which is it's capital city?
Edoras.
Rohan (Middle-earth)
The capital of Rohan is the fortified town of Edoras, on a hill in a valley of the White Mountains. "Edoras" is Old English for "enclosures". The town of Edoras was built by Rohan's second 
where is rohan in lord of the rings It is bordered to the north by the Fangorn forest, to the northeast are the walls of Emyn Mui, to the east are the mouths of the River Entwash, and the Mering Stream, to the south lie the White Mountains and to the west are the rivers Adorn and Isen. how did it get it's name? Tolkien used Old English for the kingdom's language and names.
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Rohan (Middle-earth) [SEP] Capital
The capital of Rohan is the fortified town of Edoras, on a hill in a valley of the White Mountains. "Edoras" is Old English for "enclosures". The town of Edoras was built by Rohan's second King, Brego son of Eorl the Young. The hill on which Edoras is built stands in the mouth of the valley of Harrowdale. The river Snowbourn flows past the town on its way east towards the Entwash. The town is protected by a high wall of timber. Meduseld, the Golden Hall of the Kings of Rohan, is in the centre of the town at the top of the hill.