If you have not been following the story of Corey and his bow, you’ll want to go to Corey’s page and catch up.
Part 5: Lunch with Gaspard
“Let’s have some lunch,” Gaspard proposed. “I have my lunch basket here by the tree, and we can talk. Perhaps you have some questions, and then we will retrieve your arrow.”
Lunch was wonderful – French bread with real butter and some kind of cool drink that tasted suspiciously like a light wine. Corey ate in silence, reflecting on his morning adventure.
Of course when he shot from the north, he thought, he was not moving at all – except for turning. He frowned.
“When I shot from the North Hole,” he began, “I was not moving very fast, but I was turning. If the arrow keeps my motion, why didn’t it continue to turn left when I shot it? Then it would not have gone to the right.”
Gaspard smiled. “A wise question, and the answer is not obvious.” He stopped for a moment to empty his glass, and added, shaking his head, “Pas de tout!” (Which means “Not at all.”) Then he looked up and smiled.
“The fact is that things only keep their motions in one direction. Turning is not a direction; it’s a continual correction of a motion.”
He buttered his bread as he went on. “For example, your turning, right now with my asteroid, is a motion straight east, continually corrected by gravity pulling you inwards so you don’t fly off into space. When you let go an arrow, it can only keep your eastwards motion, not your ongoing correction. It gets its own correction, of course, from its own gravity; otherwise it would fly off into space.” He looked up from his buttering and raised his bushy eyebrows a moment before continuing:
“Therefore, flying from the North Hole, the arrow carries no motion. But from anywhere else,” he hesitated and shrugged, “from anywhere else except the South Hole — there is an eastwards motion.”
Corey thought about this, closing his eyes and watching his arrows in flight. “That was a beautiful flight,” he murmured.
But then he had another question.
“So when I shot north,” he began, “why did the arrow curve around before it fell?”
Gaspard smiled. “I rather suspect,” (and he winked) “that if you had ridden on the back of the arrow, you would only have seen yourself flying eastwards. A satellite flying around your earth seems to me, from here, to be flying first east, then west, then east again. But it only flies right around, eh?”
“Yes, of course.” Corey munched thoughtfully. He sighed and took another drink.
“I have one more question then.”
“I understand north and south turning right, but what if I shoot east and west? Will those arrows also turn right, as they do at home?”
“Let’s try it,” answered Gaspard, standing up and brushing off the crumbs.
Corey stood up too and picked up his bow. He fitted an arrow and then looked around.
“Which way is west?” he asked.
Gaspard pointed to the tower. “There’s north. West is at a right angle to north,” he replied.
Corey fitted an arrow, drew back his bow and let it fly. Once again, he watched a soaring arc – turning to the right. A distant “plink” told him that it had landed on the stones of the North Park Circle, distinctly to the northwest, and indeed to the right of his aim.
He shook his head. “What happened this time?” he asked. “If I shoot west, all the motions should be the same and the arrow should fly true.”
Gaspard nodded. “The arrow flies true enough. The problem lies with you.”