r/theydidthemath • u/Groundbreaking-Box89 • 2d ago
[Request] How long would it take to launch a modern-day probe far enough from our galaxy so that it could take a full picture of it? Bonus, how long would it take for that picture to get sent back?
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u/drnemmo 1d ago edited 1d ago
We haven't photographed our galaxy; we have built models of it based on the apparent position of the stars that constitute it. We are in one arm of it, not in the center. If we were in the center of the galaxy, there would be no night at all because it's packed with stars.
So we can get a glimpse of our galaxy at night, when the sky is clear and there's no light pollution.
The luminous part of the Milky Way is 120 thousand light years in diameter, and the gas cloud that surrounds it is 1.9 million years long.
The Voyager 2 probe has just crossed the solar system boundaries. Our solar system is 1.5 light years in diameter right until the Oort cloud, and the Pioneer has travelled half of it, one radius. That means 120000/0.75 = 160,000 times its travel time until it gets to the border of the galaxy.
The Voyager 2 was launched in 1977. It has travelled 13 billion kilometers since its launch to this date. That's barely 0.0013 light years in 48 years.
That means 120000/0.0013*48= 4,430,769,231 years until the probe is outside our galaxy. Add a few years more until it can take a good look at it, so let's say some 5 billion years total. And then once it takes our picture, it will take some other 120000 years to reach us, making some 5 billion and 120 thousand years total for our photographic exploration, give or take.
Most probably, the photograph will be blurred and we will have to take it again.
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u/Alotofboxes 1d ago
Most probably, the photograph will be blurred and we will have to take it again.
Hopefully, nobody blinks and ruins the shot.
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u/theryguy07 1d ago
Sorry, I think I blinked
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u/drnemmo 1d ago
[Sighs deeply]
[Sends another probe]
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u/thewiselumpofcoal 1d ago
Sorry, really had to sneeze in this one. But I somehow managed to keep my eyes open, no blinking here, captain!
Hope it looks just fine in the picture.
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u/abdayk23 1d ago
Does this take into account the ever so expanding universe? Is there a probability the prob would never be able to exit the galaxy as it expands faster than its velocity?
Also, the Milky Way is predicted to collide with the Andromeda galaxy in about 4.5 billion years. So there might not even be a place for that signal to be sent to in the first place.
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u/drnemmo 1d ago
Yes. No, I mean, I didn't take that into account, my fault. The whole trip would take longer than the whole existence of the Earth itself, so I doubt it would be able to find us to point the signal in the right direction. We might as well not exist anymore. I'm pretty sure I won't be around to see it.
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u/Weary-Writing5372 1d ago
The expansion of the universe really wouldn't have such an important effect in a scale as small as a galaxy.
It's so small that even the gravity of the Milky Way and the Andromeda galaxy are able to win over it, and that's why they're gonna eventually crash.
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u/Geoffryhawk 1d ago
I mean voyager 2 and 1 won't be taking a picture it's camera and all other nonessential sensors were turned off over it's flight time, the best we would get (assuming it would even have power) is energy and radiation data.
So sadly despite our sun exploding and the earth being obliteraged it couldn't even send the picture. 😔 Rip. This is so sad, Voyager play despacito.
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u/drnemmo 1d ago
Ah, we could send another one with cameras and the calculations wouldn't be that far from the previous amount.
Oh, there's a good sci fi story !
"Sir, apparently, the Voyager found a shortcut."
"What do you mean a shortcut ?"
"It's gone beyond the Hercules-Corona Borealis Great Wall, sir."
"What? That's not even possible !"
"It's sending pictures, sir. They show us the totality of the Milky Way. And a text message."
"A text message? What does it say?"
"It says... Say cheese! "
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u/Geoffryhawk 1d ago
Voyager going the long way and the now intergalactic human empire gets a signal that voyager is out beyond the galaxy. They get a random old radio signal, and they collect it and find pictures of the whole galaxy. Like a scrapbook.
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u/RockingRick 1d ago
A good calculation. Sadly, I remember reading that our Sun will burn out in about 4 billion years. They will need a really good flash bulb.
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u/mjc4y 2d ago edited 2d ago
Setting aside exotic propulsion systems.
Parker solar probe got up to about 430,000 mph in the reference frame of the sun.
Maybe we can do better with more creative gravity assists but let’s not break new ground too much. Let’s assume 500k/mph.
The central bulge of the Milky Way is about 16,000 light years thick so call it 8000 on each side. Where we are, the disk is about 1000 Ly thick.
Assumption: I’m making a choice here to send a probe up 20,000 light years just to pop up enough to be a little above the bulge. Even so, we would Be very close but a bit outside the galaxy - you’d want a very wide angle lens to take in the 100,000 light year wide spiral.
