Using the best available telescopes, and assuming a typical albedo of 10%, at what distance can a 300m asteroid be seen (well enough to start plotting its course) in 1) visible and 2) infrared wavelengths?
This isn't really an answer, but it got a bit involved to put in as a comment. Anyhow, the nasa.gov site is an absolute mine of information for this sort of thing. The best way to search it is using Google with searches like (in this case) "asteroid detection limits site:nasa.gov". For example this search found articles like http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/7935/1/03-2680.pdf and http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/20572/1/98-1576.pdf both of which discuss the detection limits in some detail. As you'd expect, it's quite complicated. For example an important factor is the speed of the asteroid as an apparently stationary asteroid can't be distinguished from a faint star.
I feel as though I bang on about the NASA site quite a bit, but for all that NASA gets criticised they do an excellent job of making information public and it's always worth a quick search of their site. Of course, as a Brit it's not my tax paying for NASA; maybe that makes a difference :-)