When you astral project, you don't go to another dimension. You go to a higher plane of existence, a spiritual plane that exists alongside the physical one. Our spiritual from can temporarily leave the physical form and travel to the astral for short amounts of time.
If you can find the book, The Witch Book: The Encyclopedia of Witchcraft, Wicca, and Neo-Paganism. - Written by Raymond Buckland, it explains the astral plane and astral body quite well. If you go to the Featured Articles section, there is a thread there that explains it as well. The web address below should take you to the site article.