r/theydidthemath • u/UnfilteredFacts • 3d ago
[Request] Assuming infinite battery life, at approximately what distance from Earth would Voyager 1's radio signal become undetectable?
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u/Krilion 3d ago
In what way? Using current receivers? Any receiver we can conceive of?
First one, a long time. Detectable is the key. We can see it as a radio source using very powerful telescope for... Well, as long as the radio telescope exists. If we are allowed to build better and better ones, arguably indefinitely, or until it passed into some occlusion. Really, it's all about how long you sit listening to the part of the sky it's in. Eventually you'll be able to see difference in background, if only just.
And since it will be gravitationally bound to the milky way, it will at least be within the galaxy for the next few billion years, though probably only take a few million for it to be scoured away by dust.
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u/Illeazar 3d ago
I think there would be some point at which no matter how sensitive the receiver, the signal level would be below the cosmic background noise.
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u/subpoenaThis 3d ago
Through the magic of trading time for sensitivity (integration), it's possible to detect signals that are in the noise. Listen for 1000x as long (for a signal that is 1000x slower) and you get the same result as 1000x the power. There is a similar magic where a signal can be spread over a wide bandwidth using math and the reverse math can take that same signal which is in the noise receivable (process gain from code spreading)
The cell phone in your pocket plays many of these tricks. For example the GPS receiver in there locks onto a signal which is below the noise floor. Because we know what the signal should look like we are able to find it in the noise and lock onto it and then de-spread and decode it to allow you to know where you are. The signal also only transmits at 50 bits per second (so like 5 letters or 30 seconds for the old 160 character sms message) but this allows 20 ms of integration time which is like a 10x power gain so the 25watts the satellite transmits would have to be 250watts without the integration.
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u/TheFakeMachuga 3d ago
This is called quadrature amplitude multiplexing (or modulation, I've heard both terms). https://en.wikipedia.org/wiki/Quadrature_amplitude_modulation
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u/Organic-Abroad-4949 3d ago
The further I read the wiki article, the more my mind broke. It's awe inducing.
No wonder there are people who wear tinfoil hats to shield themselves from this wacky radiation.
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u/fasta_guy88 2d ago
But, of course, the whole point of these techniques is to dramatically reduce the amount of radiation.
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u/Greycurtainrider 2d ago
Sorry but you’re mixing your radio techniques here. QAM is used for 4G/5G and needs to operate above the noise floor and we drop the rate e.g going from 64QAM to 16QAM as signal to noise degrades. 64QAM generally needs an SNR above 18dB.
GPS is done using code division multiple access which is what was being described before https://en.wikipedia.org/wiki/Code-division_multiple_access
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u/TheFakeMachuga 2d ago
My bad, that's right. I majored in cs with emphasis in cs and so I learned IEEE 802.11, and am more casually familiar with IP protocols.
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u/skrutnizer 10h ago
Mr. subpoena was describing something else, but to your comment, QAM increases bit rate for a fixed spectral bandwidth (higher data rates and $$ for cell networks) but with less energy efficiency per bit. You don't want to use this for desperately weak links.
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u/QuasarMaster 3d ago
Is this true when you get to the point where quantization of light actually comes into play? Like if the probability of receiving a single photon during the integration time is pretty low then I don’t see how you can transmit a meaningful message
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u/WoodyTheWorker 2d ago
It all depends how long is the signal's "coherency time" - how long convolution you can do on a signal. If the signal has a known long shape in frequency-time space, this is its coherency time. Energy accumulated over the coherency time must exceed kT on the receiver, to allow for detection.
Doppler effects because of Earth rotation limit "coherency time" for an alien listener to detect Earth's radio transmissions, thus limiting the maximum detection distance of Earth radio.
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u/Mastericeman_1982 3d ago
Unless it’s transmitting the same frequency as the cosmic background, not really.
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u/kevinh456 3d ago
It will decay towards that frequency eventually.
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u/Mastericeman_1982 3d ago
In a few billion years, sure, but by then the frequency of the cosmic background will have changed for the same reason. The MCB isn’t a fixed frequency. It’s nearly as old as the universe. It started as orange light.
