What would we see back on Earth if we shot a camera off into space and watched a live-stream? I'm curious as to what we would see if we shot a camera off into space at, say, 50,000 mph and watched a live stream. Clearly in the beginning we'd be seeing things in more or less real time. But by the time the camera reaches Mars, we obviously won't be seeing what the camera sees in real time -- there would be a noticeable delay. So if we watch this live-stream in real time, how does what we see on Earth differ from what the camera sees in real-time? On Earth, would it just look like the stream we get from the camera is ever so slightly slowed down?
 A: Your "live stream" would be affected by the Doppler effect. Since the speed you mentioned is far from relativistic you don't have to consider the relativistic Doppler effect. If $t_0$ is the time when the camera was launched, $t$ is the time at which you watch a certain frame, $t_f$ is the time the events on that frame took place, $v$ is the speed of the camera and $c$ is the speed of light, they would be related according to:
$$
t_f=t_0+(t-t_0)\cdot(1-2\frac v c)
$$
The reason for the factor $2$ is that you get the effect twice since the information needs to go back and forth between Earth and the camera. Hence the lag of your video, $t-t_f$, would be given by:
$$
t-t_f=2\frac v c(t-t_0)
$$
Since $v= 50000 \,\mathrm{mph} \approx 22000 \,\mathrm{m/s}$ we have:
$$
2\frac v c\approx\frac{2\cdot 22000}{3\cdot 10^8}\approx 0.00015
$$
Hence the lag of the video would increase by approximately 1 second in two hours. You would not notice that the video was playing slower, but over time you would notice an increasing lag between the video and events taking place on Earth. The Doppler effect would also affect the wavelengths of the light captured by the camera and the wavelength of the signal with which the video was transmitted, but these effects would probably be negligible for this speed.
A: I don't know the specifics, but I do know that:
a) the feed would be red-shifted due to the Doppler effect, comparative to a firetruck's wail decreasing in pitch as it drives away, and 
b) the feed would slow down incrementally due to time dilation, moving at high speed.  This would become more severe as it entered gravitational fields also.
