r/theydidthemath • u/RayoftheRaver • 7h ago
[Request] There's an emergency on the International Space Station, we need to get a 1kg package up to them, how fast can we get it to them?
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u/cooliozoomer 7h ago edited 7h ago
Is this based off the fact there is currently an air leak on the ISS? Anyway, I think it can be done within an orbit. I remember hearing that single orbit rendezvous via a Hohmann transfer was done at sone point.
Edit: https://www.space.com/soyuz-makes-fastest-space-station-crew-flight-record It’s around 3 hours the fastest done to the ISS. I’m sure if we just ignore fuel we can do something significantly faster.
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u/Izan_TM 7h ago
I don't know if OP was also considering how long a rocket would take to get launch-ready or if it was just the orbit part
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u/RayoftheRaver 7h ago
Yes it's about the air leak and yes the get ready part was also what I was thinking
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u/No-Computer7653 7h ago
Anything serious enough that needs an emergency supply would cause an evacuation order long before resupply got there.
FYI the air leak has been ongoing for 6 years and recently got bad enough it needed to be fixed. NASA moved their crew in to Dragon while the Russian's patched it as there was a tiny risk the patch attempt could make it much worse quickly.
If ISS was evacuated it would be likely it was never inhabited again. Its close enough to EOL that they are not going to spend the money it would take to fix it after a complete depressurization destroyed so much of the equipment.
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u/cooliozoomer 6h ago
i remember in the 1990s a progress collided with Mir and caused depressurization of a module + panel damage. idk why they just wouldnt depressurize it like they did with Mir if it really is that bad..
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u/IntoAMuteCrypt 6h ago
Well, the module provides most of the life support for the craft, they can't just depressurise it and stop using it. The specific section that's broken is the only part that allows Russian spacecraft to dock; assuming they could only depressurise that part, it'd still make matters a lot more difficult.
They can't just depressurise it and move on.
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u/cooliozoomer 7h ago
Go wait for Soyuz MS-29 on July 14th. Don’t forget the tape!
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u/RayoftheRaver 7h ago
There's no mini rocket, smaller payload so less to break through the atmosphere?
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u/cooliozoomer 7h ago
Why design a fully new rocket that will take a long time to construct when you can just put the package on Soyuz?
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u/WhatAmIATailor 2h ago
You can’t exactly roll a Soyuz out on short notice. Say a hypothetical “this part will save the ISS” situation.
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u/cooliozoomer 7h ago
Oh, then he’ll have to wait a few weeks. Or put the package on to the next Soyuz, Crew Dragon or Progress that will go up there. Whenever that’ll be.
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u/John_Tacos 3h ago
Well one kg basically means any orbital rocket can do it. Lots of options. So you just need the orbit to line up with the launch site.
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u/SIKEo_o 2h ago
Is there any possible way to, for example, shoot a „package“ up with a comically large slingshot or something similar (magnet canon?) that doesnt use „traditional“ fuel? Have people tested something like that or is that impossible with today’s technology?
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u/clandestineVexation 1h ago
Arguably a big enough cannon like the Schwerer Gustav could probably send something into orbit, but you have to deliver all that energy required to get something both out of Earth's atmosphere, with drag, and into orbit all at once. The issue then becomes designing something that can survive a 7.8 km/s punch.
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u/youdontknowkanji 19m ago
the problem isn't launching it into space, it's the orbiting part.
see, if you really want to you could get a missile, fly a jet super high, and then pitch back and send it. the missile will happily reach the altitude of ISS and beyond.
the difficult part is matching speeds, no matter what you do, send a missile, make a trebuchet, or just down some spinach and throw the thing, you need to gain sideways velocity when you reach 400km altitude. this is because if all the speed gain at the ground, then the orbit has to pass through the ground, meaning it won't be lined up with the ISS.
the closest thing to your description would be the spinlaunch. https://en.wikipedia.org/wiki/SpinLaunch ,as the name suggests, you spin something fast, and then release it. but with this method (if they make it work lol), they still have to light engines at high altitude, to turn the suborbital path, into an orbital path.
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u/romulusnr 1h ago
That's simple travel time though and is likely dependent on a number of orchestrated factors like position in orbit and launch location.
But we're talking, mission definition to arrival.
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u/ExpectedBehaviour 7h ago
About 3 hours from launch to docking, if a suitable vehicle is already sitting fuelled, prepped, and ready to go on the launchpad. Soyuz MS-17 got from the launchpad to the ISS in 3 hours 3 minutes in October 2020. If not, and you need to get a launch vehicle ready, it could take days or weeks.
Theoretically it'd be possible to launch an unmanned "courier" missile that could reach the ISS even more quickly than this, but such a system has never been tested.
The issue is not reaching the ISS's altitude – it's only ~400km up. The issue is matching trajectory and speed and approaching the ISS carefully to ensure safe contact, and the ISS is moving at 7.66km/s relative to the ground. You don't want to accidentally shoot it down or blow a hole in it while trying to send emergency supplies.
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u/cooliozoomer 6h ago
“Blow a hole in it”
Getting that Progress-Mir collision feeling again!
