Hello I was watching a video recently about aircraft carriers and how they use compressed air to propel aircraft off the ship. It go me thinking if I had, maybe a 50cm x 50 cm x 50 cm spacecraft that was put into orbit. Would I be able to use compressed air as thrust to orientate the space craft? or even better would I be able to use it to give the space craft a greater distance from the Earth?
In the case of aircraft carriers the compressed air is generally a working fluid for a mechanical catapult rather than providing direct thrust like a rocket (steam is also used for the same job on carriers using steam plant).
Having said that compressed gas can be useful in providing small amounts of thrust, although air may not be the best choice because of its oxygen content and an inert gas may be preferred.
In terms of overall power to weight ratio you generally get more out of a solid/liquid fuel system as you are going from a high density phase to a gas so you don't have the additional weight of a pressure vessel. Note that for standard industrial pressurized gas containers the container may have as much mass as the gas it contains. So even if you don't have actual combustion some sort of chemical gas generation may be preferable.
Overall compressed gas is convenient, portable and simple but has fairly mediocre power density.
It's also worth considering that simple 'bottle rockets' get much more thrust when they use water to provide reaction mass while the compressed air gives the energy storage.
The problem with pure gas thrust is that the rate of conversion of potential to kinetic energy is limited by the local speed of sound and tends to be quite lossy. For jet engines this is mitigated by the fact that there is an unlimited supply of air to push through the engine from the immediate environment, rockets using fuel/oxidiser use sheer brute force of energy density of the propellant at the expense of overall efficiency and the fact that a rocket is essentially very simple so the dead weight of the engine itself is very low.
Similarly where hydrogen of oxygen are used as fuel or oxidiser they are generally liquefied rather than pressurised.
So overall there isn't a general answer, compressed gas is viable for thrust on a small scale, as for small orbital adjustments but it is less attractive for larger thrust requirements.