it is close, apparently the horizon is only 3 miles away when at sea level,
I found it fascinating while studying sea battles when I was a young lad. For example, HMS Prince of Wales opened fire on Bismarck at 26,000 yds or 13 nautical miles so you are in a situation where only sailors in the top masts can spot part of the opposing ship and shells are literally curving around the earth to hit a ship which is mostly beyond the horizon.
The ancient Greeks had already figured out the earth was round in 500 B.C.
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