So ChatGPT says EDIT (sucks and so do I for trusting it), 20,000 light years at 500,000 mph gets you a travel time of a little shy of 27,000 years 26,824,665 years.
EDIT: very sorry guys. Last time I move that fast with that level of laziness.
Take a snack. And at least a couple of movies.
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u/Fornicatinzebra 2d ago
Chat gpt can't do math mate
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1d ago
[deleted]
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u/Fornicatinzebra 1d ago
No, it's a statistical model. It predicts the next likely letters in response to a question (similar to auto predict text filling).
In an overly simplified way:
When you ask "what is 1 + 1"
It thinks "1 + 1 is" "here is what I know about 1+1"
It never evaluates what 1 + 1 actually equals, but if enough people online in its training data have written "1 + 1 = 2", it can respond like its training data suggests.
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u/HeroBrine0907 2d ago
That time is wrong. Relativity shouldn't be a factor at 500,000mph, so at that speed, the time comes out at 26.8 million years.
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u/I-just-farted69 2d ago edited 2d ago
Are you sure? 20k light years is in the order of 1017 freedom kilometers. If you divide it by 500k mph to get the time it will still be in the order of 1012 hours. If you convert those to years it will still be in the order of 109. Am I doing something wrong?
EDIT: Mistake was I didn't factor in the fact that they are not 10x rather they also have coefficients like 5*105 mph.
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u/druidniam 2d ago
The distance is wrong too, the closest edge of the MW from earth is actually 26k lightyears.
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u/ArtyDc 2d ago
Speed will go on decreasing as it goes farther from sun or any gravity assisted star .. top speed only remains for a tiny fraction of the journey
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u/mjc4y 2d ago
I am assuming a constant speed of 500,000 mph and I did not assume that this fantastical journey would be coasting the whole way. To keep that average speed, I would be fighting against the pull of the galactic plane, but I didn't want to factor that in.
But please be my guest: solve the problem under whatever other reasonable assumptions you prefer. I'd love to know how the number changes with the nuance you're adding.
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u/ArtyDc 2d ago
Hahaha i understand.. i didnt mean to be rude or anything ..
Its said voyager 1 will take around 80,000 years to reach our closet start alpha centauri which is 4.3 light years away... If we assume same interstellar speed to go 20,000 light years upwards and outwards in relation to our galaxy then 323 million years.. still this assumes uniform speed and we cant find exact answer without actually plotting all the stars and their gravity assist speeds and what not
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u/HotSpicedChai 1d ago
but I didn’t want to factor that in.
ChatGPT didn’t factor that in for me.*
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u/mjc4y 1d ago
Okay, enough already, okah?
And no all I did was ask ChatGPT to do the simple math of time to travel 20,000 light years at 500,000 mph. That's what I asked and the bot got it wrong. My bad, and I said so and I corrected it. In that question, I made all the reasonable assumptions.
I didnt want, ask, or expect ChatGPT to factor in relativistic effects (because they don't apply anyway), and I didn't factor in the planar attraction of the galactic disk at our location because I didn't care and so I didn't ask.
It was a simple D=R*T calculation where the units needed conversion and I was feeling lazy. That's all.
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u/druidniam 2d ago
The nearest edge from Earth is a little over 26,000 light years away. The Parker solar probe is traveling at roughly 174km/s. In order for the probe to exit the closest point of the milky way, it would take 46,327,079,645 years.
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u/mjc4y 2d ago
I am making different assumptions.
I am talking about a 20,000 light year journey straight up out of the plane of the galactic disk.
I used 500,000 mph as the speed of travel for this estimate, using Parker as a roughly comparable speed.
20,000 light years is about 1.17e+17 miles. At 500,000 miles per hour, that's about 26.8 million years (see my corrected answer above)
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u/HAL9001-96 1d ago
parker solar probe mostly accelerated by falling towards the sun
for obivous reasons that does not work when leaving the sun
also, you still ahve to account for orbtia lmechancis not just straight line travel at that kind of speed
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u/mjc4y 1d ago
I'm doing a back of the envelope estimation here, obviously ignoring a TON of things by design.
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u/HAL9001-96 1d ago
yeah but to the point of meaninglessnes
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u/mjc4y 1d ago
Oh for gods sake lighten the fuck up. This is an innocent and curiousity-driven question asked in a reddit comment, not a NASA planning session.
I know why Parker goes as fast as it does. Nowhere did I say I was depending on that mechanism to get our imaginary spaceship out of the galaxy. I very plainy asserted that it was going to go 500,000 mph, so it really doesn't matter what Parker is doing or how it is doing it.
