Of Particular Significance

How Can You Check that the Earth Spins?

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 02/02/2022

Well, now that we’ve seen how easily anyone who wants to can show the Earth’s a sphere and measure its size — something the classical Greeks knew how to do, using slightly more subtle methods — it’s time to face a bigger challenge that the classical Greeks never figured out. How can we check, and confirm, that the Earth is spinning daily, around an axis that passes through the north and south poles?

We definitely need techniques and knowledge that the Greeks didn’t have; the centuries of Greek astronomy included many great thinkers who were too smart to be easily fooled. The problem, fundamentally, is that it is not obvious in daily life that the Earth is spinning — we don’t feel it, for reasons worthy of a future discussion — and it’s not obvious in astronomy either, because it is hard to tell the difference between the Earth spinning versus the sky spinning. In fact, if it’s the sky that’s spinning, it’s clear why we don’t feel the motion of the Earth’s spin, whereas if the Earth is spinning then you will need to explain why we don’t feel any sense of motion. Common sense tells us that we, and the Earth, are stationary. So even though many people over the centuries did propose the Earth is spinning, it was very hard for them to convince anyone; they had neither the right technology nor a coherent understanding of basic physics.

Broken Symmetry

One way to differentiate a rotating Earth from a non-rotating one is to focus on the notion of symmetry. On a non-rotating featureless ball, even if we define it to have north and south poles, there’s no difference between East and West. There’s a symmetry: if you look at a mirror image of the ball, West and East are flipped, but there’s nothing about the ball that looks any different.

(Top) A non-rotating ball looks the same in a north-to-south mirror; it is symmetric under exchange of east and west. (Bottom) But a ball rotating west-to-east has a mirror image that rotates east-to-west; the symmetry is broken.

But if the ball rotates, this is no longer true. If the ball rotates from west to east, as our Earth does, then the mirror image of the ball rotates from east to west.

This breaking of the symmetry between the ball and its east-west mirror image allows something new to happen. On the symmetric, non-spinning ball, anything that can move eastward should be just as likely to move westward. On the asymmetric ball, this is no longer true. A rotating planet might (as ours does) have a tendency for its storms near its north and south poles to move mainly from west to east, and at other latitudes, closer to the equator, from east to west; but on a non-rotating planet there should be no such tendencies at any latitudes. The weather bands and jet streams on Earth are different when viewed in a mirror, and provide already a clear signal that the West-versus-East symmetry has been broken.

A satellite image of Earth; weather near the poles drifts eastward while near the equator it drifts westward (relative to the rotating ground.)

See for example the 7-day pattern over the United States, at a latitude where all the storms move eastward, southward or northward, but almost never westward.

But as far as I know, these weather patterns weren’t well-understood in classical Greek times or even well into the Renaissance. Perhaps this is why no one used them as evidence for a rotating Earth.

A Loophole

So the fact that weather is asymmetric east to west but not north to south is an argument that the planet must be rotating around an axis that passes through the north and south poles. But this argument, while correct, isn’t self-evident. If you thought the Earth wasn’t spinning, you’d then think the Sun goes round the Earth once a day from east to west. This motion, too, breaks the symmetry. Can we be sure that the asymmetries in the Earth’s weather aren’t simply due to this orientation of the Sun’s motion across the sky, which would cause the warmest air to be found at locations that move east to west across the Earth’s surface?

While the motion of the Sun’s warmth certainly wouldn’t cause the weather patterns we see on Earth, this isn’t immediately obvious… not unless you know a good bit of physics and geometry. And if you do, you’re already convinced the Earth rotates, so this conversation becomes unnecessary.

The point here is to give the average person who knows little or no physics, and is armed with common sense that makes physics extremely difficult to understand, an argument that doesn’t require lots of footnotes and complicated pictures. Weather patterns are a powerful argument for the Earth’s rotation, but, psychologically speaking, it would be better to find something less indirect and complex.

The Coriolis Effect

Even Isaac Newton, who was sure the Earth spins daily, wasn’t aware of a good way to prove it. He did point out that a rapidly rotating sphere, if made of a uniformly dense substance, would tend to become a bit squashed. Imagine taking a ball of pizza dough and spinning it really fast; you would expect it to become a disk. In the case of the Earth, it’s not so dramatic, but the Earth’s spin does cause the Earth to be about 1% fatter at the equator than it is on average. But this is too small an effect for ordinary people to easily check.

A much more subtle and interesting insight is called the Coriolis effect, though despite the name (Coriolis wrote his paper about this in 1835) it was already partly known in the mid-1600s. (I’m not aware of Isaac Newton commenting on it; perhaps he thought it unnecessary to point out something so obvious to him?) It was already noticed by Giovanni Battista Riccioli and by Claude Francis Milliet Dechales that on a rotating Earth, cannonballs wouldn’t appear to travel in straight lines as viewed by someone on the rotating ground. In the northern hemisphere, they’d seem to curve slightly to the right, and in the southern hemisphere to the left.

