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This question already has an answer here:

EDIT: OK, I have been asked to clarify my question(s).

  1. At what altitude do we start to see the curvature of the Earth?

  2. Distance to the horizon at this altitude.

  3. The angle between line of sight of the observer and vertical.

My reasons for these questions are:

1) I have read pilots' comments saying they cannot discern a curve at 40,000 feet. I was surprised because I have been on open sea and believed I could see the curve at the periphery of my vision. I thought about it and realised if every point on the horizon is equidistant to me, then I would probably have to get really high to see the curve. So maybe my brain created the curve, as peripheral vision is largely deduced rather than 'seen'?

2) Flat Earthers are bugging me.

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marked as duplicate by DilithiumMatrix, tpg2114, John Rennie, Jon Custer, user36790 Dec 16 '16 at 3:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Not too many flat Earther's round these parts, that I can tell you. My apologies, but I can't really follow your first paragraph. Do you mean if we say, fly high enough we will see the curve of the earth? $\endgroup$ – user108787 Nov 30 '16 at 3:41
  • $\begingroup$ Yeah, haha. Just an idea I had, that I thought some real/aspiring physicists would have an answer to. $\endgroup$ – Jimmy Jay Dec 15 '16 at 16:30
  • $\begingroup$ And that first paragraph kinda meant, "We are always at the top of the World" $\endgroup$ – Jimmy Jay Dec 15 '16 at 16:47
  • $\begingroup$ Thanks DilithiumMatrix. I apologise, as I was still editing the question(s) when you left this comment. I'm actually talking about just noticing the curve of the Earth, not seeing the whole face. Your link did give our field of vision though. Cheers $\endgroup$ – Jimmy Jay Dec 15 '16 at 18:52
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That the earth was a "sphere" had been known since ancient times, it is worth reading about Eratoshenis. They fitted data with the assumption of the earth being a sphere .

Eratosthenes, a Greek astronomer from Hellenistic Libya (276–194 BC), estimated Earth's circumference around 240 BC. He had heard that in Syene the Sun was directly overhead at the summer solstice whereas in Alexandria it still cast a shadow. Using the differing angles the shadows made as the basis of his trigonometric calculations he estimated a circumference of around 250,000 stades. The length of a 'stade' is not precisely known, but Eratosthenes's figure only has an error of around five to fifteen percent. Eratosthenes used rough estimates and round numbers, but depending on the length of the stadion, his result is within a margin of between 2% and 20% of the actual meridional circumference, 40,008 kilometres (24,860 mi). Note that Eratosthenes could only measure the circumference of the Earth by assuming that the distance to the Sun is so great that the rays of sunlight are essentially parallel.

If a sphere fits the data, a flat plane will not. The horizon a person sees is a matter of sight and instruments and one can hand wave about them. The position of the sun in the solstice is a solid observation.

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