I notice you still avoid my very simple question like the plauge:
What force is acting on the gas to accelerate it out of the back of the rocket and what is the second body involved in this?
Without some force, the gas needs to remain inside the rocket.
As you will notice, I am not even mentioning the question of vacuum - only of ever-decreasing air pressure with increasing altitudes - something I trust we can all agree about.
And you extrapolate based upon what?
You also need to focus on a vacuum, because you can't drop the pressure below 0.
The main driving force in the under-expanded regime is the pressure differential between the exhaust gas and the ambient environment.
If your exhaust gas is at 100 bar, and the ambient environment is 1 bar, that is a 99 bar driving force.
However if your exhaust gas is at 1 bar and the ambient environment is a perfect vacuum it is only a 1 bar driving force.
I also notice that this image source you use has no mention of NASA at all, so how did you determine what NASA says?
It is called under-expansion because the rocket exhaust has not yet fully expanded by the time it leaves the nozzle.
So under expansion is appropriate.
The reasons the altitudes are unspecified is because they vary depending upon the nozzle.
So in order to say very high altitudes will be a problem, you need to know what altitude the nozzle was made for, and what the effect of the pressure differential will be.
As such, your extrapolation is completely baseless.
And again, you keep jumping between so many different topics.
Are you really that incapable of defending your claims in one particular area?
Well, consider this: no honest scientists will deny that, when opening a valve between two containers (one containing air at high pressure - and the other only vacuum) the pressures in the two containers will equalize in a fraction of a second, the vacuum container 'sucking' the air to itself with tremendous, almost explosive force. (see the above density figures to understand why.)
Stop lying. No honest scientist would ever say that.
Many pressure control systems are based upon opening up valves for a fraction of a second or even longer and allowing some gas to transfer between the 2 containers.
One of the simplest regulators is a spring loaded valve where the force on the spring determines what pressure differential is required to push open the valve, which will then allow some gas through until the pressure differential drops below a critical level and the valve closes.
If what you are saying was true all our pressure based system would be completely useless.
The speed at which it will equalise depend on a multitude of factors, with keys ones being the pressure differential, the connection between the 2, and the amount of gas that needs to flow.
If you have a very large amount of gas that needs to flow through a small opening, with a small pressure differential it will take quite some time.
Imagine now the high pressure emitted by any rocket from its (always open) nozzle. As it enters the vacuum of outer space, the very same - almost explosively rapid - pressure equalization is bound to occur.
Sure "explosively rapid", with the rocket being pushed away by this explosion.
I'm afraid I'll have to cite Newton's Third Law once again.
No, that is what we have been citing repeatedly and you have been ignoring/avoiding repeatedly.
Newton's third law demands that either rockets work in a vacuum or that you can magically contain gas in a container, even with an opening in the container.
Perhaps Newton's third law should have specified (and highlighted the importance of) the relative masses of the two bodies involved. The bodies need to be of equal mass in order for the "equal in magnitude" part of this law to be true.
Pure BS.
The relative masses of the 2 bodies are irrelevant when it comes to Newton's third law.
The forces need to be equal in magnitude and opposite in direction or magically generate forces from nothing.
The mass is important in Newton's second law, F=ma.
The acceleration due to the force will depend upon the mass, and you can write it like this:
a1*m1=-a2*m2.
So if you have a large object and a small object, then the small object will be accelerated a lot while the large object does not accelerate significantly.
This is used with bullets and with rockets.
The bullet and rocket exhaust exist at very high velocities.
But lets focus on the mass shall we?
The rocket used for the Moon was a Saturn V.
It's first stage has a total mass of 2 290 000 kg.
But only 130 000 kg of that was the empty mass, that leaves 2 160 000 kg of fuel.
The total mass of the Saturn V was roughly 3 000 000 kg.
That means over 2/3 rds of that was used in the 1st stage as fuel, being shot out the back at a very high velocity.
So the comparison to a gun firing a bullet is somewhat inaccurate, as the majority of the mass is in the fuel.
To attain the so-called escape velocity of 8km/s with "recoil power" only, this is what NASA's rockets would have to do: they'd have to shoot out from behind their rockets, all at once (like a bullet from a gun) a mass equal to the mass of the vessel itself - at a velocity of 8km/s.
Please note that I have respectfully observed Newton's Third Law in my above diagram.
While you observed Newton's third law in your diagram, the argument completely rejects it.
That argument only applies if they want to actually have it reach that velocity all at once, which would kill everyone inside.
Instead, what they want to do is have it reach the required velocity over a period of time.
All that requires is providing enough force to overcome gravity and start accelerating the rocket, with that force acting for long enough to achieve the required velocity.
In order to Newton's third law you would need to accept that the gas leaving the rocket needs to accelerate the rocket.
It is interesting to note that ... was a space travel skeptic
No it isn't.
Did he provide any basis for his claim?
No.
Was he a rocket scientist?
No.
Why should what he thinks be interesting to the discussion at all?
He provided no rational argument to back up his claim. Instead all he did was dismiss it.
Without reading 9 pages of the same thing over and over, have we gotten to the "springboard" physics lesson yet?
No, that's skepti.