A rocket motor is more efficient in the atmosphere (although the entire rocket-powered vehicle may not be because of atmospheric drag).
A rocket operates most efficiently when the exit pressure equals the ambient pressure. But, it's not because the rocket pushes against the air. The outside pressure affects the expansion of the gases exiting the nozzle which affects the speed of the gases and, hence, the "reaction" that moves the rocket. In space, a rocket motor is always "over-expanding" and, therefore, not as efficient as it would be in the atmosphere.
-- Roger
Do any of you do any reading, or just go with whatever hunch passes by?
1) Energy from the fuel is lost in air drag and gravity drag and is used for the rocket to gain altitude and speed. However, much of the lost energy ends up in the exhaust.
2) 100% efficiency within the engine (engine efficiency ηc = 100%) would mean that all the heat energy of the combustion products is converted into kinetic energy of the jet. This is not possible, but the high expansion ratio nozzles that can be used with rockets come surprisingly close: when the nozzle expands the gas, the gas is cooled and accelerated, and an energy efficiency of up to 70% can be achieved. Most of the rest is heat energy in the exhaust that is not recovered.[98] The high efficiency is a consequence of the fact that rocket combustion can be performed at very high temperatures and the gas is finally released at much lower temperatures, and so giving good Carnot efficiency.
3) However, engine efficiency is not the whole story. In common with the other jet-based engines, but particularly in rockets due to their high and typically fixed exhaust speeds, rocket vehicles are extremely inefficient at low speeds irrespective of the engine efficiency.
The problem is that at low speeds, the exhaust carries away a huge amount of kinetic energy rearward. This phenomenon is termed propulsive efficiency (ηp).[98]
4) However, as speeds rise, the resultant exhaust speed goes down, and the overall vehicle energetic efficiency rises, reaching a peak of around
100% of the engine efficiency when the vehicle is travelling exactly at the same speed that the exhaust is emitted*. In this case the exhaust would ideally stop dead in space behind the moving vehicle, taking away zero energy, and from conservation of energy, all the energy would end up in the vehicle. The efficiency then drops off again at even higher speeds as the exhaust ends up travelling forwards- trailing behind the vehicle.
etc.
From these principles it can be shown that the propulsive efficiency ηp for a rocket moving at speed u with an exhaust velocity c is:
[latex] \eta_p= \frac {2 \frac {u} {c}} {1 + ( \frac {u} {c} )^2 }[/latex]
And the overall energy efficiency η is:
η = ηpηc
*It is also obvious from Newton, that must be true, but not generally realizable, so will only happen at one speed of the rocket. Other demands, and physical conditions will see that happen. Generally, a problem of "load matching". Something of which carteers are totally unaware.
All engineers, and most people, can readily understand Galilean Relativity, but also understand there is more to it than a cartoon.
http://www.internationalskeptics.com/forums/attachment.php?attachmentid=21953&stc=1&d=1303752691