# Perceiving near c speeds from a great distance

1. Dec 13, 2012

### jam.muskopf

When we look at stars that are far away from earth, they appear to be still in the sky. However, these stars are probably moving at very high velocities relative to earth; we are just so far away that they appear to be still.
What if there was a star that was very, very far away, but it was very bright, so we could see it just fine, and this star was moving .9999999c in the earth's frame of reference. However, the distance from the star is so great that appears to be moving rather slowly to people on earth. Is this situation possible? It seems to me that there should be some sort of problem with perceiving the fastest possible velocities as slow if you look at them from far away. Am I thinking about this incorrectly, or is there some sort of special relativity implication that changes this situation?

Thanks

2. Dec 13, 2012

### K^2

With the naked eye, we only see stars that are within a few hundred light years. If it was going at c, we'd notice it actually move in the sky over a few years. The only exception would be if it is heading straight for us, in which case, the Doppler shift would make it very much obvious that the star is going that fast.

Going to stars only visible in telescope, it doesn't change much. The star would still have to be in our galaxy, so that's maybe 10-20 thousand light years. That's still close enough to detect such rapid motion.

So no. None of the stars we know about could possibly be going that fast.

3. Dec 14, 2012

### PAllen

Following on K^2's observation, at 20,000 light years, lateral motion at near c would manifest as a change in position of about 65 arcseconds per year. That would be an enormously visible change (I think even milliarcseconds per year would be detectible). Then, as noted, if most of the motion was towards or away, the Doppler would be a dead giveaway.

A quick search turns up that 65 arcseconds per year is 6 times the largest angular speed observed for any star; and that largest angular speed is for Barnard's star (6 ly away), the second closest star to the sun.