How will FE explain this?
Please read Chapter 10 of Earth Not a Globe. How the sun maintains its angular size of .5 degrees or 30 arc minutes over the course of the day was described over 150 years ago by the late Dr. Samuel Birley Rowbotham. It's a known magnification effect. As the sun recedes and shrinks its magnification is caused by the intense rays of light passing through the strata of the atmosphere.
From Chapter 10 of Earth Not a Globe we read:
"IT is well known that when a light of any kind shines through a dense medium it appears larger, or rather gives a greater magnification of its image at a given distance than when it is seen through a lighter medium. This is more remarkable when the medium holds aqueous particles or vapour in solution, as in a damp or foggy atmosphere. Anyone may be satisfied of this by standing within a few yards of an ordinary street lamp, and noticing the size of the flame; on going away to many times the distance, the light upon the atmosphere will appear considerably larger. This phenomenon may be noticed, to a greater or less degree, at all times; but when the air is moist and vapoury it is more intense. It is evident that at sunrise, and at sunset, the sun's light must shine through a greater length of atmospheric air than at mid-day; besides which, the air near the earth is both more dense, and holds more watery particles in solution, than the higher strata through which the sun shines at noonday; and hence the light must be dilated or magnified, as well as modified in colour."
The next time you observe the sunset notice how the sun is much hazier, diluted, and less intense than it is overhead at noonday. This is a telltale sign that its rays are passing through a thick atmosphere, much like the light rays from a distant street lamp.
If you've ever seen a city at night you would know that distant light sources appear magnified from afar because they are shining though a dense medium. The farther you get from the source the more magnified they appear. As you move towards the source the magnified lights shrink in appearance. As you move away the lights grow in diameter again.
For example,
here is a picture of an average bustling city at night. You will immediately notice upon looking at the image that the distant lights in the scene appear magnified and intense, particularly the white ones in the upper left of the image. You should note that most of the the orange lights in the background are about as big as the orange lights in the foreground. This is entirely contradictory to what one would expect. The background lights are much farther away and the distant bulbs are all smaller than a single pixel of the screen. The orange lights maintaining their size is a great example of the magnification effect of the atmosphere balancing out the natural shrinking to perspective.
As an analogy for the enlarging of the sun at sunset, lets imagine that we are in a dark room with a flashlight. We shine the light upon the wall, creating a distinct circle of light. If we walk backwards and recede away from the wall the spot of light grows in diameter. When we walk towards the wall the spot of light becomes smaller again. The same effect happens with the distant sun at sunset. Instead of a solid surface, however, the rays of light are shining upon the semi-transparent fog of the atmosphere between the observer and the sun. The natural shrinking of the sun due to perspective is counteracted by the enlarging effect of its light upon the horizontal strata of the atmosphere. This is how the sun's diameter is maintained throughout the day.