According to the map scale provided in The Lord of the Rings, about 285 miles. You may want to double check this yourself with a ruler and map.
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Because that was where he, his father and his brother lived - it was his home. Furthermore, he wanted The One Ring to be given to Gondor (Minas Tirith is Gondor's capital), for use in defence against Sauron.
As Strider the Ranger, Aragorn is a wanderer and knowledgeable in the ways of nature. As King Elessar of Gondor, he resides in Minas Tirith, The White City.
In the film there were around 200,000 - 600,000 orcs in the book there was no real figue but according to the characters in the book it was an army with a size beyond comprehension. So i guess the films were about right.
Gandalf goes to Minas Tirith in Gondor to research the One Ring. There Lord Denethor grudgingly allowed Gandalf to search among his hoarded scrolls and books. And there he found the description of the One Ring written by Isildur.
Dain Ironfoot King Under the Mountain inherited the throne from Thorin Oakenshield after he died in the Battle of the Five Armies. He led the Dwarves from the time of the events in the Hobbit until Sauron's Attack on Erebor (which was concurrent with the Siege of Minas Tirith in Gondor).