Please try the same demonstration with the coin being held in a manner and any height that it is perceived as being "overhead" for any point on the table at all times.
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Why? Airplanes moving away get smaller...
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Any object above a plane surface would be visible from all points on that plane surface. Take the top of the coin in the example. Using a laser pointer at the top edge of the coin, any point on the table should be able to be hit by the pointer. You can try it yourself. Also, airplanes don't hit the sun. So the sun is higher than aircraft above the proposed plane surface. And with light traveling in straight lines, if a light source is sufficiently high, then it would be visible to all viewers on the plane surface.
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However, the sun does not emit light equally in all directions as the spherists claim. It is in reality much more like a flashlight: it sends out a focused spread of light that becomes less and less visible as it moves away from a given point. If you were in an airplane you would not see the light if it was focused away from you...
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But we can see the sun rise from the horizon in the east and set in the west, so therefore it can't be focused like a flashlight because a) it is still circular at sunrise/set and b)it is still shining light towards us at sunrise/set. These two points prove that the sun is spherical and not focused like a flashlight.