*
I was seized by demons and transported to an alien planet. The demons promised to allow me to return to earth if I could guess the planet's diameter, but I would have only one try.
The demons have black wings scalloped like those of a bat, and during my stay one of them used to go flying with me riding on his shoulders.
Once as we were flying above the ocean I asked how high we were and the demon answered "One mile." Far ahead of us on the horizon I could just barely make out the shore, glowing red and darkened by smoke. The locals were barbecuing the multitudes who had guessed wrong about the planet's size. I asked how far away the shore was and my host answered "A hundred miles."
"Ah," I replied, "then the diameter here is ten thousand miles." Soon thereafter I was safely returned to earth.
*
height / horizondistance=horizondistance / diameter. 1/100=100/10,000
If we had been flying at 4 mile altitude we would have been able to see things 200 miles distant. 4/200=200/10,000
In contrast to the larger planet, earth's diameter is only 7880 miles. Expressed in miles, height and distance to horizon are related by height/dist=dist/7880 and at one mile altitude the distance to horizon is a bit over 88 miles.