"Let me get this straight," Timothy frowned. "Are you saying Aristotle's argument is wrong or not?"
"The argument may be correct," Gaius wagged his finger, "but as Lucretius would say, and indeed said on different matters, the argument is not valid because you can't carry out the test properly. Not only that, but obviously Aristotle missed a chance to shine here."
"What do you mean by that?"
"Suppose you dropped the stone off a very high tower, and you could accurately locate the point vertically underneath it. With your assumption that no lateral forces came to be or passed away, which means they're conserved, then the motion at the top of the tower is faster than the bottom, so the stone will fall east, slightly. But there's more. The stone falls to the centre, but the bottom of the tower doesn't move towards the equator, so by simple geometry, the stone will also fall slightly south."
"Nobody's seen anything like that," Timothy protested.
"Because nobody's tried. According to you, logic is sufficient, and that is logical."
"It seems you have learned something from all this," Timothy nodded.
"So you have more objections?" Gaius challenged.
"Then let's get to the real heart of the problem," Timothy nodded. "You recall we discussed circular motion?"
"I do."
"As Aristotle noted, circular motion is really two motions. There is the steady falling towards the centre, and the steady moving sideways. Do you agree?"
"I've already agreed," Gaius said, "when we were discussing eclipses."
"So describe the motion of something going around the centre with no string."
"The stone, say, is falling towards the centre. It also moves aside. When it has moved aside, it has also fallen sufficiently that it is the same distance from the centre. Because it is falling towards the centre, the direction of falling has changed, but so has the direction of moving aside. Accordingly it stays at the same distance."
"Well put," Timothy nodded with approval. "Now you must see why the Earth cannot go around the sun?"
"No I do not!" Gaius responded irritably. "The Earth can fall around the Sun just as easily as the Moon fall around the Earth. The Sun is, after all, bigger than the Earth, so why shouldn't the smaller object fall around the bigger?"
"The objection is not to one object falling around the Sun," Timothy said. "Rather, the objection is to many objects falling around the Sun."
"Why not? If I take a bucket of sand, there're many objects, and they all fall when I empty the bucket."
"Exactly! And what happens when you empty a bucket of sand and stones?"
"They all fall."
"Yes, they do" Timothy said. "Now, how about a bucket of stones, and some lighter sand?"
"They still all fall," Gaius said. He was now somewhat apprehensive. This seemed to be Timothy's big point, and for the life of him, he could not see what it was.
"Of course they all fall," Timothy nodded, "as Aristotle said they would. But think about it. As Aristotle noted, objects with superior weight fall with superior speed."
"Well?" a puzzled Gaius said.
"Now you should see it," Timothy said triumphantly. "They do not all fall at the same rate. The heavy stones fall first, the lightest sand reaches the ground last."
"I'm not sure I follow." However, for the first time, he looked concerned.
"Heavier things fall fastest because by the definition of heavier, they sustain more force," Timothy emphasized. "If circular motion requires constant falling, the heaviest things with more force will receive more acceleration and hence fall the fastest, the light things the slowest, and the Earth would simply fall to pieces, or at the very least, the air would all fall slower and get left behind. Light things like air and leaves can't fall as fast, so from the night side they should stream off away from the sun, like the tail of a comet. This simply doesn't happen."
"No, it doesn't," a stunned Gaius replied.
"Except possibly for comets," Timothy added helpfully. "If you wish to say they go around the sun, I might have to agree."
"But they're not really relevant, are they," Gaius muttered.
"Oh, but they are," Timothy pointed out. "They are evidence that the streaming effect actually occurs. Clearly comets are made of heavy and light stuff. In fact the tails of comets are reasonably clear evidence that the physics outlined by the great Aristotle are correct."
Gaius remained silent, somewhat stunned by this turn of events.
"Now, think about being on a chariot," Timothy continued. "When the chariot turns a corner, you tend to be thrown to one side because there's nothing joining you to the floor of the chariot. If Aristarchus is right, and everything is that big, the Earth is travelling far faster than any chariot, but have you ever noticed being flung to one side? Or even being slightly nudged?
"And there's more," Timothy added. "Your arguments negate mine, but to properly argue for the Earth to go around the sun, you have to formulate a proposition where you say, only if the Earth goes around the sun will I see this, and then you must show it. You have not suggested anything like that."
"Give me a moment," Gaius frowned. This was impossible! He was so sure he was correct, but. . There seemed to be no answer!
"So?" Timothy eventually challenged again. "You can't win by sitting there and hoping I'll eventually die."
"I know," Gaius muttered. He was no further ahead, and he suspected he would be no further ahead tomorrow, but that did not mean he was wrong. But where? He looked up at Timothy and nodded as he said, "I'm sure you're wrong, but I can't win on this field today. Since I've lost, I'll add in twenty aureii. With that, and the fuss you made earlier, I expect you'll go."
"Expect?"
"If you wish to stay with me, you may," Gaius said. "You'll still be free, and I'll pay you more, but if you wish to leave, I fully respect that, but I think you're wrong! I don't care what you say, all that talk about the sun being stuck on a sphere, moving tens or maybe hundreds of millions of kilometers a day! Not only that, but it is so hot it should melt the disk. That's just plain wrong, but. ." Aristarchus had to be correct. After all, Athene had asked him to prove it, and what was the point of that if it were wrong?
"But?"
"I've got to admit the Earth doesn't fall to bits, and I've got to admit circular motion requires falling. Something's wrong somewhere, and one of these days I'm going to find out. It'd be nice to see your face on that day!"
"I see," Timothy stared at him. "So when do I have to decide whether to stay?"
"You don't," Gaius shrugged. "Your only decision is if, and if so, when you leave."
"And I can leave any time?"
"You're a free man," Gaius shrugged. "You can do what you wish. I want you to stay as a friend or not at all."
It was then that he remembered the expression Timothy had on his face when he first entered the room: Athene! Her expression had been, 'This has got to work.' But why? Whatever else that had been, it was not a dream. Dreams were always forgotten after a couple of days, but this had been so vivid, effectively imprinted on his mind so he would not forget. Why? Who was she? If his interpretation of her expression was correct, then whatever he did had to be important for her future as well as, or even instead of his, but how could he possibly affect someone whom he had never met, and had no conceivable mechanism for ever meeting?
Why did it matter whether planets go around the star? How could that affect his future? Or hers? Then again, perhaps it didn't. What Athene had said was that the method by which he came to understand was important, which meant. . What did it mean? Assuming it meant something, he had a few years to achieve three things. As Timothy had often remarked about slaves, he must keep going.