The easternmost land of Aman, the island of Tol Eressëa, was said to be on the edge of sight from the Isle of Meneltarma. We could - in theory - calculate from this just how far apart the islands lay. The final result would depend on the height of the Meneltarma remaining above the waves, but the distance would be of the order of about five kilometres (or three miles).
These calculations, of course, assume a round world, but it's far from clear whether that would apply to the Isle of Meneltarma. Lying relatively close to Aman, somewhere near the western end of the Straight Road into the West, the new island might very well have remained within the ancient paradigm of a flat world. In that context, Tol Eressëa might have remained visible from the Isle of Meneltarma over a much greater distance.
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