What is rocket propulsion?

Question

how rockets work at great heights where no air are present

Answer 1

I almost agree with Alcari's answer, but please do be careful. This isn't a phenomenon of energy - it's a bit unsafe talking about energy in terms of rocket propulsion because we're not dealing with a closed system, and because of that energy isn't really conserved.

A simple counterexample would work:

Consider a 1kg object and a 2kg object that a resting together. By conservation of momentum, if the 1kg object is given a speed of 2m/s in one direction, the 2kg object should gain a speed of 1m/s in the other direction. However, this means that 2kg object now has kinetic energy of 1 joule and the 1kg object now has a kinetic energy of 2 joules. Obviously, energy wasn't conserved. Be careful, because energy is almost NEVER conserved in collisions.

That being said, yes this is a consequence of Newton's Third law and the conservation of momentum. If a rocket pushes fuel out the back, then that same fuel must exert a force against the rocket, thus pushing the rocket forwards. The best way to look at the situation is that momentum must be conserved - the "backwards" momentum of the ejected fuel must be accounted for by a gain of "forwards" momentum of the rocket ship.

The interesting part about this is that as the rocket ejects more and more fuel, it becomes lighter and lighter, and so the most distinct point about rocket propulsion is that the rocket itself has a nonconstant mass. If you think about it qualitatively, what makes rocket propulsion then so efficient is that as the rocket becomes lighter, it also gains speed more easily because the same force on a lighter object causes a heavier acceleration (from a momentum standpoint, a lighter object has a smaller momentum for every velocity, and so conservation of momentum tells us that the rocket must speed up more quickly to compensate for its lighter mass).

You could work all this out mathematically from F=ma and conservation of momentum, but it requires some light calculus, and the result isn't really that insightful since you've already thought about everything qualitatively (the answer involves logarithms). In any case, I hope this helped clear everything up. Alcari was pretty much on point with her answer, but there were a few key discrepancies that you really need to take into account.

Answer 2

Rockets work on the principle that "Every action has an equal and opposite reaction"

As the rocket fuel burns, it expands and thrust out of the exhaust.

The energy it takes to thrust out of the exhaust (or nozzle) is the same ammount of energy that is pushing the rocket forward.

Imagine taking a heavy ball and throwing it away. As you throw it, you feel the ball pushing against you as well. The ammount of force you use to push the ball away also pushes against you.

A rocket works the same way, by pushing out exhaust, the exhaust also pushes against the rocket, moving it.

EDIT: to respond to JC below:

You said: "Consider a 1kg object and a 2kg object that a resting together. By conservation of momentum, if the 1kg object is given a speed of 2m/s in one direction, the 2kg object should gain a speed of 1m/s in the other direction. However, this means that 2kg object now has kinetic energy of 1 joule and the 1kg object now has a kinetic energy of 2 joules. Obviously, energy wasn't conserved. "

Actually, kinetic energy is 1/2*M*v^2.

Meaning a 1 kilo object that travels at 2m/s has 2 joules of energy, which would move the 2 kilo object as 1.41 m/s, making a perfect balance. Energy is ALWAYS conserved, it just goes elsewhere when things bend and flex, namely heat.

"Be careful, because energy is almost NEVER conserved in collisions."

It is in perfectly inflexible collisions, but that is completely beside the point, as we're not talking real collisions here, just a thought experiment.

A rocket that rear-facing exhaust of 100N will have a forward facing thrust of 100N. Pushing a (perfectly inflexible) object with 36N will make the object push back with 36N. It is that simple.