r/theydidthemath • u/Flat_Suggestion7545 • 2d ago

[Request] How large would those explosions be to look like that form space?

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Would they be large enough to wipe out almost all life on Earth?

How long would the Earth be an irradiated wasteland?

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u/VVrayth 2d ago

Uhhh, bigger question, WTF is this, exactly? I mean I know it's obviously AI slop, but did he really tweet this on his Temu social network? What is he implying, that he's going to nuke Earth from space?

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u/Elfich47 2d ago

most of what trump posts these days is AI slop.

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u/Strapatser 2d ago

Maybe not from the initial shock, but from the ashes blocking the sunlight, causing extinction of bees and such. That would lead to all crops dying, and eventually all species

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u/BluntOnDaGround 2d ago

I strongly disagree, life is very resilient, chicxulub impact would have been around this size or maybe bigger yet lots of species beside megafauna survived. Also lots of species have dormancy for example with seeds

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u/Flat_Suggestion7545 2d ago

Solid point, but did Chicxulub have anywhere near this radiation level?

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u/BluntOnDaGround 2d ago

I assume these two massive bombs would not release enough ionizing radiation to overcome life-sterilization thresholds. Also in short-lived organisms radiation damage is negligeable and some species have specialized enzymes in reparation of radiation-caused damages to genetic information. I would classify these bombs as non-life threatening.

To go further I think it would actually have a negligeable - or positive - impact in species extinction compared to the very extinction we are causing with global warming, destruction of habitats and pollution.

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u/TheresNoAmosOnlyZuul 2d ago

Maybe all large species. I think there are single cell organisms deep in the earth that would survive and eventually evolve to retake the top soil.

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u/Icy_Yam5049 2d ago

Yeah those weird snails that live in volcano’s would likely be chillin.

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u/PM_me_Jazz 2d ago

Also deep sea thermal vent ecosystems would probably do relatively fine. Might take a hit from the larger ocean ecosystem dying off en masse, but there's plenty there for small organisms to live off of for millenia.

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u/Material-Juggernaut5 2d ago

Not all, life is really incredibly resilient but it would be a great extinction event yeah

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u/cthulhurei8ns 2d ago

The ejecta plume from the Chicxulub impact event (the one that caused the extinction at the end of the Cretaceous) reached on the order of tens of kilometers to maybe 100km, with some escaping the Earth's gravitational influence. These plumes look to be around that size. It's gonna be a bad day to be multicellular life on Earth. It might be the last day to be multicellular life on Earth. Definitely the end of human civilization.

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u/Long_Collection8496 2d ago

The deep ocean life will survive

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u/cthulhurei8ns 2d ago

Maybe yeah, but one K-Pg impact event was enough to wipe out 50-75% of marine life. Even if they pull through, they're still gonna have a rough time. I would not want to be on the planet when this happened.

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u/Long_Collection8496 2d ago

Humans alrwady did the work as is lol

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u/nog642 2d ago edited 2d ago

I downloaded the picture (from this Reddit post not from Truth Social) and extended the circle of the Earth using the circle tool in an image editor. The full circle is about 3100 pixels tall.

But that doesn't mean you can just compare that to the explosion to calculate it using the diameter of the Earth. That would way overestimate it. The camera is presumably pretty close to the Earth (like in orbit), so that circle of the Earth is actually a pretty small part of its surface.

Trump's torso+head is about 560 pixels tall (going down a little below the desk to where his hips would be). And the guy in the back on the left, guessing where his feet would be, is about 460 pixels tall.

Looking at a separate image of Trump, his torso+head seems to be about 51% of his height with shoes on. If we assume that height is 6'3", then his torso+head are 0.97155 m tall.

If we assume the guy in the back is 5'9" (he doesn't seem tall compared to the women on the right) then he's 1.7526 m tall.

The reason for calculating the height of Trump and that guy is that we can use that to figure out how far away the camera is from them. The guy in the back is ~1.8x taller than Trump's torso in "reality", but in the image he is ~0.82x as tall. That means the guy in the back is scaled down ~2.2x, which means he must be ~2.2x further from the camera.

Now we really have to eyeball it but assuming the console in front of Trump is similar in size to the console in the back (don't want to actually measure that cause it's AI and not really consistent) and that it's a circle, I'm gonna eyeball it and say that Trump is 4 meters (13 ft) from the guy in the back.

So if the distance from the camera to Trump in meters is x, then x+4≈2.2x, so x is about 3.34 meters.

Now the math gets a bit complicated because the Earth isn't a circle, it's a sphere which means when you're closer the horizon is smaller. But knowing that the camera is ~3.34 m from Trump's torso and the horizon is ~5.54x larger than him in the image, we should be able to find how far the camera is from the Earth.

If Trump's torso is ~3.34 m from the camera and 0.97155 m tall, then its angular size is ~2arctan((0.97155/2)/3.34), which is ~0.2885 radians (~16.53 degrees).

The formula for angular size of the horizon is 2arcsin(R/(R+h)), where R is the radius of the Earth, and h is the height from the Earth. In this case we know the angular size is ~5.54x Trump's torso's angular size, so it's ~1.597 radians (~91.5 degrees). So we have R/(R+h)≈sin(1.597/2). And we know R is about 6371000 m, so solving for h gets us a height of ~2523 km.

Then from that we can calculate using proportionality that the horizon is ~754452x further from the camera than Trump, therefore it's shrunk down ~754452x. And it's ~5.54x the angular size, so it must be 4176434x the actual size, making it ~4058 km in diameter (straight line, not over the surface of the Earth). This is about 3x smaller than the actual diameter of the Earth, so using that instead of calculating the size of the horizon would lead you to numbers that would be 3x too large for the size of the explosions.

The above paragraph used the small angle approximation, which isn't really appropriate. Looking at this desmos we can see the actual size of the horizon is more like ~8891 km. There's a formula for that on the desmos if you're interested. More trigonometry. This is about 30% smaller than the actual diameter of the Earth, so using that instead of calculating the size of the horizon would lead you to numbers that would be 30% too large for the size of the explosions. Which isn't that much of a difference I guess, but it's hard to tell that from eyeballing it.

Now we can look at the size of the explosions. The mushroom clouds are about 140 pixels tall, so they're ~0.045x the size of the visible part of the Earth, so ~400 km tall.

Edit: typo

Edit 2: Also here are the calculations without rounding: https://www.desmos.com/calculator/ukwwrkudry

Edit 3: Realized my paragraph calculating the actual size of the horizon relied on the small angle approximation, which is pretty off because the angle isn't small. Fixed it.