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I read that there is a satellite orbiting Mars that the rovers send data to but I still find it amazing how that satellite can send signals tens of millions of miles to earth without any amplifications. How is that possible?

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How a satellite is able to communicate with Earth is better answered with How does Voyager 1 send signals to Earth? and How does NASA get information from space probes?. I'm only going to answer why it is much easier to have an orbiting satellite communicate with Earth than a rover, which I believe is the crux of your question.

First of all, there are landers that have communicated directly with Earth. Opportunity and Curiosity can both talk directly to Earth. However, they can't have as large of a dish as an orbiting satellite can. In fact, the landers don't have a steerable antenna, as that would be too difficult, and thus can only communicate with Earth when Earth is in about the right part of the sky (Directly overhead), which should happen once a day.

Communication with an orbiting spacecraft is much easier, as the distance is as much as a million times closer. Power is lost as a square of distance, thus that is a very significant factor! This allows for a lower gain antenna, which allows the two to communicate much easier, and allows the orbiting spacecraft with it's much larger steerable antenna to do the heavy lifting!

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I think the key to your question is in your pre-condition "without any amplification", in which case it would indeed be amazing, or at least surprising. However power amplifiers are always used to raise the signal strength at the transmitter so that it can be received correctly.

That point made, PearsonArtPhoto's answer and also the other referenced question/answers should be easier to understand. For example the level of amplification at both transmit and receive ends, the types of antenna at each end, frequency, bandwidth and the distance all play a role in the rate of information transfer.

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    $\begingroup$ By "without any amplification" I meant while traveling in space, not after it reaches earth, as I know the signal will lose part of its strength as it travels so I find it fascinating how a signal will travel 18 billion miles (Voyager 1) in the absence of any amplification along the way and still makes to earth. For me as a nonspecialist this is mind-blowing! $\endgroup$
    – Majid Alfifi
    Jan 18, 2017 at 5:10
  • $\begingroup$ I've added a correction, I was referring directly to a power amplifier at the transmit end. At the receive end there will be a low noise amplifier first in the chain. In fact I think your comment "amplification along the way" really makes your point clear. That's fair enough; it really is, like much of physics, quite a profound concept. $\endgroup$
    – Puffin
    Jan 18, 2017 at 19:36
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I don't know if this is an answer, but in general huge radio telescopes are used to receive signals from space probes. The transmitter that is millions of miles away might be 20 or 30 watts, this is comparable to the power of a police squad car which is 15 to 30 watts. A normal desktop radio might start to loose a 15 watt signal in a couple of miles. Radio telescopes have a huge reflective surface that is all angled to favor a precise point. With that and very sensitive receivers, they can focus on very weak signals in a tiny portion of the sky.

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