Xyius said:
If there is little to no drag in space, what is stopping us from just continuously accelerating and reaching speeds close to the speed of light? Shouldn't we just be able to just keep going faster and faster?
Let's go over these one by one.
1. There is little to no drag in space.
This is not true at relativistic velocities. Interstellar space, and even intergalactic space is not utterly void of substance. Drag due to the interstellar material is very, very small at the kinds of velocities our spacecraft have attained to date. Due to relativistic concerns, drag becomes a very significant issue at very high velocities relative to the interstellar medium.
2. What is stopping us from just continuously accelerating ...
The only way we know how to do that now is to carry the fuel needed for that acceleration with the vehicle. For now, I'll ignore relativistic concerns. Let's look at a rocket that burns all of its fuel. When all the fuel is spent the rocket continues on at a constant velocity (ignoring drag, of course). Suppose we want to make that final velocity a tiny bit faster. That means that we now have to have a tiny bit more fuel left than we would have when the rocket previously had burnt all its fuel. However, that tiny bit of extra fuel now needs to be accelerated along with the rocket. You need extra fuel to make that happen. Taking this all the way back down to the ground, a whole lot more fuel is needed at launch to make the rocket end up with a slight increase in final velocity. This is described mathematically by the ideal rocket equation. If you want to go a whole lot faster you will need a bigger fuel tank. You need to accelerate this, too. Eventually you will get to the point where you need a bigger rocket -- and you need to accelerate that as well! The ideal rocket equation places severe restrictions on how fast we can practically go, and this is without even addressing relativistic concerns.
3. ... and reaching speeds close to the speed of light?
Nasty as the ideal rocket equation is, the relativistic version of it, the relativistic rocket equation, is much, much worse. One of the key parameters in the ideal rocket equation is the velocity of the exhaust relative to the vehicle. The best that can be possibly be achieved is to have the exhaust be in the form of photons. Suppose some futuristic rocket is equipped with a photon drive. We want to use this rocket to travel to some target star. The rocket is to accelerate at 1g proper acceleration until it reaches the half-way point and then decelerate at 1g until it finally comes to a rest at the target star. To go to the nearest star (4.3 light years away), the rocket will "only" need to carry 38 kilograms of fuel for each kilogram of payload (rocket+fuel tanks+people+life support+...). To go to a star 27 light years away, that factor of 38 balloons to a factor of 886. To go to the center of the galaxy, the factor of 38 becomes 955 million.
To add insult to injury, these calculations ignore drag due to the interstellar medium.
