Will Arwen in this question leave for Valinor during the War of the Ring, or after, together with the rest of the Elves?
If she leaves only in the end: Aragorn and Arwen would not have ended up together, but that does not stop Arwen from hoping that eventually the War would be won...and with that hope Aragorn would fight on.
Otherwise: With Arwen in a whole new world altogether (relatively), Aragorn would lose the hope he holds on to in her...but still continue the battle with evil, finding hope somewhere else. But this would not be as strong as the hope he and Arwen have together.
If the West still wins in the end, Aragorn would reclaim the throne of Gondor...and rule in grief. That is, until he finds someone else to love, which I highly doubt is possible. But if he does not marry, how would the line of Luthien linger? It was said that her lineage would never be broken.
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