In the books, Gandalf and Aragorn both come to the same conclusion that answers your question. Sorry I can't remember exactly where, maybe after Aragorn looks in the Orthanc Stone (Passing of the Grey Company, Book V?). Sauron believes that the goodies have the One Ring, and that either Aragorn or some other great leader is going to use it to challenge his power. Sauron realises that it would take some time for a new user to be able to learn to wield the Ring, and so he attacks quickly, hoping to destroy Rohan and Gondor before the Ring can be used against him. This is Aragorn's main purpose in using the Palantir, to draw Sauron's attention away from Frodo. Same reason that the Army of the West attacks Sauron at the Black Gate.
Hi and welcome to the Barrow Downs, by the way. I've only been around a few days, but it's so snug and cosy I'm sure I'll stick around...
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But Gwindor answered: 'The doom lies in yourself, not in your name'.
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