Wouldn’t the size of an object that block’s Betelgeuse’s emissions from the earth be tiny, because it is so far away? It is a dot in our sky, what if we could place a basketball sized object in space at the exact distance where it blocks the star completely, and keep it in position there? Would something like that be possible?
One of the problems, as I understand it, is that some of the debris gets captured by our sun’s gravity and creates a “long period” comet. The comet then goes way out to the Ort cloud and , many years later, returns. The fact that it keeps making passes ups the chances of getting hit.
A good read is: https://www.amazon.com/Cosmic-Serpent-Victor-Clube/dp/0876633793/ref=sr_1_4?s=books&ie=UTF8&qid=1490282825&sr=1-4&keywords=the+cosmic+serpent
The idea is to use a nuke.