However, if one measures the angular diameter of the moon and the sun at these different times, one finds that they haven't changed in apparent size at all. The effect appears to be an optical illusion - your brain is fooling you into thinking them to be bigger when they are close to the horizon. There is one other effect, though. When the sun is close to the horizon, you are seeing it through a much thicker layer of atmosphere. This is why the sun is red at sunset.
Atmospheric refraction causes the sun to become slightly flattened in shape.
However, it does not appear to produce any change in the apparent size. Hey, I noticed a slight contradiction. SO, in a sense we do occupy a certain special place, even if it does not correspond to location. I agree - in a sense the universe IS very special in that it has the right properties to allow us to exist. At first sight it may sound anti-Copernican, but here goes.