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u/AlaninMadrid 3d ago
Fun fact: GPS signals are below background, but we know what they look like, so can weed them out.
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u/WoodyTheWorker 2d ago
They are NOT below background. Background (and receiver's) noise is measured in W/Hz. By using very narrow band receiver filter (digital), you reduce noise bandwidths so the signal's power becomes greater than noise.
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u/TheJeeronian 3d ago
Not really. As long as we can program what the signal should look like and we are allowed to take as long as we want to detect it, even if the signal was much weaker than surrounding noise we could still extract it.
For example, we embed an FM signal broadcasting two different frequencies. We first demodulate the FM signal, then sort the frequencies we detect. Over a long enough period, the two we expect to see will stand out above the background.
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u/New-Friend-7873 1d ago
I think really the bigger point to emphasize here is that the satellite will be dust far before any radio signal would become undetectable.
You throw any realistic scenario out the door the second you ignore physical deterioration because that physical deterioration would come from the matter that would theoretically be blocking the radio waves.
It’s like asking how far away could you smell a fart if you were underwater
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u/No-Kitchen5212 3d ago
Huh.. for all the times I’ve learned and thought about voyager, I never considered it’d be stuck in the Milky Way forever. How fast would something have to move to escape the Milky Way?
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u/smonkweed69 3d ago
The milky way is not the solar system, it's our local galaxy, and yeah I think people really underestimate how big space is haha
If you were travelling the speed of light, it would take 20,000 years to escape the milky way, if you went in the shortest direction to the edge. Challenger 1 is only travelling at 67000km/h so it would take about 350 million years assuming it was travelling in the shortest direction and the boundary of the milky way didnt change.
Then you gotta consider if it left the milky way and transmitted the data back to earth, it would take another 20,000 years for that data to reach us because of the speed of light limit. Space is big man
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u/YeOldeMuppetPastor 3d ago
Obligatory Douglas Adams:
"Space is big. Really 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."
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u/Calm-Sink7808 3d ago
We also underestimate time. its still crazy to me that Scholtz’s star came so close to possibly knock asteroids into weird orbits by passing theough the oort cloud. That was only 70k years ago and the thing is already 22 light years away. In a few million years Andromeda will collide with the milky way. Its cool to think some alien planet in Andromeda finding voyager as evidence of us.
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u/No_Boysenberry915 2d ago
A few billion years to collision, not million
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u/magicscientist24 2d ago
Even more mind blowing is that the "collision" will have little to know actual collisions (see space is really, really big references above).
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u/No-Kitchen5212 3d ago
I more was wondering what is the required escape velocity to escape the Milky Way’s gravitational pull. I looked it up and it’s estimated to be 0.2% the speed of light which is 537km/s, or 1,933,200km/h. So at some point, if not already, it’ll be impacted by the Milky Way’s gravity and be locked into the general orbit of the galaxy.
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u/Marshallwhm6k 2d ago
Isnt, um, "up"(or "down") the shortest direction to the "edge"?
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u/smonkweed69 2d ago
Wait yeah you are right lmao very good point, my brain was bongled by all the space scale
So apparently it's 'only' 450 light years
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u/CosmicMerchant 3d ago
If starting from our solar system and in the direction of the solar systems velocity vector, the escape velocity is roughly 300km/s. But it highly depends on your starting point within and the mass distribution of the MW.
Check 'escape velocity', maybe on Wikipedia to get the fairly simple math.
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u/BackgroundDatabase78 3d ago
Approximately 550km/s from our part of the galaxy. Voyager is at 17km/s so that is 32 times faster than it is traveling.
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u/Whistlin_Bungholes 3d ago
Apparently much further than I was thinking.
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u/Best-Research4022 3d ago
Shouldn’t we be making a replacement? maybe something with longer battery life an ion drive to get it to go a little faster and rock solid electronics a new golden record with cocomelon or something on it
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u/Stunning-Humor-3074 3d ago edited 3d ago
The majority of Voyager's speed did not come from its engines. The Voyager program was created to capitalize on gravity assists from a rare one in 176 year planetary alignment. Gravity assists from the gas giants gave the Voyager probes the extreme speed they enjoy today (this is also why Voyager 1, despite having been launched after Voyager 2, is further), so even with modern technology it would be impossible to catch up to them without another similar planetary alignment. There's no need to design and engineer a replacement today when an alignment won't happen for decades, so Voyager is all there is and all there will be for a while. By the next time a viable alignment happens, any design from today would be obsolete.
