Suppose we establish a moon base. This base would have some population, with some need for supplies, and needs for machinery in the early stages.
If we establish shipping lanes in space for these daily deliveries, would rocket exhaust build up in the shipping lane and cause "turbulence" (for lack of a better word) for future spacecraft using that shipping lane?
It seems like a very bad idea to have a rocket moving at Mach 10 hit a pocket of gas.
Interplanetary space is a pretty good vacuum. Any gas introduced into that vacuum will be at a higher pressure than that vacuum. Gas expands until its outward pressure is in equilibrium with the inward pressure exerted on it by its surroundings, so rocket exhaust will rapidly dissipate until there's no noticeable trace left.
The gas leaving the rocket nozzle will expand in all available directions. The pressure along the rocket's trajectory will be higher than the pressure radially outward from the trajectory, so you end up with a column of gas that epxands outward.
This photo shows a SpaceX Falcon 9 launch. You can see how quickly the plume expands, even in very low orbit - this is a timelapse photo that covers a few minutes.
The Sun ejects as Solar wind about a million metric tonnes per second.
The ejection of some tonnes per minute occasionaly from a second stage rocket engine above the atmosphere of Earth is neglible small compared to Solar wind.
A planet like Earth needs a huge mass to hold an atmosphere by its own gravity. There is no force that would hold such a gas pocket together. The gas would just spread out in the huge available space and its concentration would be incredible small when compared to the Solar wind. The Solar wind is indeed a nearly perfect vacuum at the distance of Earth from the Sun.
Gas pockets under the surface of Earth need a solid enclosure to exist. Spacecrafts need high pressure tanks to store gas or a very low temperature to store liquified gases. But in a vacuum under zero gravity gas pockets without a solid enclosure could not exist.
The short answer is no.
In space the rocket exhaust isn't really a gas it's more like a molecular dust, where all of the molecules (CO, CO2, H2O, etc) are travelling on their own divergent trajectories. In order for a 'gas' pocket to form those molecules would need to be held together in some way, and there's just nothing acting on them to do this. Instead you have a variety of factors acting to spread them apart, including their own individual momentum.
And don't forget: Space is big. Really big.
This document gives details on one LEO flight of the Falcon 9S9 (Falcon Heavy). The second stage fuel load was 107,500 kg of fuel (LOX + RP-1). 100.5 seconds of return burn accounts for the bulk of the fuel, 15.6 seconds for the landing burn used most of the remainder. Approximately half of the return burn took place above the Karman Line, and from the acceleration curve it looks like it accounts for about 45% of the expended fuel. Let's say that's on the order of 50,000 kg of combustion products spread over a couple of hundred km of trajectory in under a minute.
From the picture in Hobbes's answer you can see that the exhaust spreads out pretty quickly, and with very little to impede it that spread is going to continue. You'll end up with a curved plume of molecular 'dust', most of which will either fall back into the Earth's atmosphere or escape orbit on its own momentum. At low orbits there are enough other gas particles that most of the exhaust probably won't make it out of the magnetosphere to be swept away by the solar wind.
So yes there is a slight increase in the density of matter in low orbit, but it's extremely thin and relatively short lived. It would take some hypersensitive apparatus to detect it at all by the time of the next launch.
On the other hand, a handful of molecules may be ejected with just the right momentum to enter an elliptical orbit around the Earth. Come back in a few centuries (if we're still using combustion to get to orbit) and you might notice an effect. At worst it is probably going to require more orbital corrections per year for LEO satellites, which already have problems with the density of molecules so close to Earth's atmosphere.
I would think it would be pushed out of our solar system by the sun's radiation just as the atmosphere of mars (or earth would be if we didn't have a magnetic field).
In regards to distances further away from our sun, I believe it would act as described above. In a vacuum gas molecules dissipate.
Lets be extreme and assume the hwy gets used ALOT - would the gas clump together in the areas void of any other objects with mass?
The International Space Station leaks a little air, and enough stays in the orbit to limit the experiments that can be done there. My former colleagues in Harwell make vacuum better than that to support high power laser experiments etc. So it is possible to pollute space.
