Episode 05 - Falling Around the Earth: Newton, the Moon, and Universal Gravity

Tomlin Hawthorne

There are astronauts on the International Space Station right now, floating. You've seen the footage. Hair standing on end, a blob of orange juice drifting past a laptop. So here's the question. The station is about four hundred kilometres up. How strong is gravity up there, compared with where you're sitting? Zero? A hundredth? A half?

Tomlin Hawthorne

It's about ninety per cent. Gravity on the space station is very nearly as strong as it is in your kitchen. If you built a tower four hundred kilometres high and stood on top of it, you'd weigh a bit less than you do now and you would not float at all. So why are they floating? That's today, and the answer is the same as the answer to a much older question: why doesn't the Moon fall down?

Tomlin Hawthorne

Last time I asked you to lay a sheet of paper on top of a book and drop the book. If you did it, the paper rode all the way down as if it were glued there. On its own, it flutters. On the book, it falls like a stone, because the book is shoving the air aside for it. The paper was never slow. The air was in the way. That is Galileo's whole point in one cheap demonstration. So we ended with Galileo's two discoveries. All things fall at the same rate. And a moving object, left alone, goes straight at a steady speed for ever. Galileo died in January 1642. Isaac Newton was born that same year, on Christmas Day by the English calendar, in a farmhouse in Lincolnshire. Premature, and so small, his mother said, that he could have fitted in a quart pot. His father was already dead. When he was three, his mother remarried and left him with his grandmother. He never forgave either of them. In a list of his sins that he wrote out at nineteen, in code, one entry is threatening to burn his mother and stepfather and the house over them. I mention this because I think we should be honest about him from the start. Galileo you'd want at dinner. Newton you would not. He was secretive, suspicious, and capable of pursuing a grudge for thirty years. He had almost no friends and, as far as anyone knows, no romantic life of any kind. He spent more time on alchemy and on dating the end of the world from the Book of Daniel than he did on physics. He was also, and I don't think this is seriously disputed, the most powerful scientific mind there has been.

Tomlin Hawthorne

In 1665, plague reaches Cambridge and the university shuts. Newton, twenty-two, goes home to the farm for the better part of two years. And in that time, on his own, he invents calculus, discovers that white light is a mixture of colours, and begins to work out gravity. People were fond of pointing this out during a more recent closure of the universities. I think most of us found it unhelpful. And yes, the apple. It's one of the few legends in science that seems to be roughly true. He told the story himself in old age, to more than one person. No, it didn't hit him on the head. He saw one fall in the orchard, and it set him wondering. But it's what he wondered that matters, and it usually gets told wrong. He didn't wonder why the apple fell. Everybody knew apples fall. He wondered how far up that reaches. The pull is there at the top of the tree. It's there on top of a mountain. Does it ever stop? Could it reach as far as the Moon? And if it does reach the Moon, why doesn't the Moon come down?

Tomlin Hawthorne

Before I give you his answer, think about how the question looked to everyone before him. For two thousand years the universe had been divided into two parts, and the Moon was the border. Below it, down here, everything is made of earth, air, fire and water. Things change, decay, and move in straight lines, up or down. Above the Moon, everything is made of a fifth, perfect substance. Nothing changes. Things move in circles, eternally, because the circle is the perfect figure. So the heavens and the Earth had different physics, as they had different inhabitants. Dante's cosmos is built on this. So is most of the poetry you've read from before 1700. Asking whether an apple and the Moon obey the same rule was a bit like asking whether a king and a cabbage are subject to the same law. Newton's answer is that they are. And he shows it with a cannon. Here's the picture. It's his own, he drew it. Imagine a very high mountain, so high it pokes above the air. On top is a cannon, pointing horizontally. Fire a cannonball gently. It flies out, curves downward, and lands a little way off. Fire it harder. It goes further before it lands. Harder again. Now it's travelling so far that something new starts to matter. The Earth is round. As the ball falls, the ground curves away beneath it. So it lands further off than it would on a flat Earth. You can see where this is going. Keep firing harder. There must be one particular speed at which the ball falls toward the ground at exactly the rate the ground curves away from it. It's falling the whole time. And it never gets any closer. It goes all the way round the planet and hits the cannon in the back.

Tomlin Hawthorne

That's an orbit. That is all an orbit is. Not floating, not escaping gravity. Falling, continuously, while moving sideways so fast that you keep missing the ground. So the astronauts. The station is travelling sideways at nearly eight kilometres every second, and it is falling. The astronauts are falling with it, and so is the orange juice. They float inside for the same reason you'd float inside a lift if the cable snapped: everything is dropping together, so nothing presses on anything. They're not beyond gravity. They're in its grip, completely. They are in free fall, and have been for months. There's a line in Douglas Adams where he says the knack of flying lies in learning to throw yourself at the ground and miss. He was joking. It's also the most accurate one-sentence description of an orbit I know. And the Moon is Newton's cannonball. Remember inertia from last time: left alone, the Moon would go off in a straight line and we'd never see it again. It doesn't. Something bends its path toward us, constantly. It falls toward the Earth every second of every day, and its sideways motion carries it round. It's been falling for over four billion years.

Tomlin Hawthorne

That's a lovely picture. But a picture isn't yet physics. Newton wanted the number. And this next part is, for me, the moment the modern world starts. He asked: is it really the same pull? The very same thing that takes the apple? Here's how you'd check. The Moon is sixty times further from the centre of the Earth than the apple is. Newton had a hunch about how gravity should weaken with distance. It should spread out, the way light spreads from a candle. Stand twice as far from a candle and the light isn't half as bright, it's a quarter, because it's spread over a surface four times the size. Three times as far, a ninth. So at sixty times the distance, gravity should be weaker by sixty times sixty. Three thousand six hundred times weaker. Now, we know how far an apple falls in its first second: about five metres. So the Moon, in one second, should fall toward us by five metres divided by three thousand six hundred. A bit over a millimetre. And you can work out how far the Moon actually does fall each second, how much its path bends away from a straight line, just from the size of its orbit and the fact that it takes a month to go round. Newton did the sum. A bit over a millimetre.

