Suppose you're on the midpoint of a straight line 6e8 m long, which the dot traverses at uniform velocity.
If the dot moves at c, you would see nothing for 1s. Then there would be an instant where the first half of the line is entirely illuminated, as light from the dot at each point reaches you simultaneously.
After that, it would look like an ordinary dot moving away from you at c/2: if the dot moves for x seconds, it takes 2x seconds for the light from the dot at that point to reach you. (Note that a dot moving at c/2 would appear to be moving at c/3.)
If it's moving faster than light (say, kc, k>1), then when the dot arrives at you, you'd see a dot appear at your position, then move back to the original position at (k c / (k-1)), and vanish. (k/(k-1) is because you see it reach the start point 1s after it starts moving, and you first see it 1/k s after it starts moving.) If the dot had been stationary at that point before it began moving, you'd still see the dot there until the new one reached it, at which point they would both vanish.
Simultaneously, you'd see a dot move from your position to the end position at (k * c / (k+1)).
I'm not going to try to work out what happens if you're just standing near the path of the dot.
(I'm not sure about this, but it's what I get when I try to work it out. I'm especially not sure that I'm allowed to discount relativistic effects. I think I am because there are no massive bodies undergoing acceleration, but I don't pretend to fully understand relativity.)
Comments
Suppose you're on the midpoint of a straight line 6e8 m long, which the dot traverses at uniform velocity.
If the dot moves at c, you would see nothing for 1s. Then there would be an instant where the first half of the line is entirely illuminated, as light from the dot at each point reaches you simultaneously.
After that, it would look like an ordinary dot moving away from you at c/2: if the dot moves for x seconds, it takes 2x seconds for the light from the dot at that point to reach you. (Note that a dot moving at c/2 would appear to be moving at c/3.)
If it's moving faster than light (say, kc, k>1), then when the dot arrives at you, you'd see a dot appear at your position, then move back to the original position at (k c / (k-1)), and vanish. (k/(k-1) is because you see it reach the start point 1s after it starts moving, and you first see it 1/k s after it starts moving.) If the dot had been stationary at that point before it began moving, you'd still see the dot there until the new one reached it, at which point they would both vanish.
Simultaneously, you'd see a dot move from your position to the end position at (k * c / (k+1)).
I'm not going to try to work out what happens if you're just standing near the path of the dot.
(I'm not sure about this, but it's what I get when I try to work it out. I'm especially not sure that I'm allowed to discount relativistic effects. I think I am because there are no massive bodies undergoing acceleration, but I don't pretend to fully understand relativity.)