It turns out that any light measured under any circumstances always travels at the same speed relative to any observer. That's what Einstein meant when he said the speed of light is constant.
If you are in a ship moving at high speed and you shine a light along the direction of movement, no matter how you measure it your measurement will show that the light is moving away from your source at the speed of light ?.
If you are outside the ship and at rest with respect to the ship and you somehow measure the speed of that guy's flashlight beam, no matter how you measure it your measurements will also show the beam to be moving at the speed of light?. How to reconcile these two facts?
Lets forget that c is constant and just talk about the measurements taken of the speed of this beam of light.
If you are the guy inside the ship, you measure the speed of the beam to be, let's say, m.
If you are the guy at rest outside the ship but looking in the window, you would expect your measurement to be the speed of the beam plus the speed of the ship carrying the beam, but when you make your measurement, you find that you also measure the speed of the beam of light to be m.
Later you talk to the astronaut after he has returned, and say something like \"I measured the speed of your beam to be m, since to me, m is the speed of the beam plus the speed of your ship, then the measurement you took must be quite a bit less than m, correct?\" To which he replies \"You are a liar, sir. My measurement was m, your's must have been greater than mine, that is your measurement had to be m plus whatever my ship's speed was.\"
Let the speed of the ship = s and c = speed of light. Then you would expect your measurement to be the astronaut's measurement (m) plus the ship speed (s). Instead, your measurement is m, much slower than m+s.
Speed is measured in units of distance divided by time (d/t). Since the speed (d/t) you measured is less than it should be, the only way to account for this is that either d has decreased (constriction of length) or t has increased (dilation of time). In fact, it has been proven experimentally that both of these outlandish things happen at any speed. It's just that they aren't very noticeable until you get to speeds which are at least a fair percentage of c.
If you are the voyeur looking in on the astronaut's light experiment, if you look at his clock you will see (part of) the reason his measurement of his light beam is the same as yours. His clock will appear to be running slowly to you, which is why you measured his light beam going slower than you expected(traveling at speed m instead of speed m+s as you would expect.)
Exact amounts of length constriction and time dilation for any given speeds can be easily calculated from Einstein's field equations. Google that for more info.
or in a loop line 
Actually, I believe your mass continues to increase thus requiring more and more energy to achieve greater speed. Unlimited fuel does not necessarily give you unlimited increased thrust. Maybe somebody here with more physics can shed some light on this.
