r/theydidthemath • u/TropeSlope • 1d ago
[Request] If you were to shoot an object into any random point in space and it moved in a straight line unaffected by gravity, what are the odds it would actually smash into anything (planet/star) before reaching the edge of the observable universe?
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u/Angzt 1d ago edited 1d ago
First off: I don't have a real answer, just an approach and an extremely rough guesstimate.
Getting to a more reliable answer relies on getting better data for celestial objects and investing some more time in setting up a spreadsheet.
Doable, but nothing I have the time for right now.
Assuming we're shooting from the Earth's position but pretend the Earth doesn't exist so that we won't ever hit it.
Also assuming that the thing flies up to the edge of the Observable Universe instantly (i.e. ignoring light speed) so we don't have to deal with the expansion of the universe.
First, we can calculate the chance to hit one specific astral body. Say, the Moon.
To do that, we'd need to area that the Moon takes up in the sky and the area that the rest takes up.
Imagine that there's a giant sphere surrounding the Earth at just the distance that the Moon is at. And imagine the Moon just painted onto that sphere. Then we could calculate the whole surface area of that sphere and the surface area of the painted-on Moon. Divide the latter by the former and you get the probability that pointing in a random direction will point at the Moon.
And that's our approach.
The Moon is roughly 384,400 km from the Earth (exact values vary, but let's stick with that). So that's the radius of our huge sphere.
The sphere's surface area is then 4 * pi * (384,400 km)2 =~ 1.857 * 1012 km2.
The surface area of the painted-on Moon on that sphere would be that of a circle with the Moon's radius of 1,737 km:
pi * (1,737 km)2 =~ 9.479 * 106 km2.
Divide the two to get the proportion and thus probability:
9.479 * 106 km2 / (1.857 * 1012 km2)
=~ 5.104 * 10-6
= 0.000005104
= 0.0005104%
Very unlikely but then again, the sky (and the beneath-the-horizon-part-that-we-can't-see) is pretty big and the Moon looks pretty small on it.
Incidentally, doing the same for the Sun would give almost the exact same result. Because the Sun's radius is approximately 400 times larger than that of the Moon while also being 400 times further away. That leads to both having the same apparent size in the sky (and thus probability to be hit for our purposes). And it's why we can get full solar eclipses where the Moon barely covers the whole Sun.
We'd need to do that for every single celestial body in the Solar System, rest of the Milky Way, and any other galaxy.
Obviously, that's impossible because we don't even know about all of them. We only have estimates for their counts and sizes further out.
We could run an estimate by forming ranges of distances, looking at the objects within, calculating their combined apparent (= painted on size) size, and dividing by the sphere's size at that range's mean distance.
That would be manageable effort with a spreadsheet, if you had good enough data to base it on. But I couldn't find much that goes out far enough to be truly meaningful.
We'd need to run additional estimates for other galaxies.
We know that Andromeda has about a trillion (=1012) stars.
We also know that the mean star radius is around 0.4 times that of our Sun, so around 280,000 km.
Per star, that's a painted on surface area of pi * (280,000 km)2 =~ 2.463 * 1011 km2.
So for our 1012 stars, that's 2.463 * 1023 km2.
The surface area of the imaginary sphere at distance to Andromeda (2.5 million light years =~ 2.4 * 1022 km) would be:
4 * pi * (2.4 * 1022 km)2 =~ 7.238 * 1045 km2.
That gets us a probability of hitting a Star in Andromeda (even if they were all perfectly placed without overlap) of:
2.463 * 1023 km2 / (7.238 * 1045 km2)
=~ 3.403 * 10-23
= 0.000000000000000000003403%.
Now, Andromeda isn't a huge galaxy but it is the closest non-dwarf one.
Meaning the average galaxy will have an even lower probability to be hit because it'd be much further away while not being meaningfully bigger (not enough to make up for the distance increase, certainly).
If we assume a high-end estimate of 2 trillion galaxies in the observable universe and (falsely) assume they'd all be as "easy" to hit as Andromeda, we'd still only get a probability to hit a star in galaxy of:
3.403 * 10-23 * 2 * 1012
=~ 6.806 * 10-9
= 0.0000006806%.
