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How effective are different types of radar in space over large distances? Is radar significantly different outside of the atmosphere of Earth?

Would you need to generate a more powerful signal to cover multiple AU distances? Or would you need a more sensitive type of receiver?

Would passive radar be less effective? Do signals of opportunity even bounce off objects in space well enough to register in a passive radar system? There are a lot of loud objects in space that constantly generate noise, so I assume passive radar might actually be fairly accurate.

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    $\begingroup$ With noise it might be a problem to find its original source which would not help accuracy. $\endgroup$ – jkavalik Mar 17 '16 at 14:44
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Many questions!

How effective are different types of radar in space over large distances. Is radar significantly different outside of the atmosphere of Earth?

The only difference between a radar inside the atmosphere and in space is the lack of air to dim the signal. Instead, a usually small angular size of the target, caused by the large distances.

Would you need to generate a more powerful signal to cover multiple AU distances? Or would you need a more sensitive type of receiver?

Radar is, after all, just the same as shining a flash-light at something, just with radio waves instead of light. Both increasing the brightness of the flash-light, and the sensitivity of the receiver would naturally help, however, hitting the target accurately over such large distances is difficult, which brings us to the next question:

Would passive radar be less effective? Do signals of opportunity even bounce off objects in space well enough to register in a passive radar system?

There is in fact a lot of radio noise in space, some of which is bouncing off other objects, or disturbed by for example clouds of gas. Listening to that noise is a field known as Radio Astronomy, one of the major ways of observing far away objects.

For planetary science, radar has also been used, most notably by the Magellan probe for penetrating the thick atmosphere of Venus to generate usable images of the surface.

Arecibo

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The basic problem with using radar in space is range. When you send out a radar pulse, the amount of power that returns to the transmitter is proportional to 1/range4. So double the distance means power drops to 1/16.

On Earth, that's not a big problem. To detect objects in the atmosphere (e.g. aircraft), you can build a transmitter powerful enough to have full coverage to the edge of space and the horizon: every object that's not obscured by the Earth itself (and not very small or very stealthy, etc.) will be detected.

But space is really, really big. Radar astronomy is feasible, but limited to the solar system, and you need a giant antenna like the Arecibo dish (see the photo in Hohmannfan's answer) coupled to a powerful transmitter (the most powerful radars use transmitter in the 1-5 MW range) and a very sensitive receiver to get that far. And you can only detect large objects this way (asteroids, yes. non-giant spaceships, no).

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Spacecraft-mounted radar systems have been used extensively by the US to guide their spacecraft as they rendezvous. Gemini, Apollo, and Shuttle all had rendezvous radar systems.

Some military satellites also use radar for ocean surveillance.

On several Shuttle missions synthetic-aperture radar was used to observe the Earth.

tl;dr radar works well in space.

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    $\begingroup$ The Apollo LM rendezvous radar used a transponder in the CSM. So for the double distance power droped only to 1/4, not to 1/16. $\endgroup$ – Uwe Jun 24 '19 at 9:44

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