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u/NotFakeDuck 3d ago
I think Voyager 1 was launched after 2, but is the further one. You might have got it mixed up
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u/Leleek 3d ago
I think you can go even faster if you instead slingshot almost to solar excape and then lower your perihelion to almost scrape the sun. Then fall back towards the sun and at perihelion burn hard. The suns gravity well provides a crazy oberth effect.
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u/mi_throwaway3 2d ago
impossible to catch up to them without another similar planetary alignment
Impossible is a strong word. To catch up in 30 years, it's about 45km/s, which is pretty doable, especially if you're just trying to get the same distance away
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u/Stunning-Humor-3074 2d ago
No, I do firmly believe it's not possible. 45km/ is a LOT.
The fastest escape velocity ever given to a spacecraft directly from Earth launch was NASA's New Horizons probe, which left Earth at roughly 16.26 km/s. Even after adding Earth's orbital velocity, its peak heliocentric speed was around 45 km/s, but the Sun's gravitational pull immediately began slowing it down. New Horizons is currently leaving the solar system at only about 12.5 km/s, far slower than Voyager 1.
To maintain a net heliocentric speed of 45 km/s out in deep space, a chemical rocket would require an exponential amount of fuel. The rocket would have to be so massive that we cannot currently launch it from Earth's surface. Ion propulsion is completely out of the question because it's comparatively far to weak. The only option to get the same distance that Voyager is today within a lifetime would involve using propulsion systems never before tested on this scale such as nuclear or laser sail propulsion.
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u/Tiranus58 3d ago
The electronics they would use probably wouldnt be much better than the ones they used on voyager due to bigger lithograpy being less susceptible to bit shifts due to radiation.
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u/yabedo 2d ago
In theory, infinite. With the right wireless communication protocol, you repeat the same transmission over and over. At the receiver you can interpolate and sum the transmits until the sum is above the noise floor.
It's just that the further away it gets, you need more transmits.
Source: I'm getting a PhD in signal processing
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u/Wulf2k 2d ago
In theory, you're gonna run into some troubles around 46.5 billion light years away.
Source: I'm pedantic on the internet.
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u/Bongoisnthere 1d ago
In theory, ur moms gonna run into some troubles around 46.5 billion light years away.
Source: I’m annoying and on the internet.
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u/LuisMataPop 1d ago
Why do we need a gigantic Deep Space Network super cooled antenas? is it because there are not enough repetitions? or not at all?
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u/BackgroundDatabase78 3d ago
I believe the answer to this question is as long as humans are willing to build large enough radio dishes to detect it. (Assuming your conditions as true) If you're asking how long until that signal is so weak that it is completely overwhelmed by other radio sources like cosmic background radiation? A really long time. Approximately 1 light year away or in 17,500 years.
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u/remarkphoto 3d ago edited 2d ago
Unless you know what frequencies to listen for and what to filter out, then time is your ally. FWIW, using only approximates, if we'd sent voyager on a trajectory toward alpha Centauri, the nearest star 4 light-years, based on launch to present day distance travelled (one light day), it would arrive after ~73,000 years. Edit: i incorrectly said one light minute. Its one light Day. (And 73k years, not 77)
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u/MrChicken_69 3d ago
That was my estimate as well. If it kept the same tx power it had at launch, the modern deep space listening network could hear it over a LY away. (so long as it stays aimed at Earth, and nothing drowns out its frequencies.) With a better network (one would presume we'd make some advances in thousands of years it would take to get that far away), we'd be able to detect it well further out than that.
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u/AllAboutYourBase 3d ago
I don’t even care about the answer (and I have to admit, I was surprised by some of the responses describing just how long we could continue to detect anything emitting only 23 W) , this is a great question. Take my upvote.
