pluto is small, but it is very far from the Sun, so maybe its Hill Sphere could be surprisingly large, and if we called each particle of dust out there a "small Kuiper belt object" then this can be true.

Question: But realistically, how many solar system objects that can really qualify as a KBO are likely to enter Pluto's Hill sphere each day?

For the purposes of this question let's see if there is some way to ascertain what a KBO might be, and not focus on the helpful comment too much.

• Afaik almost all TNOs are so large they're considered 'possible dwarf planets'. Arrokoth is the only clear asteroid beyond Neptune I know of. But if a tiny meteoroid's orbit is fully within the Kuiper belt, I don't see a reason why it shouldn't be considered a KBO. Jan 19, 2021 at 14:47
• @PlutosLoyer Did you look at Wikipedia's List of trans-Neptunian objects ? The vast majority aren't considered dwarf planet candidates. Jan 19, 2021 at 17:59
• @notovny Thank you. Jan 19, 2021 at 18:20

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" $$\pi r^2 *86,400s *1km/s = 9.8 \times 10^{18} km^3= 2.9 \times 10^{-6} AU^3$$ of the Kuiper belt per day.

The Kuiper belt is described as a donut extending from 30 to 55 AU. The volume $$V$$ of a torus is $$V=2\pi^2Rr^2$$, where $$R=42.5$$ and $$r=25$$ are the major and minor radii, so the approximate volume of the Kuiper belt is $$5.24 \times 10^{5} AU^3$$. Of course, KBO's are distributed more densely near the center of the torus, and exist increasingly rarely outside the torus.

So, Pluto might sweep out about $$V_1 = 2.9 \times 10^{-6} AU^3$$ of the $$V_2=5.24 \times 10^{5} AU^3$$ volume Kuiper belt per day. That means there would have to be approximately $$V_2/V_1 \approx 1.8 \times10^{11}$$ (or 180 billion) total objects in the Kuiper belt for one to enter into Pluto's Hill sphere each day, on average. It might even need to be much higher since Pluto's orbit is more inclined then the distribution of the Kuiper Belt, as shown here: We only know of about 2000 KBOs according to this NASA site. Pitjeva and Pitjev postulate only millions of objects in the Kuiper belt, so it may be unlikely that many KBOs enter Pluto's Hill Sphere radius each day.

• – uhoh
Jan 19, 2021 at 23:23
• @uhoh It is quite interesting that the power law size distributions of the Kuiper belt don't seem to match up well with those of the Jupiter/Mars asteroid belt. Perhaps the enormous distances and slow orbital speeds in the Kuiper belt have led to fewer and less energetic collisions through the evolution of the Solar System. Jan 19, 2021 at 23:31
• The asteroid belt is at about the snow line, thus volatiles are depleted. That's not so in the Kuiper belt. Also the asteroid belt is dominated by Jupiter due to the many resonances therein. Both may slightly change the size distribution. Jan 20, 2021 at 12:13