How far away could a man-made receiver detect a signal sent from Earth?

Factual Questions
1

I’m asking this question in order to get a grasp for the (in)probability that an extraterrestrial society could pick up useful signals from the usual noise mankind produces all the time. I guess for a quick calculation, you only need the power of the strongest sender we have and the minimal input power the gain of the finest detector/receiver allows to get a useful signal. Let’s say we talk about a simple voice signal with a bandwidth of 5 khz. Does someone have those numbers and can do the math?

(if I’d remember the equations I could do it myself, I know that the most important factor is the inverse square law, but I’m unsure at the moment what other factors influence that calculation. College was a long time back, and I’ve never needed to calculate something likes this in 25 years)

2

I don’t know the equations either but…

We are getting data from Voyager 2, which has a transmitter of about 100 W (?) and is now something like 100 AU distant (15 billion km).

So we could pick up a 1,000,000 W signal at 100 times this distance, 1.5 trillion km. This is still less than half way to the nearest star.

3

You can play with a calculator here.
If you assume Arecibo-sized antennas at both ends, and a Megawatt transmitter, you get around 98 light years at 1 Kbaud.

4

Damn, that website doesn’t work for me at the moment, but I’ll check again later. But at least yours is a good ballpark figure. So the answer is: not really very far…

5

The major factor is the ability to identify the ‘desired’ signal from the background radio ‘noise’ around it.

So it’s possible for us here on Earth to pick up a signal from Voyager 2, because:

  1. we can have huge Arecibo-sized antennas (or even larger virtual ones, like recently used for black holes), and
  2. there isn’t much else in identifiable radio signals coming from that direction.

It would be much harder the other direction: for a small vehicle like that to pick out a command signal amongst all the radio noise coming off of Earth. So it’s more one-way transmission than communication.

6

What’s the context for “not really very far”? To have a conversation at this distance takes 200 years per statement exchange, from the point of view of either participant. Isn’t that prohibitive already? If it were only 20 years, would we have much conversation?

I think hearing somebody else and deducing things about them is the major thing, unless there are communicators every few light years.

7

I meant “not very far” in a universal scale. In that scale it barely scratches our own galaxy. And I wasn’t thinking firstly about communication (this may follow) but the ability to receive a signal in the first place.

8