"In his proposal, Paek used the asteroid Apophis as a theoretical test case. According to astronomical observations, this 27-gigaton rock may come close to Earth in 2029, and then again in 2036. Paek determined that five tons of paint would be required to cover the massive asteroid, which has a diameter of 1,480 feet. He used the asteroid's period of rotation to determine the timing of pellets, launching a first round to cover the front of the asteroid, and firing a second round once the asteroid's backside is exposed. As the pellets hit the asteroid's surface, they would burst apart, splattering the space rock with a fine, five-micrometer-layer of paint."
You can read the full M.I.T. article here: http://web.mit.edu/newsoffice/2012/deflecting-an-asteroid-with-paintballs-1026.html"