Nice question- one that lotís of people worry about when they first hear about rockets.
Itís not hard to explain on the basis of Newtonís 3d law: conservation of momentum.
Letís say that the rocket spits out the ions at some fixed speed (in the tail direction) with respect to itself. That makes sense because the rocket doesnít care at what speed some planet is going by- this is a matter between the rocket and its ions. Now those ions had been travelling along with the rocket, with some momentum (according to us). When they leave the rocket they are either moving backwards or at least not as fast forward, depending on how fast the rocket is going. Where did their lost momentum go? It has to go to the rest of the rocket, so that must speed up.
The key point is that even if the emitted ions are still going forward (in our frame) they arenít going forward as fast as they had been, so the rocket has to gain momentum when they leave.
If the rocketís speed with respect to us starts to get near the speed of light, c, the same argument still works but part of how the rocket gains momentum will be by picking up inertial mass rather than just by speeding up. Thatís what will keep the rocket from ever reaching c itself.
(published on 10/22/2007)