"So how far away can that new radio telescope of yours see a signal?"
This question, which I'm frequently asked, is like Spandex at the mall: odd, but remarkably commonplace. My quick answer, so often spoken that it now springs from my spinal cord, is, "to the edges of the visible universe, if the signal is strong enough."
Glib, but true. If the alien broadcasters are sufficiently motivated to build really large transmitting antennas, and aren't fazed by Homeric energy bills, they can bridge any distance. Radio astronomers have measured natural emission sent our way shortly after the Big Bang – which means that the "transmitter" is nearly 14 billion light-years away. No sweat: the universe is mostly transparent to radio waves. Alien broadcasters could, if they had the hardware and the kilowatts, reach us from anywhere.
"Sure," I sense you saying to yourself, "but be realistic for a moment. What are practical distance limits?"
One way to address this is to turn the problem around, and inquire how far our own transmissions could be heard by nosy aliens. This particular question has been on the front burner because of a recent television show in which a pontificating pundit apparently proclaimed that earthly TV broadcasts would be hopelessly scrambled after penetrating only a few light-years into space.
Well, you can forget that – it isn't true. The beefiest of our television transmitters operate at hundreds of kilowatts. They don't burp your favorite sitcoms in all directions equally, of course: The audience isn't straight up or straight down, but towards the horizon. By shaping the beam of the transmitting antenna in those directions, the signal is mildly concentrated by a factor of maybe five or ten. This is called the gain of the antenna, for readers who wish to sound literate at nerd conventions.
Another important point is that roughly one-third of a TV transmitter's power is found in thin slices of spectrum, narrow-band signal components known as carriers. They are by far the easiest parts of the broadcast to pick up.
So what's the bottom line? I'll spare you the calculation, but if aliens had a farm that was 15 miles on a side consisting of a collection of rooftop TV antennas spaced every 10 feet, and receivers as noise-free as those we build for our radio telescopes, they could pick up our TV carriers in two minutes of listening from 50 light-years away. That, incidentally, is where the earliest episodes of "I Love Lucy" are hanging out now.
The carrier would tell them we're here – that the red "on the air" sign is lit, and intelligent critters exist on planet Earth. If they found the carrier too boring, and wanted to actually watch Lucy drive Desi nuts, they'd need an antenna farm 150 times bigger in each direction. That's a large herd of antennas, approximately the size of the United States, and probably not something you'd appreciate outside your picture window. But it's hardly an unimaginable engineering feat, especially if the aliens are somewhat ahead of us in technical development.
Grote Reber built the first radio telescope in 1937, and it was 31 feet in diameter. By 2030, radio astronomers hope to have a radio telescope in Europe that's a square kilometer in size. With that rate of improvement, we should be building antennas of the dimensions needed to at least detect TV-strength signals from tens of thousands of star systems by the second half of this century. If we can do it, they can do it.
Let's consider some other earthly transmissions, for instance NASA's recent broadcast of Beatles music to Polaris (the North Star). For this, the space agency used the 210 foot Deep Space Network antenna near Madrid, Spain, and a mere 20 kilowatts of transmission power. In order for the Polarians, if there are any, to notice that this unsolicited serenade is washing over their planet, they'll need an antenna about 7 miles across. (Note to propeller-heads: I've assumed that their microwave receivers are about ten times less noisy than ours. Hardly unreasonable.) If they actually want to download the music to their iPods, they'll need heftier gear: about 500 miles on a side. Polaris, of course, is not next door. Its 430 light-years distant. This enormous span is what accounts for the large antenna requirements. The North Star is not the nearest audience for such a Beatle blast, incidentally – there are about 100,000 stellar systems that are closer. Maybe NASA chose this target because the Polarians agreed to pay royalties.
One last example, just for scale. The family-size Arecibo radio telescope in Puerto Rico is outfitted with a one megawatt radar transmitter, which it routinely switches on to study planets, asteroids, and the ionosphere. If the aliens have a similarly sized antenna at their end, they could pick up the Arecibo radar at 320 light-years in 8 seconds (roughly how much time it would take for the beamed signal to sweep across their planet as a consequence of Earth's rotation.) Note that this radar is turned on for the equivalent of about 70 days a year.
It comes down to this: When someone tells you the aliens couldn't possibly hear us, you can just smile politely. The truth is, they could. And what about us hearing them? We've only had radio for a century. Some extraterrestrials have surely had it for a hundred or thousand times longer. If our signals are detectable, theirs might be far more so.