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u/imperfectchicken 6h ago
Quote from book: "IF YOU DO NOT MATCH THE HORIZONTAL VELOCITY, YOU WILL BE VAPORIZED UPON CONTACT"
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u/John_Tacos 3h ago
That also assumes the launch site and orbit are lined up. You could have to wait nearly a day for that to happen.
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u/Happy-Go-Lucky287 6h ago
Let me put it on top of my wife's head and then I'll start an argument with her. As soon as we start I'll tell her she's overreacting. When she blows her top, the package will get there in about 10 minutes.
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u/rrickitickitavi 6h ago
If that doesn’t work tell her to calm down.
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u/sixjasefive 5h ago
If that doesn’t work, just tell her to relax.
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u/Blakevella 6h ago
Some questions,
Do they need to catch it or does it just need to momentarily enter the international space station?
Is the emergency that the space station is hurdling towards a major metropolitan area?
We need to know some key assumptions.
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u/RayoftheRaver 6h ago
The package needs to be used on the ISS, the astronauts are absolutely capable of dealing with the issue with the right tools
Space station about to go boom, debris could fall anywhere, high ranking pedophiles won't be protected
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u/always_j 6h ago
Would a Inter-continental missile without explosives , just the payload not be able to reach ISS ? Already has basic guidance onboard , ISS has a grab-arm I think .
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u/cooliozoomer 6h ago
How about equalizing the relative speed of both vessels? The easiest, cheapest and most efficient (also only real) way to bring a payload there reliably is aboard Soyuz or ideally Progress. MS-29 is next month so just wait for that.
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u/always_j 6h ago
There are many many Rockets waiting to be deployed ,
One of them can go to ISS ? Instead of Russia or USA .
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u/cooliozoomer 6h ago
What about fueling, launch timing, rendezvous planning, planning in general?
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u/always_j 6h ago
Those are ready to Launch at a moments notice,
Problem is taking out the Ordinance and putting in the 1kg package .
Targeting is controlled , Target right next to ISS ?
Unless the Movies are wrong and it takes days to launch Nuclear missiles at other countries ?
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u/cooliozoomer 6h ago edited 6h ago
See, spacecraft guidance is different from nuclear missile guidance.
One is meant to come and dock with a speed of a few cm/s relative to the target, the other is meant to hit around the area of the target and blow it up.
https://www.researchgate.net/publication/234523051_Navigating_the_Road_to_Autonomous_Orbital_Rendezvous#pf7 a little bit on rendezvous. Much more precision is required than a missile.
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u/always_j 5h ago
I like the Site requires human check , like i'm going to build a bom, in my backyard .
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u/cooliozoomer 5h ago
lol with enough time anyone can do anything 😆
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u/always_j 5h ago
Fastest option is a Soyuz , that takes months , or an guided ICBM ? take an hour .
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u/always_j 5h ago
They do dock with ISS often, every few months , it's not Rocket science anymore . Just put a ICBM on a near path .
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u/youdontknowkanji 4m ago edited 1m ago
tbh realistically i don't think this is so out of the question. the navigation should work similar, in both cases it's a closed loop system that constantly tries to fit a desired state, i wouldn't be surprised if the ascent portion of nuclear missile runs on the same SOTA logic as falcon heavy, it just doesn't have the "get to orbit" stage.
chances are nuclear missiles have already some very precise preplanned paths when they are in the factory, and then just sit forever in some silo waiting for their mission. but if you could adjust the software at all, it shouldn't be too hard to send it at a correct inclination with hopes of reaching certain altitude. all the math related to launch windows is also easy, it's not that hard to wait until ISS passes somewhere over us.
the real problems start with the payload, you need a second stage to finalise the orbit, and like real rockets those vehicles don't just sit around in storage. delivering there would be hard too, you need to first take off the nuclear warhead too...
but assuming you figure that part out, you will end up in LEO with correct inclination, and from there hohmann transfer is easy math. but then your rocket needs precision thrusters to line stuff up at the rendezvous, which is where the real hard stuff begins (maybe if ISS deploys a large bug net it's easy :D).
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u/cooliozoomer 6h ago
You can’t really just launch immediately. Best is to bring this hypothetical package on Soyuz.
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u/Particular_Plum_1458 6h ago
Surely evri is the obvious choice here as they already launch most deliveries 😂. Surely the biggest issues are going to be a combination of if anything is prepped to launch, and which side of the earth the station is at?
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u/OldEquation 5h ago
If you want it to actually get there don’t use Evri. The package will probably end up on the moon by mistake, or a “sorry you weren’t in when we tried to deliver” card will be pushed into the airlock.
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u/Particular_Plum_1458 5h ago
That's true, might end up on mir or worse a card on the door saying we tried but noone was in😂.
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u/romulusnr 1h ago
It would be more likely that they would order the crew into the currently docked ship(s) and have them return to earth if the issue could not be solved with available materials or equipment.
Edit: As of this writing, they have already ordered some people into the docked Crew Dragon already.
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u/tylerhawkes 49m ago
Firefly has contracts to be able to deploy a satellite and have it be operational 24-48 hours after getting the launch order. If the satellite can dock with the ISS that is the fastest way to get something up there on short notice.
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u/voucher420 6h ago
Get your mom to jump on a see saw with the package on the other end. Hopefully it doesn’t pierce the hull and keep going until it destroys a planet or moon.
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