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If we want to detect the distance to an object using radar, we can do it only for objects inside the solar system, otherwise the returning signal would be too weak to detect. On the other hand, we are able to detect signals from very far away, for example at redshift z=1000. How are the two things consistent?

If we will use radar for distant objects, would we be able to detect single photons of the returning signal?

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We can detect things from very distant objects because they are very very bright, and they were emitting light long ago (at the right time for that light to be reaching us now).

Take, for an analogy, the echolocation of bats.

A bat can detect by echolocation a moth that is flying a couple of metres in front of the bat. The bat can hear distant thunder from 10 km away. But the bat can't use echo detection to detect a moth, nor even a mountain that is 10km away. The squeaks that the bat makes are just too quiet to travel 10km to the mountain and back.

The apparent brightness of a distant source is proportional to $1/r^2$ (so an object that is ten times further is 100 times dimmer) However when you are bouncing a radar signal off a source, the brightness of the reflection is proportional to $1/r^4$ (An object that is ten times further is 10000 times dimmer!). The received power from distant targets is relatively very small.

Similarly we can detect photons from the cosmic microwave background, because these filled the universe 13.7 billion years ago, when they were first able to travel freely. Nothing could be brighter than filling the entire universe with hot plasma.

On the other hand we can't use radar to measure the distance to such things. Our radar-"squeaks" are not bright enough to illuminate objects that are beyond the solar system. And it would take billions of year for the photons in the radar pulse to reach the place where the CMB that we see now was first freed. And billions more years for it to get back (in fact, due to the expansion of the universe, those photons would never get back)

We can't even use radar for distant solar system bodies. The 1 MW beams are too weak to get a useful return signal from Pluto, for example.

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  • $\begingroup$ Now CMB photons are not that energetic, but what you mean is that at the time of emission they were very energetic, and that helped them to make it all the way from 13.7 billion light years away to the Earth, right? $\endgroup$
    – Halo
    Dec 12, 2021 at 18:23
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    $\begingroup$ Not really, just that they were lots of them. It doesn't matter (much) how energetic they were, or are. But still there are lots of them. There are still hundreds of times more CMB photons than every photon emitted since then. $\endgroup$
    – James K
    Dec 12, 2021 at 18:33
  • $\begingroup$ As a certain "fan-favorite" poster here and on spaceexploration pointed out recently, radar systems on exploration probes can get signals from the objects they pass by, and then tight-beam relay that back to Earth (or Medina Station) $\endgroup$ Dec 13, 2021 at 13:18
  • $\begingroup$ ooo nice hat!!! $\endgroup$
    – uhoh
    Dec 18, 2021 at 4:52

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