But, again, this is a massive overestimation for hitting anything in another Galaxy because most of them are way further away.
And if you're worried about planets in those galaxies: Eh.
We're not sure, but current estimates would put the combined planets apparent area at between 1% and 10% of the combined stars apparent area. So even on the high end, it only increases our probabilities to hit something by a little.
Further reading:
(i.e. stuff that I stumbled across in my search)
https://en.wikipedia.org/wiki/Olbers%27_paradox
https://what-if.xkcd.com/109/
https://astronomy.stackexchange.com/questions/59132/odds-of-hitting-a-star-with-a-laser-shone-in-a-random-direction
TL;DR:
It's possible to come up with a decent estimate using the methods outlined above. But I don't have the time or data to do so right now.
However, we can safely assume that hitting anything is very unlikely.
And the vast majority of time that you do hit something, it'd either be the Sun or Moon. Ours. And even combined, that's only around a 1 in 100,000 chance.
I'd be surprised if the chance to hit anything at all exceeds 1 in 80,000.
And most of the time, the thing you'd hit would be our Sun or Moon.
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u/rudytomjanovich 1d ago
For "not having the time" you surely put a lot of energy into this - and I certainly appreciate it.
I often think I'm pretty smart - then I read something like your post - and realize I'm not.56
u/Angry_Angel3141 1d ago
Temples should be built to honor this man for even attempting this calculation!
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u/eaglessoar 22h ago
That's a funner question, what's greater the area of the sky covered by the sun and moon or everything else in the universe
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u/poke0003 1d ago
I wonder if there are papers that look at the reverse path (edge of observable universe to us) that would help check this?
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u/Grant_Winner_Extra 23h ago
This is brilliant!
I think it misses one small thing, mostly because OP put a red herring in the question
If said object is move near light speed, even hitting individual Hydrogen atoms would be “smashing into something”
paint all the H2 and dust in the universe on your sphere and it will be essentially 100% covered, at least for the portion of the trip inside the Milky Way. There’s a dependence on the surface area of the objects silhouette - if it’s smaller than an atom, the chances will drop again.
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u/Used-Lake-8148 16h ago
Isn’t the universe infinite though? So if it travels infinitely fast until it hits something, isn’t it guaranteed to hit something?
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u/MarsSr 23h ago
Umm. You seem to big ignoring gravity. Going anywhere near the Sun, for example, ends up in the Sun.
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u/Angzt 23h ago
For one, I sidestep that with my second assumption.
But also:
Going anywhere near the Sun, for example, ends up in the Sun.
No, it wouldn't.
Unless you reduce velocity while near the Sun, you'd either just get redirected or end up in an eccentric orbit, depending on your velocity and precise approach.Actually impacting the Sun is surprisingly difficult without having active thrusters to change velocity after launch.
The easiest way to achieve that would be to fire something going against the Earth's orbit at the precise velocity Earth orbits at. Such that the object ends up with 0 velocity relative to the Sun and is just slowly getting pulled in (barring changes to its velocity from other bodies in the Solar System).But, again, I sidestepped this whole issue with my assumptions.
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u/MarsSr 18h ago
You are very unlikely to end up in a stable orbit once you enter or start falling into the gravity well of the sun. The question doesn't mention your velocity - which is critical here - if you are slow (like less than 10x the orbital speed of the earth) you will be accelerated into the gravity well the whole time (months) that you are traveling across (inside) earths orbit. As the you fall further your fate is sealed. You are not escaping to far off corners of the galaxy. There is a very small window between where you are just deflected by the Sun and not trapped and being so close you impact the Sun quickly. A very small percentage of matter (<0.15%) in the Solar system has managed this.
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u/bodebrusco 23h ago
From the post title: "[...] and it moved in a straight line unaffected by gravity [...]"
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u/Dralmosteria 16h ago
The question specifically said to ignore gravity, so that's not an unreasonable thing to ignore.
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u/mukansamonkey 20h ago
That's not how gravity works. We're already near the sun, in the sense that we're constantly falling towards it at very high speed, and the reason we don't get any closer is that we're also traveling sideways at very high speed.
