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In the Carl Sagan novel Contact and the 1997 film of the book, aliens from Vega have picked up TV pictures of Hitler opening the 1936 Olympics, which is depicted as the first TV signal powerful enough to reach the stars. The idea of aliens picking up our TV signals and learning human customs and languages from soap operas and commercials is well known enough to be a comedy trope.

1) How plausible is the basic idea that aliens might pick up Earth's TV or radio broadcasts in real life, assuming sentient technological aliens exist within the distance to which Earth's electromagnetic signals have penetrated? (That distance is a maximum of 79 light-years, if you agree with Sagan's view that the 1936 broadcasts were the first ones strong enough.)

2) Which types of broadcasts (in the sense of which frequency of EM radiation and type of signal modulation, amplitude or frequency) would pass through the atmosphere? My understanding is that TV and FM radio are the only realistic possibilities, as longwave radio is too weak and shortwave radio is bounced back by the ionosphere.

3) How powerful does the transmission have to be? This piece by Brian Koberlein expresses the view that a signal from earth would need a power of 110 MW to be picked up at the nearest star, Proxima Centauri, in order to be received about as well as we pick up the signals from Voyager I. UHF TV stations, he says, are limited to about 5MW, so the whole idea is unlikely. Do you agree?

4) Has humanity largely stopped sending signals that can be picked up by aliens? According to Frank Drake, the astronomer behind the Drake Equation, since nowadays "most TV and radio programmes are transmitted from satellites that typically use only 75 watts and have aerials pointing toward Earth, rather than into space" it is no longer feasible for aliens to pick up our signals. So they'll get The Twilight Zone but not Stargate.

5) If they do get Earth TV, whose TV will it mostly be? I had assumed that the US output was dominant in the early part of the peak period for broadcasting power, as the signals that are most likely to be picked up are from the late 1950s to early 1980s, when America, as the richest large country, had the largest ownership of TV sets and the largest TV industry. In the comments to this Worldbuilding SE answer Jorge Aldo disagrees. I have not been able to find good data about the historical spread of TV ownership and/or transmitter power across the world, so I might be wrong. And the answer might change if we look at FM radio rather than just TV. It is certain that latterly the amount of broadcasting in English has been equalled or surpassed by the amount in other languages such as Spanish and then Chinese. But would this be enough to counteract the effect in point (4)?

6) What other factors have I missed that might make aliens seeing our TV likely or unlikely?

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    $\begingroup$ With our luck the first thing aliens will pick up is "I Love Lucy", decide "No evidence of intelligent life on this planet!", and destroy the Earth to make way for a hyperspace bypass. I think I'll go down to the pub... $\endgroup$ – Bob Jarvis - Reinstate Monica Jun 6 '15 at 19:36
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    $\begingroup$ I've accepted AndrejaKo's superbly detailed and careful answer. But that doesn't mean that I'm no longer interested in seeing other possible answers, particularly regarding point (5), which is as much about Earth history as about aliens being able to detect us. Another point is that, even assuming that aliens on another star detecting accidentally transmitted signals from earth is unlikely, as AndrejaKo mentions that does not preclude them detecting us while passing closer to our solar system, or while actively scanning star systems nearby to them for signs of intelligence. After all, we did. $\endgroup$ – Lostinfrance Jun 8 '15 at 8:23
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    $\begingroup$ It's worth considering that a long-lived civilization with an interest in emerging intelligent life could have long ago seeded the galaxy with self-replicating observation probes, small enough to evade detection but large enough to ping their masters if anything interesting happens. Such a device could be idling out just beyond the Moon, sending detailed synopses of our TV programming halfway across the galaxy. $\endgroup$ – Maxander Sep 22 '15 at 17:13
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Since my area of expertise is telecommunications, I think that I should first try to explain a little bit about how everything works, so that we can at least do some informed speculation about what the aliens could or could not receive and what they could make out of it.

Do note that this answer is currently mostly about plausibility part.

