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In order to see the curvature, you need a 60 degree field of view and a cloud free day. From what I've read, you need to be about 35,000 feet above the surface. Find more information in this article here: http://www.howitworksdaily.com/how-high-do-you-have-to-go-to-see-the-curvature-of-the-earth/

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As a former sailor I can assure you that you can see the curvature of the earth from the crow's nest - all it takes is a calm sea. Consider a light house that stands 50 meters above sea level. If you are in the crow's nest, say 25 meters above sea level), at what distance could you first spot the top of the light house on a calm day? The problem is ...

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You could also think about the perception of this in terms of spheres of space. Lets say you are in a very small room which is hemispherical in shape. There is a 6 foot high door in the wall which seems to be very big - and relatively, it is - it takes up about 20% of overall area of the wall. Now imagine a much bigger hemispherical room that you are ...

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The size of an object while seeing it through eyes depends on the visual angle and not on the real size of the object. If the object is near to the eyes the visual angle will be higher and when it is far away the angle will be smaller. According to that, the size will differ. The size is proportional to the visual angle.

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Remember that potential energy is defined up to a constant. Here it's defined so that when $r \to \infty$ the potential energy is worth 0, for convenience. So that there's nothing special about a negative potential energy per se. What really matters here is that there's a "well", i.e. a region for $r$ where the potential energy has a minimum and that ...

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