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This answer to At what annual rate are new exoplanets being recognized? How does it compare to new asteroids? shows that the rate of new asteroid discovery is roughly two orders of magnitude higher than the rate of new exoplanet discovery, and once Vera C. Rubin comes online the disparity is likely to widen even further.

I quipped:

Thinking about the cross-over rate; at some point won't all the asteroids have been found?

there and then wondered if there is any distance limit to what is or isn't an asteroid, or are there new asteroids out there to discover all the way to the point where matter can no longer be gravitationally bound to the Sun because the pull of adjacent stars is just as strong.

Question: Are there asteroids per se in the Oort cloud, or for that matter, the Kuiper belt? Or are those basically considered comets? (trick question alert! see Do astronomers generally agree that the distinction between comets and asteroids is not so clear?)

Wikipedia sez the proposed Oort Cloud is full of icy planetesimals, and not being an astronomer I don't know how exactly to parse that.

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    $\begingroup$ Well the Oort Cloud is/was proposed as a solution to explain the isotropic distribution of comet orbits. Since a 10km Halley-sized comet out at the Oort Cloud distance is something like magnitude 61, we can't exactly directly verify it's out there... $\endgroup$ – astrosnapper Feb 5 at 16:35
  • $\begingroup$ @astrosnapper ...any time soon at least, maybe in 50 or 100 years there will be some spacecraft technology that would allow exploration, but I don't thin this SE question will be active then nor I around to accept the answer. Now I'm wondering of a short, terse answer explaining that this question can't have a definitive answer because the Oort Cloud is what it is, and isn't yet what it isn't yet? I would be inclined to accept such a terse answer to put this one to rest. $\endgroup$ – uhoh Feb 6 at 2:12
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Tl;Dr: It is a matter of consideration if you want to call Kuiper belt bodies/Oort cloud bodies "asteroids" or not.

Long answer:

The Oort cloud defines the cosmographic boundary of the Solar System and the extent of the Sun's Hill sphere and hence it is loosely bound to the Solar System, and thus is easily affected by the gravitational pull both of passing stars and of the Milky Way itself. These forces occasionally dislodge some bodies from their orbits within the cloud and send them toward the inner Solar System. This is how comets are originated. Based on their orbits, most of the short-period comets may come from the Kuiper Belt/scattered disc and the long period comets are thought to originate from the Oort cloud.

So, the general assumptions is that maximum comets(if not all) are Kuiper Belt/Oort cloud bodies but all Kuiper belt/Oort clouds bodies are not comets.

So, are they asteroids?

You "may" consider most of the KBOs and OCBs to be more like asteroids because most of the the them have fairly circular orbits around the Sun, and most of them don't come close to the Sun at all (only those which comes close to sun are considered comets). So if an object needs to have an icy composition and a highly elliptical orbit to be considered a comet, then KBOs and OCBs are more like an "icy asteroid belt and bodies" than a group of comets.

However, such classifications were done based on what we knew 60 years ago, and it's now clear that the Solar System is much more complicated. So, we need to have a better classification to avoid confusion. Now, we name celestial bodies in a very specific manner considering various factors like position, behavior, size, age, composition etc., for instance: "Main Belt Asteroids", "Kuiper Belt Objects", "Near-Earth Asteroids", "Long-Period Comets" etc., as opposed to just "asteroids" or "comets".

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