First concept that I'd like to introduce is antenna directivity. I'll start with visible light parallel before moving down the frequency axis into radio waves. Then, I'll try to explain how it allows us to compare power levels from different transmitters at different points. After that, I'll write a little bit about power spectral density and noise floor, which will allow us to compare the probabilities of detection of different types of modulations. Finally, I'll end this with a bit of my own speculation.

So imagine that you take a lighter and you light it up. You'd get a small flame which would emit light, more or less equally in all directions.

Lighter image from Wikipedia

The radio version of that would be so called "isotropic point source", that is to say infinitely small antenna that radiates equally well in all directions. Such thing, of course doesn't exist, but is sort of useful in calculations, especially when we need to compare transmitters with different power levels and different antennas. Keep in mind that it would actually radiate equally well above itself as it would radiate below and to the sides.

Here's an image of how its radiation pattern would look like: Diagram from website of PD0AC

Then we have radiation patterns of different types of antennas. Here's a radiation pattern of a Yagi-Uda array that's commonly used for TV reception in some areas:

Yagi radiation pattern from Cisco

What this image shows us is that the antenna receives the best when the "long" front side of of the antenna and has very poor reception on the very short back side. In this particular case, we have a front-to-back radio of around 25 dB. When we convert that into linear units, that means that if the front side of the antenna is pointed towards our signal source, the signal would be received some 317 time more strongly compared to the case when the same signal was being received by the back side of the antenna.

This brings us to the concept of "effective isotropic radiated power". So let's say that I have a transmitter that give out 5 W of power and that I have a receiver with an isotropic antenna, just for comparison's sake. I take my transmitter and connect it to one of my imaginary isotropic antennas, point the antenna towards the receiver and I measure EIRP of 5 W. Next, I take my Yagi antenna, from the previous example, I point it to the received antenna and do the measurement. I'd measure this way an EIRP of 158 watts. Quite a bit of difference we have there! But what if I don't point the front side of my Yagi antenna to receiver, but instead I point the side? Well from the radiation diagram we can see that on the sides, we have some -20 dB of gain, so that would give me 50 milliwatts at the sides of the antenna.

There's also a concept of "effective radiated power". The difference between ERP and EIRP is that ERP assumes that the antenna is an ideal dipole antenna in free space which has gain of 2.15 dBi. That assumption is much more closer to realistic antenna systems than the isotropic antenna and is therefore often used in broadcast industry as a measurement unit for radiated power.

So why is all of this antenna stuff important for reaching aliens? Well, the job of transmission system designers isn't to contact aliens (except when it is, but more on that later), it's to provide TV and radio to listeners, without interfering with other people doing the same thing. This means that the TV transmission antennas aren't usually going to have a radiation pattern that sends signal to the sky, they'll have a radiation pattern that tries to keep signal close to Earth. Also, the EIRP is going to be limited for safety and interference reasons. This doesn't mean that none of those many megawatts are going to reach space. They will, it's just that the power going out into space is going to be limited. Please keep in kind that someone needs to pay for all of that electricity consumed and that radio transmitters don't operate on 100% efficiency! There's a direct economical reason to keep your power as low as you can!

Next, we have power spectral density. I think this is one point that I haven't seen discussed much in detection scenarios, but which I think is of extreme importance. Let's first take a look at the name itself: Power spectral density is a density. Density of what? Of power! Over what? Spectrum. So out units are watts per hertz. Remember power from the previous post? Well here we get to see how distributed it is across the bandwidth axis of our signal and how our modulation affects that. Here, I'll give a very, very rough comparison of PAL and DVB-T, used for television, FM from broadcast VHF radio (I wanted to do DAB, but couldn't find any realistic numbers) and one special FM Morse code signal.

First, just to make calculations a bit easier and this very long answer a bit shorter, I'll assume that all modulations have a flat spectrum. This is more true for digital modulations and not so true for analog modulations.