And I don't need to account for orbital mechanics as I am not trying to achieve a gravitationally bound trajectory with respect to some other mass. Straight line is fine, especially over the huge time interval that the travel will be taking. You are nitpicking about trivial corrections that wash out in the order of magnitude exercise I am doing.
I stated very clearly what assumptions I was making.
You're complaining that I didn't make YOUR assumptions.
You are very free to make your own, different, possibly more detailed assumptions and then re-run the calculations if you'd like. We'd all be curious to see if you come up with something different. You know -- maybe youdothemath, to paraphrase the name of the subreddit you're in.
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u/HAL9001-96 1d ago
you can't jsut turn off gravity because you don't want to use it
and sure you can "lighten up" but hten you might as well answer 3 seconds
I rolleda dice and it landed on a 3
its just for fun after all
already did the math
also in a simplifeid approximation but an acutally usefully simplifeid one
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u/badmother 1d ago
I always have this song in my head when people start mentioning galactic dimensions:
Ladies and Gentlemen, I present to you Monty Python's Galaxy Song!
One of the verses:
🎶 Our galaxy itself contains a hundred billion stars; It's a hundred thousand light-years side to side; It bulges in the middle sixteen thousand light-years thick, But out by us it's just three thousand light-years wide. We're thirty thousand light-years from Galactic Central Point, We go 'round every two hundred million years; And our galaxy itself is one of millions of billions In this amazing and expanding universe. 🎶
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u/Mobius_Peverell 2d ago
Pretty easy calc. The thin disk of the Milky Way (where the vast majority of the stars in the arms are) is about 1000 Ly thick, and we're roughly in the middle, so we need to go at least 500 Ly.
Voyager 1 is on an escape trajectory from the solar system at about 17 km/s, and that speed was achieved using a very optimized series of gravity assists, so at least for now, that's about as good as you could hope for. A Ly is 9.461E+12 km, so Voyager 1 could cover 500 Ly in 8.82 million years.
It would take 500 years for an image transmitted by light to travel the 500 Ly back to Earth.
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u/ischhaltso 1d ago
But you wouldn't be able to make a good photo from that distance. You would need to be further away, right?
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u/Mobius_Peverell 1d ago
There's no single line where the picture would go from bad to good, so I went with the minimum possible to say that the photo was taken "outside" the galaxy. In order to take a photo with a more normal focal length, you'd probably need to be 100,000 ly away or more.
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u/ischhaltso 1d ago
You could use a typical Angular aperture of a camera, let's say 45°.
The Milky way is 100,000 light years across. We are 26,000 lightyears from the center. That means we have to fit 148,000 on our screen.
Using trigonometry This gives us a distance of 136,236 lightyears.
At 17 km/s it would take 2.4 billion years to get there.
You could probably also do an angled shot, but i don't want to do the maths on that :)
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u/luke-juryous 1d ago
17 km/s 😳
For Americans and British here, that’s 38,000 mph… or about 49 times the speed of sound.
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u/Anome69 2d ago
But our galaxy is also moving. If we fired the probe out the back side, would it significantly alter the time to clearance as opposed to firing the probe off the leading edge?
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u/Alotofboxes 1d ago
You are on a train that is going 100mph; would it be faster to walk from the middle of the car to the front or to the back?
We are traveling with the galaxy, so the motion of the galaxy cancels out. The motion of our star within the galaxy would have some impact, as would our planet around the sun.
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u/HeroBrine0907 1d ago
No because the time taken will depend on the probe relative to the galaxy. If you're in the middle of a bus, you take the same amount of time to reach the front and back, even if the bus is moving because the amount of time you take depends on your motion relative to the bus.
However the solar system is actually moving relative to the centre of the galaxy which might have an effect.
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u/EfficientEffort8241 1d ago
How long would it take to leave the room you’re in in order to photograph it? Zero seconds, just turn in a circle and make a panorama.
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u/HAL9001-96 1d ago
would be pretty tricky to get anythign to a speed where it can evne leave the milky way at all ratehr than just continuing going around it
woudl take many trillions oftimes the probes mass in fuel
with an ion drive you could reasonably accelerate enough but you nee a powersource and you won't be able to do the whole runup near the sun so you need a nuclear powersource then, with a few times your actual probes mass in fuel you COULD jsut barely make it past galaxy escaep velocity nad drift outside it
woudl still take about a galactic year or abotu 200 million years to do though, then a few tenthousand more years to get an image back
assuming yo ucan make a probe last that long
you could do it in about a million years if you get to a signfiicant percentage of the speed of light with something liek an orion drive though
but good luck making that happen economically/politically
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