Aragorn and Arwen Are NOT RELATED

[Mnemosyne]

Originally Posted by Appendix A

In the days of Tar-Elendil the first ships of the Numenoreans came back to Middle-earth. His elder child was a daughter, Silmarien. Her son was Valandil, first of the Lords of Andunie in the west of the land, renowned for their friendship with the Eldar. From him were descended Amandil, the last lord, and his son Elendil the Tall.

Originally Posted by Tale of Aragorn and Arwen, also Appendix A

"Estel I was called,' he said; "But I am Aragorn, Arathorn's son, Isildur's Heir, Lord of the Dunedain"; yet even in the saying he felt that his high lineage, in which his heart rejoiced, was now of little worth, and as nothing compared to her dignity and loveliness.

But she laughed merrily and said: "Then we are akin from afar. For I am Arwen Elrond's daughter, and am also named Undomiel."

...

"My son," said Gilraen, "your aim is high, even for the descendant fo many kings. For this lady is the noblest and fairest that now walks the earth. And it is not fit that mortal should wed with the Elf-kin."

"Yet we have some part in that kinship," said Aragorn, "if the tale of my forefathers is true that I have learned."

"It is true," said Gilraen, "but that was long ago and in another age of this world, before our race was diminished."

Emphases mine, but the comments on the subject are all Tolkien's.