Where does the momentum exchange happen in a rocket. Is it in the combustion chamber alone?
Consider the rocket and its fuel as single system .Now ,initially this system has 0 momentum When the fuel is burnt ,the rocket's nozzle is setup in this way so that the pressure of gas formed due to burning fuel is released in downward direction.But as we know initially it has 0 momentum ,so according to the law of conservation of momentum if gasses produced are moving downward the rocket should get the same momentum but in upward direction.That's why rocket moves in upward direction in space also.From here you can conclude that if gasses are pushed downward than rocket should be pushed upward so the net force on system remain 0 or the third law is followed(action-gasses pushed downward reaction-rocked pushed upwards.)
How does a rocket push on its exhaust and how does the exhaust push back on the rocket?
Actually, it is not the rocket that starts to push. It is the fuel. Simply outlined:
When the fuel in the fuel chamber ignites and burns, it expands due to the creation of reaction product gasses that fill more volume than the initial fuel. This expansion will push on everything around it - the pressure increases enormously. It pushes on the walls. If there is an opening - an exhaust valve or nozzle - the gas will escape through there by pushing on the opposite wall. Thereby the rocket gets a forward push. A thrust.
Also, why is the upward motion of a rocket linked to Newtons third law?
The force applied on the rocket is also felt by the fuel. This is Newton's 3rd. Fuel moves one way (out through the exhaust nozzle as combustion gasses) and the rocket moves the opposite way, since they both feel the same both opposite force.
$\begingroup$ It's the exhaust or combustion products that do the pushing. The pushing does not occur with any significance on the walls. The pushing is done in the nozzle. That's what they are for. $\endgroup$ Dec 4, 2018 at 12:01
$\begingroup$ @Steeven: thanks a lot, but in all the pictures I've seen the action is downwards and the reaction upwards. I mean the action is exerted by the rocket on the gases and as a reaction the gasses push the rocket upwards, so this still confuses me. $\endgroup$– TaofeekDec 4, 2018 at 12:08
$\begingroup$ @garyp: if the pushing only comes from the nozzle, then what about the thrust due to the imbalance of forces in the combustion chamber? $\endgroup$– TaofeekDec 4, 2018 at 12:23
1$\begingroup$ @garyp You are coorect that the nozzle is an important part of a real-world high performance rocket. However, there is nothing incorrect about Steeven's answer. The nozzle is a design detail that is used to maximise the force in the desired direction (there are rockets without nozzles...). $\endgroup$ Dec 4, 2018 at 12:51
$\begingroup$ @garyp As Oscar mentions, it doesn't really make sense to talk about the nozzle alone. An exploding blob of fuel underneath any object will propel it upwards. The rocket design, including nozzle, controls and maximizes, the utilized upwards thrust, and is therefor important to get any useful thrust, sure. I did not see that relevant in this answer. $\endgroup$– SteevenDec 4, 2018 at 14:21
When combustion of the fuel within the fuel tank occurs, exhaust gas is produced, and the particles of the exhaust gas move very quickly and collide frequently with the walls, leading to high pressure. Thus, when they exit the open end of the engine, they are at high velocities. Hence, due to the high pressure, an immense amount of force is exerted by the rocket, backwards.
Newton's third law states that for every action force, there will be a resultant reaction force acting in the opposite direction. Hence, the rocket would be propelled upwards in the opposite direction as the force exerted by the rocket.
Conservation of momentum (COM) can also be used to explain this phenomenon, but ultimately it boils down to Newton's third law because theory of COM is derived from Newton's third law.
$\begingroup$ One clarification. The momentum transfer occurs in the nozzle, not the walls of the fuel tank or combustion chamber. $\endgroup$ Dec 4, 2018 at 11:51
$\begingroup$ Yes, that's what I meant. $\endgroup$ Dec 4, 2018 at 11:52
$\begingroup$ The force of the gasses on the ground play no role at all. The reaction force of the Earth is completely irrelevant. Don't forget that rockets work perfectly well in the vast emptiness of outer space. $\endgroup$ Dec 4, 2018 at 11:56
$\begingroup$ What I meant was the backwards force. Sorry for the error there. $\endgroup$ Dec 4, 2018 at 11:59