I often hear it said that if you want to accelerate, say, a spaceship the faster it goes the more mass you have to "throw out the back" in order to sustain the same acceleration.

Is that correct?

This is what I don't understand: as you accelerate, so does your fuel, so surely it gains the exact energy that is needed to be thrown out the back. ie. your fuel is at rest relative to you, as is your spaceship. So why do fuel needs increase?

I can understand why you would need more and more energy if you were accelerating a particle in a particle accelerator. The mass of the particle increases from our perspective thus it needs more of a "kick" to be accelerated than at lower velocities.

What am I missing?

I'm a layman (as you have probably already guessed) so my question may seem naïve, but if you must lambast me for that, at least teach me at the same time. :)

kind regards
Paul

The only thing special relativity says is that the mass is corrected to

m = m₀ / <font face="symbol">g</font>.

Newton's laws are just corrected by this factor.

F = (m₀ / <font face="symbol">g</font>) a

In the frame of the spaceship: Everything looks the same at all velocities. You don't measure any mass increase. Your rockets burn at the same thrust, producing the same force, and you measure a larger and larger velocity relative to distant stars. In the limit as you approach c, you will measure yourself as moving at an infinite speed; it takes zero time, by your watch, to get anywhere in the universe. This means that, from your point of view, you can accelerate forever. F = ma seems to be correct, and in fact is correct. It doesn't take any more fuel to accelerate what you, on the ship's helm, would measure as an equal acceleration.

In the frame of a "stationary" observer: You see the ship approaching a relative speed near that of light. You see the ship becoming more massive, and F = (m₀/<font face="symbol">g</font>)a seems to hold. The ship, with its rockets running at a constant thrust, seems to be accelerating less and less.

So your idea that "you have to throw more out the back in order to sustain the same acceleration" mixes reference frames. From the perspective of the captain of the spaceship, equal forces always result in equal accelerations, just as Newton said.

If, however, you want to make yourself appear to an outside observer as having a constant acceleration, you would indeed have to continue to throttle your rockets up. Eventually, you'd have to throttle them to infinite thrust.

- Warren

Warren,
once again you supply the answer and this time I must bow to your better knowledge. Now I understand what I am missing here.

I thought, as you said, that the laws of physics hold in all reference frames which is why I couldn't understand why you would need to throw more and more mass out the back of the spaceship and how it fit in - it doesn't. It's an incorrect statement in the first place.

Thank you.

kind regards
Paul