The curvature we see in this video is based on mathematical calculations of the ‘angular declination of the horizon’.
Reality shows otherwise:
The live feed of ISS that was started recently shows the view from 4 cameras. All are pointing down to Earth. Why ? Because if they were looking straight ahead there would be no curvature, the horizon would be flat.
http://www.spaceflight101.com/uploads/6/4/0/6/6406961/_8414937_orig.jpg
The camera showing the aft view has a typical lens (not a fisheye) but it also creates the ‘curvature’. You can compare the convexity gained with a fisheye lens and a normal lens as they are next to each other on the above scheme and photo.
Here is a view from a camera attached to a balloon which doesn’t have a fisheye lens. Yet, it also causes the horizon to bend a little.
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