But in the 1600s the effect hadn’t been observed yet; it is too small in daily life and wasn’t easy to detect even by those who made a dedicated effort. In fact, in one of those lovely ironies of history, the fact that the effect hadn’t been detected (yet) was used by both Riccioli and Deschales as an argument against a rotating Earth. (Such ironies continue to the present day, as we’ll soon see.) But the effect has been easy to observe for centuries; in fact, if a nation disbelieves it, their artillery and rocketry will be inaccurate and their military will soon be defeated. As an example [apparently this widespread story is false. What’s true is that long-range artillery does need to consider the Coriolis effect, which is typically comparable in size to the effects of wind.], consider a little mix-up that confused the British navy artillery during a World War I battle with German ships in the Falkland islands, off South America. Though the British of course knew about the Coriolis effect and were correcting for it when aiming at the German ships, they were consistently missing their targets to one side. That’s because in the southern hemisphere the Coriolis effect is in the opposite direction from what the British were accustomed to in the northern hemisphere, and someone in the gunnery chain of command had failed to account for this.

It is not so hard to understand the Coriolis effect, if you are standing at the Earth’s north or south pole. If you throw anything from the north pole, it will travel south along a great circle, and since you are spinning to your left at that pole, the object you threw will appear to you to gently curve to the right. The reverse is true at the south pole, where objects will appear to curve to the left.

(Top Left) A person at the north pole throws a ball toward the equator. (Top Right) The ball travels on a great circle (a circle whose center is the Earth’s center) directly toward the equator, but as it travels, the Earth rotates underneath it, carrying the thrower around to the east. From the thrower’s viewpoint the ball’s trajectory bends to the west (the thrower’s right.) The reverse would be true at the south pole. (Bottom Left) At a lower northern latitude, a person throws a ball due east. (Bottom Right) The ball follows a great circle which will eventually cross the equator, but the thrower is dragged by the Earth on a circle which is at fixed latitude. The two circles diverge, with the ball moving to the thrower’s right. The reverse would be true at southern latitudes.

But at other latitudes, where most people observe these things, there are multiple axes and angles to keep track of, and so the connection with the Earth’s rotation becomes abstract, even though the argument is solid. And that’s the problem with the Coriolis effect — where it matters most, it’s hard to visualize. In the figure above I’ve given you the simple case of a ball thrown east, but in other directions the argument is harder to draw.

The Coriolis effect on storms is particularly dramatic, so it would be great if every child could understand it. But to see how it works, you need to convince someone that even away from the north pole, if you send a projectile off in any direction traveling in a straight line, its trajectory will seem to you as though it curves to the right (if you are in the northern hemisphere) or left (if in the southern). This is easy to see for objects moving east, as shown above, but not so easy in general. Even if you can succeed in this, to then complete the argument that it causes storms to spin counterclockwise (not clockwise, which would seem to be to the right) requires yet another discussion. So this is not easy.

The Foucault Pendulum

The original and classic method for showing the Earth rotates involves the Foucault pendulum, also known as the big big pendulum. Foucault noted that a pendulum on a rotating Earth should itself appear to rotate, and he had one installed in his home city of Paris, to great public acclaim.

Daily experience with swinging objects would lead us to expect a pendulum to swing back and forth covering the same territory over and over again. This is not exactly true on a rotating planet. Again, this is easy to explain at the north pole, but not so easy at other latitudes. At the north pole, you can understand it easily as the pendulum swinging back and forth in a fixed plane, while the Earth and its support structure rotate underneath it, making it seem to a standing observer as though the pendulum is rotating once a day.

(Left) Near the north pole, a person watches a pendulum swing. (Right) A few hours later, the apparatus holding the top of the pendulum, and the person watching, have moved to the east; but the pendulum still swings in the same plane as it did in the beginning. It seems to the person watching that the pendulum has rotated, though in fact it is the ground underneath the watcher that has rotated.

But now go, say, to New York City; why, in that location, does it take about a day and a half for a Foucault pendulum to rotate? Why does it take multiple days if you are in Panama City, or in Lima, Peru? While this is not so terribly hard to get straight if you know some vector analysis and trigonometry, it’s quite confusing if you don’t. Also, though it’s not too hard to invest in a Foucault pendulum if you are a science museum with a very high ceiling and lots of room, along with technical expertise, it’s not something you can easily do at home.

By the way, these problems bothered Foucault, too. He wanted a more intuitive, simpler method, and he invented one. But although it worked to a degree, it was too far ahead of the technology of its time. More on that in the next post.

