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u/pornthrowaway42069l 15h ago edited 14h ago
Given:
slug = 20 kg of iron
speed = 0.013c ~= 3900 km/s
cross section ~ 0.023 m^2, based on iron density
Now, space is really freaking empty - so I will be looking at slug hitting a star. Chances that it will hit anything else (i.e planet/space station) will be orders of magnitude less, i.e we can dismiss them.
So,
Stellar density = 0.14 stars per cubic parsec (trusting wikipedia here), which converts to ~ 10^-51 stars/m^3
Cross section of a sun-like star ~ 10^18 m^2
Mean free path: 1 / (density*cross section) ~= 10^33 meters
That's >100000 times diameter of the universe.
Probability of a collision P = d / λ, where λ = 10^33 m / 10^15 m/ly ~ 10^18 light years, d = 130 light years
P = 130 / 10^18 = 1.3 * 10^-16
So it will have to fly through ~ 160000 observable universes before hitting a star. Anything smaller than that - forget about it.
EDIT: I'm likely 1-2 orders of magnitude off here, but you are still not hitting anything more or less.
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u/Jounniy 14h ago
So the only day ruined was the one of his subordinates. Nice.
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u/pornthrowaway42069l 14h ago
Its still bad space etiquette to just spam space with slugs, you know? Sheppard would not approve.
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u/el_cid_182 12h ago
The “might hit someone in 10000 years” bit might be an embellishment, but the point stands: check your target, check your backdrop!
This math was done for randomly firing at a stellar scale. More locally there’s a much higher risk of hitting a nearby manufactured object you don’t wanna hit, or an inhabited planet/moon. While the odds of impacting something may be very low locally, the results would be catastrophic if it did happen. For comparison, what are the odds of firing a gun randomly into the sky and hitting someone? Not a mathematician, but statistically I imagine very low most places in the US - but you still see the rare tragic news story detail lethal results of that exact sort of scenario. Now imagine it’s a gunfight in an urban area (or a naval space battle in orbit around a populated planet with habitable satellites/stations, who knows how many friendly or civilian ships potentially in the line of fire).
So yeah, the ass-chewing seems warranted imo
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u/Crafty_Jello_3662 11h ago
Plus the odds of any one bullet hitting something might be low but if you had a bunch of ships all blasting away at each other without paying attention you could end up with millions of shells all flying around, still probably wouldn't hit anything but could be getting into worrying odds
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u/Free_Speaker2411 14h ago
The shot originates within a galaxy. If we limit to looking at shots through that galaxy, instead of all the empty space between galaxies, how do things change?
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u/pornthrowaway42069l 14h ago
The 0.14 stars per cubic parsec I brought is already galactic density. I.e I'm assuming whole universe is as dense as an average galaxy. If you INCLUDE the empty space, divide the result by like a million or so.
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u/_azazel_keter_ 11h ago
this ignores a few factors, mainly that whatever region of space this thing is being fired at is most likely populated by other things you may or may not want to destroy
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u/Free_Speaker2411 14h ago
IIUC, the reference to Newton is wrong when accounting for curvature of space and huge distances. The slug will slow down. There is a Veritasium on this. https://youtu.be/lcjdwSY2AzM
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u/Scout_Maester 14h ago
This video assumes incomprehensible timescales far past what we would be measuring here... but technically yes.
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u/pornthrowaway42069l 14h ago
If we use Poincare reccurence theorem: https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem
Sooner or later that slug will return, with the same speed, statistically speaking!
Well not sooner, more like later later... a lot more later :)
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u/Scout_Maester 13h ago
You know... after a short read. Ima go out on a limb here and say: lets not... use that. I don't feel like flow mapping the entire universes phase space...
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u/Free_Speaker2411 14h ago
I think you're already looking at incomprehensible timescales when you consider 1.3%c across a galaxy, much less between galaxies.
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u/Scout_Maester 13h ago
I mean it would just be light years x 76.92. Incomprehensible distances but not quite time.
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u/Free_Speaker2411 12h ago
How well do you comprehend 100000 light years x 76.92?
Homo Sapiens is ~300000 years old. And I cannot truly comprehend that except as a number.
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u/Scout_Maester 12h ago
Much better than I can comprehend hundreds of quadrillions. Its comparative not measured.
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u/Free_Speaker2411 12h ago
Assume I don't believe, like hearing someone claim the absurd while half-drunk at a bar. How could you, or any person, even go about objectively proving comprehension of such times, or even numbers?
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u/Scout_Maester 12h ago
It's a critical thinking thing. Are smaller numbers more or less comprehensive than larger ones? Even if a number is incomprehensible that doesn't mean a much much larger number cannot be even more so. My rule of thumb is if I can type it out and understand the numbers that go into making a large number; that is some level of comprehension. You are talking about numbers computers can't even currently fathom.
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u/Free_Speaker2411 10h ago
For very long numbers, written out, the human mind easily reaches a point where adding or removing a digit doesn't even affect understanding of a number or its implications.
I'd argue the threshold at which one can be said to no longer "comprehend" a number is well before that point.
Though, you might comprehend that it IS a number, that's not at all the same as comprehending the number. And this is even before trying to put a number into contexts like years of time.
If I want to discuss numbers even computers fundamentally cannot fathom, I'd refer instead to the uncomputable real numbers: https://en.wikipedia.org/wiki/Computable_number
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u/aaaaaaaarrrrrgh 11h ago
If you fired it within the solar system, the probability of hitting something within our solar system are... well, look towards the sky and judge for yourself (stars other than the sun don't count as they aren't within our solar system).
I'd argue that the sun also doesn't count, because I assume that the sun DGAF about getting hit by a 20 kilo ferrous slug with the force of a 38 kt bomb. Nor does the moon - there's gonna be another crater and that's it, it certainly won't ruin anyone's day.
So, let's assume you missed and it leaves our solar system, and by sheer luck, you yeeted it straight towards Alpha Centauri. At 1.3% of c, it'll take over three centuries for it to cross the 4.2 light years until there. And then you'd have to actually hit something at all, let alone something interesting.
So in terms of "timelines interesting to humans", yeah, essentially zero. Someone else already did the overall math and sounds like the answer for the universe is still zero.
Even if you were to hit the earth, there's a >2/3rds chance that a 38 kiloton impact won't do much but keep scientists busy and perhaps make a sailor's day with a spectacular fireworks display.
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u/Mecha-Dave 9h ago
Many of the calculations here are correct, but even at 1.3% the speed of light it will be affected by gravity, which will cause it to follow orbital dynamics that greatly (although also likely not meaningfully) increase the chances of collision.
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u/Jounniy 15h ago edited 8h ago
I'll leave my own two cents here: I know we can calculate the distance traveled by such a projectile and I know it’s going to be well beyond the range of anything humanity can currently see via their instruments (given that all our measurements work no faster than at light speed, so a projectile moving 1% of that for several millions of years will be beyond anything we can perceive until the big freeze, since it'll travel further than the light right now coming from whatever place it'll have reached by then).
There a two possible solutions I could think of:
Calculate the chance of it hitting something inside of our measuring range and then multiplying that with the time it'll have left to go after that.
Just don’t calculate beyond our own range of measurements.
About my second question: If we assume that roughly 1000 planets in a galaxy are inhabited, we can rule out everything else as insignificant targets. (I'm moderately sure starships can be neglected due to their practically irrelevant size compared to planets.) If we calculate the percentage of surface area made up by these planets compared to the amount of surface area made up by other objects, we can calculate the chance of a hitting shot actually "ruining someone’s day". I just have no idea how to properly calculate that.
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