Bad Astronomy. Misconceptions and Misuses Revealed, from Astrology to the Moon Landing 'Hoax'

this chapter and even had it submitted for the book, then realized what I said was essentially wrong! What you’ll read here is now correct. It’s funny, too — even people who get tides right rarely take the discussion far enough. Tides have far-reaching consequences, from locking together the Moon’s spin and orbital motion to the volcanoes on Jupiter’s moon Io. Tidal forces can even cause entire galaxies to be ripped apart, torn to shreds by even bigger galaxies.

When astronomers talk about tides, we usually don’t mean the actual movement of water. We are using the term as a shorthand for the tidal force. This is a force much like gravity, and in fact is related to gravity. We’re all aware of gravity from the first time we try to stand up and walk. As we age, we become increasingly aware of it. For me, it seems harder to get out of bed every day, and easier to drop things. Sometimes I wonder if the Earth is pulling harder on me each day.

It doesn’t really, of course. Gravity doesn’t change with time. The force of gravity, the amount that it pulls on an object, depends on only two things: the mass of the object doing the pulling, and how far away it is.

Anything with mass has gravity. You do, I do, planets do, a feather does. I can exact a minute amount of revenge on Earth’s gravity knowing that I am pulling back on the Earth as well. The amount I am pulling is pretty small, sure, but it’s there. The more massive the object, the more it pulls. The Earth has a lot more mass than I do (something like 78,000,000,000,000,000,000,000 times as much, but who’s counting?), so it pulls on me a lot harder than I do on it.

If I were to get farther away from the Earth, that force would weaken. As a matter of fact, the force drops with the square of my distance; that is, if I double my distance, the force drops by a factor of 2?2 = 4. If I triple my distance, it drops by 3?3 = 9, and so on.

That does not mean that I feel one-quarter of the gravity if I climb a ladder to twice my height, though! We don’t measure distance from the surface of the Earth, we measure it from its center. A few hundred years ago, Sir Isaac Newton, the seventeenth-century philosopher-scientist, showed mathematically that as far as distance is concerned, you can imagine that all the mass of the Earth is condensed into a tiny point at its center, so it’s from there that we measure distance.

The Earth’s radius is about 6,400 kilometers (4,000 miles), so for me to double my distance, I’d have to book a flight on a rocket: I’d need to get an additional 6,400 kilometers off the ground, nearly one-sixtieth of the way to the Moon. Only there would I feel like I weigh a quarter of what I do now. It seems like a rather drastic way to lose weight.

Because the Moon is smaller and less massive than the Earth, you would feel a gravity about one-sixth that of the Earth’s if you were standing on the lunar surface. That’s still a substantial pull. Of course, the Moon is pretty far away, so its gravitational effect here on Earth is much smaller. It orbits the Earth at an average distance of about 384,000 kilometers (240,000 miles). From that distance its gravity drops by a factor of nearly 50,000, so we can’t feel it.

But it’s there. Gravity never goes away completely. Although on the Earth the force of gravity from the Moon is terribly weak, it still extends its invisible hand, grasping our planet, pulling on it.

That grasp weakens with distance, giving rise to an interesting effect on the Earth. The part of Earth nearest the Moon feels a stronger pull than the part of the Earth farthest from the Moon. The difference in distance — the diameter of the Earth — means a difference in gravity. The near side of the Earth feels a pull about 6 percent stronger than the far side. This difference in pull tends to stretch the Earth a little bit. It’s because the gravity is different from one side of the Earth to the other, so we call it differential gravity.

Gravity always attracts, so the force of lunar gravity is always a pull toward the Moon. So, you would think, since the near side of the Earth feels a stronger pull, water would pile up there, giving us a high tide. On the far side of the Earth there should be a low tide, a flattening, perhaps, because even though the force is weaker, it still points toward the Moon.

But we know that’s not right. There are two high and two low tides a day. That means at any one time there must be a high tide on the opposite side of the Earth from the Moon as well. How can this be?

Clearly, differential gravity isn’t enough to explain tides. For the complete picture, we have to look once again to the Moon.

Allow me to digress for a moment.

A couple of years ago, my two good friends Ben and Nicky got married. They asked my then-three-year-old daughter Zoe to be the flower girl. The ceremony was lovely, and afterwards at the reception we all danced. Zoe wanted to dance with me, and what proud father could say no?

So I took her hands and we danced in a circle. I had to lean backwards a little to make sure we didn’t topple over, and as I swung her around I couldn’t help noticing that the circle she made on the floor was big, and the one I made was small. Since my mass was about five times what hers was, she made a circle five times bigger than mine.

So what does this have to do with tides? Everything. Our little dance is a tiny version of the same tango in which the Earth and Moon participate. Instead of holding each other’s hands, the Earth and Moon use gravity to embrace. And just like Zoe and me, they both make circles.

Since the Moon’s mass is one-eightieth the mass of the Earth, the effect of the Moon’s pull on the Earth is one-eightieth the effect of the Earth’s pull on the moon. Like my daughter making a bigger circle on the dance floor than I did, the Moon makes a big circle around the Earth, but the Earth also makes a little circle at the same time.

This means that the Moon and the Earth are actually orbiting a point in between the two bodies, as if all the mass in the Earth-Moon system is concentrated there. This point is called the center of mass, or technically the barycenter. Since the Earth is about 80 times the mass of the Moon, the center of mass of the whole system is about one-eightieth of the way from the center of the Earth to the center of the Moon. That’s about 4,800 kilometers (3,000 miles) or so from the center of the Earth, or about 1,600 kilometers (1,000 miles) beneath the Earth’s surface. If you could watch the Earth from outer space, you’d see it make a little circle centered on a point 1,600 kilometers beneath its surface, once every month. In a very real sense, the center of mass of the Earth (which is basically the center of the Earth itself) is orbiting the center of mass of the Earth-Moon system, making that little circle once a month.

This has some interesting implications. To see this, think about the astronauts on board the space station. They float freely, as if there is no gravity. In fact, they feel gravity almost as strongly as we do here on the surface of the Earth; after all, they are only a few hundred kilometers high, not much compared to the 6,400-kilometer radius of the Earth. The astronauts float because they are in free fall; the Earth is pulling them down, so they fall. But they have so much sideways velocity that they basically keep missing the Earth. Their orbit carries them along a curve that has the same curvature of the Earth, so they continuously fall but never get any closer to the ground.

An astronaut standing on a scale in the space station would measure her weight as zero because she is falling around the center of the Earth. Gravity affects her, but she cannot feel it. This is always true for an orbiting object.

But remember, the center of the Earth is orbiting the Earth-Moon barycenter, too. So even though the center of the Earth is affected by gravity from the Moon, someone standing there would not actually feel that force. They would be in free fall!

But someone standing under the Moon on the Earth’s surface would feel the Moon’s pull. Someone standing on the opposite side would, too, but more weakly. But since the force felt from the Moon’s gravity is zero at the Earth’s center, we can measure the Moon’s gravity relative to the center of the Earth. To someone on the side of the Earth nearest the Moon, there would be a force felt toward the Moon. Someone in the center of the Earth feels no force (remember, they are in free fall). But the person on the far side of the Earth feels less force toward the Moon than the person at the center of the Earth. But what’s smaller than zero force? A negative force; in other words, a positive force in the other direction, away from the Moon.

It seems paradoxical that gravity can act in such a way as to make something feel a force away from an object, but in this case it’s because we are measuring that force relative to the center of the Earth. When you do