The 21st Century Night Sky and a Rotating Earth

Here’s a completely different approach. We started with the observation that if the Earth rotates, then there should be something different about west-to-east than east-to-west — something other than the direction of the Sun’s motion across the sky. If we can find evidence of something that differentiates these two directions but has nothing to do with the Sun’s heating and weather, we might be convinced that the Earth is rotating.

So head out in the middle of the night and stare up at the stars, the Moon, and the planets. Of course, just as the ancient Greeks did, you’ll see these objects in the sky move slowly across the sky. But by looking at these ancient objects, you will not learn anything the Greeks did not know, and they were unable to prove that the Earth rotates.

There is something, however, that you can see that the classical Greeks could not. More and more commonly, as near-Earth orbits fill with thousands of satellites and pieces of space junk, you will see rapidly moving bright objects that don’t flicker like a plane but aren’t near-stationary like a star; they cross the sky in just a few minutes as they orbiting the entire Earth once every hour and a half or so. If you watch for a while, you’ll see some moving from north to south. You’ll see some moving from south to north. You’ll see some moving from west to east. And you’ll see some moving from eas… NO YOU WON’T!!

Don’t take my word for it; try it yourself. No matter what part of the Earth you live on, you’ll almost never see a satellite moving from east to west. Or if you haven’t the time, look at this satellite tracker; you’ll see that all the satellites are moving either on polar orbits (northward or southward) or on eastward-trending orbits. Nothing moves westward.

Now, what is the cause of that?! Why would satellite operators all around the world, from all the space-faring countries, only send up their satellites moving from west to east? Is it a conspiracy? A cultish, religious conviction that satellites moving into the light must always see the Sun rise in the east? A strange coincidence? Of course not. The reason to send satellites from west to east is completely practical. Sending up a satellite is extremely expensive, and one of the main costs is fuel (and the weight of that fuel, which requires even more fuel). Going west to east saves a lot of fuel, and therefore saves tons of money.

The reason it saves fuel is that an orbiting satellite relatively near the Earth’s surface (meaning within a few hundred miles, as is the case for the various space stations that are or were in orbit) must travel at 17000 miles per hour (28000 km per hour) relative to the Earth’s center in order to remain in a roughly circular orbit. (You can estimate this speed yourself, by timing satellites as they pass overhead.) But the Earth’s equator, near to the European Space Agency launching site in French Guiana, is already rotating 1040 miles per hour (1670 kph) from west to east relative to the Earth’s center. (At Florida latitudes, the location of Cape Canaveral, it is rotating at 914 mph, 1470 kph) This west-to-east motion gives a rocket launching toward the east a head start. Since is already moving west to east relative to the Earth’s center, the extra speed it has to obtain, if it heads eastward, is not a full 17000 mph; it need gain only about 16000 mph. That saves fuel! If instead it were to head east to west, the Earth’s spin would actually be a handicap, meaning that the rocket would need to change its speed by 18000 mph, and thus require much more fuel. (And more fuel at launch means the rocket is heavier, and that too requires more fuel!) So unless you’re crazy, or drowning in free money and fuel, you’d never launch your orbital satellite on a rocket heading east to west. And indeed, nobody does.

With the Earth rotating west-to-east, giving locations at the equator a speed of about 1000 mph (1600 kph), an eastward launch (green) gets a head-start from the Earth’s rotation, while a westward launch (orange) actually has to slow and stop heading east before it can begin to head west. It’s much more fuel-efficient to launch east than west, and this is why few if any satellites move across the sky from east to west.

This, then, is a strong intuitive logical proof, one that any person can check for themselves by staring at the night sky, that the Earth is rotating west to east, and rather rapidly. If the Earth were not rotating at all, or if its rotation were very slow compared to 17000 mph, then there would be no fuel benefit to launching west-to-east satellites versus east-to-west ones, and so some countries might do it one way and others might do it the other way depending on their convenience. There would be no reason to expect east-to-west satellites to be absent. And since it’s easy to check for yourself (as I showed you) that the Earth’s circumference is about 25000 miles (40000 km), you can confirm yourself that a 24 hour rotation period gives the equator the speed I quoted above — more than 1000 mph (1600 kph), enough that rocket engineers would not ignore it.

I challenge you to come up with an alternative explanation. But still, this is an argument, not a proof, and it doesn’t by itself tell you how fast the Earth spins, or around which axis. The best demonstration, though barely within reach of modern technology, is much clearer and simpler than a Foucault pendulum… and Foucault knew all about it. That’s for next time.

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14 Responses

  1. The phases of the moon -alone- not much help. The timing or measure of the tides -alone- not much help in showing that the Earth rotates. But the relationship between the tides and the phases of the moon are apparent to many non-experts. That relationship along with an open mind may suggest that the Sun and the Moon produce the tides OR that the tides regulate the course of the Sun and the Moon. Now if it were only the moon, one might blame the motion of the moon on the tides. But the Moon and the Sun both keyed to the tides— now we can not claim their movement is dictated by the sloshing of the seas. Can we? Sure, if we both believe the Earth is the center of the Universe; we can claim what-ever and get away with doing so.