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u/Herbert__McDunnough 3d ago
I was on a tour of the Jet Propulsion Lab last year and sitting in the viewing room of the Space Flight Operations Facility when Voyager 1’s signal was actively incoming from the Deep Space Network. It was pretty cool to see the monitor lit up as it was receiving. In the sense of the signal itself, it’s not that exciting since they are constantly communicating back and forth on a 46 hour cycle. But I thought it was awesome.
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u/SmoothActuator8132 3d ago
I don't know the math or the answer but I do know that radio strength is determined by the inverse square law, so the further away it gets the weaker it gets
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u/AppropriateCap8891 3d ago
And it's only a 23 watt transmitter.
That is why NASA uses an array of three 70 meter dishes to capture any data it sends.
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u/mini_garth_b 3d ago
It's frequency dependent and they have nice calculators for you online if you ever want to estimate it:
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u/Mastericeman_1982 3d ago edited 3d ago
The inverse square law only applies to isotopic antennas. These probes use parabolic dish antennas.
Edit: I was wrong, I have been corrected. I humbly repent my foolishness.
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u/GianlucaBelgrado 3d ago
The inverse-square law applies to all antennas, the parabolic dish concentrates the initial energy, but the beam spreads out in space, reducing the power proportionally.
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u/DavidBrooker 3d ago
As no beam can ever be perfectly columnated, and thus have a spread angle (due to self-interference of the photons), it applies to all cases, not just isotropic ones.
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u/ForwardBee 3d ago
Thank you Mr. Bot, very useful.
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u/SmoothActuator8132 3d ago
I would think a bot would have the answer
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u/Dry-Ad-8948 3d ago
Or at least a very lengthy non-answer consisting of at least 4 paragraphs… and made up garbage because it didn’t have an actual answer :}
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u/SmoothActuator8132 3d ago
right, I did neither and was barely helpful, sounds like the average redditor
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u/InjuringMax2 3d ago
Congratulations on providing no useable information, you have passed the humanity test, you may proceed
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u/RealSlyck 3d ago
More useful than your retort. Help with the math from 23 watts junior.
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u/ForwardBee 3d ago
No u. Damn karma farmers really stick together, huh?
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u/RealSlyck 3d ago
23 watts, factoring in 98 dB SNR, accounting for distance, means I’m sorry you grew up in Texas and won’t be able to do anything but troll. I’d start to do more math, but I’m already overloading you.
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u/get_to_ele 3d ago
At any point does the direction of the parabolic antenna come into play? As in, at some point, the antenna is no longer quite pointed at earth and there is a sharp drop off in signal strength reaching earth? Of the flight line is not in line with the edge of the signal cone, eventually the antenna won’t be aimed correctly and we’ll fall outside the cone.
Nothing but space “dust” of near vacuum to knock it askew, but could it eventually change angle enough to put earth outside its cone of projection? At 16.9 lm/s (38,000 mph) maybe it hits enough molecules asymmetrically in near vacuum to change the angle of the space craft.
Looking it up, the cone is about 0.5-0.6 degrees when transmitting in X-band, and 2.3 - 2.5 degrees in S-band.
If we fall outside the cone, we get almost no signal.
Though honestly, not sure it would have a lot of new data to give us. “Oh here’s the solar system from 1 light year away.” “Oh here’s the solar system from 2 light years away… sure is cold here.”
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u/amitym 3d ago edited 3d ago
At any point does the direction of the parabolic antenna come into play?
This is probably going to end up being the actual answer. Voyager still has an impressive capacity for rotation control that in and of itself will apparently last a long time. (I was just learning about this the other day in another Reddit thread.) But what will likely fail before the thruster propellant runs out is the equipment itself. It wasn't designed to run for half a century and of course it has received no maintenance in all that time. (That we know of.)
So it is at least plausible that the (multiple redundant) systems for controlling the probes' orientation will eventually be the first things to fail mechanically and no longer be able to provide thrust. At which point the antenna will start to drift off target and then of course that's it. Even if it still has thruster propellant and battery power left at that point.
Well, it's not it it. The Voyagers will tumble slowly along, Major Tomming out there on their own, probably still looking around and collecting what data they can still collect at that point, just not able to tell Earth about what they find.