So let's start with PAL. Our channel, in UHF band, and I'm restricting myself to UHF band, since low parts of VHF band can have problems getting out of atmosphere, is around 8 MHz wide. There's also a version that's 6 MHz wide. So let's see the "idealized" power spectral density. For power levels, I'll just use some info from a local transmitter, so that we can get some real-life values. This transmitter, while it was transmitting PAL, had for one particular channel ERP of 250 kW. When we divide 250 kW by 8 MHz, we get 31.25 milliwatts per hertz of power spectral density. The same transmitter is now transmitting DVB-T channel with ERP of 25 kW. This gives us 3.125 milliwatts per hertz power spectral density. Much lower!

The same transmitter is running an FM radio station at 15 kW. The bandwidth of the station is around 300 kHz, so this gives us PSD of around 500 milliwatts per hertz. Much higher than analog TV!

Next, I'd like to mention the Morse message. This was actually a test of an interplanetary radar, but it's here as an representative of so-called Active SETI. So they have frequency modulation with 62,5 Hz deviation and maximum input signal frequency of less than 1 Hz. I'll use 1 Hz for calculation. According to Carson's rule, we can get an estimate of bandwidth in which 98% of power of FM signal is contained. It gives us bandwidth of 125 Hz. ERP of transmission was 50 kW. This gives us PSD of 392 watts per hertz! Way higher than FM radio, but on the other hand, a test transmission and therefore not continuous.

Now why did I go into this basic explanations about PSD? Well in order to detect that we have a signal, we first need a good enough signal to noise radio. Our noise could be coming from numerous sources, such as thermal noise, shot-noise etc. It is going to be a property of the receiver and it itself is also characterized by power spectral density. One common thing about receivers is that usually, we can easily affect their reception bandwidth. The lower reception bandwidth we have, the lower is our noise power at the receiver. In an ideal world, our receiver will have a filter matched to the bandwidth of our transited signal. So basically, this means that if our power is constant, it's going to be easier to detect a signal with lower bandwidth than a signal with higher bandwidth, as illustrated in this drawing:

Signal PSD

So basically, my idea is that the aliens, if they are going to detect out signals in the first place, are most likely to detect Active SETI attempts, if they happen to be looking for them at the moment. Otherwise, I think that FM radio has better chance of being picked up than TV. Furthermore, in an analog TV signal, not all components are transmitted with same power! Part of signal carrying color (chroma components) is usually weaker than part that carries black and white signal (luma). Also, depending on implementation, it might be possible to get audio signals from TV even if video reception is not possible.

EDIT1:

As a response to comment, let's say that we have a space ship in Earth's orbit with a TV transmitter on-board. Let's also say that our spaceship is pointing its antenna towards our listeners and is emitting the program with 5 MW of ERP and uses a 6 MHz wide channel. Let's say that we're transmitting at frequency of 430 MHz (not in TV band, but close by, chosen due to available data) and that our aliens built their own version of Arecibo with same specifications, that is to say 60,5 dBi gain on 430 MHz. Let us also say that noise floor is −106 dBm for our channel at the receiver.

The Friis transmission equation goes something like this: Prx=GtxGrx(λ/4πR)^2*Ptx, where:
Prx is the power at the receiver and should be -106 dBm,
Gtx is the gain of transmitter antenna, Grx is the gain of the receiver antenna, Ptx is the power of the transmmitter, λ is the wavelength, R is the distance.

From this equation, we should derive R and change it so that we take into account mixture of decibels and linear units. Do note that in our case, we have 5 MW of ERP, so in order to convert that to EIRP, we are going to use transmission antenna with gain of -2,15 dBi. Also note that the upper edge of our signal is at 436 MHz, which have wavelength of around 0.688 m.

We divide everything with the antenna gains and transmit power and we take 10*lg of everything to get to decibels. So we have:

10lg(Prx)-10lg(Ptx)-10lg(Grx)-10lg(Gtx)=20lg(λ/4πR)

Now we put our numbers into that:
96.9897 dBm + 106 dBm +2,15 dBi -60,5 dBi=20lg(λ/4πR)

Now we can use one of those handy Friis Transmission equation calculators and get a number for the range. Using this one, I get range of 638 420 000 000 m, that's 638.42 Gm or 4,26 AU.
That's very, very little! Even if we take much better values for system noise temperature, such as for example 100 K, or maybe even lower, we'll still have very low ranges. So for TV, we don't really have a big chance of having aliens receive a signal.

