Lehpron: Momentum; I do believe that I may have forgotten the definition of which. What was it again, mass times velocity? Force per unit time? Isn't that an impulse, like a burst or a pulsed detonation? Technically in any of those four scenarios, momentum should be conserved.
, that is, you´re introducing a force
(with a rocket, by means of a chemical/thermic reaction).
Conservation of momentum is based on a force-less situation.
Lehpron: LAMO! Are you freaking kidding me? Dude, if you've got thrust leaving slower than it came in, that sounds like a drag engine. You're not accelerating, you're DEaccelerating!
No, actually not.
Your problem is that you´re thinking from the external
reference system. But what´s happening is that in "throwing the first ball" you´re exerting a force coming from chemical energy (converted in your arm muscles) to accelerate the whole vehicle, including the unburnt fuel / balls that haven´t been thrown yet
When you´re picking up the next ball, it is already moving along with the vehicle from the first acceleration (very slowly
And when you´re throwing it backwards, you´re converting more chemical energy into an impulse to the vehicle (and to the ball you´ve thrown, that´s where action/reaction comes in). You´ll have no more energy or no more balls to throw, at some point, but as long as you´ve got some of both left, you can accelerate indefinitely
The trick is that you´re pumping some of the energy from your muscles into the forward momentum by pushing the "exhaust mass" backwards. None of those factors has any dependency on how fast you´re already going relative to the ground
- it only depends on:
a) how much mass
you´re throwing (the mass flow rate)
b) the acceleration
of that mass
That´s why you can have the same effect by accelerating a large mass
at a slower rate
or a smaller mass
at a higher rate
to achieve the same net effect... basically what a rocket engine
distinguishes from an ion engine
. The rocket engine uses its fuel for both energy source and exhaust mass, the ion engine uses electrical energy from solar cells (thereby eliminating the need to carry the energy source with it) and very small amounts of a chemically inert, ionized gas as exhaust mass (the only really exhaustable resource).
Both could get you to any speed if there was only enough energy and mass (and no drag or relativistic effects). The only reference system is the ship; The earth´s reference system (ideally) just doesn´t come into the equation any more when you´re moving through the vacuum of space. (close to the planet, you´ll still have drag and gravitation to overcome, of course.)
The only relevant factor is the impulse
generated by the acceleration of mass. The relative speeds
are basically irrelevant
Aircraft engines, by contrast, constantly interact with the earth´s inertial reference system because they´re hitting the air (drag) and using it for mass flow (different here, because the air is standing still, not moving along with the plane), injecting more mass and the energy through the chemical fuel (which at least moves at the speed of the plane, already, although that doesn´t make a big difference here due to the massive amount of drag, by comparison).
[Edited 2004-02-24 22:28:00]