# How far would a radio signal propagate in free space as compared to Earth's atmosphere?

A curiosity question.

Radio Propagation within Earth's atmosphere is via atmosphere. Broadly speaking a signal loses strength between bouncing off the ionized layer, and absorption by various earthy elements.

If an identical signal were to be produced in free space, how far would it travel as compared to it's range within Earth's atmosphere?

EDIT: A commercial FM transmitter on Earth probably has a range no more than 25 miles where the listener uses a broadcast receiver. For the purpose of elaboration assume the the receiver being placed in static orbit - how far out could the same signal be generated, and still be intelligible?

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I wonder how information is conveyed to satellites.(THIS is an answer to your question) –  Nix Jul 9 '13 at 12:12
Another thing to think about: The spacecraft 'Voyager 1' was launched in 1977. It is now at a distance of $1.866 × 10^{10}$km, and it communicates to the earth by means of radio signals. –  mikhailcazi Jul 9 '13 at 12:36
The question is ill-posed. You don't specify noise conditions, receiver sensitivity, and initial signal's ERP to get a sensible answer as to the maximum ranges at which both signals will be detected. –  Deer Hunter Jul 9 '13 at 12:42
The main problem in radio communications is being able to recover the transmitted signal from the received, noisy signal; and it is mainly a channel coding problem. also, because the distances between spacecrafts (or stations, etc.)in space are very large, the transmission power is not too important and the successful communication depends on error-correction methods used. –  Mostafa Jul 9 '13 at 12:47
@mikhailcazi: The Voyagers use the Deep Space Network; apparently using PSK. My query is about the range of a system in space relative to the range of the same system on Earth. –  Everyone Jul 10 '13 at 1:28

## 1 Answer

First, no, "radio propagation" is not "via atmosphere". Different wavelengths get absorbed, reflected, or simply passed by different parts of the atmosphere. There is no one general rule. Many of our radio communications within the atmosphere are pretty much like they would be in free space, for example.

Second, all radio waves propagate infinitely in free space. There is no finite end to the propagation. What does matter in a practical sense is signal to noise ratio. Below some signal to noise ratio for whatever information encoding scheme is used, that information can't be recovered. Or more accurately, the error rate goes up as the signal to noise ratio goes down. At some point the errors in the information make is useless or "unreceivable" in a practical sense.

## Added:

You are now asking specifically about "commercial FM", which I take to mean radio at around 100 MHz (3 meter wavelength). The primary mechanism limiting reception distance of such commercial FM stations is the curvature of the earth. The wavelength is too short for significant refraction around the earth, as happens with commercial AM at around 1 MHz (300 meters). Note that when you are in a car listening to a FM station at the fringe of its range, it will come and go as you get to tops of hills or dip between them.

Another factor is that here on earth there is significant interference from all kinds of unintentional broad-band radiators. Eventually at some distance the intended signal becomes too small relative to this background noise for the signal to be picked up well enough for your liking.

In the end, there are no hard limits and reception is about signal to noise ratio. That means you can extend the useful range of a transmission by reducing noise or selectively amplifying the signal. Note that spaceprobes usually emit only a few Watts or tens of Watts, whereas commercial FM stations usually a few kW. One important difference is that spaceprobe signals are picked up with highly directional antennas and extra low noise receivers. You wouldn't want to pay for one of those receivers in your car. The narrow beam of the receiving antenna greatly increases signal to noise ratio. Since the signal is coming from a point, the same signal is still picked up along a narrow beam. But, only a tiny fraction of the noise that is coming from all around is picked up along that same beam.

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Pretty close to the answer I wished to learn; I've elaborated on the question a bit ... –  Everyone Jul 10 '13 at 1:46
Hm.. the reference to an FM signal was merely for the purpose of illustration –  Everyone Jul 10 '13 at 16:29