Of Particular Significance

Category: Particle Physics

How to Figure Out the Distance to the Moon Yourself

Last time I described an easy way for you to determine the size of the Moon — easier than the famous techniques used by the classical Greeks. (We don’t need to know the Earth’s circumference, as they did, if we’re ok with a moderately precise estimate.) Once you’ve done that, there’s an simple method, well known since classical times, for figuring out how far away the Earth’s companion is. That’s what I’ll describe in this short post.

(What’s not so easy is to determine the distance and size of the Sun. The classical Greeks failed in their efforts. We’ll need a more modern approach… but that’s for next week.)

Size Versus Distance

Even the early classical Greeks knew something about the Sun, just from the fact that the Moon and Sun appear roughly the same size to our eyes — that is, they occupy about the same amount of sky. If the Sun is twice as far away as the Moon, its diameter must be twice as big, in order that it appear the same size. That’s illustrated in the figure below. If it is ten times as far away, its diameter must be ten times as big. If it’s four hundred times as far away, its diameter is four hundred times as big. (Spoiler: that last one’s the truth; but we’ll get to it later.)

If the Moon is a distance L away from you, and another object twice as far away appears to be the same size in the sky, then that object’s diameter must be twice the Moon’s diameter D. This logic applies more generally to objects further and nearer than the Moon.

You can run this logic in the other direction; if something perfectly blocks the Moon, then if it’s ten times closer than the Moon its diameter must be ten times smaller. If it’s a billion times closer than the Moon, it must be a billion times smaller.

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POSTED BY Matt Strassler

ON February 18, 2022

How to Figure Out the Size of the Moon Yourself

Having confirmed we live on a spherical, spinning Earth whose circumference, diameter and radius are roughly 25000, 8000, and 4000 miles (40000, 13000, and 6500 km) respectively, it’s time to ask about the properties of the objects that are most obvious in the sky: the Sun and Moon. How big are they, and how far away?

If the Moon were close to Earth, then at any one time it would only be visible over a small part of the Earth, as indicated in light blue. But in fact (except at new moon) about half the Earth can see it at a time.

Historically, many peoples thought they were quite close. With our global society, it’s clear that neither can be, because they can be seen everywhere around the world. Even the highest clouds, up to 10 miles high, can only be seen by those within a couple of hundred miles or so. If the Moon were close, only a small fraction of us could see it at any one time, as shown in the figure at right. But in fact, almost everyone in the nighttime half of the Earth can see the full Moon at the same time, so it must be much further away than a couple of Earth diameters. And since the Moon eclipses the Sun periodically by blocking its light, the Sun must be further than the Moon.

The classical Greeks were expert geometers, and used eclipses, both lunar and solar, to figure out how big the Moon is and how far away. (To do this they needed to know the size of the Earth too, which Eratosthenes figured out to within a few percent.) They achieved this and much more by working carefully with the geometry of right-angle triangles and circles, and using trigonometry (or its precursors.)

The method we’ll use here is similar, but much easier, requiring no trigonometry and barely any geometry. We’ll use eclipses in which the Moon goes in front of a distant star or planet, which are also called “occultations”. I’m not aware of evidence that the Greeks used this method, though I don’t know why they wouldn’t have done so. Perhaps a reader has some insight? It may be that the empires they were a part of weren’t quite extensive enough for a good measurement.

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POSTED BY Matt Strassler

ON February 17, 2022

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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POSTED BY Matt Strassler

ON February 14, 2022

Why Simple Explanations of Established Facts Have Value

I’ve received various comments, in public and in private, that suggest that quite a few readers are wondering why a Ph.D. physicist with decades of experience in scientific research is spending time writing blog posts on things that “everybody knows.” Why discuss unfamiliar but intuitive demonstrations of the Earth’s shape and size, and why point out new ways of showing that the Earth rotates? Where’s all the discussion of quantum physics, black holes, Higgs bosons, and the end of the universe?

One thing I’m not doing is trying to convince flat-earthers! A flat-earther’s view of the world is so full of conceptual holes that there’s no chance of filling them. Such an effort would be akin to trying to convince a four-year-old Santa Claus devotee that the jolly fellow can’t actually fly through the air and visit half a billion homes, stopping to eat the cookies left for him in every one, all in one night. Logic has no power on a human whose mind is already made up. (If you’re an adult, don’t be that human.)

Instead my goals are broader, and more contemplative than corrective. Here are a few of them.

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POSTED BY Matt Strassler

ON February 11, 2022

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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POSTED BY Matt Strassler

ON February 7, 2022

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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POSTED BY Matt Strassler

ON February 2, 2022

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Category: Particle Physics

How to Figure Out the Distance to the Moon Yourself

Size Versus Distance

POSTED BY Matt Strassler

How to Figure Out the Size of the Moon Yourself

POSTED BY Matt Strassler

Hey! Where are you Headed Today?

POSTED BY Matt Strassler

Why Simple Explanations of Established Facts Have Value

POSTED BY Matt Strassler

The Best Proof that the Earth Spins

The Magic Star-Pointing Wand

POSTED BY Matt Strassler

How Can You Check that the Earth Spins?

Broken Symmetry

POSTED BY Matt Strassler

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Buy The Book

Reading My Book?

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