The idea here is that any radio energy that does not end up in the vicinity of the target was wasted and at 21 billion Km that gives you plenty of opportunity for mis-alignment.
Receiving the signal has similar challenges, with the added complication that this time the sender is sending with a power level that puts its signal under the noise floor by the time it reaches Earth.
https://en.wikipedia.org/wiki/Noise_floor
Fun fact: this goes for the GPS satellites as well by the time their signal reaches your pretty little hand-held receiver and it takes nothing short of magic (to me, not to the people that design that stuff) to recover the signal.
Edit: TLDR: for the amount of money required to design, build and deploy such relay satellite in geosynchronous or such orbit you can do several manned missions to mars or some other planet of your choosing
As for your edit: very heavy satellites cost (including launch) ~$250M whereas a manned Mars mission is estimated to cost $6B.
I really don't see how you could do 'several manned missions to Mars or another planet of your choosing' for the same budget as a single relay satellite, even a large one.
The problems I see with such a design are simply that it does not give you any advantage for spending all that money and actually stands a fair chance of making things worse. More stuff, so more stuff that can go wrong and if it does it is in a place where you can't fix it. Limited life-span as well compared to the Voyager itself because of the larger complexity (must keep two antenna's aimed at the same time while moving itself).
Uplink path of DSN is capable of significantly higher power levels than 20kW, several orders of magnitude more. Also the whole transceiver electronics are especially fiddly, with various cryogenically cooled and/or high-power microwave valves without meaningful solid-state replacements, which is not something you want to have in GSO without any chance of mainteance.
Yes, that's exactly what I wrote upthread, that's the hard requirement. And that is what will fail and then you've got a very expensive doorstop in an orbit outside of any repair capability. Inability do do maintenance / repairs is the killer.
On the other hand it is certainly true that RCS of such satellite would require exceedingly large stores of RCS supplies which will invariably run out and have to be somehow replenished.
Edit: even hall thrusters require stores of xenon and with the precision required the amount consumed is far from practical.
For missions where that makes sense (mars probes, STS, ISS and IIRC even original Apollo moon landings) relay satellites or even networks of them are/were used. To some extent for such constructions to be useful it has to be constructed of satellites that orbit something which is near to target of the probe, which is impractical for probes that are on highly eliptical orbits around sun, not to say probes that are on exit trajectory like Voyager.
The Voyagers have a 3.7m diameter parabolic radio dish, larger than the Hubble space telescope's mirror even. That alone provides a huge amount of gain on communications. Additionally, the spacecraft have 10s of watts of power available for transmitting signals, which is a fair bit considering (while on the other end the ground stations have up to hundreds of thousands of watts to transmit). The ground-stations in the deep space network (DSN) are tens of meters across, a small antenna is 34m, the biggest ones are 70m across. That also provides a huge amount of gain alone. It means that there is more area to collect signals from the spacecraft and it means that the beam from the ground station to the spacecraft is much tighter, concentrating the total transmission power into a smaller cross-sectional area at the distance of the spacecraft.
The spacecraft also uses error correcting codes, which involve transmitting many more bits than the underlying data, but in such a way that errors due to noise are not only detectable but correctable.
On top of all of that you have the state of the art low noise amplifiers in the DSN antennae. A typical low noise amplifier is a carefully built electronics assembly made by experts. The DSN amplifiers? They use 99.95% purity ruby rods chilled to 4 degrees above absolute zero to form microwave MASER based amplifiers.
There's a neat little video (series) here on the DSN and contacting the Voyagers: https://www.youtube.com/watch?v=FzRP1qdwPKw
"Low-Noise Systems in the Deep Space Network" Edited by Macgregor S. Reid
https://descanso.jpl.nasa.gov/monograph/series10/Reid_DESCAN...
It's published by the JPL as part of the "Deep Space Communictions and Navigation Series". The rest of the books in the series, listed in the book's front matter, have some fascinating titles.
They mentioned that the received signal from the Voyager spacecraft is actually stronger than the signals from several closer craft, because the Voyagers have such good antennas.
The videos of their decoder screen brings back memories of doing very similar things with oilfield tools. The same sorts of techniques are used to get data from deep below the earth, though not with RF but mud pulse telemetry instead. Same digital encoding types and decoders. I got to work with the guys who designed all of the telemetry systems and wrote the decoders for that stuff too.
Curiously, those codes are now superseded by other, more modern approaches, for example Turbo Codes [1] which are used not only in deep space probes, but also in cellular communications and other applications that we consider normal these days.
[0] https://en.m.wikipedia.org/wiki/Concatenated_error_correctio...
So, starting from a system that can communicate from Earth to the moon, if you can find a way to add 64 decibels then it can work from Earth to Voyager. Ways to add decibels include using more directional antennas on one or both ends or transmitting with more power. Alternatively, you can make up some of those decibels by communicating much slower.
The interesting thing about the inverse square law is that it's insensitive to the scales involved. For instance, going from 10 meters to 20 meters results in a 6db loss, and going from 1 light year to 2 light years also results in a 6db loss. This is much different from, say, light in a fiber optic cable, which would experience a 6db loss from impurities in the glass each time the light traveled some constant distance.
If you could send a perfectly parallel beam, it would effectively be an antenna with infinite gain. As far as I know, that's not possible but getting as close as you can is a good strategy. There's also antenna aiming limitations to consider -- it's possible to have too much gain if it exceeds your ability to point in the right direction.
The opposite extreme is an isotropic radiator, which emits equally in all directions. (That isn't possible either, but it's a good theoretical baseline.) Antenna gain is usually described relative to an isotropic radiator. So, an antenna with a gain of 12dbi means that in the direction it sends its strongest beam, it's 12 decibels stronger than it would be if the antenna were an isotropic radiator.
I think that's the crucial point. While transmission through a cable etc. has exponential decay, transmission through vacuum has quadratic decay, so much more feasible.
The more interesting part is that Voyager can send signals we can receive (with giant, huge radio dishes, but still).
Keep in mind that there are inefficiencies in simply transmitting with more power. The more you amplify, the more noise you introduce. No matter what you do, you can never improve the size and hardware that you're transmitting to.
I don't work much with RF, but, with optical transmissions, the major innovations I've seen are from better receivers that are better able to separate signal from noise at lower power levels. On the earth side of things, we can use massive dishes connected to modern hardware that have very advanced signal processing capabilities. Ultimately, Voyager is 1960s-era hardware with very very very minimal ability to change the software in any way.
If they wanted to (and had the funding to) build a dish on earth that was 10x larger to receive the signals from Voyager with hugely advanced signal processing, that's a totally doable thing. On the other hand, there is virtually nothing you can do to make voyager hear better.
Ultimately, its a lot easier to amplify something faint than it is to shout louder.
Yes, but since you are amplifying the noise right along with the signal if the other side shouts louder it really helps. As does a very good directional antenna (parabolic, very solid mount, very precise control of its orientation).
https://space.stackexchange.com/questions/958/how-does-voyag...
(Searched for "voyager communication" on DDG, top hit.)
I was surprised to learn that it's a ground-based system. I'd think they would need antennas in space (on satellites) so that you can both send extremely powerful signals without disturbing others, and receive without having to go through the atmosphere. Instead, there are just three ground stations at approximately 120° around the earth for continuous communication.