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

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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
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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:

[tex]f_{observed} = f_{source}\sqrt{\frac{1 + v/c} {1 - v/c}}[/tex]

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

[tex]f_{observed} = 4.36 f_{source}[/tex]

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.
 
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Exactly what I thought, thanks.
 
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ghwellsjr
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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.
Yes, it would be like watching a video sped up except that everything would be horribly blue shifted so you couldn't actually see what currently is visible to the naked eye. But you could have some sort of electronic telescope with a monitor that could detect the images and put them in the visible range.

Now as you're traveling toward this planet, presumably orbiting another distant star, at near light speed, you will see it age as it existed X years ago up to the present time during the first half of your trip and then during the second half of your trip you will see it age another X years into the future, as defined by the common rest frame between you and the planet before you started your trip. If you go fast enough, you would only age a little bit. Take your pick, however long you want the trip to last, there is a speed that will get you there in that amount of time.
 

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