# You approach a planet at a velocity near c, what do you see?

## Main Question or Discussion Point

I think about this every time I look up at the stars and think about the fact that what we're seeing is the sky as it existed X years ago, depending on how far away the star is. So let's say we're traveling toward a planet at near light speed, do you watch it age at a rate relative to the time dilation you are experiencing? I can't help but think it would be like watching a video of a planet sped up.

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jtbell
Mentor
So let's say we're traveling toward a planet at near light speed, do you watch it age at a rate relative to the time dilation you are experiencing?
If you literally mean "watch" as in "watch through a telescope", what you would see is determined by the relativistic Doppler effect. In terms of frequency:

$$f_{observed} = f_{source}\sqrt{\frac{1 + v/c} {1 - v/c}}$$

If you are approaching the planet at v = 0.9c, then

$$f_{observed} = 4.36 f_{source}$$

So if you were to watch a clock on the planet, through your telescope, you would see it as running 4.36 times faster than your own clock.

If you were traveling away from the planet at the same speed, you would see that clock as running at a rate 1/4.36 = 0.229 of your own clock.

Exactly what I thought, thanks.

ghwellsjr