Tomlin Hawthorne

He wrote later that he found the two numbers to answer pretty nearly. Which may be the greatest understatement in the English language. Think what has just happened. A thing you can hold in your hand in a Lincolnshire orchard, and a world a quarter of a million miles away, turn out to be doing the same thing for the same reason, and the arithmetic agrees. The border at the Moon is gone. There's one physics, here and everywhere. He called it universal gravitation. Every piece of matter attracts every other piece. The more mass, the stronger. The further apart, the weaker, by the square of the distance. You are, at this moment, gravitationally attracting the Moon. Very slightly. But it's mutual. I should give you his three laws of motion as well, and they'll take thirty seconds, because you already have them. One. A thing keeps doing what it's doing, still or moving in a straight line, unless something pushes it. That's Galileo's inertia. Two. A push changes the motion. The harder the push, the bigger the change. The more massive the thing, the smaller the change. That's why you can shove a shopping trolley and not a lorry. Three. If you push something, it pushes back on you equally hard. Push a wall while standing on a skateboard and you'll find out. Those three, plus gravity. He published them in 1687, in a book usually called the Principia, which is in Latin and was made as difficult as he could manage, on purpose, he said, to keep away people who knew a little mathematics and would bother him. And for the next two hundred years, those four rules explained very nearly everything. The tides. Why the Earth bulges at the equator. The paths of comets. Let me give you the two predictions that made people gasp. Newton's friend Edmond Halley, who had paid for the printing of the Principia out of his own pocket, by the way, used the theory on a comet he'd seen in 1682. He worked out that it was the same one that had been seen in 1607 and in 1531, coming round on a long loop. And he predicted it would return at the end of 1758. He knew he wouldn't live to see it. He asked, a little wistfully, that posterity remember it was first predicted by an Englishman. On Christmas night, 1758, a German farmer and amateur astronomer spotted it. Halley had been dead nearly seventeen years. And the second. By the 1840s, the planet Uranus was drifting off its predicted path. Slightly. Either Newton was wrong, or something unseen was tugging on it. A young Frenchman, Urbain Le Verrier, sat down and calculated where an unknown planet would have to be to cause exactly that drift. He wrote to the observatory in Berlin with the co-ordinates. They looked that same night. In under an hour they found Neptune, less than one degree from where he'd said. A new world, found with a pen. One of Le Verrier's colleagues said he had discovered a planet at the tip of his quill. Please remember this story. In episode forty-four the same thing happens again, on a far larger scale, and this time nobody has found the planet.

Tomlin Hawthorne

Now, the reaction. And here I'm on your ground. The poets took it personally. Alexander Pope wrote an epitaph that treats Newton as a second act of creation, nature lying hidden in night until God sends Newton and all is light. In France, Voltaire turned Newton into a hero of the Enlightenment, and his companion, Émilie du Châtelet, who was a far better mathematician than Voltaire and knew it, produced the French translation of the Principia. She finished it in 1749, days before she died following childbirth. It is still the standard French edition. And then the mood turned. William Blake's famous image of Newton shows him naked on a rock at the bottom of the sea, bent over a pair of compasses, staring at a diagram, with his back to everything alive. For Blake, Newton had reduced the world to measurement. And at a rowdy dinner in 1817, Keats and Charles Lamb drank a toast to the confusion of mathematics, on the grounds that Newton had destroyed the poetry of the rainbow by explaining it. I'd like you to notice what you make of that. Does knowing the Moon is falling make it less wonderful, or more? I think more, as you can probably tell. But the Romantics weren't fools, and we'll put their case properly in the final episode.

Tomlin Hawthorne

The myth of the week we've already met: that there's no gravity in space. It's everywhere. It's what holds the station up there, and the Moon, and the Earth round the Sun. Weightlessness isn't the absence of gravity. It's what gravity feels like when you stop resisting it. What you feel as weight, sitting there, is the chair pushing up on you.

Tomlin Hawthorne

And a question to end Part One on. Newton could tell you, to many decimal places, how gravity behaves. He could not tell you what it is. How does the Earth reach across a quarter of a million miles of nothing and take hold of the Moon? There's no rope. Nothing in between. This troubled him badly. He wrote to a friend that the idea of one body acting on another across empty space, with nothing in between to carry the action, was so great an absurdity that no competent thinker could ever fall into it. And he had just built his entire system on it. When pressed, he said, in Latin, that he framed no hypotheses. He would describe, and he would not pretend to explain. So here's the question. If a theory predicts everything, comets, planets, tides, to the limit of measurement, but doesn't tell you why, is that an explanation? Or is it a superb description? And is there a difference? What more would you want? Hold on to that. The answer to Newton's worry takes two hundred and thirty years to arrive, it comes from a patent clerk, and it is stranger than anything Newton feared. Your challenge this week is a sentence to read. Here is Newton's law of gravity as he might write it today. The force equals a constant, times the first mass, times the second mass, divided by the distance squared. Don't calculate anything. Just read it like a line of verse and ask what it claims. What happens to the force if you double one of the masses? If you double the distance? If there is nothing else in the universe but two specks of dust, a billion miles apart, does it say they attract? It does. Every equation in this series can be read that way, and that's how we're going to read them. Next time we start Part Two, with the oddest idea in physics that everyone thinks they understand. We'll ask what energy is, and discover that nobody knows, and that it's the most reliable thing in the universe anyway.