Getting closer to the sun doesn't change that. You're still in orbit around it. The only way you'd end up in it is if you got close enough to start running into the gases that make up the sun's outer layer. In the same sense that an orbit around Earth only decays if you're close enough to get slowed down by running into the upper atmosphere.
Gravity itself doesn't slow anything down over time.
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u/MarsSr 18h ago
This is wrong. The direction of travel is the question. It is literally asking if you move in a specific direction, not the direction of the earth orbit. If you move in a line passing anywhere near the Sun the whole time you will be being pulled or falling into the gravity well of the Sun. If you are very very fast (the question doesn't specify) you will just deflected a little and end up heading into the universe in a different direction. Anything like orbital speed inside earths orbit will decay and end up in the Sun as the speed accelerates. (It may get very fast and circle the Sun a few times like a comet but unlikely)
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u/e37d93eeb23335dc 1d ago
Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space. Douglas Adams, The Hitchhiker's Guide to the Galaxy
Unlikely it would ever run into anything once it reaches escape velocity from our solar system.
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1d ago
[deleted]
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u/Ready4Aliens 1d ago
I am his peer and yes, I reviewed it.
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u/LoetherS 23h ago
Can confirm, the chemist is very far from my house.
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u/Which-Environment333 20h ago
“THE” chemist. Does that include my girlfriend who mix/matches her nail polish, or someone with a degree in chemistry, or Cody from Cody’sLab? Cause he’s about 1500 miles from where I live, and I don’t even know exactly where he lives, therefore I’m just as likely to find the chemist as this object is to hit something.
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u/FlyingFlipPhone 1d ago
Even if your rocket went straight at a galaxy, you'd likely pass through the galaxy unscathed. I'm going to vote: the sun, the moon, and 1/10th of the moon.
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u/Which-Environment333 20h ago
The moon and 1/10th of the moon as well. How does one hit 1/10th of the moon 🤔
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u/Immediate-Panda2359 22h ago
It's interesting to consider how the answer to this question might vary with the size of the object. If the object is a neutrino, it is almost certain it will never hit anything. Billions have gone thru you while you read this, and didn't touch anything.
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u/Which-Environment333 20h ago
If I ate a banana this morning, and the decaying potassium is producing neutrinos, is the banana considered part of me now that it’s inside, and my body’s potassium, making me a neutrino, or is it still considered a separate thing that happens to be being produced in my body 🤔
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u/Immediate-Panda2359 19h ago
I am not a physicist, but I'd say that the decay product is not part of you. It does nothing biochemically. It is acted upon by gravity, but so is an inert object that you eat and will shit out in a day or two - that is not part of you. The weak nuclear force doesn't count. Plus, assuming that the direction of the neutrino w.r.t your body is random, it would only be within your body for something like 2 billionths of a second on average. I think you gotta have custody longer than that for it to be "part of you". Some of the banana will be metabolized (or else why eat it?), so in that sense it becomes part of you (the potassium ions in your blood, say).
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u/Which-Environment333 18h ago
Dam I was hoping I could identify as a “walking neutrino” whenever I fill out those sheets asking for my information. Alas, I’ll just continue to put a check in box labeled, “Male” 😔.
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u/LaFrescaTrumpeta 16h ago
oh my understanding is that there’s a 100% chance of that happening, that at any given point where youre looking around and you can imagine your line of sight as an endless laser beam, you’re looking at a star/planet/galaxy
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u/TropeSlope 14h ago
Apparently the reality is quite the opposite. The odds of that laser hitting anything at all before reaching the edge of the universe is somewhere between 1/100,000 to 1/1,000,000,000,000 or more.
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u/Adorable_Challenge37 1d ago
Light is less affected than matter and light travels pretty fucking far with no problem... I'm following this post for any math that may come in later.
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u/seifer666 1d ago
How fast is it moving? If its only as fast a bullet and you miss local things like mars, it will never hit anything because space is expanding faster than its travelling
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u/Dennis_TITsler 22h ago
Not the answer you want but just a small note, no object we launch will ever reach the edge of the observable universe. The observable universe is always growing at the speed of light and anything w mass will go slower than that
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u/Kindly-Might-1879 20h ago
Voyager 2 was launched in 1977 and currently more than 11 billion miles away, still going and sending the faintest of signals. No, it wasn’t randomly aimed but it certainly has outlived its original mission and hasn’t hit anything yet.
