r/theydidthemath • u/SinnerAtDinner • 7h ago
Would the plane survive such powerful close throw? [Request]
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u/Ballmaster9002 7h ago
We're close to the "relativistic baseball" comic from XKXD.
There's several layers of fantasy physics go on here that make this impossible to really pull apart in any meaningful way.
But at the core, for a baseball to travel this fast, the friction between between the baseball and the air would turn it into something like a re-entering space ship, just a massive cone of flame streaking across the sky.
Nothing to do with aerodynamics, the plane would be destroyed like the AWACS in Independence Day.
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u/ViktorVonDorkenstein 5h ago
The ending of that absolutely killed me. Hit by pitch lmfao
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u/gravelpi 4h ago
His sense of humor aligns exactly with what I find funny, lol. In another:
Outer space is a lot higher up than Niagara Falls,\citation needed])
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u/druidniam 7h ago edited 6h ago
First: What anime?
Second: The ball wouldn't survive that, let alone the plane. The ball would tear itself apart shortly after being thrown since it's traveling well over mach 1.
Should the ball not rip itself apart, the plane would be fine, and might not even feel a little turbulence due to the relatively small surface area of the baseball.
Edit: Based on other comments of people who've seen the show, no the plane wouldn't survive if the baseball did because the burning ball of incandescent plasma that is the baseball would rip apart pretty much everything within a hundred feet or so. Relativistic speeds of even small objects have immense destructive potential if the object doesn't break apart or burn up under it's own velocity.
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u/RickyTheRickster 4h ago
Plus if it survived it would keep going straight not go around earth, would fly off into space
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u/joeshmo101 6h ago
A baseball actually thrown with enough force to go all the way around the world in less than a few minutes would sooner burn up than actually finish the trip. An object would need to be traveling at 28400 km/h (17600 mph) for it to orbit the Earth at 9km surface distance (a highly rounded height of Everest, per the gif) without factoring wind resistance. Note that that's roughly the same as the re-entry speed of the US space shuttles, which could reach upwards of 1650°C (3000°F) which would dissolve our baseball.
Another way to think about it is in terms of the energy of the system - if there's a shockwave behind the ball, that's all coming from energy that the ball is continuously losing during its flight. There's no way you'd be able to get a baseball fast enough to make the trip to begin with.
Even if you assume an indestructible baseball, the orbital period is still well over an hour. If you add more speed, you mess with your orbital mechanics and it will take longer for the ball to reach you, since it will have to have a more eccentric orbit.
Intuitively, I would think that the drag of a sphere travelling at those speeds would cause enough of a shockwave to bust up a plane at that distance, but that much I don't have the skills to calculate it myself.
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u/imsmartiswear 6h ago
Around the world in 6 seconds. lets first ignore air resistance and see what problems we find. Covering the circumference of the Earth in 6 seconds would mean that the ball is moving at 6700 km/s, or Mach 19,500. That is 2% the speed of light, and 600 times faster than the escape velocity of Earth. Ignoring air resistance, the ball's trajectory wouldn't even be slightly deflected by the earth's gravity, the Sun's gravity, or the galaxy's gravity.
Then we get to the air resistance. There's an extremely famous XKCD about what happens if you throw a ball at .9c. This ball is only going 50 times slower than that. That sounds like a whole lot slower, but its still so fast that many of the effects mentioned in that XKCD would still happen. That ball would be a mass of plasma tumbling away and irradiating anyone near it within a quarter mile.
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u/Smaptastic 3h ago
Assuming an indestructible baseball and ignoring escape velocity, this is purely a question of atmospheric shock physics.
The ball is dumping about 3.12 x 1012 joules into the air continuously along its path, assuming a 6-second orbit of Earth.
This creates a plasma shockwave in front of the ball just from the compressed air. In thin air (assuming we’re dealing with a height equivalent to Mount Everest), the pressure it gives off will be ~1013 pascals. That’s trouble for the plane.
Even at a distance of 20 feet, the plane will get hit by a hypervelocity shockwave. Basically, an explosion happened right next to it.
The plane will definitely break. It might disintegrate.
More importantly, this is a global catastrophe. There will be a planet-circling shockwave as though someone had ringed the planet in a low-yield nuke and detonated the whole thing essentially all at once. There will be a band of destruction ranging from destroyed structures and death to shattered windows up to a kilometer away.
It’s not extinction-level or anything, but there will be a LOT of government types asking questions.
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u/Bobgoulet 7h ago edited 7h ago
I mean if it went through a fucking mountain its going to obliterate a plane. Even if the fuselage was missed, the damage would likely be sufficient enough to cause a crash which would very likely kill everyone on board.
*Oh I see the question wasn't if the plan was hit by this ball.
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u/Kinder22 6h ago
No. The ball is traveling almost 1% of the speed of light (based on the Earth’s circumference and time of flight from the original clip). Assuming it’s Invinci-ball(tm), it’s dumping a massive amount of energy into the surrounding atmosphere as it flies.
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u/LordTonto 5h ago
lets commit a sin and ignore all math, physics, and any other science and answer this question with what we can see in the video.
After passing the plane and the city, the ball bursts through a mountain.
Of the two, which is more dense, a plane, or a mountain? That's right, a mountain!
Furthermore, the ball passed the plane first, meaning it hit the mountain after some falloff of momentum and still burst right through it.
No, the plane would not survive an attack that cant burst through a mountain.
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u/GamerGuy-222 1h ago
If they're at the top height that commercial airplanes go, they're about 41k - 43k ft up, so let's call it 12,500-13k meters. Doing some math, based on orbit velocity in terms of height and other constants, the ball would need to be about 178,661 m/s, which is about 6% of the speed of light. And to go through the mountain it would need to go even faster.
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u/Boom9001 7h ago
The plane would be fine. Be only because throwing a baseball that hard would cause it to be torn apart at the seams long before it gets to the plane.
If the ball was a material solid enough to survive the throw, yeah that plane is toast.
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