Aragorn is quite possibly the strongest warrior in the whole of the War of the Ring, and is certainly the only one who could have risen to the throne of Gondor, and united the kingdoms in an era of peace in the days after Sauron’s demise. Aragorn is a unique blend of everything that opposes Sauron, being a Dunedain of Numenorian blood, descended from both Luthien who once defeated the dark lord, and Isildur who cut the ring of power from his finger, and of course, being in cahoots with some of Sauron’s greatest foes, including Gandalf, Galadriel, and Elrond.
Aragorn acts in both the books and the film adaptations of the trilogy as the pinnacle of the race of men, one whose heart is noble and true, whose loyalty to his friends is the greatest challenge for the dark lord to face, whose very genes allow him to summon an unconquerable army of the dead, and whose will has been trained towards the purpose of beating Sauron for all of his years of existence. All other men in the trilogy, even the underestimated and underappreciated Faramir, and his mighty brother Boromir, fall short of Aragorn’s heroism.
That is why Aragorn is the only one who could challenge Sauron in the Palantir, and win. In the film version, Gandalf confides in Aragorn “The rumor has reached him. The heir of Numenor still lives. Sauron fears you Aragorn. He fears what you may become.” this spurs Aragorn to take up the Palantir and wrestle with Sauron for its control. The audience already knows that this is a very dangerous thing to attempt, because of the previous scene in which Pippin picked up the Palantir and was almost driven insane by it. A well as nearly cracking his mind, the dark lord could also have learned of the ring, and Frodo’s quest to destroy it, which would have meant the end of Middle Earth as it is known, ensuring Sauron’s victory. Aragorn knowingly takes on this risk when he battles Sauron’s will, for if he loses, it would mean the end for everyone and everything he holds dear.
Peter Jackson’s decision to include the scene in which Aragorn wrestles for control of the Orthanc Palantir was an interesting one, because in the books, Aragorn does this alone, and then tells the others of his triumph after the fact. The film depicts some of the struggles, with Aragorn showing the reforged blade Anduril, which first cut the ring from Sauron’s finger, and Sauron retaliating by showing a vision of Arwen dead as her light and immortality fades in conjunction with the rings of power. It is not clear in the films that Aragorn has won the battle, and achieved the incredible feat of controlling the Palantir despite Sauron’s long and strong hold of it, because in the films he drops the Palantir and the Evenstar alongside it, but win he does. The book describes it this way:
“He beheld me. Yes, Master Gimli, he saw me, but in another guise than you see me here. If that will aid him, then I have done ill. But I do not think so. To know that I lived and walked the earth was a blow to his heart, I deem; for he knew it not till now. The eyes in Orthanc did not see through the armor of Théoden; but Sauron has not forgotten Isildur and the sword of Elendil. Now in the very hour of his great designs the heir of Isildur and the Sword are revealed; for I showed the blade re-forged to him. He is not so mighty yet that he is above fear; nay, doubt ever gnaws him.”
So in essence, Aragorn challenges Sauron in the Palantir for two reasons. The first is to strike some fear into Sauron’s heart, both by warning him that the heir of Numenor has returned and is leading the opposition against him, and by showing him the sword that brought about his undoing in the past. The second reason for the fight in the Palantir was to goad Sauron into acting rashly, to trick him into striking the kingdoms of men before he was truly ready, thus giving the fellowship and their allies the advantage of being more prepared than Sauron’s forces.
This, like many of the ploys and tactics used by the allies during the war of the ring, keeps Sauron’s attention focused on them, and away from the 2 hobbits desperately trying to make their way through the lands of Mordor undetected. No matter how many lives are lost in the big battles against the orc army, the true assault is taking place beneath Sauron’s eye, with Frodo and Sam needing as much time and help as they can get, and what better place to start helping them than by winning a Palantir?