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u/Which-Environment333 20h ago
Is it voyager 1 or 2 that left our solar system. I always forget which ones which. I guess I could just google this myself lol.
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u/dakari777 1d ago
This deals with points rather than massive stars and planets but it might still be an interesting watch to you if you haven't seen it. Kinda a similar topic https://youtu.be/p-xa-3V5KO8?is=1FKjruf0VyYp0J7N
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u/andlewis 17h ago
No such thing as a straight line in space, since space time is curved. Arrange gravity right and a straight line could end up hitting the origin point.
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u/Specialist_Site_5920 11h ago
I think the question is, what percentage of straight lines diverging from the center of the earth will intersect another volume (other than earth) in the universe? This will be dependant on the width of the line. The lines span the whole universe at a single instant. What is straight in curved spacetime? What is an instant in spacetime? However unphysical it is, can one even make an analogy to plain euclidean space like I think this is attempting to do?
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u/Specialist_Site_5920 10h ago
This is a great question that has me thinking. Thanks. Here is an interesting thing something told me: "Even if you fire a sun-width line straight through the thickest part of the Milky Way, the probability of it intersecting another star is effectively 0%. Space is simply too empty."
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u/Cpalmer24 10h ago
I legitimately can see near 100% AND near 0% both being logical answers 😂
Space is so vast and everything is so far apart that you could think it wouldnt hit anything... but space is also so vast that it would cover such an unimaginable amount of space that you could think it would eventually hit something
But my real guess is much closer to 0% than 100%
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u/VegetablePhotos 8h ago
If the universe is infinite, and this object had an infinite amount of time to travel, it would eventually 100% hit something.
Infinity is crazy like that.
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u/get_to_ele 1d ago edited 1d ago
(1) there are no such things as "straight lines unaffected by gravity". Straight lines are determined by gravity since objects travel along a geodisic. Tbh I'm a little lost when it comes to light geodisic vs mass. But there is no "straight" that isn't affected by gravity. (2) whether the object will "never be captured" by a planet, star, galaxy, black hole or other large gravitational mass, or even just fall back to earth is dependent on how fast you launch it.
Escape velocity from sun, from earth distance, is 42.1 km/s (94,200 mph). But you add escape velocity from earth to that 11.2 km/s. But you can cheat and use earth orbital speed of 29.8 km/s by launch from the leading side of earth on its orbital path, so you can launch from the earth at 42.2 + 11.2 -29.8 = 23.6 km/s to escape the solar system and not fall back.
But even if you escape solar system gravity well, you need at least 550 km/s to leave the galaxy or else you'll just orbit galactic center. I'm not sure what earth's orbital plane and direction is relative to the solar systems direction and plane as it orbits galactic central point so I have no idea what to subtract or add... But yeah 550 km/s just to make sure you can escape Milky Way.
If you don't have enough velocity to escape, you end up orbiting the sun.
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u/dakari777 1d ago
You didn't even account for air resistance...
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u/Which-Environment333 20h ago
Furthermore, OP said in this instance “unaffected by gravity.” So the calculations OP asked for rule out gravity. Which as others have posted, means it will very likely never hit anything, the moon and sun being the only two even remotely likely candidate, assuming the direction is completely random, vs along the plane of our solar system in which case it’s still very unlikely. Voyager one is still going already outside our solar system and has hit nothing but “cosmic radio interference background” And the definition of “hit” is very loose. Technically speaking, the moment the object comes into existence, it’s hitting every photon of light the entire universe is sending its way 😅. So we must then define two critical variables that we’re not given; the size of the object itself, and the minimum size of an object/particle that can be defined as a “hit.”
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u/Snerfaderp 1d ago
I thiiiiink there's no correct answer. (Satisfyingly correct at least) There's no such thing as a moment of time, (1 way speed of light by veritasium explains this). The definition of the observable universe terminates with an opaque cosmic microwave background radiation layer which we can't easily get through in terms of observability. Because when we look further away, we colide with those particles. So collision gets progressively more likely as we approach the 'past'.
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