[Spiral Galaxy M81 image credit: Adam Block/Mount Lemmon SkyCenter/University of Arizona]
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I learned a thing!
Wherein I learn a thing
A habit I’ve tried to get into recently is thinking about the origin of odd words or phrases when I use them. I’ve found that more often than not, something weird and interesting comes up when I look up the etymology.
I was writing about Rigel, a star that’s on the opposite corner of Orion from Betelgeuse, and wrote that it’s “catty-corner”. After I did, I looked at the word for a moment, then remembered that some people say “kitty-corner”. Why is that? So I looked it up and got a surprise.
The word is actually “cater-corner” (sometimes without the dash). It comes from the French word for four (quatre) and before that the Latin (quattuor), sometimes referring to the four sides of a quadrilateral, and eventually coming to mean diagonally placed. The word “cater” referred to the four pips representing 4 on a six-sided die, of all things.
Catty-corner and kitty-corner are corruptions of that, slight mispronunciations that caught on, and having nothing to do with cats. I think we used kitty-corner when I was a kid; my memory is vague but that sounds right. It never occurred to me until now to find out why.
And that’s why I like looking into such things. It’s fun! I like it even more when it’s surprising, especially when the history of a word takes a weird turn like this one did.
Because I think math is cool, and I think that because it is
A few weeks ago, about in the middle of the time Colorado was locked down due to the COVID-19 pandemic, my wife noticed the air was clearer.
I had been thinking that myself. We live just east of the Rockies, and can usually see down quite a ways. But haze and air pollution limit that view, some days worse than others. Boulder is in a valley, so heavier air tends to sit there, making it hazier, but our view of the famous Flatirons was unusually crisp. This, we figured, was due to the much lower number of cars on the road.
At around that same time I went out to run errands — we keep those to a minimum, of course, but sometimes you gotta go — and while driving south on a highway I spotted a mountain obviously very far away. I pulled over to get a shot of it with my phone:
[Pike’s Peak from 150 km away. Credit: Phil Plait]
We sometimes see it when the air is clearer, but this was the best view I’ve had of it; despite the low resolution in this cropped zoom you can see some detail including where it’s covered in snow and where it isn’t.
It turns out that’s Pike’s Peak, about 150 km south of where I took that shot. I had to double check the map to make sure, but yup, that’s it.
I was surprised I could see so much of it from so far away. But then I did the math… which, it turns out, isn’t that hard. In fact, let me show you!
In 2018 I wrote an article about how far away you can see a meteor, and made a diagram for it. That same diagram works here!
[Diagram showing the Earth and the top of the atmosphere — but it also works for any object of height h. Credit: Phil Plait]
Here R is the radius of the Earth, d is the distance to an object, and h is the height of that object. In our case, h is the height of Pike’s Peak. I looked that up (4.3 km), as well as the radius of the Earth (6400 km). I can then calculate d, which is the maximum distance I can see the top of the mountain. If my actual distance (150 km) is less than that, then I can not only see the top but also part of the mountain below it.
The equation is on that linked page. When I do the math, I get that the maximum distance I should see it is 230 km. That’s farther than my actual distance of 150 km, so not only can I see the top of the mountain but a significant portion below it, too.
If I futz with the math a little to solve for h, and saying my distance is 150 km, I can figure out how much of the mountain I could see. For that distance I can see everything above a height of 1.7 km — anything below that elevation is below my horizon. Pike’s Peak is 4.3 km high, so that photo shows something like the top 4.3 – 1.7 = 2.6 km of the mountain.
These numbers are rough, and I made a bunch of assumptions, but I think it’s pretty close (the biggest issue is I don’t know the elevation of where I was when I took that photo, and that has a big effect on how far away the horizon is). You can clearly see quite a bit of the mountain, so it does seem to all fit together.
It’s still little surprising that I can see something that far away, but I also know that math is math. Reality has very little need to cater to our preconceptions. We are the ones who must change our conceptions to fit reality.
It’s probably a pretty good idea to extrapolate that as needed, folks.
What I’ve recently written on the blog, ICYMI
[A stunning image of a protoplanetary disk where a newly forming planet is orbiting the star AB Aurigae. From Wednesday’s post. Credit: ESO/Boccaletti et al.]
Monday 11 May, 2020: Two huge blobs in Earth’s mantle are fighting it out over our magnetic pole
Tuesday 12 May, 2020: Do aliens exist? Probably. Are they intelligent? Probably not.
Wednesday 12 May, 2020: A spectacular image of a kinky spiral points toward a baby planet forming
Thursday 13 May, 2020: NASA renames new space telescope after pioneering astronomer Nancy Grace Roman
Friday 14 May, 2020: No, NASA did not discover a parallel universe where time runs backwards
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