    1. Still, the fact that the Moon and Sun create the tides (which is not as obvious as you may believe — Galileo disagreed, presumably because in the Mediterranean tides are not so simple as at most ocean beaches) doesn’t directly prove the Earth spins. I believe that a person who thought Moon and Sun orbit the Earth would still conclude that there should be tides… because they are generated by the fact that the two bodies’ gravitational effects vary from one side of the Earth to the other, a fact which does not depend on the Earth’s rotation. However, the details might perhaps be different. I should try to work out those details. Tides are not intuitive; every argument I’ve found on-line that tries to explain to general readers why tides occur twice per day gets it wrong. Even NASA’s page is wrong. And I understand why; I don’t have an easy way to explain it yet either.

  2. Would not a simple Doppler effect be the simplest proof: observe a very small sharp (in frequency) astronomical radio emission line source in evening and at dawn. Or better measure the pulse rate of a pulsar at dusk and dawn. Or try to observe a temperature difference in the cosmic microwave background looking east versus west (hard from the earth’s surface)?

    Separately: where’s that “correct and complete” one for tides?

    1. Oh, if we’re willing to use high-precision modern technology, then of course it is easy to show the Earth’s spinning. The question is whether you can demonstrate it to a non-expert, say a child of 14, or an interested but skeptical adult who has flat-earthers in the family. In fact Doppler effects aren’t needed, as I’ll explain in the next post; there are much easier ways. We’ll come back to Doppler effects when it is time to debate the Earth’s orbit.

      Re: the tides, https://www.vialattea.net/content/tides-and-centrifugal-force/ .

  3. Tides and the phases of the moon. Using “clocks” of the time one could make a good case for the Earth’s rotation. But I doubt that anyone who was convinced that the Earth was the center of the Universe would be persuaded. Much like today; Earth centric individuals accept the whole “Big Bang” story.

    1. Clearly phases of the Moon won’t work; the Greeks knew and understood those phases perfectly, as a purely geometric effect. They don’t tell you if the Earth is spinning or the Moon and Sun are orbiting the Earth. As for tides, I don’t think they tell you the difference either, but maybe there’s a subtlety I’m not considering? What’s the argument? (In any case, it will not be easy to explain to a non-expert; almost every brief explanation of the Earth’s tides on the internet is wrong, and the only correct and complete one I’ve been able to find involved some hard work in rotating reference frames…)

  4. Pendulum represents SU(2) symmetry group. But whatever written, including the Mathematics represents the 2D, a local symmetry breaking or Holographic?

    1. Mass Parameters are Abelian at “right angle” (like poppig out & in from nothing), a Hidden-variable thus a non-Abelian like gauge invariance making the Einstein’s-hypotenuse to cancel (Maxwell equations transform in this way).?

        1. Thanks..
          The mirror image symmetry breaking is not the same but digitally Same (2D holographic). So the circumference is the square (two triangles) at right angles (starting and finishing = rotation) where the Mass Parameter Einstein’s-hypotenuse = 0 ?

  5. Hi Matt. It’s been about a decade since my last comments on your blog. I like your arguments and hope never to meet someone who should be persuaded by them, but I have met someone once who thought that the Sun is hollow and that some people live inside of it (the worse case of home-schooling by religious parents I hope).

    Anyway, there are a couple errors to correct. The parenthetical sentence about Florida has mpr twice. The paragraph above the rotating earth graphic concludes: “you’d never launch your orbital satellite on a rocket heading west to east. And indeed, nobody does.” You really mean the opposite. And I would change Earth “size” to circumference.

    1. Hi Vincent — first, thanks for the corrections, and second, it’s nice to hear from you again!

      As for persuasion: I don’t claim one can ever persuade an adult who is fanatical, crazy, or fundamentally illogical; such people will make the world fit their beliefs, rather than the other way round. It’s much the same with certain religious beliefs; persuasion is not relevant. The people you can convince are the ones who haven’t made up their minds, especially young people who are at the questioning stage. That’s why the strongest, clearest arguments need to be made to be available to them, and to their parents and science teachers. The best arguments are always those which are simple, intuitive, and easy to check for oneself.

      In my view, the Coriolis force (and related phenomena like the spinning of storms and the rotation of a Foucault pendulum) don’t quite meet that standard, and that’s why more direct checks are needed for the Earth’s rotation. For the spherical Earth and its size, it’s not quite as important since there are photographs and clues from air travel; but even so, it’s reassuring to the skeptical or uniformed to learn that one can check these things very easily for oneself, without traveling to space or taking a round-the-world flight.

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