Re: [Phys-l] Rocket Hovering and Conservation of Momentum

[Leigh Palmer <palmer@sfu.ca>]

On 25-Jul-06, at 9:00 Zeke Kossover wrote:

> Howdy-
>
> A student asked me this question recently, and I am not
> sure about my answer.
>
> He asked, "Imagine a rocket hovering off the ground,
> applying a thrust equal to the rocket's weight. Gas is
> moving downwards getting downwards momentum. What is
> getting upwards momentum?"

I haven't read any of the ensuing discussion, but I will give my  
completely predictable response to this question. I will note in  
passing that the hovering rocket is Jonathan Archibald Wheeler's  
favorite example of the principle of equivalence, and mine as well.  
Without looking out the window, an astronaut aboard the rocket cannot  
tell the difference between his situation in Earth's gravitational  
field and that of an astronaut in outer space in an accelerating  
rocket producing the same thrust. The forces acting upon the  
astronauts are the same in both cases, though some misguided folk  
would characterize one of those forces as "fictitious".

Oh yes, my answer: have your student apply the principle of momentum  
conservation in the context to which it is constrained. The momentum  
of an isolated system is conserved. In this case the phrase "getting  
downwards momentum" implies that momentum is a real entity, a common  
cognitive error.

Momentum is not a real thing. It should not be looked upon as being  
acquired in this case. As your student quite correctly observes and  
illustrates, that idea is sterile. It leads to no physical  
enlightenment; it is just confusing. We should listen more carefully  
to our students' questions. In many cases they may have been lead to  
the glib application of concepts with which they do not fully  
understand and appreciate. Rather than constructing elaborate  
justifications for misapplying such concepts we might better serve  
them by returning to the basics.

Two things are evidently wrong with the idea that the momentum of the  
exhaust gas is a real thing. In the first place, the momentum of this  
particular gas must be defined relative to some particular frame of  
reference. That is not the case, for example, with a real physical  
entity like electric charge or mass. Also one must marvel as well at  
the fact that the "downwards momentum" of the gas seems to increase  
with time as the gas descends in Earth's gravitational field. Odd  
behavior for a real entity.

One must go through the analysis systematically: define the system,  
assure that it is isolated, and calculate the momentum of the system  
before and after a given process. If you have chosen wisely you will  
get the same answer for each calculation. Sounds dull, perhaps, but  
it is a very powerful tool.

I will not extend this already prolix note farther because there is  
no need to. Do the analysis!

Leigh