Would Radio Communications Between Parties Experiencing Time Differently Be Compressed/Stretched This is a contrived and extreme example that is likely not even possible, but I'm hoping the answer will help me understand something about communications across relative time.
Imagine two individuals attempting to communicate by radio.
One is stationary at a fixed point and the other is on a spacecraft orbiting the other at 80% light speed.  Lets say the distance between the two is 1 light hour.
The distance between the two does not change appreciably.
However, because of the tremendous velocity of the moving person, time would be experienced differently between the two.
While neither would perceive anything unusual about themselves or their immediate surroundings:

*

*Time would be much slower for the moving person relative to the stationary person.

*Time would be much faster for the stationary person relative to the moving person.

Since light is constant, once any component of the message is sent it should arrive in exactly 1 hour.
However, I would think that the length of the message, or rather the time spent transmitting the message, would change based on the sender.
If the moving person sends a message wouldn't the message be "stretched" when received by the stationary person?  Since the stationary person experiences time much faster, relatively speaking, wouldn't a message of length 1 minute, sent in real time from the moving person, be received over a period of time much longer than 1 minute by the stationary person?  Wouldn't this make any message unintelligible or not even recognizable as a message, given the extreme difference in time?
Could such a message be aggregated by the stationary person over time and compressed such that it could be understood, or is there something I'm missing?
The reverse is, if the stationary person sends a message, wouldn't the moving person see that message compressed to a period of time much less than 1 minute?
I'm also assuming this would mean that, if the moving person were moving at a speed approaching the speed of light, it would be impossible to communicate since time would almost stop for the moving person relative to the stationary person.
How could we calculate the perceived "length" of the message at different relative speeds and at different distances?
 A: Say an orbit, as measured from earth, takes one hour as measured from earth.  Then during that hour the clock on board spacecraft advances by .6 hours.  So:

*

*A video that takes one hour to play on earth will arrive at the ship over a period of time when the ship's clock is advancing .6 hours.  The video will appear to be playing in fast-forward.


*A video that plays on the ship over the course of a single orbit (and hence .6 hours on the ship's clock) will arrive on earth over a period of one hour.  The video will appear to be playing in slow motion.


*Of course either party can record the message as it arrives and play it back at a different speed.


*The person on the spacecraft will always say "the video that is arriving now is playing at 5/3 its normal speed".  But in his instantaneous frame, he will always say that the video that arrived, say, half an hour ago, arrived at some other speed --- because the craft he was on half an hour ago was moving relative to the craft he's on now.  He'll say in fact that the video arrived at 5/3 normal speed according to his own watch but that his watch was running slow at the time (though it's running perfectly well now).  He'll also have a very different opinion now than he did then about what time the video started to arrive.
A: If the moving person sends a signal, it will be redshifted according to the relativistic Doppler effect. For the case of uniform circular motion the source around the receiver, the received frequency $f_r$ is related to the source frequency $f_s$ by
$$f_r = \frac{f_s}{\gamma}$$
where $\gamma=\dfrac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ is the Lorentz factor. Since we can assume that the receiver of the signal knows these formulae, they would be able to adjust the received signal to account for the Doppler shift and then interpret it normally. The same goes for the case of a stationary source and moving receiver, but with a blueshift ($f_r=\gamma f_s$) instead of a redshift.
