Light: Speed and Sight Dilemma

[Zencapop]

Ok,

Here is a problem that I have been thinking about. Let me know what you guys think its going to look like.

For this problem, we assume that faster than light speed travel is possible and that we have a telescope that can see a spaceship 1 light year away.

Imagine that a spaceship comes and docks 1 light-year away from Earth. It stays there for about 5 minutes, and then travels at 2 times the speed of light, reaching Earth in 6 months. It then stays docked on Earth for 6 more months.

My question is, what will the journey look like from Earth? It should be strange because the light from the ship when it initially docked would reach Earth 1 year later. But the ship would already be on Earth after 6 months. After a year, will we see two ships for five minutes, one docked on Earth and one docked 1 light year away? What will the movement of the ship look like after a year, as it would have started moving then, at least the movement from its light would start reaching us. But, the ship would have already started becoming visible much earlier, as it was traveling towards us.

Its mind boggling, isn't it?

 

[Lsos]

You would not be able to see the ship until it got here, because it would be outrunning its own light. Just go to an airshow and see what happens when an airplane travels close to the speed of sound. You can't hear it until it's right on top of you.

So it's kind of easy to imagine...except for the fact that it's impossible.

 

[Zencapop]

I don't agree with Lsos' answer. Even if it will be outrunning its own light, light from it 1 year ago will reach us today. This will show two ships, one docked 1 light year away and one docked on Earth for the past 6 months.

 

[diazona]

But the ship was not docked one year ago, it was docked 6 months ago. You're right that light from the ship 1 year ago would reach us today, if the ship were 1 light-year away at that time. But it wasn't.

What would actually happen (if you take what is probably the simplest option for how you break the rules to allow FTL travel) is that, as Lsos said, you wouldn't see the ship until it arrived at Earth. From that moment, you would see two images of the ship, one docked on Earth and one that appeared to be traveling backwards away from you toward the space station. After (6 months-5 minutes), you would see yet another image of the ship appear docked at the space station, and that image would persist for 5 minutes. At the end of the 5 minutes, the backward-moving image would "merge" with the space-station-docked image and they would both disappear, leaving only the one image of the ship docked on Earth.

Here's a spacetime diagram that demonstrates how it works. Time is on the vertical axis and space is on the horizontal axis. The red line is the path of the ship and the blue and green lines are the paths of light rays.