For FM radio on the other hand, if we take a 100 kW ERP transmitter at 97 MHz, based on some USA limitations for power, and we imagine that the aliens have a 60,5 dBi gain antenna for FM with system temperature of 35 K we get a much nicer result of 5 349 800 000 000 m or 5,349 Tm or 35,76 AU. Still, it's quite short range. The range is much greater, but still not very sufficient to reach nearby star systems, assuming that system temperature is reasonable.

So TL;DR:

I do not believe that it is feasible that accidentally transmitted analog TV or radio signals would be able to reach a nearby star system in a reasonably-detectable state, but that depends also a lot on their detection capabilities. I do believe that aliens passing near the edges of our Solar system might be able to detect our transmissions.

Also note that a 100 kW radio signal has longer range than 5 MW TV signal, so keep in mind that not everything is in transmitter power.

It should be noted that for intentional active SETI signals, especially if digital, situation might be somewhat different. We'd have much higher powers, we'd have gains from error correction codes, assuming aliens can decode them. I also used signal to noise radio of 0 dB as the lower limit for analog system reception. In real life, it has been proven that decoding digital signals is possible at signal to noise rations a bit below 0 dB, so that could also make some impact.

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    $\begingroup$ For extra credit: It might be possible to get an estimate of path-loss through Earth's atmosphere and then use the Friis equation to get the received signal strength at a distant location. It might be also possible to use for example Thermal noise to get the minimum noise PSD at the alien's receiver and use that to get an estimate of maximum range. This could give some hints about number 3. $\endgroup$ – AndrejaKo Jun 6 '15 at 16:33
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    $\begingroup$ Also it might be interesting to research a bit about our own reception systems such as Arecibo telescope or Deep Space Network. The reception not only depends on our transmission capabilities, but also on the aliens' antenna system and its coverage. $\endgroup$ – AndrejaKo Jun 6 '15 at 16:39
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    $\begingroup$ Very thorough analysis. Well done. Do you think you could add a TL;DR section to summarize your answer? $\endgroup$ – Frostfyre Jun 6 '15 at 16:53
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    $\begingroup$ @Frostfyre It's definitely a good idea! $\endgroup$ – AndrejaKo Jun 6 '15 at 16:53
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    $\begingroup$ Path loss due to atmosphere is so small compared to the geometric loss (inverse square law) due to the deep space distances that it might be ignored. Just apply friis equation to the signal and verify if the signal strenght received would be above the usual noise floor of the frequency at hand. $\endgroup$ – Jorge Aldo Jun 6 '15 at 16:55
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I just saw a presentation at SETI explained how near-future receiver arrays will be sensitive enough to pick up our aircraft radar from hundreds of lightyears. That's leakage of common use. We also have interplanetary radar that's occasionally beamed out.

So to answer your question, look at the opposite end: what are SETI researchers expecting to be able to detect, modeling the situation of our own technological history?

While radio is power-saving and subtle, radar by its nature must be bright enough to reflect off passive targets. So much more detectable.

Here is a press release:

Unprecedented scope

The program will include a survey of the 1,000,000 closest stars to Earth. It will scan the center of our galaxy and the entire galactic plane. Beyond the Milky Way, it will listen for messages from the 100 closest galaxies. The telescopes used are exquisitely sensitive to long-distance signals, even of low or moderate power:

  • If a civilization based around one of the 1,000 nearest stars transmits to us with the power of common aircraft radar, Breakthrough Listen telescopes could detect it.

  • If a civilization transmits from the center of the Milky Way, with any more than 12 times the output of interplanetary radars we use to probe the Solar System, Breakthrough Listen telescopes could detect it.

  • From a nearby star (25 trillion miles away), Breakthrough Listen’s optical search could detect a 100-watt laser (energy output of normal household light bulb).

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