# Communication with a Relativistic Rocket

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#### Ishimura_

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A spacecraft is travelling at 0.99c away from the Earth and ground control on earth wants to communicate with the spacecraft, so they send a signal. When the signal reaches the craft would the gamma difference cause the ground control speech to be faster by a factor of gamma? More generally, would there be any technical issues with communication to and from the relativistic spacecraft (e.g. - would the speech need to be sped up or slowed down by a computer prior to sending)?

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#### theridane

##### Guest
Yes, it would. It's an amusing idea to think about they would have to slow it down about 7 times to get it back into sync.

On top of that they would have to deal with a redshift of the wavelength - at ship travelling at 0.99c away from the sender would perceive a 434 MHz radio carrier as 30 MHz - which means that not only would they need to pack a wide-band radio system (basically covering the whole spectrum from their nominal frequency downwards), but also use significantly reduced baud rates (30 MHz gets you a lower bitrate than 434 MHz).

If you think about it, these two problems sort of solve each other - as the ship accelerates, the frequency goes down, which means the ground needs to send data slower in order to fit into the decreasing bandwidth. But that's a good thing, since the ship needs to slow it down anyway.

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#### Ishimura_

##### Guest
Thanks for the answer, similar to what I thought, but I hadn't thought about the redshift. I intuitively figured it would be like playing a record on the wrong speed :-D

Another question. If the rocket receeds from Earth at 0.99c and the signal is traveling at c. Does the signal take 100 times longer to reach the rocket than if the rocket were stationary? I ask because from the perspective of the rocket, it would measure the speed of the signal to Earth at c, and Earth would measure the speed of its signal at c, but the rocket is moving relative to the Earth. So how long would it take a signal to reach the rocket? To reach the Earth?

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#### theridane

##### Guest
From Earth's point of view, it would work pretty much like in Newtonian physics (so it would take 100 times longer).

(I'm not 100% sure about the following)
From the rocket's POV though, the universe around it would appear contracted. From their point of view the photon would fly at c, but it would travel through a much shorter distance to reach them.

Another way of looking at things is using time - the photon is travelling at c, but since the outside clock ticks 7x faster, a photon covers 7 light-seconds during a single "onboard" second (this is why lengths contract).

Mhh... I'm getting lost in this. :shock: requesting assistance :lol:

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#### emperor_of_localgroup

##### Guest
Ishimura_":1a7dimvg said:
A spacecraft is travelling at 0.99c away from the Earth and ground control on earth wants to communicate with the spacecraft, so they send a signal. When the signal reaches the craft would the gamma difference cause the ground control speech to be faster by a factor of gamma? More generally, would there be any technical issues with communication to and from the relativistic spacecraft (e.g. - would the speech need to be sped up or slowed down by a computer prior to sending)?

Interesting problem. I have crunched some numbers from earth point of view.

1) If a signal is sent from earth 1 day after departure, the signal will be received 10 days later. If the signal is sent 1 year later, the signal will reach the space-craft 10 years later.

2) If signal is sent at 1MHz (1 Mega bits/sec) rate from earth, the time difference between arrival of the first bit and the second bit would be 10micro sec (instaed of 1 micro sec). In other words, the craft will take 10 sec to completely receive a 1 sec long signal from earth.

I haven't done the math for what happens when the space-craft sends a signal to earth. I'll try next.

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