If we get a rocket into space with an extremely large fuel supply, will it be possible to get its velocity to the speed of light or more?
Answers
The quick answer is that it would require an almost infinite amount of fuel and take an almost infinite amount of time, to get almost infinitely close to the speed of light.
Let’s look at it, though. When you say “fuel” you are talking about impulse engines, the standard rocket where you throw out a gas molecule behind you at a fast speed, and gain a little forward velocity because of Newton’s first law.
The heavier the rocket, the less kick that gas molecule gives you. Fuel has mass. So, when you say “if you had enough fuel” you are saying, “if you start with a very massive rocket”. The more fuel you take, the less speed you will get by burning a gram of fuel. The fact that you are taking so much fuel is acting against you as you try to gain speed.
When you get to high speed, relativity comes into play. Your ship’s mass is increasing because the ship is getting faster. Yes, you are throwing off fuel, but what remains is more massive than it used to be because the mass of an object depends on its velocity (as measured by an observer looking at it from “outside”).
Another way of looking at it is that since kinetic energy has an “m” in the formula, and mass approaches infinity as the object gets close to the speed of light, the energy required to give the rocket that almost speed of light speed you mentioned in your question is itself almost infinite.
Better is to bounce external objects, like the photons in a strong laser beam, off a very light rocket to accelerate it. Of course, the farther from earth your little rocket gets, fewer photons from the massive laser back at the starting point will hit it. And, thanks to relativity again, your ship is getting more massive. Too bad!