Wow. I'm not sure if I should be honored or just embarrassed. But anyway, thanks for such a comprehensive response. It's going to take me a while to go over it all.
Coincidentally, I was thinking about this today. And I remembered something that I heard when I was very young. I may not even be remembering it correctly. But it was something like; The horizon is 14 miles away when you're standing on deck.
I guess I just took it for granted that that was true. However. And this I do know for a fact. When I was sailing a boat across the Atlantic. I remember approaching the Azores and seeing the clouds that marked the islands well before seeing the island. For what that's worth.
I wonder if there are any clear photographs of Catalina island from the mainland through a high powered telescope. If you could see the hull of a sail boat near the island in such a picture. I would be forced to concede that I've been misled and misguided all my life. Theoretically, you should only be able to see part of the masts and sails.

One other thing very quickly. And I'm not certain that it has any relevance at all. But if you spray a garden hose straight up in the air and focus on the droplets of water. They always form spheres as they reach the zenith of their trip. And when you blow a soap bubble or a bubble of air underwater. They tend to be rather spheroid. It just seems like some stuff just naturally wants to form spheres. Especially in the absence of gravity .

Last thing. I promise. If the sun is going around a center pole. Wouldn't it always be visible to some degree from anywhere on the plane?

Anyway. Thanks again for all the information. I'll be busy checking it out.