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This was done with the moon: Radio Dishes Peer Beneath Moon's Surface

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It is important to understand how this process works. The method described in your article is known as Bistatic Radar. In effect, a transmitter sends out a signal (generally a radio telescope in the microwave region) which hits the surface of some body and bounces off to be received back on Earth by a second, separate radio telescope. Now, because a microwave's wavelength is so long ($\sim 0.1-100\:cm$) the microwaves don't bounce off from the exact surface, but instead are able to penetrate slightly into the subsurface before being reflected. This means the receiver gets a reflection of the subsurface of the body.

In the case you linked, they used the Arecibo Telescope to provide the transmitted signal to the Moon and the Green Bank Telescope to receive the signal. A similar process could be done to other bodies besides our Moon. However, you run into the problem that the farther away an object is, the harder it will be to detect the returning signal.

I believe that most objects within our solar system (and certainly all objects outside it) are outside the distance where this method will work. I was able to find an instance where someone used this method for an asteroid that passed by the Earth at a distance 11 times that of the Moon. I'm not sure what the limit is to how far away something must be before this method no longer works, but I imagine it wouldn't work even for Mars unless we seriously upgrade our technology and power.

Of course your question seems to presuppose the transmitter and receiver are both on Earth. If your transmitter is much closer, say a satellite orbiting that planet, then it is certainly feasible. Here is a source which discusses the concept of using Bistatic Radar probing via a satellite, which also goes into the history a bit on what has been done before.

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  • $\begingroup$ Thank you very much!! So could we improve our technology in the future to see the subsurface of other planets from ground based astronomy radars and radio telescopes? And would this increased radio signals or the radiowaves that improved radiotelescopes would detect be able to penetrate some cm of metal (i.e aluminium)? $\endgroup$
    – Noduagg
    Commented Sep 1, 2016 at 10:42
  • $\begingroup$ And a last thing, do you know if the asteroid you said bounced the signals in the subsurface? So do we see what is under its surface? $\endgroup$
    – Noduagg
    Commented Sep 1, 2016 at 10:51
  • $\begingroup$ @Noduagg In theory yes, if our technology was good enough we could use bistatic radar from Earth to look at Mars, for example. Although it's probably simpler to just send a satellite there. I can't say though if the radio waves could penetrate metal, that would require some serious physics calculations. As for the asteroid, technically they probably penetrated the subsurface a bit, but I think you may have a wrong impression of the process. It's not that they're x-raying the ground with superman vision, they're just getting an image of the ground, reflected back a few cm down. $\endgroup$
    – zephyr
    Commented Sep 1, 2016 at 13:05
  • $\begingroup$ Yes but because they have penetrated few cm in the ground we'd be able to "see" that depth isn't it? And a last thing, if the radiowaves find a piece of metal (i.e aluminium) it would depend of the frequency (depth skin effect). So they would be weaken. But imagine we'd have a 2cm thick aluminium piece. Would the skin effect be enough powerful to stop the waves (the frequency used by arecibo)? Or would some of them pass through and tell us what is behind? $\endgroup$
    – Noduagg
    Commented Sep 1, 2016 at 15:46
  • $\begingroup$ @Noduagg As I said, I can't know how deep a microwave can penetrate into aluminum to know if their signal can "see through" it without doing in depth physics calculations. However, I suspect the "skin depth" for aluminum is far shorter than 2 cm. Consider for example, that the microwaves emitted by your standard kitchen microwave cannot penetrate the thin film of metal on your microwave door, letting you safely see through the door without being hit by doses of microwaves. $\endgroup$
    – zephyr
    Commented Sep 1, 2016 at 15:53
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Yes, but not Earth-based ones.

SHARAD (Shallow Radar) is an instrument on the Mars Reconnaissance Orbiter which performs subsurface imaging of Mars.

Here is an image from Wikipedia of deposit layers on Mars's north pole, taken by SHARAD:

Mars north pole deposit layers

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