move in elliptical—or oval—orbits with the sun at one focus. He also pointed out that the speed of a planet is greatest when it is closest to the sun, and that the farther a planet’s orbit is from the sun the slower it moves. Not until Kepler’s time was it actually stated that the earth was a planet just like other planets. Kepler also emphasized that the same physical laws apply everywhere throughout the universe.”
“How could he know that?”
“Because he had investigated the movements of the planets with his own senses instead of blindly trusting ancient superstitions. Galileo Galilei, who was roughly contemporary with Kepler, also used a telescope to observe the heavenly bodies. He studied the moon’s craters and said that the moon had mountains and valleys similar to those on earth. Moreover, he discovered that the planet Jupiter had four moons. So the earth was not alone in having a moon. But the greatest significance of Galileo was that he first formulated the so-called Law of Inertia.”
“And that is?”
“Galileo formulated it thus: A body remains in the state which it is in, at rest or in motion, as long as no external force compels it to change its state.”
“If you say so.”
“But this was a significant observation. Since antiquity, one of the central arguments against the earth moving round its own axis was that the earth would then move so quickly that a stone hurled straight into the air would fall yards away from the spot it was hurled from.”
“So why doesn’t it?”
“If you’re sitting in a train and you drop an apple, it doesn’t fall backward because the train is moving. It falls straight down. That is because of the law of inertia. The apple retains exactly the same speed it had before you dropped it.”
“I think I understand.”
“Now in Galileo’s time there were no trains. But if you roll a ball along the ground—and suddenly let go...”
“... it goes on rolling ...”
“... because it retains its speed after you let go.”
“But it will stop eventually, if the room is long enough.”
“That’s because other forces slow it down. First, the floor, especially if it is a rough wooden floor. Then the force of gravity will sooner or later bring it to a halt. But wait, I’ll show you something.”
Alberto Knox got up and went over to the old desk. He took something out of one of the drawers. When he returned to his place he put it on the coffee table. It was just a wooden board, a few millimeters thick at one end and thin at the other. Beside the board, which almost covered the whole table, he laid a green marble.
“This is called an inclined plane,” he said. “What do you think will happen if I let go the marble up here, where the plane is thickest?”
Sophie sighed resignedly.
“I bet you ten crowns it rolls down onto the table and ends on the floor.”
“Let’s see.”
Alberto let go of the marble and it behaved exactly as Sophie had said. It rolled onto the table, over the tabletop, hit the floor with a little thud and finally bumped into the wall.
“Impressive,” said Sophie.
“Yes, wasn’t it! This was the kind of experiment Galileo did, you see.”
“Was he really that stupid?”
“Patience! He wanted to investigate things with all his senses, so we have only just begun. Tell me first why the marble rolled down the inclined plane.”
“It began to roll because it was heavy.”
“All right. And what is weight actually, child?”
“That’s a silly question.”
“It’s not a silly question if you can’t answer it. Why did the marble roll onto the floor?”
“Because of gravity.”
“Exactly—or gravitation, as we also say. Weight has something to do with gravity. That was the force that set the marble in motion.”
Alberto had already picked the marble up from the floor. He stood bowed over the inclined plane with the marble again.
“Now I shall try to roll the marble across the plane,” he said. “Watch carefully how it moves.”
Sophie watched as the marble gradually curved away and was drawn down the incline.
“What happened?” asked Alberto.
“It rolled sloping because the board is sloping.”
“Now I’m going to brush the marble with ink ... then perhaps we can study exactly what you mean by sloping.”
He dug out an ink brush and painted the whole marble black. Then he rolled it again. Now Sophie could see exactly where on the plane the marble had rolled because it had left a black line on the board.
“How would you describe the marble’s path?”
“It’s curved ... it looks like part of a circle.”
“Precisely.”
Alberto looked up at her and raised his eyebrows.
“However, it is not quite a circle. This figure is called a parabola.”
“That’s fine with me.”
“Ah, but why did the marble travel in precisely that way?”
Sophie thought deeply. Then she said, “Because the board was sloping, the marble was drawn toward the floor by the force of gravity.”-
“Yes, yes! This is nothing less than a sensation! Here I go, dragging a girl who’s not yet fifteen up to my attic, and she realizes exactly the same thing Galileo did after one single experiment!”
He clapped his hands. For a moment Sophie was afraid he had gone mad. He continued: “You saw what happened when two forces worked simultaneously on the same object. Galileo discovered that the same thing applied, for instance, to a cannonball. It is propelled into the air, it continues its path over the earth, but will eventually be drawn toward the earth. So it will have described a trajectory corresponding to the marble’s path across the inclined plane. And this was actually a new discovery at the time of Galileo. Aristotle thought that a projectile hurled obliquely into the air would first describe a gentle curve and then fall vertically to the earth. This was not so, but nobody could know Aristotle was wrong before it had been demonstrated.”
“Does all this really matter?”
“Does it matter? You bet it matters! This has cosmic significance, my child. Of all the scientific discoveries in the history of mankind, this is positively the most important.”
“I’m sure you are going to tell me why.”
“Then along came the English physicist Isaac Newton, who lived from 1642 to 1727. He was the one who provided the final description of the solar system and the planetary orbits. Not only could he describe how the planets moved round the sun, he could also explain why they did so. He was able to do so partly by referring to what we call Galileo’s dynamics.”
“Are the planets marbles on an inclined plane then?”
“Something like that, yes. But wait a bit, Sophie.”
“Do I have a choice?”
“Kepler had already pointed out that there had to be a force that caused the heavenly bodies to attract each other. There had to be, for example, a solar force which held the planets fast in their orbits. Such a force would moreover explain why the planets moved more slowly in their orbit the further away from the sun they traveled. Kepler also believed that the ebb and flow of the tides— the rise and fall in sea level—must be the result of a lunar force.”
“And that’s true.”
“Yes, it’s true. But it was a theory Galileo rejected. He mocked Kepler, who he said had given his approval to the idea that the moon rules the water. That was because Galileo rejected the idea that the forces of gravitation
