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This answer to "How fast is fuel escaping a rocket for it to reach escape velocity 11km/s?" includes the following:

From Rocket and Spacecraft Propulsion: Principles, Practice and New Developments

Rocket and Spacecraft Propulsion: Principles, Practice and New Developments

It can be seen in Figure 1.6 that the rocket can travel faster than the speed of its exhaust. This seems counter-intuitive when thinking in terms of the exhaust pushing against something. In fact, the exhaust is not pushing against anything at all, and once it has left he nozzle of the rocket engine it has no further effect on the rocket. All the action takes place inside the rocket, where a constant accelerating force is being exerted on the inner walls of the combustion chamber and the inside of the nozzle. So while the speed of the rocket depends on the magnitude of the exhaust velocity, as shown in Figure 1.6, it can itself be much greater. A stationary observer sees the rocket and its exhaust passing by, both moving in the same direction, although the rocket is moving faster than the exhaust.

original screenshot

I wrote the comment:

Your choice of quotes is excellent! "All the action takes place inside the rocket..." is the clearest most concise sentence I've read all year. This is an "Aha!" answer.

but now I'm having second thoughts about elevating the word "action" from an everyday word to its use in physics:

In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived through the principle of stationary action. Action is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensions of [energy]⋅[time] or [momentum]⋅[length], and its SI unit is joule-second. Action is only of interest when the total energy of the system is conserved.

Question: Can we say that this kind of action actually takes place inside a rocket along with the Newton's 3rd law action/reaction or "stuff that happens that's important and makes the rocket go" kind of action?

Skaters_showing_newtons_third_law Illustration of Newton's "action" Source

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    $\begingroup$ In my limited understanding, this "action" is a mathematical tool. It doesn't actually represent "something that happens" $\endgroup$
    – user20574
    Commented Oct 13, 2020 at 12:03
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    $\begingroup$ @user253751 I think you are right; I should have linked to Newton's action not Euler's. $\endgroup$
    – uhoh
    Commented Oct 13, 2020 at 12:36
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    $\begingroup$ en.wikipedia.org/wiki/Action_(physics) appears to be a somewhat different concept from Newton's usage of the same word. My understanding is that in Newton's day, "action" was the term for what we now call "force". Newton's 3rd law in modern English is For every force, there's an equal and opposite force - IDK why it's not taught that way, using the same terminology as the rest of physics instruction, except for the history-of-science aspect of what Newton actually said / wrote in barely-modern English. "Force" is less prone to lame paraphrasing using "action" as e.g. cause/effect. $\endgroup$
    – Peter Cordes
    Commented Oct 13, 2020 at 13:00
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    $\begingroup$ That doesn't answer your question about whether en.wikipedia.org/wiki/Action_(physics) might have been meant, but I don't think it was intended that way either; the technical language is in the next clause, using the word "force". $\endgroup$
    – Peter Cordes
    Commented Oct 13, 2020 at 13:02
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    $\begingroup$ The action in the answer is an informal way of saying "all forces on the rocket", not the action as defined in the stationary action principle. $\endgroup$
    – user65081
    Commented Oct 13, 2020 at 14:51

1 Answer 1

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The answer depends on where one draws the system boundary. If one draws the boundary at the exit plane from the rocket then what happens inside the rocket is irrelevant. All that matters is the effective exhaust velocity and the difference between the pressure at the exit plane and ambient pressure.

If on the other hand one one draws the boundary at the physical surfaces between solid and gas, then what happens "inside the rocket" happens at those physical surfaces. That is no longer inside the rocket from this point of view. From this point of view, the action-reaction occurs at the boundary of inside the rocket and outside the rocket.

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  • $\begingroup$ Interesting! To double check, is the exit plane defined by the end of the nozzle? Is "pressure difference" the difference between some average pressure across that plane and infinity (vacuum for example, if this is in space)? $\endgroup$
    – uhoh
    Commented Oct 13, 2020 at 23:53
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    $\begingroup$ The exit plane is defined by the end of the nozzle. The pressure difference is the between the pressure at the exit plane versus ambient pressure. The exhaust is ideally exhausted if the pressure at the exit plane is equal to the ambient pressure, underexpanded if the pressure at the exit plane exceeds ambient pressure, and overrexpanded if the pressure at the exit plane is less than ambient pressure. $\endgroup$
    – David Hammen
    Commented Oct 14, 2020 at 3:52
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    $\begingroup$ Surely the pressure difference across any plane is 0 because it's infinitely thin? $\endgroup$
    – user20574
    Commented Oct 14, 2020 at 16:58
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    $\begingroup$ @user253751 I reworded the answer to clarify. It's the difference between the pressure of the exhaust as it leaves the nozzle and ambient pressure, not across the plane. $\endgroup$
    – David Hammen
    Commented Oct 15, 2020 at 10:31

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