# How would be tv reception in a spaceship travelling close to speed of light?

My little brother has made me a tough question (specially for a computer science engineer).

Imagine that there is a spaceship orbiting earth close at nearly speed of light (say 99%). Someone in earth transmits a tv signal to spaceship.

What will the astronauts see in their television?

• Nothing?
• Accelerated version of what was recorded? (My best guess)
• Normal speed of what was recorded long time ago?

## 1 Answer

Relativistic motion in a circle is a surprisingly subtle problem to treat. You might want to have a look at Distance in relativistic circular motion in invariant spacetime, which addresses a related problem. That answer contains a link to a paper that goes into the problem in more detail.

The end result is that the observer on the Earth sees time moving slowly for the astronaut, while the astronaut sees time moving fast for the people on Earth. The factor by which time runs fast or slow is $\gamma$ where:

$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

The factor $\gamma$ is greater than 1 for any non-zero velocity $v$ and it tends to infinity as $v$ tends to the speed of light. So if the Earth broadcasts a programme lasting 1 hour the spaceship will receive the whole broadcast in 1/$\gamma$ hours so the programme will appear to the astronauts to be speeded up.

NB the TV transmission from the Earth would be blue shifted, so a normal TV couldn't receive it. However I'm assuming the astronaut's TV is sophisticated enough to receive the changed frequency and cope with the timing changes needed to decode the picture.

• "Relativistic mass" isn't a concept that's used much these days because it can be very misleading. For example students tend to think if the mass increases the gravitation field of the object should increase and it should ultimately turn into a black hole. See for example physics.stackexchange.com/questions/28422. – John Rennie Aug 23 '12 at 14:46