I just want to get some clarifications regarding the transmission and receiving of a radio waves between planets as a means of communication with aliens for story building.

1. Is it better to transmit the signal from the surface of the earth or by placing any beacon or antenna in outer space? it is said that atmosphere has placed some limitations for sending messages.

2. Does a FM or AM radio wave transmitted to outer space gets dispersed while it propagates through outer space? lets consider that a message is transmitted to a planet of our nearest star. if disperses, can that signal be detected from any other planets of the same star?

3. To detect transmitted FM or AM signal from any other planets, do we need to point the telescope exactly towards that location? lets consider a radio signal being directed towards earth. let it be towards Arecibo Observatory. can we detect that signal from Arecibo telescope even if that telescope is pointed towards some other sources?

4. do we require big dishes or need the method of interferometry for detecting the radio signals or does the size of the telescope helps us to get better resolution of the detected radio signal?

• Hint: the Deep Space Network consists of ground-based antennas. You don't have to speculate about how we'd solve the problem if we needed to, you can just look at the solutions that are actually in use. – Emilio Pisanty Nov 29 '17 at 13:01

Is it better to transmit the signal from the surface of the earth or by placing any beacon or antenna in outer space? it is said that atmosphere has placed some limitations for sending messages.

It is, theoretically, better to transmit from space. As others have noted, the atmosphere blocks a wide variety of wavelengths. Of course, building them on the ground is orders of magnitude easier. So that's what we do.

Almost. What we also do is convince ourselves that it's a good idea to build them on the ground. Here's the reasoning:

1. all life requires water
2. EM frequencies are the easiest to generate in massive quantities
3. only certain EM frequencies easily penetrate water in gas or plasma form
4. using our level of technology, we can only see signals that are EXTREMELY powerful
5. the only reason to broadcast something we could see in (4) would be to deliberately be detected
6. any civilization doing (5) realizes that they will be talking to dummies limited by (3)
7. therefore, the aliens will broadcast in a specific range of frequencies that dummies can receive

That set of frequencies is known as "the water hole". This is also a useful set of frequencies because it is between two "obvious" radiators in space, OH and H, which combine to form water, which we assume everyone needs.

You can question any one of these assumptions, and should! However, the real key to understanding the chain of logic is (4). This isn't really a statement about what we think aliens would actually do, its a statement about what we can do with today's technology. Of course, that is always changing - it used to be hard to generate microwaves so we used VHF. Now, not so much. And it all depends on (1), if the aliens in question are not water based and think all life requires carbon, then they would select some other set of frequencies and we would never see them. And that's fine, because, again, this is a statement of what we can do, not what the aliens would do.

Does a FM or AM radio wave transmitted to outer space gets dispersed while it propagates through outer space?

Of course, but I suspect you already knew that.

lets consider that a message is transmitted to a planet of our nearest star. if disperses, can that signal be detected from any other planets of the same star?

Yes. Controlling dispersion to a planet-sized object at the distance of the next star would require an antenna about the size of the solar system. This is the diffraction limit, a fundamental physical fact of our universe.

To detect transmitted FM or AM signal from any other planets, do we need to point the telescope exactly towards that location

This is sort of the same as...

do we require big dishes or need the method of interferometry for detecting the radio signals or does the size of the telescope helps us to get better resolution of the detected radio signal?

Here comes the second set of assumptions...

The universe is filled with objects that give off massive amounts of radio signals, quasars are a good example. So if we're going to find the ones from the aliens, we have to look for ones with some sort of special quality.

One of the qualities these background sources have is that tend to be broadband, so if we point our telescope at it we see signal across a wide band. So, if we're going to be able to detect it, the alien signal would have to be narrowband. Really narrow.

And while we think that signal would be in the water hole, that's still a lot of bandwidth to cover if the signal is really narrow. So if you're going to break that signal down into "channels" and examine each one, you're going to need a whole lot of signal to work with, otherwise there's just not enough signal left in each channel.

And that's the reason we use telescopes. Not for resolution, but simply to get a big signal so we can look at each part of it and still have enough energy to work with. The amount of signal is basically the area of the scope, so bigger is better.

Now you don't need one big scope to do that. If you break the water hole down into, say, 1000 channels, then 1000 small telescopes is just as good as one a thousand times larger. Which is the whole idea behind the Allen Telescope Array, which has 42 small telescopes of the originally planned 360. The idea is that it would be way cheaper to build a bunch of small scopes than one 360 times larger. However, such a scope has limited uses outside of SETI, it it's been very difficult to maintain funding.

So now the former question - does the signal have to be in the direction we're pointing. Yes, because that's what scopes do. However, the Earth turns. So the idea is just to wait. Sooner or later you'll end up covering most of the sky.

Is it better to transmit the signal from the surface of the earth or by placing any beacon or antenna in outer space? -

Ionosphere is opaque to radio waves with wavelength more than 1010 nano meters. Reflection and absorption of radio waves in this layer is due to presence of free electrons in ionosphere. So for radio waves, it will be better to put an antenna in space and transmit.

Does a FM or AM radio wave transmitted to outer space gets dispersed while it propagates through outer space?

Radio Waves propagates in all direction from the source of signal. They are supposed to reach the right place in right time. Detection depends on the strength of signal, the instrument used for detecting signal, and transmission losses in the medium.

To detect transmitted FM or AM signal from any other planets, do we need to point the telescope exactly towards that location?

We do not need telescope to detect FM or AM signal. We need the right kind of antenna.

Do we require big dishes or need the method of interferometry for detecting the radio signals or does the size of the telescope helps us to get better resolution of the detected radio signal?

The formula for calculating antenna length is given as length in meters =300 / frequency in MHz. Radio waves have frequency range in 300 GHz to as low as 3 kHz.