> The Arecibo Observatory and FAST could each detect the TV carrier wave leakage out to a distance of about sixteen lightyears. That’s a little bit further away than Tau Ceti is.

https://www.forbes.com/sites/quora/2017/01/27/how-far-into-s...

That's for detecting a TV broadcast. But how far away could one Arecibo observatory detect another Arecibo?

> The answer is, that except for obscuration and dust in certain places, it could be anywhere in the galaxy and we would pick up the signals. That means at least one hundred billion stars that you can listen to for signs of extraterrestrial intelligence.

https://www.rollingstone.com/culture/culture-news/carl-sagan...

How far away can our own technologies detect our own transmissions? If a planet 100 light years away was making as much RF noise as us, could we detect it? I thought we could.

One easy way to think about this is:

If our radio signals would make it to a planet 100 light-years away (even if you ignore Inverse-square law), you could probably power them down and still reach all of earth. Why would one pay for that extra, unneeded, power?

Because antenna gain is a function of both the transmitter and receiver, and detection is different from getting a high-quality signal. Most high-power radio signals on earth are aimed at transmitting to fairly low power, small, cheap devices which need to recover a good amount of information from the signal. This is very different from the requirements of a radio telescope (which has a gain many orders of magnitude higher because it has a much larger space, power, and cost budget) detecting a signal (which requires far lower signal-to-noise than reconstructing something high quality from it).