What is the maximum transmission distance of the radio signal in the outer space which could still be understood?
I’ll put this question in a form of a physics problem:
Transmitter at a point A sends a signal to a receiver at a point B. What is the longest distance in light years from points A to B for which receiver can still understand the signal?
- Signal type: electromagnetic wave.
- Signal frequency: frequency for which signal fades the least - probably radio.
- Signal form:
- Variant 1: beam of highest concentration possible.
- Variant 2: full sphere.
- Transmitter power: power of the most powerful transmitter known to be built in the Earth.
- Receiver: sensitivity of the most sensitive receiver known to be built in the Earth.
- Transmission medium: interstellar space.
- Understanding of a signal:
- Variant A: Can detect that the signal is not a noise.
- Variant B: Can decode the information in the signal.
Depends a lot on what the signal is. Some signals are quite like noise theirselves. You should clarify a bit. Simplest understandable signal is just a train of pulses, periodic, and it can not carry information.
http://physics.stackexchange.com/a/87997/30000 - check out this related question. As radio transmitters are just another variety of light sources when astronomy is concerned, we will need transmitters comparable in power to stars to make them visible on the inter-star distances (we can gain some signal power through focusing, but even best focusing will still require 1 millionth of "hot Jupiter" power output, which is rather huge).
Related: What is a link budget, and how do I make one? on Amateur Radio (if you know the receiver sensitivity, frequency and distance, you can figure out the effective radiated power needed; then just add antenna gains to taste) and the last part of my answer to What is the farthest a spacecraft has traveled away from earth? on Space Exploration, which just so happens to deal with talking to Voyager 1 over the Deep Space Network. The critical figure in free-space loss calculations is distance in wavelengths.
With this question I am interested in what kind of transmitters and receivers we would need to communicate with a human colony or aliens in say the planet of the nearest star (e.g. Alpha Centauri).
Spark gap transmitters carried information just fine: https://en.wikipedia.org/wiki/Spark-gap_transmitter - Marconi ,1896.
It cannot be said correctly, since we humans have hardly traveled to the moon and sent space probes to explore other planets in our solar system. So, theoretically anything might be possible. I'm trying to be a bit practical here. The only man made object that has gone really far is Voyager 1, which is at a distance of 18.7 billion kilometers (125.3 AU) from the sun. Although launched in 1977, it is the only live transmitter and receiver which is that far.
The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System. The communication system includes a 3*.7 meters (12 ft) diameter parabolic dish high-gain antenna* to send and receive radio waves via the three Deep Space Network stations on the Earth. Voyager 1 normally transmits data to Earth over Deep Space Network Channel 18, using a frequency of either 2296.481481 MHz or 8420.432097 MHz, while signals from Earth to Voyager are broadcast at 2114.676697 MHz.
As of 2013, signals from Voyager 1 take over 17 hours to reach Earth.
I agree that there are powerful transmitters in the world than what is present in the Voyager 1, but, most of them still remain untested. So, we can be exact with the measurements.
This feels somewhat empty and unsatisfying. The entire field of Astronomy is about measuring and theorizing about places we have never been. Surely we know something about the physics of radio signals in a vacuum and can surmise the effects of interstellar space on signal degradation. Maybe the author didn't provide enough information to define the problem, but saying "don't know because we haven't been there yet" just feels a bit lacking. No offense; I just don't think your opening premise is correct.
The reason is there are too many variables!
Any signal that passes by a sun or pulsar can be totally wiped out by the strong electromagnetic noise they produce. Another problem is that decay of radio signals even without interference is not a simple thing to calculate, it really requires testing in the environment the signal will encounter.
Anyway it's really all for naught because radio waves are completely useless for interstellar communication. They are moving way too slow for any meaningful use. Even the nearest solar system would take 4 years to send a signal and 4 more years to get a reply.