Had Arwen sailed for elvenhome, whither Aragorn?

[Lhundulinwen]

Um, excuse me if I'm completly wrong here, but didn't Aragorn think Arwen was dead after Elrond's little visit before he went on the paths of the dead? Its been a while since I've read ROTK in its entirety, so I'm not sure if that's the book's version or PJ's.

Anyway, I think Aragorn would have went to Mordor and fought, but he may have been.... (how do I say this?) less careful with himself if he didn't think there was his true love waiting for him. Yes, Aragorn is an idealized version of mankind, but he was still a man who had a heart that could break. If Arwen left, I truely think Aragorn's heart would have broke, and he would have fulfilled his 'duty' to mankind and fought at Mordor, but his heart wouldn't have been anywhere near the battle.