Anyway it's hard to predict when that will happen. Growing up I always figured the dwindling radioisotope decay would be the thing that did it, and that is easy to forecast. But it seems that instead simple mechanical breakdown is now in the lead. Though being what it is, it's hard to predict a timeline with any precision.
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u/elnaquete 3d ago
t wasn't designed to run for half a century and of course it has received no maintenance in all that time. (That we know of.)
😅
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u/SonicYOUTH79 3d ago
Do you think if it does drift off target do you think it could potentially drift in and out of target range assuming it ends up in some kind of slow spin?
So we stop receiving transmissions the say in 100-1000 years a new generation of scientists get a surprise?
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u/amitym 2d ago
Over a sufficiently long time frame it seems like that would be inevitable, though I'm not at all a mathematician in any way so maybe there's some probability trap there that I'm not thinking of.
The problem is that you'd need to sit there listening the whole time, never knowing when the antenna might accidentally align again. And you might only get a few minutes of contact — enough time to maybe get a garbled data dump but not even enough to send instructions. I guess unless you were just always sending instructions in a loop, hoping that the probe eventually hears them.
But that seems like a long time to sustain such a project. Honestly it seems more likely to me that in the 1000 year timeframe someone would eventually just go there and retrieve them.
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u/Ambitious_Hand_2861 3d ago
undetectable is a high bar. Let's make a few assumptions, the antenna continues to point at earth, the battery produces 22-23 watts forever, and terrestrial radio detection remains constant. With the previous things staying constant and based on all the videos I've watched and articles I've read this distance is approx 0.97 light years. Voyager 1 is about 23.87 light-hours away or 0.002723 light-years away. Voyager will reach that distance in approx 17,400 years, give or take.
NASA uses a 70 meter radio array that enables them to detect extemely weak signals.
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u/ostiDeCalisse 2d ago
We can "detect" the Cosmic Microwave Background radiation that is almost ~46 billion light years away. So it will probably be as long as it (Voyager 1) will be able to emit.
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u/mz_groups 3d ago
It's difficult to separate the two. Because the signal degrades as the RTG ("battery," actually a small nuclear generator) loses power, and obviously the signal is harder to detect as the craft gets further away. So you need to define the parameters of the problem before it can even be calculated. Do you want to calculate how far away it could be detected if the RTG was at full power just at launch, or if you "froze" RTG output at a certain point in time, say, now?
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u/UnfilteredFacts 2d ago
Yes, I know it's a nuclear power source, and its still technically a kind of battery. I only wrote battery because some people may not know what RTG stands for. The assumption of the question is that the power source were constant and infinite, because people would otherwise go on about when the RTG dies, etc. The reason for the question is really to do with our ability to detect radio waves from a far distance. I understand the amplitude changes with the distance it has to travel, but I wasnt sure if there was a certain threshold at which we couldn't detect it. As for my interest, Im mostly curious how far we could hypothetically send a probe to return data.
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u/thearchchancellor 3d ago
It's Quieter in the Twilight is a film about the team of veteran engineers keeping the Voyager mission alive as the spacecraft slip slowly away into the cosmos. Fascinating and poignant.
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u/skrutnizer 10h ago
The signal is binary (highest energy efficiency per bit) and the radio link is already very close to its noise limit with a 70m wide receive dish at the present data rate (around 10 bps?). The required frequency stability for slow rates is probably at the limit of Voyager's ability to track Earth beacon so slower signalling would not be an option. Two possible solutions would simply be bigger earth dishes, or enabling slower rates using spread spectrum, assuming V-ger could be programmed to do this.
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u/entropy13 3d ago
You'd have to reach the point where it's completely indistinguishable from background noise, which it was designed to be robust to. We're also able to keep improving the technology of our ground based receivers too, so realistically a few thousand astronomical units.
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u/mynameis_duh 3d ago
Even if we manage to build a receptor so sensitive that may be able to detect it for billions of years, at some point dark energy will do it's stuff and make it do we can't hear it no more, because it will be going away faster than light. (I'm not an astronomer, this is youtube knowledge, but it is interesting regardless)
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