# Relative increase in fuel mass

1. Sep 28, 2011

### schonovic

if a rocketship in space is approaching the speed of light and its relative mass is increasing then i assume the fuel mass is increasing which would make it more potent the closer the ship gets to the speed of light which would give it infinite force when the ship reaches the speed of light. what happens to prevent this from being true?

2. Sep 28, 2011

### Naty1

The simple answer from the external frame of reference you imply:

As the mass of the fuel, and the rocketship itself, approaches an arbitrarily large value, so too does the force (or energy) required to accelerate it.

Wikipedia explains related aspects:

.." As seen from the center of momentum frame, the relativistic mass is also the invariant mass.....For other frames, the relativistic mass ...... includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the center of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. ..."

http://en.wikipedia.org/wiki/Relativistic_mass

3. Sep 28, 2011

### Staff: Mentor

The relativistic mass of a rocket always decreases, never increases. This is for the same reason that the non-relativistic mass of a non-relativistic rocket always decreases: you are spewing lots of mass off the back end. That effect is always greater than the relativistic mass effect.

Also, the quantity of interest is not the force, but the impulse. You can make an arbitrarily high force by reducing the duration of your burn, but that doesn't change the impulse. If you work out the math, the impulse available from the remaining fuel is always strictly decreasing and always finite.

4. Sep 28, 2011

### ?????

If you are in a stationary reference frame and watching the ship accelerate, then the mass of fuel on board the ship increases relativistically as the ship goes faster. If you are on board the ship, the fuel mass stays the same as it always was (not counting the mass that's expelled out the rocket engine), being the same density as if the ship had no velocity.