…stackexchange.com/…/assuming-a-flat-world-and-no…

Basically, you could see for a long way but your eyeballs suck so it largely doesn’t matter. Even with the best telescope and optics on a perfect day you will be limited by the gasses in the atmosphere which scatter light.

Also, Barad-dûr was destroyed when Frodo threw the One Ring into the fires of Mount Doom so it wouldn’t be there.