Hubble nucleus

This week’s CQW is a guest post by Phillip Helbig: Read the question then, without calculating or estimating anything, first make a quick guess as to the result. Then work out the result (an order of magnitude or two is close enough). Neglect gravity and other types of interactions and imagine the entire observable universe being compressed into a ball (rather like a movie of the expanding universe played in reverse). There are about a hundred billion stars per galaxy on average, and at least a hundred billion galaxies in the observable universe. Or think of the Hubble Deep Field, which has the angular size of a small rice grain held at arm’s length, full of galaxies - and this was intentionally chosen because it was apparently empty! The sky is about 25 million times larger. What is the size of the ball when the density is equal to the density of nuclear matter?