There's no definitive answer, but most fans believe that Obi-Wan knew how to destroy the Death Star without the help of the st. The key may have been his knowledge of Darth Vader and the dark side of the Force. By luring Vader into a trap on the Death Star, Obi-Wan may have been hoping to use Vader's own anger and hatred against him. In this scenario, Obi-Wan would know that Vader would try to stop him, which would give Obi-Wan an opportunity to strike a fatal blow.