Hey! Where are you Headed Today?

Even if you’re working from home, so that you’re spending the day at a fixed location on the Earth’s surface, you’re not at a fixed location relative to the Earth’s center. As the Earth turns daily, it carries you around with it. So where are you headed today? Presumably Earth’s spin takes you around in a big circle, right?

That’s great. Which circle?

Point to it, right now.

Let me ask that again, in case that wasn’t clear. With your feet on the ground, looking whichever direction you choose, please show me the circle you’ll be taking today on your travels.

Most people who hazard a guess imagine that if they face east (toward the rising Sun, which here is into the plane of your screen), they are traveling on a circle that cuts vertically into the ground. But this is true for very few of us.

No idea? In my experience, many people have never even thought about it. Those who are willing to hazard a guess have to think for a moment to figure out that the Earth is rotating west to east — that’s why the Sun appears to rise in the east and set in the west. Once they are clear on that point, many people face east, and then indicate a circle that goes straight ahead, which would be combination of east and then down, as you can see in the figure.

To say that another way, if you imagine the circle of travel as being the edge of a disk, that disk would face east-west and slice directly down into the ground.

For the vast majority of us, it turns out this guess is not correct.

So where are we headed? People located at the equator or the poles can answer this more easily than the rest of us, so let’s start with them.

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The Best Proof that the Earth Spins

In my last post I gave you a way to check for yourself, using observations that are easy but were unavailable to ancient scientists, that the Earth is rotating from west to east. The clue comes from the artificial satellites and space junk overhead. You can look for them next time you have an hour or so under a dark night sky, and if you watch carefully, you’ll see none of them are heading west. Why is that? Because of the Earth’s rotation. It is much more expensive to launch rockets westward than eastward, so both government agencies and private companies avoid it.

In this post I want to describe the best proof I know of that the Earth rotates daily, using something else our ancestors didn’t have. Unlike the demonstration furnished by a Foucault pendulum, this proof is clear and intuitive, involving no trigonometry, no complicated diagrams, and no mind-bending arguments.

The Magic Star-Pointing Wand

Let’s start by imagining we owned something perfect (almost) for demonstrating that the Earth is spinning daily. Suppose we are given a magic wand, with an amazing occult power: if you point it at a distant star, any star (excepting the Sun), from any location on the Earth, it will forever stay pointed at that star. Just think of all the wonderful things you could do with this device!

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How Can You Check that the Earth Spins?

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.

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