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I recall reading an article where the moon, could be detected via radar and that orbiting radar satellites could map out the surface of mars, and in some cases even parts of Venus (the lattermost might be a false memory).

I am curious, what would be a large enough radar to put into space (and perhaps also at what distance from the sun), that would allow us to detect MOST Kuiper belt objects, Sednoids, and the Oort Cloud. Is this the kind of thing that could be afforded under $\\\$100\times 10^9$?

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    $\begingroup$ This question might also have a home in space-exploration stackexchange due to its speculative nature. $\endgroup$
    – Sidharth Ghoshal
    Commented Apr 5 at 16:10
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    $\begingroup$ You might be interested in reading mdpi.com/2072-4292/15/23/5605 for a recap of current radar capabilities $\endgroup$
    – planetmaker
    Commented Apr 5 at 16:25
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    $\begingroup$ I'm not saying that this is impossible, but radar, which depends on a signal being transmitted, then reflecting back, obeys a inverse 4th power rule, that is, if the object is 10 times further, it is 10000 times less bright in radar. On the other hand, our ability to detect incredibly weak radio signals is marvelous, so I note caution, but not despair, at least not until someone runs the numbers. $\endgroup$
    – James K
    Commented Apr 5 at 20:41
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    $\begingroup$ @planetmaker I will review the paper! $\endgroup$
    – Sidharth Ghoshal
    Commented Apr 6 at 0:43
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    $\begingroup$ @SidharthGhoshal: Putting the radar in the Kuiper Belt itself is not a good idea, as these objects are incredibly far from each other. Such a radar would be much further from KBOs on the other side of the Sun than a similar radar placed at Earth. $\endgroup$
    – Pierre Paquette
    Commented Apr 6 at 6:05

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An answer can perhaps be given in terms of the capabilities of the now defunct Arecibo radar facility. This was the most powerful radar system, as summarised in Venditti et al. (2023).

Arecibo had a 1MW transmitter, with a beam of 2 arcminutes. It was capable of studying near Earth asteroids of size $\sim 140$ m out to distances of 0.1 au. It has been used to study the more distant Galilean moons of Jupiter and Titan around Saturn. I cannot find evidence that it has been used to observe Pluto or any Trans-Neptunian Objects (TNOs).

The signal to noise (SN) of a radar observation depends on the inverse 4th power of the distance to the reflecting object and (roughly) on the square of the object's radius. If 140m asteroids can be studied with a SN$=50$ at $d=0.1$ au (Venditti et al.), then they might be barely detected with SN$=5$ at 0.18 au.

If we now put these objects at say 50 au, then the minimum size of a detectable object would be $10^7$ m in radius. i.e. an object larger than the Earth would be barely detectable.

To even detect a Pluto-sized object at 50 au would need a radar with about 100 times the power or a dish with 100 times the collecting area.

Then, bear in mind that this is only looking at a patch of sky of a few square arcminutes. i.e. It is not mapping the sky, it is pointing at a known position of an object and the whole sky comprises of more than 10 million sky patches of this size, each one of which would need a beamed 100 MW radar signal to be sent towards it.

Never say never, but I think it can be safely ruled out with current technology and 100 billion dollars (you possibly couldn't even provide the power required for 100 billion dollars, it depends how long each observation lasts).

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    $\begingroup$ "I cannot find evidence that it has been used to observe Pluto or any Trans-Neptunian Objects (TNOs)." Round-trip time to Pluto is about 500 minutes, i.e. Earth turns by 120°. But Arecibo could point within only +- 18° from Zenith - that's not enough even with the most favorable position of Pluto in the sky. I'd expect anything further out than 10 AU to be pretty much impossible. $\endgroup$
    – asdfex
    Commented Apr 7 at 15:05
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    $\begingroup$ @asdfex good point - a network would be required. $\endgroup$
    – ProfRob
    Commented Apr 7 at 15:24
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    $\begingroup$ @ProfRob slightly related to that: Why was the 100m Green Bank dish needed together with DSN's 70m Goldstone dish to detect Chandrayaan-1 in lunar orbit? It's "academic" now since Arecibo is no longer with us, but I think there are also examples of astronomical observations where transmit and receive were done with different dishes. But I'm not sure why I think so right now. $\endgroup$
    – uhoh
    Commented Apr 7 at 23:49
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    $\begingroup$ hot off the press: What are the technologies needed to make deep space LIDAR competitive with RADAR? Any plans for tests, prototypes or "pathfinder" systems? $\endgroup$
    – uhoh
    Commented Apr 11 at 3:11
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    $\begingroup$ @SidharthGhoshal I don't think so; "empty interplanetary space" is really full of electrons, so interaction with the plasma as well as interplanetary scintillation would be big obstacles as they might tend to further de-cohere the microwave signal. Also, the optical half of of the beam has to travel in the same optical path length. You would need a coil of optical fiber long enough to stretch to the Kuiper belt and back to Earth (divided by ~1.5, the index of refraction of silica) before the two are recombined to recover information. $\endgroup$
    – uhoh
    Commented Jun 3 at 21:29

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