When The Lord of the Rings fans got their first glimpse of Minas Tirith, it was breathtaking. Gandalf was riding on Shadowfax with Pippin in front of him. As they crested a grassy knoll, the white city stood gleaming before them. They soon found out that Minas Tirith had been darkened by Denethor's unhealable corruption, but that corruption was washed away when Sauron was defeated. Thus, Minas Tirith's glory was renewed with Aragorn as its king.
Aragorn ruled over Gondor for 120 years, and it was an era of glorious peace. He and Arwen had a number of children during their reign, but they only had one son: Eldarion. Eldarion was his father's heir, and he ended up ruling from Minas Tirith just like his father. But there's an important question that needs to be answered. If Eldarion's mother was Arwen Undómiel, then would he have been part Elf?
Was Aragon's Son Part Elf?
In The Lord of the Rings, there were only a few instances where an Elf married a human. The first instance was when Beren married Lúthien, and the second famous pairing was when Eärendil married Elwing. The children of those unions were called Peredhil, or half-elven. They had to choose between a mortal life and an Elven life. Eärendil and Elwing's children were named Elrond and Elros, but the two brothers chose differently. Elros chose to be a mortal, while Elrond chose to be counted as an Elf.
Elrond's daughter, Arwen Undómiel, married Aragorn (a decedent of Elros) in The Lord of the Rings. They pledged their love when Arwen gave Aragorn her Evenstar necklace. By Peredhel rules, Eldarion and the rest of Aragorn and Arwen's children should have chosen between being an Elf or a human. However, that wasn't the case. Arwen chose to abandon her status as an immortal Elf before she and Aragorn came together. Thus, their children were the product of the union between two regular humans. Eldarion wasn't even slightly Elvish. He was the consummation of the line of Peredhel because he was the product of both Elrond and Elros' descendants.
Eldarion Was Nearly Part of Tolkien's Next Era
Not much is known about Eldarion because he wasn't alive during LOTR. But he was nearly the subject of Tolkien's next work. After LOTR's release, Tolkien started working on a sequel called The New Shadow. It was set about 100 years after the defeat of Sauron and the Fall of the Black Tower. Its premise was to show the resurgence of the Cult of Melkor while Eldarion was ruling over Gondor.
That would have been a great way to open a new part of the LOTR story. But Tolkien abandoned the book after writing 13 pages. In a 1964 letter to Colin Bailey, he explained why he dropped the project: "I could have written a 'thriller' about the plot and its discovery and overthrow — but it would have been just that. Not worth doing." From that, it seems pretty clear that he wanted LOTR to end on a good and happy note. Pulling in more evil after Sauron's defeat would have cheapened the ending of LOTR and the sacrifices that the Fellowship made. So, in the end, Eldarion was considered a good and wise king, but because The New Shadow's canonicity is debated, not much about his reign is known for certain.