Newly Found Planetoid Possibly Larger than Quaoar
I am Jack's username writes "A newly discovered planetoid (Google news cluster) 2004 DW in the Edgeworth-Kuiper belt, where some think objects larger than Pluto exist, may be larger than Quaoar - making it the second largest known trans-Neptunian object and 18th largest object in the solar system."
Yeah, because the most distant galaxies are about 1000000000 (not exact, but you get the point) times larger and brighter than an asteroid 40au from earth. An asteroid or comet only reflects light, so the farther it is from the sun the harder it is to see. A galaxy on the other hand, will have billions of stars, each billions and billions of times brighter than what's reflected from an asteroid.
You need some mechanism to "increase" the apparent area of the (in this case KBO.) Unfortunately, KBOs are just small rocks, with not too much interesting going on. (Planets that eclipse their own star are easier to see, because they are fixed in the angle they explore on the sky relative to the star.)
If you're looking for some kind of "eclipse" effect on the background stars, the best way to increase the effective area of your object is to make it heavy enough that it can gravitationally lens something behind it. The lensing effect increases the angular size of the "sweet spot." See the various MACHO searches.
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Well, let me address (although not outright answer) the question you actually posted: the chances of a given KBO occulting a given star are pretty small. Particularly if the star doesn't lie close to the ecliptic...
That said, the odds of a KBO occulting a star or, perhaps better, any KBO occulting any star aren't all that tiny. Pluto occults stars on occasion. That's how we get data on the atmospheric structure, after all. Admittedly, astronomers keenly search for these occultations, but they do happen every few years or so. Now, mind you, Pluto is a big KBO so that it has a much higher probablity of passing in front of a star than most of the others. Recall that it is, in fact, one of the very few KBOs that have been resolved in our images. (I believe that Quaoar, Charon, Varuna, and perhaps one or two others have been. It's because we have not resolved many of these that we don't know the albedoes/sizes of KBOs that well.)
The next question is why should we look for occultations? Using them as a means to detect KBOs is probably a waste of time. Occultations can give you a profile of the atmosphere which might not be interesting for most KBOs, although a non-detection would at least tell us something about KBOs in general. (i.e. - That they don't have atmospheres. Not that I think people would be generally stunned by this.)
While Dyson was more of a mathematical theory person, his claim to fame is in physics, and along the school of "when your ownly tool is a hammer, everything looks like a nail", that setup is very reminiscent of a particle detector.