With high powered radio transmitters.
The same way you can use your car radio to tune into a radio stations miles and miles away.
Big radio receivers here on earth can pick up the signals that those space craft are sending out.
The mars Rovers can be a bit more complex, since this radio communication needs a direct “line of sight” so if earth is on one side of arms, and the rover is on the other side of mars, then mars itself blocks our radio signal. So the rovers will first send their signal up to a satellite orbiting mars, and then that satellite will pass the information back along to us.
One thing that helps with these extremely long distance communications is that we know exactly where the signal is coming from. We even know the math to adjust for the time it takes for that signal to travel the long distances between there and Earth. So we can point a transmitter and receiver exactly where it needs to be in order to send/receive signals. Some averaging helps even out background noise, allowing us to see signals even if the received power is below the noise level.
The same way you can see Mars from Earth. Radio waves act just like visible light, both being a part of the electromagnetic spectrum. You get a wave in the spectrum with enough energy to escape the atmosphere, and you’ve got yourself a wave that will continue on until it hits something that stops it. And as long as you can recover enough of that energy at the other end to be able to tell what it originally was, you’ve got yourself a radio message (or a visible planet).
Light shows us what things look like by using different wavelengths which our brain interprets as colors. Radio waves, depending on the method used, do much the same thing by either varying the frequency (and therefore the wavelength) or phase (voltage) of the wave. You don’t need the whole radio wave to receive the message on the other end, just enough to distinguish between the frequency or phase differences. Sure, they take bit more power than your wifi uses, but it’s the same concept.
Radio signals are just a form of light that we can’t see. Light in a ~vacuum travels at the speed of light (obviously). Distance affects signal quality and how much data you can transmit but when traveling at relativistic speeds (ie the speed of light) the distance we are transmitting and receiving from isn’t really that crazy especially with nothing like air or water in the way to diffuse the signal.
Energy cannot be destroyed and there is almost nothing in space that can absorb a radio signal. So a radiosignal can go on pretty much forever in space.
The main thing that makes a radiosignal weaker is that all that energy it had at the moment of transmission spreads out over a larger surface. If you send it omni-directionally (in every direction) that energy forms like a bubble of radio energy. Since radiowaves travel at the speed of light (or close to it) that “bubble” becomes bigger pretty fast so the radio energy gets really spread out (and weak).
There are two ways of making it better at reaching long distances.
The first way is that you can direct the radio energy in a single direction. So instead of forming a big balloon bubble of radio energy it’s more like a very narrow flashlight. The narrower you make the beam the more energy is concentrated at a single point, but concentrating radio energy is pretty tough and you could also miss your target if you don’t point it in the right direction. Long distance communication almost always use Directional antennas (high gain antennas) that send their signal in a narrow cone.
The second way is to build a giant radio-dish on the receiving end (google what a radio telescope looks like). That radar dish will gather up all of the radio energy that hits the dish and bounce it towards a single point. The bigger the radio-dish is the more energy is concentrated and a weaker signal can be detected. The radio-dishes that we use to listen to stuff like the Mars Rover or Voyager, and send back instructions, are pretty big compared to antennas we use to communicate on earth (compare the size of a radio telescope to the satellite dish people use to get Satellite TV. And Satellite TV signals aren’t very concentrated compared to the signal communication satellites at mars send out)
Radio, no big mystery there.
Well, a little mystery perhaps, what is often overlooked is just what kind of antennae are used to receive the signals from distant and low powered devices across solar system [https://spacenews.com/increasing-demands-putting-pressure-on-deep-space-network/](https://spacenews.com/increasing-demands-putting-pressure-on-deep-space-network/) check the little service buildings next to antennae for scale.
Size and directionality of antenna make a massive difference for how far away you can extend a connection. Take common wifi devices and replace the tiny antennas with something more like satellite TV dishes and you can basically have wifi connection however far you can find line of sight, it’ll work for hundreds of km if you point the antennas to each other. And that’s with wifi which is very demanding because of how much data it pushes through.
Accept lower data rates and you can reduce the demands for the antenna and transmitter power significantly. With LoRa its possible to have satellite connection with small undirected antennas and very low power transmissions, it’s just that the datarates are puny, nothing like what you have for wifi [https://harmvandenbrink.medium.com/tracking-and-receiving-messages-from-satellites-with-lora-afafd875e005](https://harmvandenbrink.medium.com/tracking-and-receiving-messages-from-satellites-with-lora-afafd875e005)
Now if you combine large highly directional antennas, puny data rates and fairly high powered transmission, then Voyager probes can phone home no problem.
Even more capable than radio would be laser comms, your typical handheld laser pointer can be seen from space with a naked eye if you point it right. That’s because it’s directionality is a lot higher than what a radio antenna can manage, you don’t need to put out much power if it’s all going the right way.
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