"The spinning Earth is in air," Timothy frowned.
"I have here a bucket of water and I'll put it on this potter's wheel and spin it," Gaius offered. He had been ready for this argument, and had brought the potter's wheel and put it in the corner of the room. "Watch! The water quickly catches up with the bucket."
"So?"
"Aristotle made the excellent point that everything, no matter how light, falls to the centre. So does air, but because of Archimedes' principle, it's on top. Outside that, there is void, and the bodies and air move with eternal motion. There's no contrary wind because there is nothing on the outside and the air has caught up with the Earth, just as the water does in that bowl. Furthermore," he added, and wagged a finger at Timothy, "we can prove there's nothing out there."
"We can?" Timothy gave an even more perplexed look.
"Yes! Watch stars come up from the horizon. They really shimmer, and that must be because of the air. Now, as the ancients noted, stars go behind the Moon quite sharply. The reason there're no clouds on the Moon is simply because there's no air there. The Moon is not in air, so its motion is eternal!"
Timothy gave Gaius a look that seemed as if it was true respect, then he nodded and said, "That was good logic. I concede that if there is a void, the argument of the winds is not valid, and there's no way to prove there is air around the Moon." He paused, then added, "How about this?
"Let's suppose for a moment the Earth travels around the sun. It must therefore move with two motions. Think of going around a table in a circle. You go left to right and front to back"
"So?"
"Think of people scattered around a field, and you walk a circle. Sometimes, someone will seem to be to the left of someone else, then as you keep walking they may appear to pass in front and end up on the right. That does not happen with the stars. No matter what, they are always in the same position relative to each other."
"If you're far enough away, and the stars are far enough apart, you wouldn't notice," Gaius said. He had seen this argument, and was prepared. "If Democritus is correct, and the stars are other suns, to get that dim they have to be very far away." He paused, then continued, "Added to which, something like that does happen to the paths of the planets."
"First, the planets," Timothy nodded. "They are on separate spheres, which travel around the Earth at different speeds and at times meet epicycles, so yes, your argument about the planets is correct, but in different forms it is the same for both explanations."
"Except for one point," Gaius frowned.
"Which is?"
"If the planets are on different spheres, one inside the other, how come you can see through them to the outer spheres? Why is nothing shaded?"
"The spheres are made of material you can see through," Timothy shrugged.
"There's nothing like that on Earth," Gaius shrugged, "which is clear enough and strong enough."
"Firstly, there's glass, and secondly there's no reason why the material of the heavens can't be different from on Earth."
"Firstly, as you put it," Gaius smiled, "there's good reason to believe the material of the heavens are the same as those of Earth. Bits of meteors have been found, and they comprise stone and iron. In your model, these fall to the centre, and would break anything like glass, or would never reach the Earth."
"They could fall through holes in the lowest sphere," Timothy pointed out.
"That's little better than resorting to magic," Gaius countered, "and there's no reason to resort to that when there's the perfectly simple explanation of everything falling to the centre, in this case the sun."
"But the Moon falls around the Earth?"
"While both of them are falling around the Sun," Gaius replied. "Smaller falls around bigger. And there's more. Let's suppose the Sun moves around the Earth on your spheres, and the Moon does also. There is now the issue of eclipses."
"I thought we'd dealt with them," Timothy frowned. "We agreed that eclipses happen when the Moon, being closer, crosses the Earth — Sun line, with a solar eclipse when the Moon is on the sun side and. ."
"We agree the cause of eclipses," Gaius interposed. "It's just that this can't happen with your spheres."
"And why not?" Timothy said in a puzzled tone. "This is usually thought to be the stronger point of the argument about the spheres."
"Because if the Moon falls around the Earth, and does so to also pull on the tides, it must move with two motions."
"So?" Timothy opened is hands as if he could not understand.
"Once the bodies get back into the same positions, the same thing should happen, but it doesn't. Eclipses are rather rare," Gaius pointed out. "No frequent repeating cycle means your moon has to move with three motions, one of which has to be like a pendulum. There's no physical cause for that, but on the other hand, if the Moon goes around the Earth on a plane different from that on which the Earth goes around the Sun, then eclipses occur when the three bodies are fortuitously in line."
"Interesting," Timothy shrugged, then said, "Let's deal with this spinning Earth. For the Earth to spin, it needs a continual applied force and. ."
"That assumes there is a contrary to overcome," Gaius replied. "If it is spinning in a void, nothing will slow it down. It would be like a top, going on forever."
"Then if it were spinning," Timothy continued, "there would be a natural tendency for light things like leaves not to be able to keep up. ."
"If the air keeps up by friction, so do they," Gaius countered.
"Hmmm. In that case, what about this," Timothy said. "Suppose I throw a stone straight up in the air. Force from the hand causes energy to come to be and the stone rises in the air. The energy slowly passes away until the stone reaches a point where it has no energy, then it begins to fall towards the centre. More energy comes to be, the stone speeds up, then it hits the ground and the energy passes away again. Do you agree so far?"
Gaius thought for a moment, then remembering Timothy' tactics, he said, "Perhaps, perhaps not, but for the moment let's assume that is so."
Timothy gave him a smile, then continued, "Think of the geometry. If the Earth is spinning, then the stone is travelling horizontally at a speed of, say, v, such that v times twenty-four hours equals 2πr, where r is the radius of the Earth. Now, let me throw the stone high in the air, say to a height h. At that point, it has to travel 2π(r+h) in twenty-four hours. Since no force has been added other than in the up and down direction, it cannot speed up in terms of rotation, so it should slip back on its path. But no matter how high you throw such a stone, it always falls back to where you threw it up."
"That depends on no lateral forces coming to be or passing away."
"What's the objection to that?" Timothy asked.
"Nothing. I'm just thinking," Gaius admitted. "I also note that, except at the equator, your line of length r and your line h have an angle between them. I also note your h is very small compared with r."
"Agreed, but so what? The distance you can measure on the ground is of a similar distance compared with the circumference of the planet."
"Perhaps," Gaius said. He paused, then added confidently, "You define the perpendicular as the point from where you drop something so that it lands in the desired spot. Obviously if you stand on that spot and throw something in such a way as it just reaches that point and effectively stops, it will fall back to your spot, and the motion will have been perpendicular by definition."