Ok, here we go again... Sorry for the crude graphics, but it's much fasterthis way than fiddling with graphing applications.
To illustrate my, point, the one and only thing that can move a rocket (or any other thing) upwards is a FORCE exerted in the same direction as the desired movement. That's physics 101.
As we're dealing with gases, the one and only way a gas can exert a force upon a solid body is by means of PRESSURE. We're not absolutely concerned about action-reaction and such niceties, because we don't need to know how much and how fast the gas is ejected. That is just a nice-to-know datum, but what we want is just to have the maximum possible force applied to our dear rocket. Right?
So, as we see in the graphic, the most important thing is to build a huge pressure in the combustion chamber. Being it a closed recipient except for one end (where the gases exit), assuming a more or less homogeneous pressure, the horizontal components of the force neutralize themselves leaving only the vertical component, that would be dependent upon the throat's surface, as only in this part of the chamber pressure is zero or near zero.
The same would happen also for the nozzle, but forces there would be much less, as it is the pressure.
Now, the problem is whether it's possible to maintain such pressure in the combustion chamber in a vacuum, or the gases would be effectively 'sucked' out of it as soon as they're generated. And no pressure, no thrust! It's that simple.
I've looked at the purported parameters of a 'real' rocket engine as the Merlin 1C:
https://en.wikipedia.org/wiki/Merlin_(r ... #Merlin_1C
This thing is supposedly capable of generating 480 kN of thrust, roughly 48 tons of weight. To make an idea of it, that's enough to lift three 15 ton fully loaded articulated trucks. Yet, I cannot see any massive attachment fixtures capable of sustaining such a force and transmit it to the rocket's structure. Another issue is that most of the force is applied to the combustion chamber, which de facto would be 'pulling' from the inside.
Also, the purported pressure inside the combustion chamber is 6.7 MPa. So if we want to have a forward thrust of 480 kN, we need a 'zero pressure' area in the bottom of the chamber of 0.07 sq. meters, what tells us that the throat should have a radius of 0,011m, or 11 cm, which more or less could match the photo.
Now, all what rests is to find out whether such pressure in the chamber can be maintained in vacuum conditions. In fact, that would be a near-perfect implementation of the Joule-Thompson box experiment!
As a corollary, it's quite funny that all discussions verse about the 3rd law, the gas exit speed and so on, which are absolutely irrelevant points.